Nadim · Golowasch · Bucher
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Rotstein HG, Olarinre M and Golowasch J (2016) Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models. J Neurophysiol 116(5):2431-2452. PubMed
Rhythmic oscillation in neurons can be characterized by various attributes, such as the oscillation period and duty cycle. The values of these features depend on the amplitudes of the participating ionic currents, which can be characterized by their maximum conductance values. Recent experimental and theoretical work has shown that the values of these attributes can be maintained constant for different combinations of two or more ionic currents of varying conductances, defining what is known as level sets in conductance space. In two-dimensional conductance spaces, a level set is a curve, often a line, along which a particular oscillation attribute value is conserved. In this work, we use modeling, dynamical systems tools (phase-space analysis), and numerical simulations to investigate the possible dynamic mechanisms responsible for the generation of period and duty-cycle levels sets in simplified (linearized and FitzHugh-Nagumo) and conductance-based (Morris-Lecar) models of neuronal oscillations. A simplistic hypothesis would be that the tonic balance between ionic currents with the same or opposite effective signs is sufficient to create level sets. According to this hypothesis, the dynamics of each ionic current during a given cycle are well captured by some constant quantity (e.g., maximal conductances), and the phase-plane diagrams are identical or are almost identical (e.g., cubic-like nullclines with the same maxima and minima) for different combinations of these maximal conductances. In contrast, we show that these mechanisms are dynamic and involve the complex interaction between the nonlinear voltage dependencies and the effective time scales at which the ionic current's dynamical variables operate.
Daur N, Nadim F and Bucher D (2016) The complexity of small circuits: the stomatogastric nervous system. Curr Opin Neurobiol 41:1-7. Journal
The crustacean stomatogastric nervous system is a long-standing test bed for studies of circuit dynamics and neuromodulation. We give a brief update on the most recent work on this system, with an emphasis on the broader implications for understanding neural circuits. In particular, we focus on new findings underlining that different levels of dynamics taking place at different time scales all interact in multiple ways. Dynamics due to synaptic and intrinsic neuronal properties, neuromodulation, and long-term gene expression-dependent regulation are not independent, but influence each other. Extensive research on the stomatogastric system shows that these dynamic interactions convey robustness to circuit operation, while facilitating the flexibility of producing multiple circuit outputs.
Chen Y, Li X, Rotstein HG and Nadim F (2016) Membrane potential resonance frequency directly influences network frequency through electrical coupling. J Neurophysiol doi: 10.1152/jn.00361.2016. [Epub ahead of print]. PubMed
Oscillatory networks often include neurons that membrane potential resonance, a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (fres). Although fres has been correlated to the network frequency (fnet) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift fres, without changing other attributes of the impedance profile, also shift fnet in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsically oscillatory (O) and resonator (R) neurons. Using a two-cell model of such a network, we show increasing fres of R directly increases fnet and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of fres on fnet is independent of the parameters that define the oscillator, or the combination of parameters in R that produce the shift in fres, so long as this combination produces the same impedance vs. frequency relationship. We experimentally verify the model predictions, using the dynamic clamp technique, by connecting a model resonator to the pacemaker PD neurons of the crab Cancer borealis pyloric network, using electrical synapses, and show that the pyloric network frequency can be shifted by changing fres in the resonator. Our results provide compelling evidence that resonance frequency and amplitude strongly influence the network oscillation frequency and therefore modulators may target these attributes in order to modify rhythmic activity.
Kintos N, Nusbaum MP, and Nadim F (2016) Convergent neuromodulation onto a network neuron can have divergent effects at the network level. J Comput Neurosci 40(2):113-135. PubMed
Different neuromodulators often target the same ion channel. When such modulators act on different neuron types, this convergent action can enable a rhythmic network to produce distinct outputs. Less clear are the functional consequences when two neuromodulators influence the same ion channel in the same neuron. We examine the consequences of this seeming redundancy using a mathematical model of the crab gastric mill (chewing) network. This network is activated in vitro by the projection neuron MCN1, which elicits a half-center bursting oscillation between the reciprocally-inhibitory neurons LG and Int1. We focus on two neuropeptides which modulate this network, including a MCN1 neurotransmitter and the hormone crustacean cardioactive peptide (CCAP). Both activate the same voltage-gated current (I MI ) in the LG neuron. However, I MI-MCN1 , resulting from MCN1 released neuropeptide, has phasic dynamics in its maximal conductance due to LG presynaptic inhibition of MCN1, while I MI-CCAP retains the same maximal conductance in both phases of the gastric mill rhythm. Separation of time scales allows us to produce a 2D model from which phase plane analysis shows that, as in the biological system, I MI-MCN1 and I MI-CCAP primarily influence the durations of opposing phases of this rhythm. Furthermore, I MI-MCN1 influences the rhythmic output in a manner similar to the Int1-to-LG synapse, whereas I MI-CCAP has an influence similar to the LG-to-Int1 synapse. These results show that distinct neuromodulators which target the same voltage-gated ion channel in the same network neuron can nevertheless produce distinct effects at the network level, providing divergent neuromodulator actions on network activity.
Gray M and Golowasch J (2016) Voltage dependence of a neuromodulator-activated ionic current. eNeuro doi: 10.1523/ENEURO.0038-16.2016. PubMed
The neuromodulatory inward current (IMI) generated by crab Cancer borealis stomatogastric ganglion neurons is an inward current whose voltage dependence has been shown to be crucial in the activation of oscillatory activity of the pyloric network of this system. It has been previously shown that IMI loses its voltage dependence in conditions of low extracellular calcium, but that this effect appears to be regulated by intracellular calmodulin. Voltage dependence is only rarely regulated by intracellular signaling mechanisms. Here we address the hypothesis that the voltage dependence of IMI is mediated by intracellular signaling pathways activated by extracellular calcium. We demonstrate that calmodulin inhibitors and a ryanodine antagonist can reduce IMI voltage dependence in normal Ca(2+), but that, in conditions of low Ca(2+), calmodulin activators do not restore IMI voltage dependence. Further, we show evidence that CaMKII alters IMI voltage dependence. These results suggest that calmodulin is necessary but not sufficient for IMI voltage dependence. We therefore hypothesize that the Ca(2+)/calmodulin requirement for IMI voltage dependence is due to an active sensing of extracellular calcium by a GPCR family calcium-sensing receptor (CaSR) and that the reduction in IMI voltage dependence by a calmodulin inhibitor is due to CaSR endocytosis. Supporting this, preincubation with an endocytosis inhibitor prevented W7 (N-(6-aminohexyl)-5-chloro-1-naphthalenesulfonamide hydrochloride)-induced loss of IMI voltage dependence, and a CaSR antagonist reduced IMI voltage dependence. Additionally, myosin light chain kinase, which is known to act downstream of the CaSR, seems to play a role in regulating IMI voltage dependence. Finally, a Gβγ-subunit inhibitor also affects IMI voltage dependence, in support of the hypothesis that this process is regulated by a G-protein-coupled CaSR.
Mouser C, Bose A and Nadim F (2016) The role of electrical coupling in generating and modulating oscillations in a neuronal network. Math Biosci 278:11-21. PubMed
A simplified model of the crustacean gastric mill network is considered. Rhythmic activity in this network has largely been attributed to half center oscillations driven by mutual inhibition. We use mathematical modeling and dynamical systems theory to show that rhythmic oscillations in this network may also depend on, or even arise from, a voltage-dependent electrical coupling between one of the cells in the half-center network and a projection neuron that lies outside of the network. This finding uncovers a potentially new mechanism for the generation of oscillations in neuronal networks.
Bucher D (2015) Contribution of axons to short-term dynamics of neuronal communication.In: Axons and Brain Architecture (Rockland KS, ed). Elsevier, Boston. Google books
Bucher D, Haspel G, Golowasch J, and Nadim F (2015) Central Pattern Generators. In: Encyclopedia of Life Sciences, John Wiley & Sons. eLS
Essential behaviours such as walking or breathing are rhythmic, that is, characterised by repetitive activation of muscles in a specific temporal sequence. A basic version of the underlying neural activity is generated in the central nervous system by networks called central pattern generators (CPGs). CPGs can produce these patterns even in the absence of inputs that carry specific timing information. The core rhythmic activity can be based on intrinsic oscillatory properties of pacemaker neurons or emerge from the synaptic connectivity of nonoscillatory neurons. In both cases, other neurons are recruited into this rhythmic activity to generate a whole pattern. Neuronal and synaptic properties underlying the precise temporal patterning of sequential bursting activity are shaped by neuromodulators to generate different versions of motor patterns. The circuitry controlling rhythmic behaviours of a whole animal is organised in modules that control different body parts and can be coordinated in different ways to generate different behaviours.
Garcia VJ, Daur N, Temporal S, Schulz DJ, and Bucher D (2015) Neuropeptide receptor transcript expression levels and magnitude of ionic current responses show cell type-specific differences in a small motor circuit. J Neurosci 35:6786-6800. PubMed
We studied the relationship between neuropeptide receptor transcript expression and current responses in the stomatogastric ganglion (STG) of the crab, Cancer borealis. We identified a transcript with high sequence similarity to crustacean cardioactive peptide (CCAP) receptors in insects and mammalian neuropeptide S receptors. This transcript was expressed throughout the nervous system, consistent with the role of CCAP in a range of different behaviors. In the STG, single-cell qPCR showed expression in only a subset of neurons. This subset had previously been shown to respond to CCAP with the activation of a modulator-activated inward current (IMI), with one exception. In the one cell type that showed expression but no IMI responses, we found CCAP modulation of synaptic currents. Expression levels within STG neuron types were fairly variable, but significantly different between some neuron types. We tested the magnitude and concentration dependence of IMI responses to CCAP application in two identified neurons, the lateral pyloric (LP) and the inferior cardiac (IC) neurons. LP had several-fold higher expression and showed larger current responses. It also was more sensitive to low CCAP concentrations and showed saturation at lower concentrations, as sigmoid fits showed smaller EC50 values and steeper slopes. In addition, occlusion experiments with proctolin, a different neuropeptide converging onto IMI, showed that saturating concentrations of CCAP activated all available IMI in LP, but only approximately two-thirds in IC, the neuron with lower receptor transcript expression. The implications of these findings for comodulation are discussed.
Bucher D and Anderson PAV (2015) Evolution of the first nervous systems – what can we surmise? J Exp Biol 218:501-503. Journal
Tseng HA, Martinez D and Nadim F (2014) The frequency preference of neurons and synapses in a recurrent oscillatory network. J Neurosci 34:12933-45. PubMed
A variety of neurons and synapses shows a maximal response at a preferred frequency, generally considered to be important in shaping network activity. We are interested in whether all neurons and synapses in a recurrent oscillatory network can have preferred frequencies and, if so, whether these frequencies are the same or correlated, and whether they influence the network activity. We address this question using identified neurons in the pyloric network of the crab Cancer borealis. Previous work has shown that the pyloric pacemaker neurons exhibit membrane potential resonance whose resonance frequency is correlated with the network frequency. The follower lateral pyloric (LP) neuron makes reciprocally inhibitory synapses with the pacemakers. We find that LP shows resonance at a higher frequency than the pacemakers and the network frequency falls between the two. We also find that the reciprocal synapses between the pacemakers and LP have preferred frequencies but at significantly lower values. The preferred frequency of the LP to pacemaker synapse is correlated with the presynaptic preferred frequency, which is most pronounced when the peak voltage of the LP waveform is within the dynamic range of the synaptic activation curve and a shift in the activation curve by the modulatory neuropeptide proctolin shifts the frequency preference. Proctolin also changes the power of the LP neuron resonance without significantly changing the resonance frequency. These results indicate that different neuron types and synapses in a network may have distinct preferred frequencies, which are subject to neuromodulation and may interact to shape network oscillations.
Akcay Z, Bose A and Nadim F (2014) Effects of synaptic plasticity on phase and period locking in a network of two oscillatory neurons. J Math Neurosci 4:8. PubMed
We study the effects of synaptic plasticity on the determination of firing period and relative phases in a network of two oscillatory neurons coupled with reciprocal inhibition. We combine the phase response curves of the neurons with the short-term synaptic plasticity properties of the synapses to define Poincare maps for the activity of an oscillatory network. Fixed points of these maps correspond to the phase-locked modes of the network. These maps allow us to analyze the dependence of the resulting network activity on the properties of network components. Using a combination of analysis and simulations, we show how various parameters of the model affect the existence and stability of phase-locked solutions. We find conditions on the synaptic plasticity profiles and the phase response curves of the neurons for the network to be able to maintain a constant firing period, while varying the phase of locking between the neurons or vice versa. A generalization to cobwebbing for two-dimensional maps is also discussed.
Golowasch J (2014) Ionic Current Variability and Functional Stability in the Nervous System. BioScience 64:570-580. Journal
Identified neurons in different animals express ionic currents at highly variable levels (population variability). If neuronal identity is associated with stereotypical function, as is the case in genetically identical neurons or in unambiguously identified individual neurons, this variability poses a conundrum: How is activity the same if the components that generate it—ionic current levels—are different? In some cases, ionic current variability across similar neurons generates an output gradient. However, many neurons produce very similar output activity, despite substantial variability in ionic conductances. It appears that, in many such cells, conductance levels of one ionic current vary in proportion to the conductance levels of another current. As a result, in a population of neurons, these conductances appear to be correlated. Here, I review theoretical and experimental work that suggests that neuronal ionic current correlation can reduce the global ionic current variability and can contribute to functional stability.
Nadim F and Bucher D (2014) Neuromodulation of neurons and synapses. Curr Opin Neurobiol 29C:48-56. PubMed
Neuromodulation underlies the flexibility of neural circuit operation and behavior. Individual neuromodulators can have divergent actions in a neuron by targeting multiple physiological mechanisms. Conversely, multiple neuromodulators may have convergent actions through overlapping targets. The divergent and convergent neuromodulator actions can be unambiguously synergistic or antagonistic, but neuromodulation often entails balanced adjustment of nonlinear membrane and synaptic properties by targeting ion channel and synaptic dynamics rather than just excitability or synaptic strength. In addition, neuromodulators can exert effects at multiple timescales, from short-term adjustments of neuron and synapse function to persistent long-term regulation. This short review summarizes some highlights of the diverse actions of neuromodulators on ion channel and synaptic properties.
Bose A, Golowasch J, Guan Y and Nadim F (2014) The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations. J Comput Neurosci 32:229-242. PubMed
Neuronal oscillatory activity is generated by a combination of ionic currents, including at least one inward regenerative current that brings the cell towards depolarized voltages and one outward current that repolarizes the cell. Such currents have traditionally been assumed to require voltage-dependence. Here we test the hypothesis that the voltage dependence of the regenerative inward current is not necessary for generating oscillations. Instead, a current I NL that is linear in the biological voltage range and has negative conductance is sufficient to produce regenerative activity. The current I NL can be considered a linear approximation to the negative-conductance region of the current-voltage relationship of a regenerative inward current. Using a simple conductance-based model, we show that I NL , in conjunction with a voltage-gated, non-inactivating outward current, can generate oscillatory activity. We use phase-plane and bifurcation analyses to uncover a rich variety of behaviors as the conductance of I NL is varied, and show that oscillations emerge as a result of destabilization of the resting state of the model neuron. The model shows the need for well-defined relationships between the inward and outward current conductances, as well as their reversal potentials, in order to produce stable oscillatory activity. Our analysis predicts that a hyperpolarization-activated inward current can play a role in stabilizing oscillatory activity by preventing swings to very negative voltages, which is consistent with what is recorded in biological neurons in general. We confirm this prediction of the model experimentally in neurons from the crab stomatogastric ganglion.
Rotstein HG and Nadim F (2014) Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. J Comput Neurosci 37:9-28. PubMed
Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g 1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g L - g 1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g 1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.
Kintos N and Nadim F (2014) A modeling exploration of how synaptic feedback to descending projection neurons shapes the activity of an oscillatory network. SIAM J Appl Dyn Syst 13:1239-1269. Journal
Rhythmic activity which underlies motor output is often initiated and controlled by descending modulatory projection pathways onto central pattern generator (CPG) networks. In turn, these descending pathways receive synaptic feedback from their target CPG network, which can influence the CPG output. However, the mechanisms underlying such bidirectional synaptic interactions are mostly unexplored. We develop a reduced mathematical model, including both feed-forward and feedback circuitry, to examine how the synaptic interactions involving two projection neurons, MCN1 and CPN2, can produce and shape the activity of the gastric mill CPG in the crab stomatogastric nervous system. We use simplifying assumptions that are based on the behavior of the biological system to reduce this model down to 2 dimensions, which allows for phase plane analysis of the model output. The model shows a distinct activity for the gastric mill rhythm that is elicited when MCN1 and CPN2 are coactive compared to the rhythm elicited by MCN1 activity alone. Furthermore, the presence of feedback to the projection neuron CPN2 provides a distinct locus of pattern generation in the model which does not require reciprocally inhibitory interactions between the gastric mill CPG neurons, but is instead based on a half-center oscillator that occurs through a trisynaptic pathway that includes CPN2. Our modeling results show that feedback to projection pathways may provide additional mechanisms for the generation of motor activity. These mechanisms can have distinct dependence on network parameters and may therefore provide additional flexibility for the rhythmic motor output.
Harris RM, Otopalik AG, Smith CJ, Bucher D, Golowasch J and Hofmann HA (2014) Single-Neuron Gene Expression Analysis Using the Maxwell® 16 LEV System in the Neural Systems and Behavior Course. Promega Corporation Web Site Promega
Gene expression analysis from single cells has become increasingly prominent across biological disciplines; thus, it is important to train students in these approaches. Here, we present an experimental and analysis pipeline that we developed for the Neural Systems & Behavior (NS&B) course at Marine Biological Laboratory. Our approach used the Maxwell® 16 LEV simplyRNA Tissue Kit and GoTaq® 2-Step RT-qPCR System for gene expression analysis from single neurons of the crustacean stomatogastric ganglion, a model system to study the generation of rhythmic motor patterns. We used double-stranded RNA to knockdown expression of a putative neuromodulator-activated sodium channel. We then examined the electrophysiological responses to known neuromodulators and confirmed that the response was reduced. Finally, we measured how mRNA levels of several ion channel genes changed in response. Our results provide new insights into the neural mechanisms underlying the generation and modulation of rhythmic motor patterns..
Bose A and Nadim F (2014) Multistability Arising from Synaptic Dynamics. In: Encyclopedia of Computational Neuroscience. (Jaeger D, Jung R, eds) Springer, New York. PDF
Fox DM, Rotstein HG and Nadim F (2014) Bursting in Neurons and Small Networks. In: Encyclopedia of Computational Neuroscience. (Jaeger D, Jung R, eds) Springer, New York. PDF
Golowasch J and Nadim F (2014) Capacitance, Membrane. In: Encyclopedia of Computational Neuroscience. (Jaeger D, Jung R, eds) Springer, New York. PDF
Martinez D, Matveev V and Nadim F (2014) Short-Term Synaptic Plasticity in Central Pattern Generators. In: Encyclopedia of Computational Neuroscience. (Jaeger D, Jung R, eds) Springer, New York. PDF
Nadim F (2014) Invertebrate Pattern Generation: Overview. In: Encyclopedia of Computational Neuroscience. (Jaeger D, Jung R, eds) Springer, New York. PDF
Bucher D and Marder E (2013) SnapShot: Neuromodulation. Cell 155:482-482 e1. PubMed
Rotstein HG and Nadim F (2013) Neurons and Neural Networks: Computational Models. In: Encyclopedia of Life Sciences. John Wiley & Sons. Wiley
Oh M, Zhao S, Matveev V and Nadim F (2012) Neuromodulatory changes in short-term synaptic dynamics may be mediated by two distinct mechanisms of presynaptic calcium entry. J Comput Neurosci 33:573-85. PubMed
Although synaptic output is known to be modulated by changes in presynaptic calcium channels, additional pathways for calcium entry into the presynaptic terminal, such as non-selective channels, could contribute to modulation of short term synaptic dynamics. We address this issue using computational modeling. The neuropeptide proctolin modulates the inhibitory synapse from the lateral pyloric (LP) to the pyloric dilator (PD) neuron, two slow-wave bursting neurons in the pyloric network of the crab Cancer borealis. Proctolin enhances the strength of this synapse and also changes its dynamics. Whereas in control saline the synapse shows depression independent of the amplitude of the presynaptic LP signal, in proctolin, with high-amplitude presynaptic LP stimulation the synapse remains depressing while low-amplitude stimulation causes facilitation. We use simple calcium-dependent release models to explore two alternative mechanisms underlying these modulatory effects. In the first model, proctolin directly targets calcium channels by changing their activation kinetics which results in gradual accumulation of calcium with low-amplitude presynaptic stimulation, leading to facilitation. The second model uses the fact that proctolin is known to activate a non-specific cation current I ( MI ). In this model, we assume that the MI channels have some permeability to calcium, modeled to be a result of slow conformation change after binding calcium. This generates a gradual increase in calcium influx into the presynaptic terminals through the modulatory channel similar to that described in the first model. Each of these models can explain the modulation of the synapse by proctolin but with different consequences for network activity.
Zhao S and Golowasch J (2012) Ionic current correlations underlie the global tuning of large numbers of neuronal activity attributes. J Neurosci 32:13380-8. PubMed
Ionic conductances in identified neurons are highly variable. This poses the crucial question of how such neurons can produce stable activity. Coexpression of ionic currents has been observed in an increasing number of neurons in different systems, suggesting that the coregulation of ionic channel expression, by thus linking their variability, may enable neurons to maintain relatively constant neuronal activity as suggested by a number of recent theoretical studies. We examine this hypothesis experimentally using the voltage- and dynamic-clamp techniques to first measure and then modify the ionic conductance levels of three currents in identified neurons of the crab pyloric network. We quantify activity by measuring 10 different attributes (oscillation period, spiking frequency, etc.), and find linear, positive and negative relationships between conductance pairs and triplets that can enable pyloric neurons to maintain activity attributes invariant. Consistent with experimental observations, some of the features most tightly regulated appear to be phase relationships of bursting activity. We conclude that covariation (and probably a tightly controlled coregulation) of ionic conductances can help neurons maintain certain attributes of neuronal activity invariant while at the same time allowing conductances to change over wide ranges in response to internal or environmental inputs and perturbations. Our results also show that neurons can tune neuronal activity globally via coordinate expression of ion currents.
Maffei A, Bucher D and Fontanini A (2012) Homeostatic plasticity in the nervous system. Neural Plast 2012:913472. PubMed
Unal CT, Golowasch JP and Zaborszky L (2012) Adult mouse basal forebrain harbors two distinct cholinergic populations defined by their electrophysiology. Front Behav Neurosci 6:21. PubMed
We performed whole-cell recordings from basal forebrain (BF) cholinergic neurons in transgenic mice expressing enhanced green fluorescent protein (eGFP) under the control of the choline acetyltransferase promoter. BF cholinergic neurons can be differentiated into two electrophysiologically identifiable subtypes: early and late firing neurons. Early firing neurons ( approximately 70%) are more excitable, show prominent spike frequency adaptation and are more susceptible to depolarization blockade, a phenomenon characterized by complete silencing of the neuron following initial action potentials. Late firing neurons ( approximately 30%), albeit being less excitable, could maintain a tonic discharge at low frequencies. In voltage clamp analysis, we have shown that early firing neurons have a higher density of low voltage activated (LVA) calcium currents. These two cholinergic cell populations might be involved in distinct functions: the early firing group being more suitable for phasic changes in cortical acetylcholine release associated with attention while the late firing neurons could support general arousal by maintaining tonic acetylcholine levels.
Temporal S, Desai M, Khorkova O, Varghese G, Dai A, Schulz DJ and Golowasch J (2012) Neuromodulation independently determines correlated channel expression and conductance levels in motor neurons of the stomatogastric ganglion. J Neurophysiol 107:718-27. PubMed
Neuronal identity depends on the regulated expression of numerous molecular components, especially ionic channels, which determine the electrical signature of a neuron. Such regulation depends on at least two key factors, activity itself and neuromodulatory input. Neuronal electrical activity can modify the expression of ionic currents in homeostatic or nonhomeostatic fashion. Neuromodulators typically modify activity by regulating the properties or expression levels of subsets of ionic channels. In the stomatogastric system of crustaceans, both types of regulation have been demonstrated. Furthermore, the regulation of the coordinated expression of ionic currents and the channels that carry these currents has been recently reported in diverse neuronal systems, with neuromodulators not only controlling the absolute levels of ionic current expression but also, over long periods of time, appearing to modify their correlated expression. We hypothesize that neuromodulators may regulate the correlated expression of ion channels at multiple levels and in a cell-type-dependent fashion. We report that in two identified neuronal types, three ionic currents are linearly correlated in a pairwise manner, suggesting their coexpression or direct interactions, under normal neuromodulatory conditions. In each cell, some currents remain correlated after neuromodulatory input is removed, whereas the correlations between the other pairs are either lost or altered. Interestingly, in each cell, a different suite of currents change their correlation. At the transcript level we observe distinct alterations in correlations between channel mRNA amounts, including one of the cell types lacking a correlation under normal neuromodulatory conditions and then gaining the correlation when neuromodulators are removed. Synaptic activity does not appear to contribute, with one possible exception, to the correlated expression of either ionic currents or of the transcripts that code for the respective channels. We conclude that neuromodulators regulate the correlated expression of ion channels at both the transcript and the protein levels.
Daur N, Bryan AS, Garcia VJ and Bucher D (2012) Short-term synaptic plasticity compensates for variability in number of motor neurons at a neuromuscular junction. J Neurosci 32:16007-17. PubMed
We studied how similar postsynaptic responses are maintained in the face of interindividual variability in the number of presynaptic neurons. In the stomatogastric ganglion of the lobster, Homarus americanus, the pyloric (PY) neurons exist in variable numbers across animals. We show that each individual fiber of the stomach muscles innervated by PY neurons received synaptic input from all neurons present. We performed intracellular recordings of excitatory junction potentials (EJPs) in the muscle fibers to determine the consequences of differences in the number of motor neurons. Despite the variability in neuron number, the compound electrical response of muscle fibers to natural bursting input was similar across individuals. The similarity of total synaptic activation was not due to differences in the spiking activity of individual motor neurons across animals with different numbers of PY neurons. The amplitude of a unitary EJP in response to a single spike in a single motor neuron also did not depend on the number of PY neurons present. Consequently, the compound EJP in response to a single stimulus that activated all motor axons present was larger in individuals with more PY neurons. However, when axons were stimulated with trains of pulses mimicking bursting activity, EJPs facilitated more in individuals with fewer PY neurons. After a few stimuli, this resulted in depolarizations similar to the ones in individuals with more PY neurons. We interpret our findings as evidence that compensatory or homeostatic regulatory mechanisms can act on short-term synaptic dynamics instead of absolute synaptic strength.
Ballo AW, Nadim F and Bucher D (2012) Dopamine modulation of Ih improves temporal fidelity of spike propagation in an unmyelinated axon. J Neurosci 32:5106-19. PubMed
We studied how conduction delays of action potentials in an unmyelinated axon depended on the history of activity and how this dependence was changed by the neuromodulator dopamine (DA). The pyloric dilator axons of the stomatogastric nervous system in the lobster, Homarus americanus, exhibited substantial activity-dependent hyperpolarization and changes in spike shape during repetitive activation. The conduction delays varied by several milliseconds per centimeter, and, during activation with realistic burst patterns or Poisson-like patterns, changes in delay occurred over multiple timescales. The mean delay increased, whereas the resting membrane potential hyperpolarized with a time constant of several minutes. Concomitantly with the mean delay, the variability of delay also increased. The variability of delay was not a linear or monotonic function of instantaneous spike frequency or spike shape parameters, and the relationship between these parameters changed with the increase in mean delay. Hyperpolarization was counteracted by a hyperpolarization-activated inward current (I(h)), and the magnitude of I(h) critically determined the temporal fidelity of spike propagation. Pharmacological block of I(h) increased the change in delay and the variability of delay, and increasing I(h) by application of DA diminished both. Consequently, the temporal fidelity of pattern propagation was substantially improved in DA. Standard measurements of changes in excitability or delay with paired stimuli or tonic stimulation failed to capture the dynamics of spike conduction. These results indicate that spike conduction can be extremely sensitive to the history of axonal activity and to the presence of neuromodulators, with potentially important consequences for temporal coding.
Zhang Y, Bucher D and Nadim F (2012) Modeling and prediction of conduction delay in an unmyelinated axon. BMC Neurosci 13 (Suppl1):81. PDF
Zhao S, Sheibanie AF, Oh M, Rabbah P and Nadim F (2011) Peptide neuromodulation of synaptic dynamics in an oscillatory network. J Neurosci 31:13991-4004. PubMed
Although neuromodulation of synapses is extensively documented, its consequences in the context of network oscillations are not well known. We examine the modulation of synaptic strength and short-term dynamics in the crab pyloric network by the neuropeptide proctolin. Pyloric oscillations are driven by a pacemaker group which receives feedback through the inhibitory synapse from the lateral pyloric (LP) to pyloric dilator (PD) neurons. We show that proctolin modulates the spike-mediated and graded components of the LP to PD synapse. Proctolin enhances the graded component and unmasks a surprising heterogeneity in its dynamics where there is depression or facilitation depending on the amplitude of the voltage waveform of the presynaptic LP neuron. The spike-mediated component is influenced by the baseline membrane potential and is also enhanced by proctolin at all baseline potentials. In addition to direct modulation of this synapse, proctolin also changes the shape and amplitude of the presynaptic voltage waveform which additionally enhances synaptic output during ongoing activity. During ongoing oscillations, proctolin reduces the variability of cycle period but only when the LP to PD synapse is functionally intact. Using the dynamic clamp technique we find that the reduction in variability is a direct consequence of modulation of the LP to PD synapse. These results demonstrate that neuromodulation of synapses involves complex and interacting influences that target different synaptic components and dynamics as well as the presynaptic voltage waveform. At the network level, modulation of feedback inhibition can result in reduction of variability and enhancement of stable oscillatory output.
Zhang Y and Golowasch J (2011) Recovery of rhythmic activity in a central pattern generator: analysis of the role of neuromodulator and activity-dependent mechanisms. J Comput Neurosci 31:685-99. PubMed
The pyloric network of decapods crustaceans can undergo dramatic rhythmic activity changes. Under normal conditions the network generates low frequency rhythmic activity that depends obligatorily on the presence of neuromodulatory input from the central nervous system. When this input is removed (decentralization) the rhythmic activity ceases. In the continued absence of this input, periodic activity resumes after a few hours in the form of episodic bursting across the entire network that later turns into stable rhythmic activity that is nearly indistinguishable from control (recovery). It has been proposed that an activity-dependent modification of ionic conductance levels in the pyloric pacemaker neuron drives the process of recovery of activity. Previous modeling attempts have captured some aspects of the temporal changes observed experimentally, but key features could not be reproduced. Here we examined a model in which slow activity-dependent regulation of ionic conductances and slower neuromodulator-dependent regulation of intracellular Ca(2+) concentration reproduce all the temporal features of this recovery. Key aspects of these two regulatory mechanisms are their independence and their different kinetics. We also examined the role of variability (noise) in the activity-dependent regulation pathway and observe that it can help to reduce unrealistic constraints that were otherwise required on the neuromodulator-dependent pathway. We conclude that small variations in intracellular Ca(2+) concentration, a Ca(2+) uptake regulation mechanism that is directly targeted by neuromodulator-activated signaling pathways, and variability in the Ca(2+) concentration sensing signaling pathway can account for the observed changes in neuronal activity. Our conclusions are all amenable to experimental analysis.
Nadim F, Zhao S, Zhou L and Bose A (2011) Inhibitory feedback promotes stability in an oscillatory network. J Neural Eng 8:065001. PubMed
Reliability and variability of neuronal activity are both thought to be important for the proper function of neuronal networks. The crustacean pyloric rhythm ( approximately 1 Hz) is driven by a group of pacemaker neurons (AB/PD) that inhibit and burst out of phase with all follower pyloric neurons. The only known chemical synaptic feedback to the pacemakers is an inhibitory synapse from the follower lateral pyloric (LP) neuron. Although this synapse has been studied extensively, its role in the generation and coordination of the pyloric rhythm is unknown. We examine the hypothesis that this synapse acts to stabilize the oscillation by reducing the variability in cycle period on a cycle-by-cycle basis. Our experimental data show that functionally removing the LP-pyloric dilator (PD) synapse by hyperpolarizing the LP neuron increases the pyloric period variability. The increase in pyloric rhythm stability in the presence of the LP-PD synapse is demonstrated by a decrease in the amplitude of the phase response curve of the PD neuron. These experimental results are explained by a reduced mathematical model. Phase plane analysis of this model demonstrates that the effect of the periodic inhibition is to produce asymptotic stability in the oscillation phase, which leads to a reduction in variability of the oscillation cycle period.
Johnson BR, Brown JM, Kvarta MD, Lu JY, Schneider LR, Nadim F and Harris-Warrick RM (2011) Differential modulation of synaptic strength and timing regulate synaptic efficacy in a motor network. J Neurophysiol 105:293-304. PubMed
Neuromodulators modify network output by altering neuronal firing properties and synaptic strength at multiple sites; however, the functional importance of each site is often unclear. We determined the importance of monoamine modulation of a single synapse for regulation of network cycle frequency in the oscillatory pyloric network of the lobster. The pacemaker kernel of the pyloric network receives only one chemical synaptic feedback, an inhibitory synapse from the lateral pyloric (LP) neuron to the pyloric dilator (PD) neurons, which can limit cycle frequency. We measured the effects of dopamine (DA), octopamine (Oct), and serotonin (5HT) on the strength of the LP-->PD synapse and the ability of the modified synapse to regulate pyloric cycle frequency. DA and Oct strengthened, whereas 5HT weakened, LP-->PD inhibition. Surprisingly, the DA-strengthened LP-->PD synapse lost its ability to slow the pyloric oscillations, whereas the 5HT-weakened LP-->PD synapse gained a greater influence on the oscillations. These results are explained by monoamine modulation of factors that determine the firing phase of the LP neuron in each cycle. DA acts via multiple mechanisms to phase-advance the LP neuron into the pacemaker's refractory period, where the strengthened synapse has little effect. In contrast, 5HT phase-delays LP activity into a region of greater pacemaker sensitivity to LP synaptic input. Only Oct enhanced LP regulation of cycle period simply by enhancing LP-->PD synaptic strength. These results show that modulation of the strength and timing of a synaptic input can differentially affect the synapse's efficacy in the network.
Bucher D and Goaillard JM (2011) Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon. Prog Neurobiol 94:307-46. PubMed
Most spiking neurons are divided into functional compartments: a dendritic input region, a soma, a site of action potential initiation, an axon trunk and its collaterals for propagation of action potentials, and distal arborizations and terminals carrying the output synapses. The axon trunk and lower order branches are probably the most neglected and are often assumed to do nothing more than faithfully conducting action potentials. Nevertheless, there are numerous reports of complex membrane properties in non-synaptic axonal regions, owing to the presence of a multitude of different ion channels. Many different types of sodium and potassium channels have been described in axons, as well as calcium transients and hyperpolarization-activated inward currents. The complex time- and voltage-dependence resulting from the properties of ion channels can lead to activity-dependent changes in spike shape and resting potential, affecting the temporal fidelity of spike conduction. Neural coding can be altered by activity-dependent changes in conduction velocity, spike failures, and ectopic spike initiation. This is true under normal physiological conditions, and relevant for a number of neuropathies that lead to abnormal excitability. In addition, a growing number of studies show that the axon trunk can express receptors to glutamate, GABA, acetylcholine or biogenic amines, changing the relative contribution of some channels to axonal excitability and therefore rendering the contribution of this compartment to neural coding conditional on the presence of neuromodulators. Long-term regulatory processes, both during development and in the context of activity-dependent plasticity may also affect axonal properties to an underappreciated extent.
Nadim F, Zhao S and Bose A (2011) A PRC description of how inhibitory feedback promotes oscillation stability. In: Phase Response Curves in Neuroscience (Butera RJ, Prinz A and Schultheiss NW, eds). Springer, New York. Springer
Tseng HA and Nadim F (2010) The membrane potential waveform of bursting pacemaker neurons is a predictor of their preferred frequency and the network cycle frequency. J Neurosci 30:10809-19. PubMed
Many oscillatory networks involve neurons that exhibit intrinsic rhythmicity but possess a large variety of voltage-gated currents that interact in a complex fashion, making it difficult to determine which factors control frequency. Yet these neurons often have preferred (resonance) frequencies that can be close to the network frequency. Because the preferred frequency results from the dynamics of ionic currents, it can be assumed to depend on parameters that determine the neuron's oscillatory waveform shape. The pyloric network frequency in the crab Cancer borealis is correlated with the preferred frequency of its bursting pacemaker neurons anterior burster and pyloric dilator (PD). We measured the preferred frequency of the PD neuron in voltage clamp, which allows control of the oscillation voltage range and waveforms (sine waves and realistic oscillation waveforms), and showed that (1) the preferred frequency depends on the voltage range of the oscillating voltage waveform; (2) the slope of the waveform near its peak has a strongly negative correlation with the preferred frequency; and (3) correlations between parameters of the PD neuron oscillation waveform and its preferred frequency can be used to predict shifts in the network frequency. As predicted by these results, dynamic clamp shifts of the upper or lower voltage limits of the PD neuron waveform during ongoing oscillations changed the network frequency, consistent with the predictions from the preferred frequency. These results show that the voltage waveform of oscillatory neurons can be predictive of their preferred frequency and thus the network oscillation frequency.
Ballo AW, Keene JC, Troy PJ, Goeritz ML, Nadim F and Bucher D (2010) Dopamine modulates Ih in a motor axon. J Neurosci 30:8425-34. PubMed
We studied the axons of the pyloric dilator neurons in the stomatogastric nervous system of the lobster. The several-centimeters-long portions of these axons in the motor nerves depolarize in response to low concentrations of dopamine (DA) and exhibit peripheral spike initiation in the absence of centrally generated activity. This effect is inhibited by blockers of hyperpolarization-activated inward current (I(h)). We show here that peripheral spike initiation was also elicited by D(1)-type receptor agonists and drugs that increase cAMP. This suggests that DA acts via a D(1)-type receptor mechanism to modulate hyperpolarization-activated cyclic nucleotide-gated channels. We used two-electrode voltage clamp of the axon to directly study the effect of DA on I(h). Surprisingly, DA decreased the maximal conductance. However, because of a shift of the activation curve to more depolarized potentials, and a change in the slope, conductance was increased at biologically relevant membrane potentials. These changes were solely caused by modulation of I(h), as DA had no discernible effect when I(h) was blocked. In addition, they were not induced by repeated activation and could be mimicked by application of drugs that increase cAMP concentration. DA modulation of I(h) persisted in the presence of a protein kinase A inhibitor and is therefore potentially mediated by a phosphorylation-independent direct effect of cAMP on the ion channel. A computer model of the axon showed that the changes in maximal conductance and voltage dependence were not qualitatively affected by space-clamp problems.
Zhao S, Golowasch J and Nadim F (2010) Pacemaker neuron and network oscillations depend on a neuromodulator-regulated linear current. Front Behav Neurosci 4:21. PubMed
Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current I(MI), which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of I(MI) for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs.
Oh M, Tseng H-a and Nadim F (2010) Synapses showing a preferred frequency in a reciprocally inhibitory neuronal network. BMC Neurosci 11:194. PDF
Huang X, Nadim F and Bose A (2010) Using feed-forward networks to infer the activity of feed-back neuronal networks. BMC Neurosci 11:48. PDF
Ballo AW and Bucher D (2009) Complex intrinsic membrane properties and dopamine shape spiking activity in a motor axon. J Neurosci 29:5062-74. PubMed
We studied the peripheral motor axons of the two pyloric dilator (PD) neurons of the stomatogastric ganglion in the lobster, Homarus americanus. Intracellular recordings from the motor nerve showed both fast and slow voltage- and activity-dependent dynamics. During rhythmic bursts, the PD axons displayed changes in spike amplitude and duration. Pharmacological experiments and the voltage dependence of these phenomena suggest that inactivation of sodium and A-type potassium channels are responsible. In addition, the "resting" membrane potential was dependent on ongoing spike or burst activity, with more hyperpolarized values when activity was strong. Nerve stimulations, pharmacological block and current clamp experiments suggest that this is due to a functional antagonism between a slow after-hyperpolarization (sAHP) and inward rectification through hyperpolarization-activated current (IH). Dopamine application resulted in modest depolarization and "ectopic" peripheral spike initiation in the absence of centrally generated activity. This effect was blocked by CsCl and ZD7288, consistent with a role of IH. High frequency nerve stimulation inhibited peripheral spike initiation for several seconds, presumably due to the sAHP. Both during normal bursting activity and antidromic nerve stimulation, the conduction delay over the length of the peripheral nerve changed in a complex manner. This suggests that axonal membrane dynamics can have a substantial effect on the temporal fidelity of spike patterns propagated from a spike initiation site to a synaptic target, and that neuromodulators can influence the extent to which spike patterns are modified.
Bucher D (2009) Central pattern generators. In: Encyclopedia of Neuroscience. (Squire L, ed) Academic Press, Oxford.
Golowasch J, Thomas G, Taylor AL, Patel A, Pineda A, Khalil C and Nadim F (2009) Membrane capacitance measurements revisited: dependence of capacitance value on measurement method in nonisopotential neurons. J Neurophysiol 102:2161-75. PubMed
During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.
Oh M, Zhao S and Nadim F (2009) A mechanism underlying short-term synaptic dynamics regulated by neuromodulator based on kinetics of Ca currents. BMC Neurosci 10:222. PDF
Zhang Y, Khorkova O, Rodriguez R and Golowasch J (2009) Activity and neuromodulatory input contribute to the recovery of rhythmic output after decentralization in a central pattern generator. J Neurophysiol 101:372-86. PubMed
Central pattern generators (CPGs) are neuronal networks that control vitally important rhythmic behaviors including breathing, heartbeat, and digestion. Understanding how CPGs recover activity after their rhythmic activity is disrupted has important theoretical and practical implications. Previous experimental and modeling studies indicated that rhythm recovery after central neuromodulatory input loss (decentralization) could be based entirely on activity-dependent mechanisms, but recent evidence of long-term conductance regulation by neuromodulators suggest that neuromodulator-dependent mechanisms may also be involved. Here we examined the effects of altering activity and the neuromodulatory environment before decentralization of the pyloric CPG in Cancer borealis on the initial phase of rhythmic activity recovery after decentralization. We found that pretreatments altering the network activity through shifting the ionic balance or the membrane potential of pyloric pacemaker neurons reduced the delay of recovery initiation after decentralization, consistent with the recovery process being triggered already during the pretreatment period through an activity-dependent mechanism. However, we observed that pretreatment with neuromodulators GABA and proctolin, acting via metabotropic receptors, also affected the initial phase of the recovery of pyloric activity after decentralization. Their distinct effects appear to result from interactions of their metabotropic effects with their effects on neuronal activity. Thus we show that the initial phase of the recovery process can be accounted for by the existence of distinct activity-and neuromodulator-dependent pathways. We propose a computational model that includes activity- and neuromodulator-dependent mechanisms of the activity recovery process, which successfully explains the experimental observations and predicts the results of key biological experiments.
Zhang Y, Bose A and Nadim F (2009) The influence of the A-current on the dynamics of an oscillator-follower inhibitory network. SIAM J Appl Dyn Syst 8:1564-1590. PubMed
The transient potassium A-current is present in almost all neurons and plays an essential role in determining the timing and frequency of action potential generation. We use a three-variable mathematical model to examine the role of the A-current in a rhythmic inhibitory network, as is common in central pattern generation. We focus on a feed-forward architecture consisting of an oscillator neuron inhibiting a follower neuron. We use separation of time scales to demonstrate that the trajectory of the follower neuron within each cycle can be tracked by analyzing the dynamics on a 2-dimensional slow manifold that as determined by the two slow model variables: the recovery variable and the inactivation of the A-current. The steady-state trajectory, however, requires tracking the slow variables across multiple cycles. We show that tracking the slow variables, under simplifying assumptions, leads to a one-dimensional map of the unit interval with at most a single discontinuity depending on g(A), the maximal conductance of the A-current, or other model parameters. We demonstrate that, as the value of g(A) is varied, the trajectory of the follower neuron goes through a set of bifurcations to produce n:m periodic solutions where the follower neuron becomes active m times for each n cycles of the oscillator. Using a generalized Pascal triangle, each n:m trajectory can be constructed as a combination of solutions from a higher level of the triangle.
Tohidi V and Nadim F (2009) Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency. J Neurosci 29:6427-35. PubMed
Network oscillations typically span a limited range of frequency. In pacemaker-driven networks, including many central pattern generators (CPGs), this frequency range is determined by the properties of bursting pacemaker neurons and their synaptic connections; thus, factors that affect the burst frequency of pacemaker neurons should play a role in determining the network frequency. We examine the role of membrane resonance of pacemaker neurons on the network frequency in the crab pyloric CPG. The pyloric oscillations (frequency of approximately 1 Hz) are generated by a group of pacemaker neurons: the anterior burster (AB) and the pyloric dilator (PD). We examine the impedance profiles of the AB and PD neurons in response to sinusoidal current injections with varying frequency and find that both neuron types exhibit membrane resonance, i.e., demonstrate maximal impedance at a given preferred frequency. The membrane resonance frequencies of the AB and PD neurons fall within the range of the pyloric network oscillation frequency. Experiments with pharmacological blockers and computational modeling show that both calcium currents I(Ca) and the hyperpolarization-activated inward current I(h) are important in producing the membrane resonance in these neurons. We then demonstrate that both the membrane resonance frequency of the PD neuron and its suprathreshold bursting frequency can be shifted in the same direction by either direct current injection or by using the dynamic-clamp technique to inject artificial conductances for I(h) or I(Ca). Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.
Daur N, Nadim F and Stein W (2009) Regulation of motor patterns by the central spike-initiation zone of a sensory neuron. Eur J Neurosci 30:808-22. PubMed
Sensory feedback from muscles and peripheral sensors acts to initiate, tune or reshape motor activity according to the state of the body. Yet, sensory neurons often show low levels of activity even in the absence of sensory input. Here we examine the functional role of spontaneous low-frequency activity of such a sensory neuron. The anterior gastric receptor (AGR) is a muscle-tendon organ in the crab stomatogastric nervous system whose phasic activity shapes the well-characterized gastric mill (chewing) and pyloric (filtering) motor rhythms. Phasic activity is driven by a spike-initiation zone near the innervated muscle. We demonstrate that AGR possesses a second spike-initiation zone, which is located spatially distant from the innervated muscle in a central section of the axon. This initiation zone generates tonic activity and is responsible for the spontaneous activity of AGR in vivo, but does not code sensory information. Rather, it is sensitive to the neuromodulator octopamine. A computational model indicates that the activity at this initiation zone is not caused by excitatory input from another neuron, but generated intrinsically. This tonic activity is functionally relevant, because it modifies the activity state of the gastric mill motor circuit and changes the pyloric rhythm. The sensory function of AGR is not impaired as phasic activity suppresses spiking at the central initiation zone. Our results thus demonstrate that sensory neurons are not mere reporters of sensory signals. Neuromodulators can elicit non-sensory coding activity in these neurons that shapes the state of the motor system.
Clewley R, Soto-Trevino C and Nadim F (2009) Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron. J Comput Neurosci 26:75-90. PubMed
The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on "scales of dominance," to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation--tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.
Bucher D (2009) Neuronal homeostasis: does form follow function or vice versa?. Curr Biol 19:R64-7. PubMed
Nerve cells adjust their electrical excitability and the overall strength of synaptic connections to maintain their functional identity. A recent study suggests that they may also regulate dendritic branch patterns to compensate for the variability of synaptic contacts and help ensure appropriate connectivity in the brain.
Zhang Y, Bose A and Nadim F (2008) Predicting the activity phase of a follower neuron with A-current in an inhibitory network. Biol Cybern 99:171-84. PubMed
The transient potassium A-current is present in most neurons and plays an important role in determining the timing of action potentials. We examine the role of the A-current in the activity phase of a follower neuron in a rhythmic feed-forward inhibitory network with a reduced three-variable model and conduct experiments to verify the usefulness of our model. Using geometric analysis of dynamical systems, we explore the factors that determine the onset of activity in a follower neuron following release from inhibition. We first analyze the behavior of the follower neuron in a single cycle and find that the phase plane structure of the model can be used to predict the potential behaviors of the follower neuron following release from inhibition. We show that, depending on the relative scales of the inactivation time constant of the A-current and the time constant of the recovery variable, the follower neuron may or may not reach its active state following inhibition. Our simple model is used to derive a recursive set of equations to predict the contribution of the A-current parameters in determining the activity phase of a follower neuron as a function of the duration and frequency of the inhibitory input it receives. These equations can be used to demonstrate the dependence of activity phase on the period and duty cycle of the periodic inhibition, as seen by comparing the predictions of the model with the activity of the pyloric constrictor (PY) neurons in the crustacean pyloric network.
Nadim F, Brezina V, Destexhe A and Linster C (2008) State dependence of network output: modeling and experiments. J Neurosci 28:11806-13. PubMed
Emerging experimental evidence suggests that both networks and their component neurons respond to similar inputs differently, depending on the state of network activity. The network state is determined by the intrinsic dynamical structure of the network and may change as a function of neuromodulation, the balance or stochasticity of synaptic inputs to the network, and the history of network activity. Much of the knowledge on state-dependent effects comes from comparisons of awake and sleep states of the mammalian brain. Yet, the mechanisms underlying these states are difficult to unravel. Several vertebrate and invertebrate studies have elucidated cellular and synaptic mechanisms of state dependence resulting from neuromodulation, sensory input, and experience. Recent studies have combined modeling and experiments to examine the computational principles that emerge when network state is taken into account; these studies are highlighted in this article. We discuss these principles in a variety of systems (mammalian, crustacean, and mollusk) to demonstrate the unifying theme of state dependence of network output.
Smolinski T, Soto-Treviño C, Rabbah P, Nadim F and Prinz A (2008) Systematic selection of model parameter values matching biological behavior under different simulation scenarios. BMC Neurosci 9:53. PDF
Agbanusi I, Yarahmadi A, Bose A, Golowasch J and Nadim F (2008) Approximating the phase response curves of square wave bursting neurons. BMC Neurosci 9 (Suppl I):24. PDF
Mouser C, Nadim F and Bose A (2008) Maintaining phase of the crustacean tri-phasic pyloric rhythm. J Math Biol 57:161-81. PubMed
We construct and analyze a model network of the pyloric rhythm of the crustacean stomatogastric ganglion consisting of an oscillator neuron that inhibits two reciprocally inhibitory follower neurons. We derive analytic expressions that determine the phase of firing of the follower neurons with respect to the oscillator. An important aspect of the model is the inclusion of synapses that exhibit short-term synaptic depression. We show that these type of synapses allow there to be a complicated relationship between the intrinsic properties of the neurons and the synapses between them in determining phase relationships. Our analysis reveals the circumstances and ranges of cycle periods under which these properties work in concert with or independently from one another. In particular, we show that phase maintenance over a range of oscillator periods can be enhanced through the interplay of the two follower neurons if the synapses between these neurons are depressing. Since our model represents the core of the oscillatory pyloric network, the results of our analysis can be compared to experimental data and used to make predictions about the biological network.
Kintos N, Nusbaum MP and Nadim F (2008) A modeling comparison of projection neuron- and neuromodulator-elicited oscillations in a central pattern generating network. J Comput Neurosci 24:374-97. PubMed
Many central pattern generating networks are influenced by synaptic input from modulatory projection neurons. The network response to a projection neuron is sometimes mimicked by bath applying the neuronally-released modulator, despite the absence of network interactions with the projection neuron. One interesting example occurs in the crab stomatogastric ganglion (STG), where bath applying the neuropeptide pyrokinin (PK) elicits a gastric mill rhythm which is similar to that elicited by the projection neuron modulatory commissural neuron 1 (MCN1), despite the absence of PK in MCN1 and the fact that MCN1 is not active during the PK-elicited rhythm. MCN1 terminals have fast and slow synaptic actions on the gastric mill network and are presynaptically inhibited by this network in the STG. These local connections are inactive in the PK-elicited rhythm, and the mechanism underlying this rhythm is unknown. We use mathematical and biophysically-realistic modeling to propose potential mechanisms by which PK can elicit a gastric mill rhythm that is similar to the MCN1-elicited rhythm. We analyze slow-wave network oscillations using simplified mathematical models and, in parallel, develop biophysically-realistic models that account for fast, action potential-driven oscillations and some spatial structure of the network neurons. Our results illustrate how the actions of bath-applied neuromodulators can mimic those of descending projection neurons through mathematically similar but physiologically distinct mechanisms.
Blitz DM, White RS, Saideman SR, Cook A, Christie AE, Nadim F and Nusbaum MP (2008) A newly identified extrinsic input triggers a distinct gastric mill rhythm via activation of modulatory projection neurons. J Exp Biol 211:1000-11. PubMed
Neuronal network flexibility enables animals to respond appropriately to changes in their internal and external states. We are using the isolated crab stomatogastric nervous system to determine how extrinsic inputs contribute to network flexibility. The stomatogastric system includes the well-characterized gastric mill (chewing) and pyloric (filtering of chewed food) motor circuits in the stomatogastric ganglion. Projection neurons with somata in the commissural ganglia (CoGs) regulate these rhythms. Previous work characterized a unique gastric mill rhythm that occurred spontaneously in some preparations, but whose origin remained undetermined. This rhythm includes a distinct protractor phase activity pattern, during which a key gastric mill circuit neuron (LG neuron) and the projection neurons MCN1 and CPN2 fire in a pyloric rhythm-timed activity pattern instead of the tonic firing pattern exhibited by these neurons during previously studied gastric mill rhythms. Here we identify a new extrinsic input, the post-oesophageal commissure (POC) neurons, relatively brief stimulation (30 s) of which triggers a long-lasting (tens of minutes) activation of this novel gastric mill rhythm at least in part via its lasting activation of MCN1 and CPN2. Immunocytochemical and electrophysiological data suggest that the POC neurons excite MCN1 and CPN2 by release of the neuropeptide Cancer borealis tachykinin-related peptide Ia (CabTRP Ia). These data further suggest that the CoG arborization of the POC neurons comprises the previously identified anterior commissural organ (ACO), a CabTRP Ia-containing neurohemal organ. This endocrine organ thus appears to also have paracrine actions, including activation of a novel and lasting gastric mill rhythm.
Rabbah P and Nadim F (2007) Distinct synaptic dynamics of heterogeneous pacemaker neurons in an oscillatory network. J Neurophysiol 97:2239-53. PubMed
Many rhythmically active networks involve heterogeneous populations of pacemaker neurons with potentially distinct synaptic outputs that can be differentially targeted by extrinsic inputs or neuromodulators, thereby increasing possible network output patterns. To understand the roles of heterogeneous pacemaker neurons, we characterized differences in synaptic output from the anterior burster (AB) and pyloric dilator (PD) neurons in the lobster pyloric network. These intrinsically distinct neurons are strongly electrically coupled, coactive, and constitute the pyloric pacemaker ensemble. During pyloric oscillations, the pacemaker neurons produce compound inhibitory synaptic connections to the follower lateral pyloric (LP) and pyloric constrictor (PY) neurons, which fire out of phase with AB/PD and with different delay times. Using pharmacological blockers, we separated the synapses originating from the AB and PD neurons and investigated their temporal dynamics. These synapses exhibited distinct short-term dynamics, depending on the presynaptic neuron type, and had different relative contributions to the total synaptic output depending on waveform shape and cycle frequency. However, paired comparisons revealed that the amplitude or dynamics of synapses from either the AB or PD neuron did not depend on the postsynaptic neuron type, LP or PY. To address the functional implications of these findings, we examined the correlation between synaptic inputs from the pacemakers and the burst onset phase of the LP and PY neurons in the ongoing pyloric rhythm. These comparisons showed that the activity of the LP and PY neurons is influenced by the peak phase and amplitude of the synaptic inputs from the pacemaker neurons.
Matveev V, Bose A and Nadim F (2007) Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map. J Comput Neurosci 23:169-87. PubMed
Out-of-phase bursting is a functionally important behavior displayed by central pattern generators and other neural circuits. Understanding this complex activity requires the knowledge of the interplay between the intrinsic cell properties and the properties of synaptic coupling between the cells. Here we describe a simple method that allows us to investigate the existence and stability of anti-phase bursting solutions in a network of two spiking neurons, each possessing a T-type calcium current and coupled by reciprocal inhibition. We derive a one-dimensional map which fully characterizes the genesis and regulation of anti-phase bursting arising from the interaction of the T-current properties with the properties of synaptic inhibition. This map is the burst length return map formed as the composition of two distinct one-dimensional maps that are each regulated by a different set of model parameters. Although each map is constructed using the properties of a single isolated model neuron, the composition of the two maps accurately captures the behavior of the full network. We analyze the parameter sensitivity of these maps to determine the influence of both the intrinsic cell properties and the synaptic properties on the burst length, and to find the conditions under which multistability of several bursting solutions is achieved. Although the derivation of the map relies on a number of simplifying assumptions, we discuss how the principle features of this dimensional reduction method could be extended to more realistic model networks.
Gansert J, Golowasch J and Nadim F (2007) Sustained rhythmic activity in gap-junctionally coupled networks of model neurons depends on the diameter of coupled dendrites. J Neurophysiol 98:3450-60. PubMed
Gap junctions are known to be important for many network functions such as synchronization of activity and the generation of waves and oscillations. Gap junctions have also been proposed to be essential for the generation of early embryonic activity. We have previously shown that the amplitude of electrical signals propagating across gap-junctionally coupled passive cables is maximized at a unique diameter. This suggests that threshold-dependent signals may propagate through gap junctions for a finite range of diameters around this optimal value. Here we examine the diameter dependence of action potential propagation across model networks of dendro-dendritically coupled neurons. The neurons in these models have passive soma and dendrites and an action potential-generating axon. We show that propagation of action potentials across gap junctions occurs only over a finite range of dendritic diameters and that propagation delay depends on this diameter. Additionally, in networks of gap-junctionally coupled neurons, rhythmic activity can emerge when closed loops (re-entrant paths) occur but again only for a finite range of dendrite diameters. The frequency of such rhythmic activity depends on the length of the path and the dendrite diameter. For large networks of randomly coupled neurons, we find that the re-entrant paths that underlie rhythmic activity also depend on dendrite diameter. These results underline the potential importance of dendrite diameter as a determinant of network activity in gap-junctionally coupled networks, such as network rhythms that are observed during early nervous system development.
Marder E and Bucher D (2007) Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu Rev Physiol 69:291-316. PubMed
Studies of the stomatogastric nervous systems of lobsters and crabs have led to numerous insights into the cellular and circuit mechanisms that generate rhythmic motor patterns. The small number of easily identifiable neurons allowed the establishment of connectivity diagrams among the neurons of the stomatogastric ganglion. We now know that (a) neuromodulatory substances reconfigure circuit dynamics by altering synaptic strength and voltage-dependent conductances and (b) individual neurons can switch among different functional circuits. Computational and experimental studies of single-neuron and network homeostatic regulation have provided insight into compensatory mechanisms that can underlie stable network performance. Many of the observations first made using the stomatogastric nervous system can be generalized to other invertebrate and vertebrate circuits.
Rotstein HG and Nadim F (2007) Neurons and Neural Networks: Computational Models. In: Encyclopedia of Life Sciences. John Wiley & Sons. Wiley
Mouser C, Nadim F and Bose A (2007) Maintaining phase of the tri-phasic crab pyloric rhythm. BMC Neurosci 8:97. PDF
Smolinski T, Soto-Treviño C, Rabbah P, Nadim F and Prinz A (2007) Systematic computational exploration of the parameter space of the multi-compartment model of the lobster pyloric pacemaker kernel suggests that the kernel can achieve functional activity under various parameter configurations. BMC Neurosci 8:164. PDF
Zhang Y, Bose A and Nadim F (2007) Determining the effect of the A-current on the activity phase of a follower neuron in an inhibitory network. BMC Neurosci 8:48. PDF
Nadim F and Bose A (2007) Dynamics of central pattern generating networks: Locus of control. SIAM News 40:151. PDF
Smolinski T, Soto-Treviño C, Rabbah P, Nadim F and Prinz A (2007) Analysis of biological neurons via modeling and rule mining. International J of Info Tech and Intelligent Computing 1:293-302.
Khorkova O and Golowasch J (2007) Neuromodulators, not activity, control coordinated expression of ionic currents. J Neurosci 27:8709-18. PubMed
Electrical activity in identical neurons across individuals is often remarkably similar and stable over long periods. However, the ionic currents that determine the electrical activity of these neurons show wide animal-to-animal amplitude variability. This seemingly random variability of individual current amplitudes may obscure mechanisms that globally reduce variability and that contribute to the generation of similar neuronal output. One such mechanism could be the coordinated regulation of ionic current expression. Studying identified neurons of the Cancer borealis pyloric network, we discovered that the removal of neuromodulatory input to this network (decentralization) was accompanied by the loss of the coordinated regulation of ionic current levels. Additionally, decentralization induced large changes in the levels of several ionic currents. The loss of coregulation and the changes in current levels were prevented by continuous exogenous application of proctolin, an endogenous neuromodulatory peptide, to the pyloric network. This peptide does not exert fast regulatory actions on any of the currents affected by decentralization. We conclude that neuromodulatory inputs to the pyloric network have a novel role in the regulation of ionic current expression. They can control, over the long term, the coordinated expression of multiple voltage-gated ionic currents that they do not acutely modulate. Our results suggest that current coregulation places constraints on neuronal intrinsic plasticity and the ability of a network to respond to perturbations. The loss of conductance coregulation may be a mechanism to facilitate the recovery of function.
Drover JD, Tohidi V, Bose A and Nadim F (2007) Combining synaptic and cellular resonance in a feed-forward neuronal network. Neurocomputing 70:2041-2045. PubMed
We derive a mathematical theory to explain the subthreshold resonance response of a neuron to synaptic input. The theory shows how a neuron combines information from its intrinsic resonant properties with those of the synapse to determine the neuron's generalized resonance response. Our results show that the maximal response of a postsynaptic neuron can lie between the preferred intrinsic frequency of the neuron and the synaptic resonance frequency. We compare our theoretical results to parallel findings on experiments of the crab pyloric central pattern generator.
Zhang Y and Golowasch J (2007) Modeling Recovery of Rhythmic Activity: Hypothesis for the role of a calcium pump. Neurocomputing 70:1657-1662. PDF
Bucher D, Johnson CD and Marder E (2007) Neuronal morphology and neuropil structure in the stomatogastric ganglion of the lobster, Homarus americanus. J Comp Neurol 501:185-205. PubMed
The stomatogastric nervous system (STNS) has long been used as a model system for the study of central pattern generation, neuromodulation, and network dynamics. Anatomical studies of the crustacean stomatogastric ganglion (STG) in different species have mostly been restricted to subsets of neurons and/or general structural features. For the first time, we describe the morphology of all STG neurons belonging to the two circuits that produce the well-described pyloric and gastric rhythms in the lobster, Homarus americanus. Somata sit on the dorsal and lateral surface of the STG and send a single primary neurite into the core of the neuropil, which is mostly made up of larger lower order branches. The perimeter of the neuropil consists mostly of finer higher order branches. Immunohistochemical labeling for synaptic proteins is associated with the small diameter branches. Somata positions are not constant but show preferred locations across individuals. The number of copies is constant for all neuron types except the PY and GM neurons (PY neuron number ranges from 3 to 7, and GM neuron number ranges from 6 to 9). Branch structure is largely nondichotomous, and branches can deviate substantially from cylindrical shape. Diameter changes at branch points can be as large as 20-fold. Clearly, the morphology of a specific neuron type can be quite variable from animal to animal.
Zhou L, Zhao S and Nadim F (2007) Neuromodulation of short-term synaptic dynamics examined in a mechanistic model based on kinetics of calcium currents. Neurocomputing 70:2050-2054. PubMed
Network plasticity arises in large part due to the effects of exogenous neuromodulators. We investigate the neuromodulatory effects on short-term synaptic dynamics. The synapse from the lateral pyloric (LP) to the pyloric dilator (PD) neuron in the pyloric network of the crab C. borealis has both spike-mediated and non-spike-mediated (graded) components. Previous studies have shown that the graded component of this synapse exhibits short-term depression. Recent results from our lab indicate that in the presence of neuromodulatory peptide proctolin, low-amplitude presynaptic stimuli switch the short-term dynamics of this graded component from depression to facilitation. In this study, we show that this facilitation is correlated with the activation of a presynaptic inward current that is blocked by Mn(2+) suggesting that it is a slowly-accumulating Ca(2+) current. We modify a mechanistic model of synaptic release by assuming that the low-voltage-activating Ca(2+) current in our system is composed of two currents with fast (I(CaF)) and slow (I(CaS)) kinetics. We show that if proctolin adjusts the activation rate of I(CaS), this leads to accumulation of local intracellular Ca(2+) in response to multiple presynaptic voltage stimuli which, in turn, results in synaptic facilitation. Additionally, we assume that proctolin increases the maximal conductances of Ca(2+) currents in the model, consistent with the increased synaptic release found in the experiments. We find that these two presynaptic actions of proctolin in the model are sufficient to describe its actions on the short-term dynamics of the LP to PD synapse.
Ambrosio-Mouser C, Nadim F and Bose A (2006) The effects of varying the timing of inputs on a neural oscillator. SIAM J Appl Dyn Syst 5:108-139. PubMed
The gastric mill network of the stomatogastric ganglion of the crab Cancer borealis is comprised of a set of neurons that require modulatory input from outside the stomatogastric ganglion and input from the pyloric network of the animal in order to oscillate. Here we study how the frequency of the gastric mill network is determined when it receives rhythmic input from two different sources but where the timing of these inputs may differ. We find that over a certain range of the time difference one of the two rhythmic inputs plays no role what so ever in determining the network frequency, while in another range, both inputs work together to determine the frequency. The existence and stability of periodic solutions to model sets of equations are obtained analytically using geometric singular perturbation theory. The results are validated through numerical simulations. Comparisons to experiments are also presented.
Bucher D, Taylor AL and Marder E (2006) Central pattern generating neurons simultaneously express fast and slow rhythmic activities in the stomatogastric ganglion. J Neurophysiol 95:3617-32. PubMed
Neuronal firing patterns can contain different temporal information. It has long been known that the fast pyloric and the slower gastric motor patterns in the stomatogastric ganglion of decapod crustaceans interact. However, the bidirectional influences between the pyloric rhythm and the gastric mill rhythm have not been quantified in detail from preparations that spontaneously express both patterns in vitro. We found regular and stable spontaneous gastric and pyloric activity in 71% of preparations of the isolated stomatogastric nervous system of the lobster, Homarus americanus. The gastric [cycle period: 10.96 +/- 2.67 (SD) s] and pyloric (cycle period: 1.35 +/- 0.18 s) patterns showed bidirectional interactions and coordination. Gastric neuron firing showed preferred phases within the reference frame of the pyloric cycle. The relative timing and burst parameters of the pyloric neurons systematically changed within the reference frame of the gastric cycle. The gastric rhythm showed a tendency to run at cycle periods that were integer multiples of the pyloric periods, but coupling and coordination between the two rhythms were variable. We used power spectra to quantify the gastric and pyloric contributions to the firing pattern of each individual neuron. This provided us with a way to analyze the firing pattern of each gastric and pyloric neuron type individually without reference to either gastric or pyloric phase. Possible functional consequences of these network interactions for motor output are discussed.
Nadim F and Golowasch J (2006) Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter. J Neurophysiol 95:3831-43. PubMed
We analyze simple morphological configurations that represent gap-junctional coupling between neuronal processes or between muscle fibers. Specifically, we use cable theory and simulations to examine the consequences of current flow from one cable to other gap-junctionally coupled passive cables. When the proximal end of the first cable is voltage clamped, the amplitude of the electrical signal in distal portions of the second cable depends on the cable diameter. However, this amplitude does not simply increase if cable diameter is increased, as expected from the larger length constant; instead, an optimal diameter exists. The optimal diameter arises because the dependency of voltage attenuation along the second cable on cable diameter follows two opposing rules. As cable diameter increases, the attenuation decreases because of a larger length constant yet increases because of a reduction in current density arising from the limiting effect of the gap junction on current flow into the second cable. The optimal diameter depends on the gap junction resistance and cable parameters. In branched cables, dependency on diameter is local and thus may serve to functionally compartmentalize branches that are coupled to other cells. Such compartmentalization may be important when periodic signals or action potentials cause the current flow across gap junctions.
Zhou L, LoMauro R and Nadim F (2006) The interaction between facilitation and depression of two release mechanisms in a single synapse. Neurocomputing 69:1001-1005. ScienceDirect
The synapse from the lateral pyloric (LP) to the pyloric dilator (PD) neuron in the stomatogastric nervous system of the crab Cancer borealis has both a graded and a spike-mediated component. These two components have opposite short-term dynamics: the spike-mediated component is usually facilitating, while the graded component is depressing. We built a model of these two synaptic components and their interactions, based on the concept of quantal release evoked by calcium influx. This model is able to accurately predict the postsynaptic response of the PD neuron to any temporally patterned presynaptic LP neuron activity.
Haedo RJ and Golowasch J (2006) Ionic mechanism underlying recovery of rhythmic activity in adult isolated neurons. J Neurophysiol 96:1860-76. PubMed
Neurons exhibit long-term excitability changes necessary for maintaining proper cell and network activity in response to various inputs and perturbations. For instance, the adult crustacean pyloric network can spontaneously recover rhythmic activity after complete shutdown resulting from permanent removal of neuromodulatory inputs. Dissociated lobster stomatogastric ganglion (STG) neurons have been shown to spontaneously develop oscillatory activity via excitability changes. Rhythmic electrical stimulation can eliminate these oscillatory patterns in some cells. The ionic mechanisms underlying these changes are only partially understood. We used dissociated crab STG neurons to study the ionic mechanisms underlying spontaneous recovery of rhythmic activity and stimulation-induced activity changes. Similar to lobster neurons, rhythmic activity spontaneously develops in crab STG neurons. Rhythmic hyperpolarizing stimulation can eliminate, but more commonly accelerate, the emergence of stable oscillatory activity depending on Ca(2+) influx at hyperpolarized voltages. Our main finding is that upregulation of a Ca(2+) current and downregulation of a high-threshold K(+) current underlies the spontaneous homeostatic development of oscillatory activity. However, because of a nonlinear dependence on stimulus frequency, hyperpolarization-induced oscillations appear to be inconsistent with a homeostatic regulation of activity. We find no difference in the activity patterns or the underlying ionic currents involved between neurons of the fast pyloric and the slow gastric mill networks during the first 10 days in isolation. Dynamic-clamp experiments confirm that these conductance modifications can explain the observed activity changes. We conclude that spontaneous and stimulation-induced excitability changes in STG neurons can both result in intrinsic oscillatory activity via regulation of the same two conductances.
Rabbah P and Nadim F (2005) Synaptic dynamics do not determine proper phase of activity in a central pattern generator. J Neurosci 25:11269-78. PubMed
Rhythmic motor activity often requires neuronal output to the muscles to arrive in a particular sequence. At the pattern-generator level, this requires distinct activity phases in different groups of constituent neurons. The phase differences between rhythmically active neurons in a network are thought to arise from the interplay between their intrinsic properties and the temporal dynamics of synapses among these neurons. In the rhythmically active pyloric network of the lobster Panulirus interruptus, synaptic connections from the pacemaker ensemble to the follower neurons [lateral pyloric (LP) and pyloric constrictor (PY)] are thought to be primarily responsible for the proper phase of activity (pacemaker-LP-PY) across all frequencies (0.5-2 Hz) of the pyloric rhythm. We test this hypothesis by characterizing the synapses from the pacemaker ensemble to the LP and PY neurons. Paired comparisons show that these two synapses are not significantly different in strength or in the extent of short-term depression. To examine the level to which intrinsic properties of the follower neurons determine their relative activity phase, we block all chemical synapses within the network and drive the LP and PY neurons rhythmically using artificial synaptic currents with identical strength and dynamics implemented with the dynamic-clamp technique. In response to these identical synaptic inputs, the LP and PY neurons maintain the proper relative phase of activity. These results strongly indicate that the relative phase of activity among these follower neurons within the pyloric network is not dictated by their synaptic inputs but is solely determined by their distinct intrinsic properties.
Soto-Trevino C, Rabbah P, Marder E and Nadim F (2005) Computational model of electrically coupled, intrinsically distinct pacemaker neurons. J Neurophysiol 94:590-604. PubMed
Electrical coupling between neurons with similar properties is often studied. Nonetheless, the role of electrical coupling between neurons with widely different intrinsic properties also occurs, but is less well understood. Inspired by the pacemaker group of the crustacean pyloric network, we developed a multicompartment, conductance-based model of a small network of intrinsically distinct, electrically coupled neurons. In the pyloric network, a small intrinsically bursting neuron, through gap junctions, drives 2 larger, tonically spiking neurons to reliably burst in-phase with it. Each model neuron has 2 compartments, one responsible for spike generation and the other for producing a slow, large-amplitude oscillation. We illustrate how these compartments interact and determine the dynamics of the model neurons. Our model captures the dynamic oscillation range measured from the isolated and coupled biological neurons. At the network level, we explore the range of coupling strengths for which synchronous bursting oscillations are possible. The spatial segregation of ionic currents significantly enhances the ability of the 2 neurons to burst synchronously, and the oscillation range of the model pacemaker network depends not only on the strength of the electrical synapse but also on the identity of the neuron receiving inputs. We also compare the activity of the electrically coupled, distinct neurons with that of a network of coupled identical bursting neurons. For small to moderate coupling strengths, the network of identical elements, when receiving asymmetrical inputs, can have a smaller dynamic range of oscillation than that of its constituent neurons in isolation.
Beenhakker MP, DeLong ND, Saideman SR, Nadim F and Nusbaum MP (2005) Proprioceptor regulation of motor circuit activity by presynaptic inhibition of a modulatory projection neuron. J Neurosci 25:8794-806. PubMed
Phasically active sensory systems commonly influence rhythmic motor activity via synaptic actions on the relevant circuit and/or motor neurons. Using the crab stomatogastric nervous system (STNS), we identified a distinct synaptic action by which an identified proprioceptor, the gastropyloric muscle stretch receptor (GPR) neuron, regulates the gastric mill (chewing) motor rhythm. Previous work showed that rhythmically stimulating GPR in a gastric mill-like pattern, in the isolated STNS, elicits the gastric mill rhythm via its activation of two identified projection neurons, modulatory commissural neuron 1 (MCN1) and commissural projection neuron 2, in the commissural ganglia. Here, we determine how activation of GPR with a behaviorally appropriate pattern (active during each gastric mill retractor phase) influences an ongoing gastric mill rhythm via actions in the stomato gastric ganglion, where the gastric mill circuit is located. Stimulating GPR during each retractor phase selectively prolongs that phase and thereby slows the ongoing rhythm. This selective action on the retractor phase results from two distinct GPR actions. First, GPR presynaptically inhibits the axon terminals of MCN1, reducing MCN1 excitation of all gastric mill neurons. Second, GPR directly excites the retractor phase neurons. Because MCN1 transmitter release occurs during each retractor phase, these parallel GPR actions selectively reduce the buildup of excitatory drive to the protractor phase neurons, delaying each protractor burst. Thus, rhythmic proprioceptor feedback to a motor circuit can result from a global reduction in excitatory drive to that circuit, via presynaptic inhibition, coupled with a phase-specific excitatory input that prolongs the excited phase by delaying the onset of the subsequent phase.
Bucher D, Prinz AA and Marder E (2005) Animal-to-animal variability in motor pattern production in adults and during growth. J Neurosci 25:1611-9. PubMed
Which features of network output are well preserved during growth of the nervous system and across different preparations of the same size? To address this issue, we characterized the pyloric rhythms generated by the stomatogastric nervous systems of 99 adult and 12 juvenile lobsters (Homarus americanus). Anatomical studies of single pyloric network neurons and of the whole stomatogastric ganglion (STG) showed that the STG and its neurons grow considerably from juvenile to adult. Despite these changes in size, intracellularly recorded membrane potential waveforms of pyloric network neurons and the phase relationships in the pyloric rhythm were very similar between juvenile and adult preparations. Across adult preparations, the cycle period and number of spikes per burst were not tightly maintained, but the mean phase relationships were independent of the period of the rhythm and relatively tightly maintained across preparations. We interpret this as evidence for homeostatic regulation of network activity.
Johnson BR, Schneider LR, Nadim F and Harris-Warrick RM (2005) Dopamine modulation of phasing of activity in a rhythmic motor network: contribution of synaptic and intrinsic modulatory actions. J Neurophysiol 94:3101-11. PubMed
The phasing of neuronal activity in a rhythmic motor network is determined by a neuron's intrinsic firing properties and synaptic inputs; these could vary in their relative importance under different modulatory conditions. In the lobster pyloric network, the firing of eight follower pyloric (PY) neurons is shaped by their intrinsic rebound after pacemaker inhibition and by synaptic input from the lateral pyloric (LP) neuron, which inhibits all PY neurons and is electrically coupled to a subset of them. Under control conditions, LP inhibition is weak and has little influence on PY firing. We examined modulation that could theoretically enhance the LP's synaptic contribution to PY firing. We measured the effects of dopamine (DA) on LP-->PY synapses, driving the LP neuron with trains of realistic waveforms constructed from prerecorded control and DA LP oscillations, which differed in shape and duration. Under control conditions, chemical inhibition underwent severe depression and disappeared; in the mixed synapses, electrical coupling dominated. Switching between control and DA LP waveforms (with or without DA present) caused only subtle changes in synaptic transmission. DA markedly enhanced synaptic inhibition, reduced synaptic depression and weakened electrical coupling, reversing the sign of the mixed synapses. Despite this, removal of the LP from the intact network still had only weak effects on PY firing. DA also enhances PY intrinsic rebound properties, which still control the onset of PY firing. Thus in a rhythmic network, the functional importance of synaptic modulation can only be understood in the context of parallel modulation of intrinsic properties.
Marder E and Bucher D (2005) Robustness in Neuronal Systems: The Balance Between Homeostasis, Plasticity, and Modulation. In: Robust Design: A Repertoire of Biological, Ecological, and Engineering Case Studies (Jen E, ed). Oxford University Press, New York. Google full text
Mamiya A and Nadim F (2005) Target-specific short-term dynamics are important for the function of synapses in an oscillatory neural network. J Neurophysiol 94:2590-602. PubMed
Short-term dynamics such as facilitation and depression are present in most synapses and are often target-specific even for synapses from the same type of neuron. We examine the dynamics and possible functions of two synapses from the same presynaptic neuron in the rhythmically active pyloric network of the spiny lobster. Using simultaneous recordings, we show that the synapses from the lateral pyloric (LP) neuron to the pyloric dilator (PD; a member of the pyloric pacemaker ensemble) and the pyloric constrictor (PY) neurons both show short-term depression. However, the postsynaptic potentials produced by the LP-to-PD synapse are larger in amplitude, depress less, and recover faster than those produced by the LP-to-PY synapse. The main function of the LP-to-PD synapse is to slow down the pyloric rhythm. However, in some cases, it slows down the rhythm only when it is fast and has no effect or to speeds up when it is slow. In contrast, the LP-to-PY synapse functions to delay the activity of the PY neuron; this delay increases as the cycle period becomes longer. Using a computational model, we show that the short-term dynamics of synaptic depression observed for each of these synapses are tailored to their individual functions and that replacing the dynamics of either synapse with the other would disrupt these functions. Together, the experimental and modeling results suggest that the target-specific features of short-term synaptic depression are functionally important for synapses efferent from the same presynaptic neuron.
Ambrosio C, Bose A and Nadim F (2005) The effect of modulatory neuronal input on gastric mill frequency. Neurocomputing 65:623-631. ScienceDirect
We study the crustacean stomatogastric nervous system to gain insight in the interaction of oscillators of different intrinsic frequencies. We show how fast inhibition from the pyloric network interacts with a slow modulatory input to control the frequency of the gastric mill rhythm. We deduce that the timing of the pyloric input is crucial in determining what effect it will have on the frequency of the gastric network. Over one set of timings, the modulatory input and the pyloric input work together to determine the frequency and over another set of timings, the effect of the pyloric input is mitigated by the modulatory input.
Marder E, Bucher D, Schulz DJ and Taylor AL (2005) Invertebrate central pattern generation moves along. Curr Biol 15:R685-99. PubMed
Central pattern generators (CPGs) are circuits that generate organized and repetitive motor patterns, such as those underlying feeding, locomotion and respiration. We summarize recent work on invertebrate CPGs which has provided new insights into how rhythmic motor patterns are produced and how they are controlled by higher-order command and modulatory interneurons.
Pulver SR, Bucher D, Simon DJ and Marder E (2005) Constant amplitude of postsynaptic responses for single presynaptic action potentials but not bursting input during growth of an identified neuromuscular junction in the lobster, Homarus americanus. J Neurobiol 62:47-61. PubMed
As lobsters grow from early juveniles to adults their body size increases more than 20-fold, raising the question of how function is maintained during these ongoing changes in size. To address this question we studied the pyloric 1 (p1) muscle of the stomach of the lobster, Homarus americanus. The p1 muscle receives multiterminal innervation from one motor neuron, the lateral pyloric neuron of the stomatogastric ganglion. Staining with antibodies raised against synaptotagmin showed that as the muscle fibers increased in length, the spacing between the terminal innervation increased proportionally, so the number of synaptic contact regions/muscle fiber did not change. Muscle fibers were electrically coupled in both juveniles and adults. The amplitude of single intracellularly recorded excitatory junctional potentials evoked by motor nerve stimulation was the same in both juveniles and adults. Nonetheless, the peak depolarizations reached in response to ongoing pyloric rhythm activity or in response to high-frequency trains of stimuli similar to those produced during the pyloric rhythm were approximately twofold larger in juveniles than in adults. This suggests that homeostatic regulation of synaptic connections may operate at the level of the amplitude of the single synaptic potential rather than on the summed depolarization evoked during strong rhythmic activity.
Rabbah P, Golowasch J and Nadim F (2005) Effect of electrical coupling on ionic current and synaptic potential measurements. J Neurophysiol 94:519-30. PubMed
Recent studies have found electrical coupling to be more ubiquitous than previously thought, and coupling through gap junctions is known to play a crucial role in neuronal function and network output. In particular, current spread through gap junctions may affect the activation of voltage-dependent conductances as well as chemical synaptic release. Using voltage-clamp recordings of two strongly electrically coupled neurons of the lobster stomatogastric ganglion and conductance-based models of these neurons, we identified effects of electrical coupling on the measurement of leak and voltage-gated outward currents, as well as synaptic potentials. Experimental measurements showed that both leak and voltage-gated outward currents are recruited by gap junctions from neurons coupled to the clamped cell. Nevertheless, in spite of the strong coupling between these neurons, the errors made in estimating voltage-gated conductance parameters were relatively minor (<10%). Thus in many cases isolation of coupled neurons may not be required if a small degree of measurement error of the voltage-gated currents or the synaptic potentials is acceptable. Modeling results show, however, that such errors may be as high as 20% if the gap-junction position is near the recording site or as high as 90% when measuring smaller voltage-gated ionic currents. Paradoxically, improved space clamp increases the errors arising from electrical coupling because voltage control across gap junctions is poor for even the highest realistic coupling conductances. Furthermore, the common procedure of leak subtraction can add an extra error to the conductance measurement, the sign of which depends on the maximal conductance.
Buschges A, Ludwar B, Bucher D, Schmidt J and DiCaprio RA (2004) Synaptic drive contributing to rhythmic activation of motoneurons in the deafferented stick insect walking system. Eur J Neurosci 19:1856-62. PubMed
A general feature of motor patterns for locomotion is their cyclic and alternating organization. In walking, for example, rhythmic activity in leg motoneurons innervating antagonistic muscles of a joint is primarily antiphasic within each cycle. We investigate which role central pattern generating networks play in the generation of leg motoneuron activity in the absence of sensory feedback. We elicited activity in antagonistic flexor and extensor tibiae motoneurons in the deafferented mesothoracic ganglion of the stick insect by mechanically stimulating the head or abdomen, while recording intracellularly from their neuropilar processes. In most cases, tactile stimulation induced coactivation of tibial motoneurons. However, in approximately 25% of the trials, tibial motoneurons generated alternating cycles consisting of bursts of action potentials that were terminated by strong inhibitory synaptic inputs. Injection of depolarizing current increased the amplitude of the inhibitory phase of the oscillation, while hyperpolarizing current decreased it and revealed a tonic depolarization of the motor neurons during the bout of rhythmic motor activity. The same results were gathered from recording tibial leg motoneurons during 'twitching' motor activity in decerebrated animals. Our results indicate that alternating rhythmic motoneuron activity in the deafferented stick insect walking system results from phasic inhibitory drive provided by central pattern generating networks. This inhibitory input patterns the firing of the motoneurons that results from a tonic depolarizing drive. This tonic depolarizing drive was also observed in tibial motoneurons of the deafferented mesothoracic ganglion during walking movements of the intact ipsilateral front leg.
Wood DE, Manor Y, Nadim F and Nusbaum MP (2004) Intercircuit control via rhythmic regulation of projection neuron activity. J Neurosci 24:7455-63. PubMed
Synaptic feedback from rhythmically active neuronal circuits commonly causes their descending inputs to exhibit the rhythmic activity pattern generated by that circuit. In most cases, however, the function of this rhythmic feedback is unknown. In fact, generally these inputs can still activate the target circuit when driven in a tonic activity pattern. We are using the crab stomatogastric nervous system (STNS) to test the hypothesis that the neuronal circuit-mediated rhythmic activity pattern in projection neurons contributes to intercircuit regulation. The crab STNS contains an identified projection neuron, modulatory commissural neuron 1 (MCN1), whose tonic stimulation activates and modulates the gastric mill (chewing) and pyloric (filtering of chewed food) motor circuits in the stomatogastric ganglion (STG). During tonic stimulation of MCN1, the pyloric circuit regulates both gastric mill cycle frequency and gastropyloric coordination via a direct synapse onto a gastric mill neuron in the STG. However, when MCN1 is spontaneously active, it has a pyloric-timed activity pattern attributable to synaptic input from the pyloric circuit. This pyloric-timed activity in MCN1 provides the pyloric circuit with a second pathway for regulating the gastric mill rhythm. At these times, the direct STG synapse from the pyloric circuit to the gastric mill circuit is not necessary for pyloric regulation of the gastric mill rhythm. However, in the intact system, these two pathways play complementary roles in this intercircuit regulation. Thus, one role for rhythmicity in modulatory projection neurons is to enable them to mediate the interactions between distinct but related neuronal circuits.
Prinz AA, Bucher D and Marder E (2004) Similar network activity from disparate circuit parameters. Nat Neurosci 7:1345-52. PubMed
It is often assumed that cellular and synaptic properties need to be regulated to specific values to allow a neuronal network to function properly. To determine how tightly neuronal properties and synaptic strengths need to be tuned to produce a given network output, we simulated more than 20 million versions of a three-cell model of the pyloric network of the crustacean stomatogastric ganglion using different combinations of synapse strengths and neuron properties. We found that virtually indistinguishable network activity can arise from widely disparate sets of underlying mechanisms, suggesting that there could be considerable animal-to-animal variability in many of the parameters that control network activity, and that many different combinations of synaptic strengths and intrinsic membrane properties can be consistent with appropriate network performance.
Mamiya A and Nadim F (2004) Dynamic interaction of oscillatory neurons coupled with reciprocally inhibitory synapses acts to stabilize the rhythm period. J Neurosci 24:5140-50. PubMed
In the rhythmically active pyloric circuit of the spiny lobster, the pyloric dilator (PD) neurons are members of the pacemaker group of neurons that make inhibitory synapses onto the follower lateral pyloric (LP) neuron. The LP neuron, in turn, makes a depressing inhibitory synapse to the PD neurons, providing the sole inhibitory feedback from the pyloric network to its pacemakers. This study investigates the dynamic interaction between the pyloric cycle period, the two types of neurons, and the feedback synapse in biologically realistic conditions. When the rhythm period was changed, the membrane potential waveform of the LP neuron was affected with a consistent pattern. These changes in the LP neuron waveform directly affected the dynamics of the LP to PD synapse and caused the postsynaptic potential (PSP) in the PD neurons to both peak earlier in phase and become larger in amplitude. Using an artificial synapse implemented in dynamic clamp, we show that when the LP to PD PSP occurred early in phase, it acted to speed up the pyloric rhythm, and larger PSPs also strengthened this trend. Together, these results indicate that interactions between these two types of neurons can dynamically change in response to increases in the rhythm period, and this dynamic change provides a negative feedback to the pacemaker group that could work to stabilize the rhythm period.
Bose A, Manor Y and Nadim F (2004) The activity phase of postsynaptic neurons in a simplified rhythmic network. J Comput Neurosci 17:245-61. PubMed
Many inhibitory rhythmic networks produce activity in a range of frequencies. The relative phase of activity between neurons in these networks is often a determinant of the network output. This relative phase is determined by the interaction between synaptic inputs to the neurons and their intrinsic properties. We show, in a simplified network consisting of an oscillator inhibiting a follower neuron, how the interaction between synaptic depression and a transient potassium current in the follower neuron determines the activity phase of this neuron. We derive a mathematical expression to determine at what phase of the oscillation the follower neuron becomes active. This expression can be used to understand which parameters determine the phase of activity of the follower as the frequency of the oscillator is changed. We show that in the presence of synaptic depression, there can be three distinct frequency intervals, in which the phase of the follower neuron is determined by different sets of parameters. Alternatively, when the synapse is not depressing, only one set of parameters determines the phase of activity at all frequencies.
Bucher D, Thirumalai V and Marder E (2003) Axonal dopamine receptors activate peripheral spike initiation in a stomatogastric motor neuron. J Neurosci 23:6866-75. PubMed
We studied the effects of dopamine on the stomatogastric ganglion (STG) of the lobster, Homarus americanus. The two pyloric dilator (PD) neurons are active in the pyloric rhythm, have somata in the STG, and send axons many centimeters to innervate muscles of the stomach. Dopamine application to the stomatogastric nervous system when the PD neurons were rhythmically active evoked additional action potentials during the PD neuron interburst intervals. These action potentials were peripherally generated at a region between the STG and the first bilateral branch, approximately 1 cm away from the STG, and traveled antidromically to the neuropil and orthodromically to the pyloric dilator muscles. Focal applications of dopamine to the nerves showed that spikes could be initiated in almost the entire peripheral axon of the PD neurons. Dopamine also evoked spikes in isolated peripheral axons. The concentration threshold for peripheral spike initiation was at or below 10-9 m dopamine. Thus, the peripheral axon can play an important role in shaping the output signaling to the muscles by the motor neuron.
Luther JA, Robie AA, Yarotsky J, Reina C, Marder E and Golowasch J (2003) Episodic bouts of activity accompany recovery of rhythmic output by a neuromodulator- and activity-deprived adult neural network. J Neurophysiol 90:2720-30. PubMed
The pyloric rhythm of the stomatogastric ganglion of the crab, Cancer borealis, slows or stops when descending modulatory inputs are acutely removed. However, the rhythm spontaneously resumes after one or more days in the absence of neuromodulatory input. We recorded continuously for days to characterize quantitatively this recovery process. Activity bouts lasting 40-900 s began several hours after removal of neuromodulatory input and were followed by stable rhythm recovery after 1-4 days. Bout duration was not related to the intervals (0.3-800 min) between bouts. During an individual bout, the frequency rapidly increased and then decreased more slowly. Photoablation of back-filled neuromodulatory terminals in the stomatogastric ganglion (STG) neuropil had no effect on activity bouts or recovery, suggesting that these processes are intrinsic to the STG neuronal network. After removal of neuromodulatory input, the phase relationships of the components of the triphasic pyloric rhythm were altered, and then over time the phase relationships moved toward their control values. Although at low pyloric rhythm frequency the phase relationships among pyloric network neurons depended on frequency, the changes in frequency during recovery did not completely account for the change in phase seen after rhythm recovery. We suggest that activity bouts represent underlying mechanisms controlling the restructuring of the pyloric network to allow resumption of an appropriate output after removal of neuromodulatory input.
Bucher D (2003) Bitter taste. J Exp Biol 206:3307-3308. JEB
Bucher D (2003) Carbs or fat? Nerve cells that control glycolysis in locust flight muscles. J Exp Biol 206:2094. JEB
Bucher D (2003) From dusk till dawn: diurnal rhythm of neurogenesis in lobsters. J Exp Biol 206:1103. JEB
Bucher D (2003) Inspiration from the legs. J Exp Biol 206:6. JEB
Manor Y, Bose A, Booth V and Nadim F (2003) Contribution of synaptic depression to phase maintenance in a model rhythmic network. J Neurophysiol 90:3513-28. PubMed
In many rhythmic neuronal networks that operate in a wide range of frequencies, the time of neuronal firing relative to the cycle period (the phase) is invariant. This invariance suggests that when frequency changes, firing time is precisely adjusted either by intrinsic or synaptic mechanisms. We study the maintenance of phase in a computational model in which an oscillator neuron (O) inhibits a follower neuron (F) by comparing the dependency of phase on cycle period in two cases: when the inhibitory synapse is depressing and when it is nondepressing. Of the numerous ways of changing the cycle period, we focus on three cases where either the duration of the active state, the inactive state, or the duty cycle of neuron O remains constant. In each case, we measure the phase at which neuron F fires with respect to the onset of firing in neuron O. With a nondepressing synapse, this phase is generally a monotonic function of cycle period except in a small parameter range in the case of the constant inactive duration. In contrast, with a depressing synapse, there is always a parameter regime in which phase is a cubic function of cycle period: it decreases at short cycle periods, increases in an intermediate range, and decreases at long cycle periods. This complex shape for the phase-period relationship arises because of the interaction between synaptic dynamics and intrinsic properties of the postsynaptic neuron. By choosing appropriate parameters, the cubic shape of the phase-period curve results in a small variation in phase for a large interval of periods. Consequently, we find that although a depressing synapse does not produce perfect phase maintenance, in most cases it is superior to a nondepressing synapse in promoting a constant phase difference.
Nadim F, Booth V, Bose A and Manor Y (2003) Short-term synaptic dynamics promote phase maintenance in multi-phasic rhythms. Neurocomputing 52-4:79-87. ScienceDirect
We show that in an inhibitory rhythmic network synaptic depression promotes phase constancy. As cycle period increases, the synapse recovers from depression and becomes more effective in delaying the postsynaptic cell. As a result, the delay between the pre- and postsynaptic bursts increases as cycle period increases. We discuss the dependence of the bursting phase of the postsynaptic cell on the strength and kinetics of the depressing synapse.
Mamiya A, Manor Y and Nadim F (2003) Short-term dynamics of a mixed chemical and electrical synapse in a rhythmic network. J Neurosci 23:9557-64. PubMed
In the rhythmically active pyloric circuit of the spiny lobster, the synapse between the lateral pyloric (LP) neuron and pyloric constrictor (PY) neuron has an inhibitory depressing chemical and an electrical component. To understand how the dynamics of the LP-->PY synapse affect the relative firing times between these two neurons in an ongoing rhythm, we characterized the dynamics of the LP-->PY synapse after a pharmacological block of ongoing activity. When a train of voltage pulses was applied to the voltage-clamped LP neuron, the inhibitory chemical component of the postsynaptic potential (PSP) in the PY neuron rapidly depressed. Thus, after the first few pulses, the PSP was either hyperpolarizing or depolarizing, depending on the interpulse duration, with shorter interpulse durations producing depolarizing PSPs. To characterize the synaptic response during rhythmic activity, we played back prerecorded realistic waveforms in the voltage-clamped LP neuron. After an initial transient, the resulting PSP in PY was always depolarizing, suggesting that in an ongoing rhythm, the electrical component of the synapse is dominant. However, our results indicate that the chemical component of the synapse acts to delay the peak time of the PSP and to reduce its amplitude, and that these effects become more important at slower cycle periods.
Bucher D, Akay T, DiCaprio RA and Buschges A (2003) Interjoint coordination in the stick insect leg-control system: the role of positional signaling. J Neurophysiol 89:1245-55. PubMed
Interjoint coordination is essential for proper walking behavior in multi-jointed insect legs. We have shown previously that movement signals from the femur-tibia (FT) joint can shape motor activity of the adjacent coxa-trochanter (CT) joint in the stick insect, Carausius morosus. Here, we present data on the role of position signals from the FT-joint on activity generated in motoneurons (MNs) of the CT-joint. We show that the probability of occurrence of stance (with depression in the CT-joint) or swing movements (with levation in the CT-joint) at the start of walking sequences is influenced by the angle of the FT-joint in the resting animal. We tested the influence of FT-joint angle on pharmacologically induced rhythmic activity of CT-joint depressor (DprTr) and levator (LevTr) MNs. The burst duration, mean spike rate within bursts, and duty cycle for each MN pool were found to depend on FT position. For LevTr MNs, these parameters progressively increased as the FT-joint was moved from extension to flexion, and the opposite was true for DprTr MNs. The cycle period of CT-MN rhythmicity also depended on FT position. In addition, we sometimes observed that the motor output shifted completely to one MN pool at extreme positions, suggesting that the central rhythm-generating network for the CT-joint became locked in one phase. These results indicate that position signals from the FT-joint modulate rhythmic activity in CT-joint MNs partly by having access to central rhythm generating networks of the CT-joint.
Golowasch J, Goldman MS, Abbott LF and Marder E (2002) Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol 87:1129-31. PubMed
Parameters for models of biological systems are often obtained by averaging over experimental results from a number of different preparations. To explore the validity of this procedure, we studied the behavior of a conductance-based model neuron with five voltage-dependent conductances. We randomly varied the maximal conductance of each of the active currents in the model and identified sets of maximal conductances that generate bursting neurons that fire a single action potential at the peak of a slow membrane potential depolarization. A model constructed using the means of the maximal conductances of this population is not itself a one-spike burster, but rather fires three action potentials per burst. Averaging fails because the maximal conductances of the population of one-spike bursters lie in a highly concave region of parameter space that does not contain its mean. This demonstrates that averages over multiple samples can fail to characterize a system whose behavior depends on interactions involving a number of highly variable components.
Nadim F and Manor Y (2002) Neurons and neural networks: Computational models. In: Encyclopedia of Life Sciences. Macmillan, London.
Marder E and Bucher D (2001) Central pattern generators and the control of rhythmic movements. Curr Biol 11:R986-96. PubMed
Central pattern generators are neuronal circuits that when activated can produce rhythmic motor patterns such as walking, breathing, flying, and swimming in the absence of sensory or descending inputs that carry specific timing information. General principles of the organization of these circuits and their control by higher brain centers have come from the study of smaller circuits found in invertebrates. Recent work on vertebrates highlights the importance of neuro-modulatory control pathways in enabling spinal cord and brain stem circuits to generate meaningful motor patterns. Because rhythmic motor patterns are easily quantified and studied, central pattern generators will provide important testing grounds for understanding the effects of numerous genetic mutations on behavior. Moreover, further understanding of the modulation of spinal cord circuitry used in rhythmic behaviors should facilitate the development of new treatments to enhance recovery after spinal cord damage.
Manor Y and Nadim F (2001) Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity. J Neurosci 21:9460-70. PubMed
When depressing synapses are embedded in a circuit composed of a pacemaker neuron and a neuron with no autorhythmic properties, the network can show two modes of oscillation. In one mode the synapses are mostly depressed, and the oscillations are dominated by the properties of the oscillating neuron. In the other mode, the synapses recover from depression, and the oscillations are primarily controlled by the synapses. We demonstrate the two modes of oscillation in a hybrid circuit consisting of a biological pacemaker and a model neuron, reciprocally coupled via model depressing synapses. We show that across a wide range of parameter values this network shows robust bistability of the oscillation mode and that it is possible to switch the network from one mode to the other by injection of a brief current pulse in either neuron. The underlying mechanism for bistability may be present in many types of circuits with reciprocal connections and synaptic depression.
Goldman MS, Golowasch J, Marder E and Abbott LF (2001) Global structure, robustness, and modulation of neuronal models. J Neurosci 21:5229-38. PubMed
The electrical characteristics of many neurons are remarkably robust in the face of changing internal and external conditions. At the same time, neurons can be highly sensitive to neuromodulators. We find correlates of this dual robustness and sensitivity in a global analysis of the structure of a conductance-based model neuron. We vary the maximal conductance parameters of the model neuron and, for each set of parameters tested, characterize the activity pattern generated by the cell as silent, tonically firing, or bursting. Within the parameter space of the five maximal conductances of the model, we find directions, representing concerted changes in multiple conductances, along which the basic pattern of neural activity does not change. In other directions, relatively small concurrent changes in a few conductances can induce transitions between these activity patterns. The global structure of the conductance-space maps implies that neuromodulators that alter a sensitive set of conductances will have powerful, and possibly state-dependent, effects. Other modulators that may have no direct impact on the activity of the neuron may nevertheless change the effects of such direct modulators via this state dependence. Some of the results and predictions arising from the model studies are replicated and verified in recordings of stomatogastric ganglion neurons using the dynamic clamp.
Nadim F, Manor Y and Bose A (2001) Control of network output by synaptic depression. Neurocomputing 38-40:781–787. ScienceDirect
In a network of an excitatory and an inhibitory neuron, depression in the inhibitory synapse can produce two distinct oscillatory regimes. In one regime, the network has a short period cell-dominated solution; in the other regime, the solution has much longer period and is synapse-dominated. These regimes overlap to produce an interval of bistability. Neuromodulatory input that targets one of multiple parameters in the network can switch the network control between the intrinsic properties of cells and the dynamics of the synapses.
Bose A, Manor Y and Nadim F (2001) Bistable Oscillations Arising from Synaptic Depression. SIAM J Appl Math 26:706–727. Journal
Synaptic depression is a common form of short-term plasticity in the central and peripheral nervous systems. We show that in a network of two reciprocally connected neurons a single depressing synapse can produce two distinct oscillatory regimes. These distinct periodic behaviors can be studied by varying the maximal conductance, $\gbarinh$, of the depressing synapse. For small $\gbarinh$, the network has a short-period solution controlled by intrinsic cellular properties. For large $\gbarinh$, the solution has a much longer period and is controlled by properties of the synapse. We show that in an intermediate range of $\gbarinh$ values both stable periodic solutions exist simultaneously. Thus the network can switch oscillatory modes either by changing (g) over bar (inh) or, for fixed (g) over bar (inh), by changing initial conditions.
Manor Y and Nadim F (2001) Frequency regulation demonstrated by coupling a model and a biological neuron. Neurocomputing 38-40:269–278. ScienceDirect
Using a 2-cell reciprocally inhibitory network consisting of a biological pacemaker neuron and a model neuron integrated in real time, we show that if both synapses are depressing there is a wide range of bistability in the system. The two stable outputs are both oscillatory, but one is controlled by the intrinsic properties of the biological pacemaker neuron, whereas the other is controlled by the strength of the depressing synapses.
Bucher D, Scholz M, Stetter M, Obermayer K and Pfluger HJ (2000) Correction methods for three-dimensional reconstructions from confocal images: I. Tissue shrinking and axial scaling. J Neurosci Methods 100:135-43. PubMed
We show here, using locust wholemount ganglia as an example, that scaling artifacts in three-dimensional reconstructions from confocal microscopic images due to refractive index mismatch in the light path and tissue shrinking, can account for dramatic errors in measurements of morphometric values. Refractive index mismatch leads to considerable alteration of the axial dimension, and true dimensions must be restored by rescaling the Z-axis of the image stack. The appropriate scaling factor depends on the refractive indices of the media in the light path and the numerical aperture of the objective used and can be determined by numerical simulations, as we show here. In addition, different histochemical procedures were tested in regard to their effect on tissue dimensions. Reconstructions of scans at different stages of these protocols show that shrinking can be avoided prior to clearing when dehydrating ethanol series are carefully applied. Fixation and mismatching buffer osmolarity have no effect. We demonstrate procedures to reduce artifacts during mounting and clearing in methyl salicylate, such that only isometric shrinkage occurs, which can easily be corrected by rescaling the image dimensions. Glycerol-based clearing agents produced severe anisometric and nonlinear shrinkage and we could not find a way to overcome this.
Bucher D and Pfluger H (2000) Directional sensitivity of an identified wind-sensitive interneuron during the postembryonic development of the locust. J Insect Physiol 46:1545-1556. PubMed
Simultaneous extracellular recordings from both locust abdominal connectives show a differential activation of both bilateral homologues of an identified long projection interneuron (A4I1) in response to wind stimuli from different directions. Despite the previously shown extensive structural dynamics of sensory afferents and synaptic rearrangement of the direct afferent-to-interneuron connections during postembryonic development, a directional sensitivity is already present in first instar nymphs. Only quantitative changes in the strength of the directional response can be detected. Intracellular stainings of the A4I1 interneuron in first instar nymphs and adults show that general morphological features do not change during postembryonic development, in contrast to the presynaptic sensory afferents. This also holds for general morphological features of pleuroaxillary flight motoneurons. The output connections of A4I1 to these motoneurons and an unidentified intersegmental interneuron are already present in flightless nymphs.
Swensen AM, Golowasch J, Christie AE, Coleman MJ, Nusbaum MP and Marder E (2000) GABA and responses to GABA in the stomatogastric ganglion of the crab Cancer borealis. J Exp Biol 203:2075-92. PubMed
The multifunctional neural circuits in the crustacean stomatogastric ganglion (STG) are influenced by many small-molecule transmitters and neuropeptides that are co-localized in identified projection neurons to the STG. We describe the pattern of gamma-aminobutyric acid (GABA) immunoreactivity in the stomatogastric nervous system of the crab Cancer borealis and demonstrate biochemically the presence of authentic GABA in C. borealis. No STG somata show GABA immunoreactivity but, within the stomatogastric nervous system, GABA immunoreactivity co-localizes with several neuropeptides in two identified projection neurons, the modulatory proctolin neuron (MPN) and modulatory commissural neuron 1 (MCN1). To determine which actions of these neurons are evoked by GABA, it is necessary to determine the physiological actions of GABA on STG neurons. We therefore characterized the response of each type of STG neuron to focally applied GABA. All STG neurons responded to GABA. In some neurons, GABA evoked a picrotoxin-sensitive depolarizing, excitatory response with a reversal potential of approximately -40 mV. This response was also activated by muscimol. In many STG neurons, GABA evoked inhibitory responses with both K(+)- and Cl(-)-dependent components. Muscimol and beta-guanidinopropionic acid weakly activated the inhibitory responses, but many other drugs, including bicuculline and phaclofen, that act on vertebrate GABA receptors were not effective. In summary, GABA is found in projection neurons to the crab STG and can evoke both excitatory and inhibitory actions on STG neurons.
Nadim F and Manor Y (2000) The role of short-term synaptic dynamics in motor control. Curr Opin Neurobiol 10:683-90. PubMed
During the past few years, much attention has been given to the role of short-term synaptic plasticity, in particular depression and facilitation, in sculpting network activity. A recent study shows that synaptic depression in rhythmic motor networks could switch the control of network frequency from intrinsic neuronal properties to the synaptic dynamics. Short-term synaptic plasticity is also involved in the stabilization and reconfiguration of motor circuits and in the initiation, maintenance and modulation of motor programs.
Bartos M, Manor Y, Nadim F, Marder E and Nusbaum MP (1999) Coordination of fast and slow rhythmic neuronal circuits. J Neurosci 19:6650-60. PubMed
Interactions among rhythmically active neuronal circuits that oscillate at different frequencies are important for generating complex behaviors, yet little is known about the underlying cellular mechanisms. We addressed this issue in the crab stomatogastric ganglion (STG), which contains two distinct but interacting circuits. These circuits generate the gastric mill rhythm (cycle period, approximately 10 sec) and the pyloric rhythm (cycle period, approximately 1 sec). When the identified modulatory projection neuron named modulatory commissural neuron 1 (MCN1) is activated, the gastric mill motor pattern is generated by interactions among MCN1 and two STG neurons [the lateral gastric (LG) neuron and interneuron 1]. We show that, during MCN1 stimulation, an identified synapse from the pyloric circuit onto the gastric mill circuit is pivotal for determining the gastric mill cycle period and the gastric-pyloric rhythm coordination. To examine the role of this intercircuit synapse, we replaced it with a computational equivalent via the dynamic-clamp technique. This enabled us to manipulate better the timing and strength of this synapse. We found this synapse to be necessary for production of the normal gastric mill cycle period. The synapse acts, during each LG neuron interburst, to boost rhythmically the influence of the modulatory input from MCN1 to LG and thereby to hasten LG neuron burst onset. The two rhythms become coordinated because LG burst onset occurs with a constant latency after the onset of the triggering pyloric input. These results indicate that intercircuit synapses can enable an oscillatory circuit to control the speed of a slower oscillatory circuit, as well as provide a mechanism for intercircuit coordination.
Nadim F, Manor Y, Kopell N and Marder E (1999) Synaptic depression creates a switch that controls the frequency of an oscillatory circuit. Proc Natl Acad Sci U S A 96:8206-11. PubMed
Synaptic depression is a form of short-term plasticity exhibited by many synapses. Nonetheless, the functional significance of synaptic depression in oscillatory networks is not well understood. We show that, in a recurrent inhibitory network that includes an intrinsic oscillator, synaptic depression can give rise to two distinct modes of network operation. When the maximal conductance of the depressing synapse is small, the oscillation period is determined by the oscillator component. Increasing the maximal conductance beyond a threshold value activates a positive-feedback mechanism that greatly enhances the synaptic strength. In this mode, the oscillation period is determined by the strength and dynamics of the depressing synapse. Because of the regenerative nature of the feedback mechanism, the circuit can be switched from one mode of operation to another by a very small change in the maximal conductance of the depressing synapse. Our model was inspired by experimental work on the pyloric network of the lobster. The pyloric network produces a simple motor rhythm generated by a pacemaker neuron that receives feedback inhibition from a depressing synapse. In some preparations, elimination of the synapse had no effect on the period of the rhythm, whereas in other preparations, there was a significant decrease in the period. We propose that the pyloric network can operate in either of the two modes suggested by the model, depending on the maximal conductance of the depressing synapse.
Manor Y, Nadim F, Epstein S, Ritt J, Marder E and Kopell N (1999) Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons. J Neurosci 19:2765-79. PubMed
We describe a novel mechanism by which network oscillations can arise from reciprocal inhibitory connections between two entirely passive neurons. The model was inspired by the activation of the gastric mill rhythm in the crab stomatogastric ganglion by the modulatory commissural ganglion neuron 1 (MCN1), but it is studied here in general terms. One model neuron has a linear current-voltage (I-V) curve with a low (L) resting potential, and the second model neuron has a linear current-voltage curve with a high (H) resting potential. The inhibitory connections between them are graded. There is an extrinsic modulatory excitatory input to the L neuron, and the L neuron presynaptically inhibits the modulatory neuron. Activation of the extrinsic modulatory neuron elicits stable network oscillations in which the L and H neurons are active in alternation. The oscillations arise because the graded reciprocal synapses create the equivalent of a negative-slope conductance region in the I-V curves for the cells. Geometrical methods are used to analyze the properties of and the mechanism underlying these network oscillations.
Golowasch J, Bedrax-Weiss T and Palacios A (1999) Words go missing in cyberspace. Nature 398:186. PubMed
Golowasch J, Manor Y and Nadim F (1999) Recognition of slow processes in rhythmic networks. Trends Neurosci 22:375-377. PubMed
Golowasch J, Casey M, Abbott LF and Marder E (1999) Network stability from activity-dependent regulation of neuronal conductances. Neural Comput 11:1079-96. PubMed
Activity-dependent plasticity appears to play an important role in the modification of neurons and neural circuits that occurs during development and learning. Plasticity is also essential for the maintenance of stable patterns of activity in the face of variable environmental and internal conditions. Previous theoretical and experimental results suggest that neurons stabilize their activity by altering the number or characteristics of ion channels to regulate their intrinsic electrical properties. We present both experimental and modeling evidence to show that activity-dependent regulation of conductances, operating at the level of individual neurons, can also stabilize network activity. These results indicate that the stomatogastric ganglion of the crab can generate a characteristic rhythmic pattern of activity in two fundamentally different modes of operation. In one mode, the rhythm is strictly conditional on the presence of neuromodulatory afferents from adjacent ganglia. In the other, it is independent of neuromodulatory input but relies on newly developed intrinsic properties of the component neurons.
Marder E, Golowasch J, Richards KS, Soto-Treviño C, Miller WL and Abbott LF (1999) Self-assembly of oscillatory neurons and networks. In: Lecture Notes in Computer Science (Mira M and Sánchez-Andrés JV, eds). Springer, Berlin.
Golowasch J, Abbott LF and Marder E (1999) Activity-dependent regulation of potassium currents in an identified neuron of the stomatogastric ganglion of the crab Cancer borealis. J Neurosci 19:RC33. PubMed
Identified neurons of the stomatogastric ganglion of the crab Cancer borealis were voltage-clamped, and the current densities of three K+ currents were measured. The current densities of each of the three K+ currents varied twofold to fivefold in inferior cardiac (IC) neurons from different animals. Conventionally, this degree of variability has been attributed to experimental artifacts. Instead, we suggest that it reflects a natural variability that may be related to an underlying process of plasticity. First, we found that there is no fixed ratio among the three K+ currents. Second, we found that several hours of stimulation with depolarizing current pulses (0.5 sec duration at 1 Hz) altered the current density of the Ca2+-dependent outward current, IK(Ca), and the transient outward current, IA. This stimulation paradigm mimics the normal pattern of activity for these neurons. The effect of stimulation on the IA current density was eliminated when Ca2+ influx was blocked by extracellular Cd2+. In contrast, the K+ current densities of the lateral pyloric (LP) neuron were unaffected by the same pattern of stimulation, and the currents expressed by both the IC and the LP neurons were insensitive to hyperpolarizing pulses at the same frequency. We conclude that the conductance densities expressed by neurons may vary continually depending on the recent history of electrical activity in the preparation, and that intracellular Ca2+ may play a role in the processes by which activity influences the regulation of current densities in neurons.
Nadim F, Manor Y, Nusbaum MP and Marder E (1998) Frequency regulation of a slow rhythm by a fast periodic input. J Neurosci 18:5053-67. PubMed
Many nervous systems contain rhythmically active subnetworks that interact despite oscillating at widely different frequencies. The stomatogastric nervous system of the crab Cancer borealis produces a rapid pyloric rhythm and a considerably slower gastric mill rhythm. We construct and analyze a conductance-based compartmental model to explore the activation of the gastric mill rhythm by the modulatory commissural neuron 1 (MCN1). This model demonstrates that the period of the MCN1-activated gastric mill rhythm, which was thought to be determined entirely by the interaction of neurons in the gastric mill network, can be strongly influenced by inhibitory synaptic input from the pacemaker neuron of the fast pyloric rhythm, the anterior burster (AB) neuron. Surprisingly, the change of the gastric mill period produced by the pyloric input to the gastric mill system can be many times larger than the period of the pyloric rhythm itself. This model illustrates several mechanisms by which a fast oscillatory neuron may control the frequency of a much slower oscillatory network. These findings suggest that it is possible to modify the slow rhythm either by direct modulation or indirectly by modulating the faster rhythm.
Marder E, Manor Y, Nadim F, Bartos M and Nusbaum MP (1998) Frequency control of a slow oscillatory network by a fast rhythmic input: pyloric to gastric mill interactions in the crab stomatogastric nervous system. Ann N Y Acad Sci 860:226-38. PubMed
The stomatogastic nervous system of the crab, Cancer borealis, produces a slow gastric mill rhythm and a fast pyloric rhythm. When the gastric mill rhythm is not active, stimulation of the modulatory commissural ganglion neuron 1 (MCN1) activates a gastric mill rhythm in which the lateral gastric (LG) neuron fires in antiphase with interneuron 1 (Int1). We present theoretical and experimental data that indicate that the period of the MCN1 activated gastric mill rhythm depends on the strength and time course of the MCN1 evoked slow excitatory synaptic potential (EPSP) in the LG neuron, and on the strength of inhibition of Int 1 by the pacemaker of the pyloric network. This work demonstrates a new mechanism by which a slow network oscillator can be controlled by a much faster oscillatory neuron or network and suggests that modulation of the slow oscillator can occur by direct action on the neurons and synapses of the slow oscillator, or indirectly by actions on the fast oscillator and its synaptic connection with the slow oscillator.
Liu Z, Golowasch J, Marder E and Abbott LF (1998) A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J Neurosci 18:2309-20. PubMed
Membrane channels are subject to a wide variety of regulatory mechanisms that can be affected by activity. We present a model of a stomatogastric ganglion (STG) neuron in which several Ca2+-dependent pathways are used to regulate the maximal conductances of membrane currents in an activity-dependent manner. Unlike previous models of this type, the regulation and modification of maximal conductances by electrical activity is unconstrained. The model has seven voltage-dependent membrane currents and uses three Ca2+ sensors acting on different time scales. Starting from random initial conditions over a given range, the model sets the maximal conductances for its active membrane currents to values that produce a predefined target pattern of activity approximately 90% of the time. In these models, the same pattern of electrical activity can be produced by a range of maximal conductances, and this range is compared with voltage-clamp data from the lateral pyloric neuron of the STG. If the electrical activity of the model neuron is perturbed, the maximal conductances adjust to restore the original pattern of activity. When the perturbation is removed, the activity pattern is again restored after a transient adjustment period, but the conductances may not return to their initial values. The model suggests that neurons may regulate their conductances to maintain fixed patterns of electrical activity, rather than fixed maximal conductances, and that the regulation process requires feedback systems capable of reacting to changes of electrical activity on a number of different time scales.
Glowik RM, Golowasch J, Keller R and Marder E (1998) D-glucose-evoked inhibition of CHH-containing X-organ neurons of the crab Cancer borealis. Ann NY Acad Sci 839:406-408. Wiley
Nadim F and Calabrese RL (1997) A slow outward current activated by FMRFamide in heart interneurons of the medicinal leech. J Neurosci 17:4461-72. PubMed
The endogenous neuropeptide FMRFamide (Phe-Met-Arg-Phe-NH2) can accelerate the oscillation of reciprocally inhibitory pairs of interneurons that pace heartbeat in the medicinal leech. A model based on all available biophysical data of a two-cell heart interneuron oscillator provides a theoretical basis for understanding this modulation. Previously observed modulation of K+ currents by FMRFamide cannot account for this acceleratory effect in the model. This observation prompted the present reexamination of K+ currents in heart interneurons. We devised better methods for separation of the various components of K+ current and more accurately measured their activation and deactivation kinetics. Moreover, we demonstrated that FMRFamide activates a previously undetected K+ current (IKF), which has very slow activation and deactivation kinetics. Addition of physiologically measured amounts of IKF to the model two-cell oscillator can account for the acceleratory effect of FMRFamide.
Manor Y, Nadim F, Abbott LF and Marder E (1997) Temporal dynamics of graded synaptic transmission in the lobster stomatogastric ganglion. J Neurosci 17:5610-21. PubMed
Synaptic transmission between neurons in the stomatogastric ganglion of the lobster Panulirus interruptus is a graded function of membrane potential, with a threshold for transmitter release in the range of -50 to -60 mV. We studied the dynamics of graded transmission between the lateral pyloric (LP) neuron and the pyloric dilator (PD) neurons after blocking action potential-mediated transmission with 0.1 microM tetrodotoxin. We compared the graded IPSPs (gIPSPs) from LP to PD neurons evoked by square pulse presynaptic depolarizations with those potentials evoked by realistic presynaptic waveforms of variable frequency, amplitude, and duty cycle. The gIPSP shows frequency-dependent synaptic depression. The recovery from depression is slow, and as a result, the gIPSP is depressed at normal pyloric network frequencies. Changes in the duration of the presynaptic depolarization produce nonintuitive changes in the amplitude and time course of the postsynaptic responses, which are again frequency-dependent. Taken together, these data demonstrate that the measurements of synaptic efficacy that are used to understand neural network function are best made using presynaptic waveforms and patterns of activity that mimic those in the functional network.
Golowasch J and Corey DP (1997) Patch Clamp. In: Encyclopedia of Neuroscience, 2nd edition (Adelman G, ed). Birkhäuser, Boston.
Glowik RM, Golowasch J, Keller R and Marder E (1997) D-glucose-sensitive neurosecretory cells of the crab Cancer borealis and negative feedback regulation of blood glucose level. J Exp Biol 200:1421-31. PubMed
We studied the effects of glucose on cultured X-organ neurons of the crab Cancer borealis using single-electrode current- and voltage-clamp techniques. A subpopulation of the cells responded to D-glucose with a hyperpolarization. These cells, but not glucose-insensitive cells, showed immunoreactivity to crustacean hyperglycemic hormone (CHH), the hormone responsible for the elevation of blood glucose levels in crustaceans. Glucose-sensitive cells were also inhibited by serotonin and gamma-aminobutyric acid but were not affected by dopamine and Leu-enkephalin. The response was specific for D-glucose, with an EC50 of 0.25 mmoll-1. No response was seen to L-glucose, sucrose, galactose, mannose or fructose. The glucose response persisted in the absence of extracellular Na+ and in low-Ca2+/Mn2+ saline. In voltage-clamp experiments, D-glucose evoked a small current with a reversal potential close to that of voltage-dependent K+ currents. We conclude that D-glucose activates a K+ current in CHH-immunoreactive cells that, in normal saline, induces a hyperpolarization. We propose that this enables glucose to regulate directly the release of CHH into the hemolymph, thus constituting a negative feedback mechanism regulating hemolymph glucose concentration.
Marder E, Abbott LF, Turrigiano GG, Liu Z and Golowasch J (1996) Memory from the dynamics of intrinsic membrane currents. Proc Natl Acad Sci U S A 93:13481-6. PubMed
Almost all theoretical and experimental studies of the mechanisms underlying learning and memory focus on synaptic efficacy and make the implicit assumption that changes in synaptic efficacy are both necessary and sufficient to account for learning and memory. However, network dynamics depends on the complex interaction between intrinsic membrane properties and synaptic strengths and time courses. Furthermore, neuronal activity itself modifies not only synaptic efficacy but also the intrinsic membrane properties of neurons. This paper presents examples demonstrating that neurons with complex temporal dynamics can provide short-term "memory" mechanisms that rely solely on intrinsic neuronal properties. Additionally, we discuss the potential role that activity may play in long-term modification of intrinsic neuronal properties. While not replacing synaptic plasticity as a powerful learning mechanism, these examples suggest that memory in networks results from an ongoing interplay between changes in synaptic efficacy and intrinsic membrane properties.
Olsen O, Nadim F, Hill AA and Edwards DH (1996) Uniform growth and neuronal integration. J Neurophysiol 76:1850-7. PubMed
1. The cable equations were analyzed to determine the effects of two patterns of uniform growth on the passive and active integrative properties of neurons. 2. During uniform isoelectrotonic growth, the diameters of all neuronal processes increase as the square of their increase in length, while the specific electrical properties and branch terminal conditions of the neuron remain constant. An analytic inductive proof is given to show that, for any neuron, uniform isoelectrotonic growth increases the input conductance everywhere by the cube of the growth factor, but leaves the active and passive spread of membrane potential within the neuron unchanged. The spread of membrane voltage is unchanged because this pattern of growth enables both the axial and membrane currents everywhere in the cell to increase by the cube of the growth factor. Synaptic inputs would evoke the same responses in the isoelectrotonically larger cell as in the smaller cell if the total postsynaptic conductance of the synapse increased with the dendritic membrane area. 3. During uniform isometric growth, the diameter and lengths of all processes increase by the same factor, while the specific electrical properties and branch terminal conditions remain constant. This pattern of uniform growth increases the input conductance by the square of the growth factor, and also increases the attenuation, delay, and low-pass filtering of the cell's responses. Voltage attenuation increases with isometric growth because the axial current increases in proportion to growth, while the membrane current increases in proportion to the square of the growth factor. Isometric growth reduces the ability of distal synaptic inputs to affect the membrane potential at proximal integrating sites, even after the synaptic conductance has increased to compensate for the increased input conductance. 4. These two patterns of uniform growth help define the consequences of all types of uniform growth for neuronal integration and responsiveness.
Olsen OH, Nadim F and Calabrese RL (1995) Modeling the leech heartbeat elemental oscillator. II. Exploring the parameter space. J Comput Neurosci 2:237-57. PubMed
In the previous paper, we described a model of the elemental heartbeat oscillator in the leech. Here, the parameters of our model are explored around the baseline canonical model. The maximal conductances of the currents and the reversal potential of the leak current are varied to reveal the effects of individual currents and the interaction between synaptic and intrinsic currents in the model. The model produces two distinct modes of oscillation as the parameters are varied, S-mode and G-mode. These two modes are defined, their origin is identified, and the parameter space is mapped into S-mode and G-mode oscillation and no oscillation. Finally, we will make predictions for how the period can be modulated in heart interneurons.
Nadim F, Olsen OH, De Schutter E and Calabrese RL (1995) Modeling the leech heartbeat elemental oscillator. I. Interactions of intrinsic and synaptic currents. J Comput Neurosci 2:215-35. PubMed
We have developed a biophysical model of a pair of reciprocally inhibitory interneurons comprising an elemental heartbeat oscillator of the leech. We incorporate various intrinsic and synaptic ionic currents based on voltage-clamp data. Synaptic transmission between the interneurons consists of both a graded and a spike-mediated component. By using maximal conductances as parameters, we have constructed a canonical model whose activity appears close to the real neurons. Oscillations in the model arise from interactions between synaptic and intrinsic currents. The inhibitory synaptic currents hyperpolarize the cell, resulting in activation of a hyperpolarization-activated inward current Ih and the removal of inactivation from regenerative inward currents. These inward currents depolarize the cell to produce spiking and inhibit the opposite cell. Spike-mediated IPSPs in the inhibited neuron cause inactivation of low-threshold Ca++ currents that are responsible for generating the graded synaptic inhibition in the opposite cell. Thus, although the model cells can potentially generate large graded IPSPs, synaptic inhibition during canonical oscillations is dominated by the spike-mediated component.
Golowasch J, Paupardin-Tritsch D and Gerschenfeld HM (1995) Enhancement by muscarinic agonists of a high voltage-activated Ca2+ current via phosphorylation in a snail neuron. J Physiol 485 ( Pt 1):21-8. PubMed
1. In previous work we have shown that in the snail Helix aspersa neuron F1 carbamylcholine (CCh) and other muscarinic agonists enhance the inward current carried through high voltage-activated Ca2+ channels by Ba2+ (HVA-ICa). It was also found that cyclic nucleotides, inositol trisphosphate or arachidonic acid are not involved in this modulation. Moreover, despite the effect of CCh being blocked by intracellular injection of EGTA, neither protein kinase C nor Ca(2+)-calmodulin-dependent protein kinase II appeared to play a role. 2. In the present paper, the intracellular mechanism of this muscarinic modulation was investigated further by studying the effects of inhibitors of Ser-Thr protein phosphatases (PP) on both the HVA-ICa of neuron F1 and its enhancement by CCh. 3. Intracellular injections in the F1 neuron of either microcystin LR or okadaic acid, both inhibitors of PP1 and PP2A, mimic the action of CCh on the HVA-ICa and occlude the effects of CCh on this current. In contrast, cyclosporin A, an inhibitor of PP2B (calcineurin), affects neither the HVA Ca2+ current itself nor its modulation by CCh. 4. The efficacy of PP inhibitors was tested in F1 neurons in which serotonin (5-HT) induces an inward current involving intracellular increases in cAMP and a protein kinase A-dependent closing of K+ channels. We found that intracellular injection of either microcystin LR or okadaic acid mimicked the 5-HT-induced inward current and occluded the effect of further application of 5-HT.(ABSTRACT TRUNCATED AT 250 WORDS)
Calabrese RL, Nadim F and Olsen OH (1995) Heartbeat control in the medicinal leech: a model system for understanding the origin, coordination, and modulation of rhythmic motor patterns. J Neurobiol 27:390-402. PubMed
We have analyzed in detail the neuronal network that generates heartbeat in the leech. Reciprocally inhibitory pairs of heart interneurons form oscillators that pace the heartbeat rhythm. Other heart interneurons coordinate these oscillators. These coordinating interneurons, along with the oscillators interneurons, form an eight-cell timing oscillator network for heartbeat. Still other interneurons, along with the oscillator interneurons, inhibit heart motor neurons, sculpting their activity into rhythmic bursts. Critical switch interneurons interface between the oscillator interneurons and the other premotor interneurons to produce two alternating coordination states of the motor neurons. The periods of the oscillator interneurons are modulated by endogenous RFamide neuropeptides. We have explored the ionic currents and graded and spike-mediated synaptic transmission that promote oscillation in the oscillator interneurons and have incorporated these data into a conductance-based computer model. This model has been of considerable predictive value and has led to new insights into how reciprocally inhibitory neurons produce oscillation. We are now in a strong position to expand this model upward, to encompass the entire heartbeat network, horizontally, to elucidate the mechanisms of FMRFamide modulation, and downward, to incorporate cellular morphology. By studying the mechanisms of motor pattern formation in the leech, using modeling studies in conjunction with parallel physiological experiments, we can contribute to a deeper understanding of how rhythmic motor acts are generated, coordinated, modulated, and reconfigured at the level of networks, cells, ionic currents, and synapses.
Nusbaum MP, Weimann JM, Golowasch J and Marder E (1992) Presynaptic control of modulatory fibers by their neural network targets. J Neurosci 12:2706-14. PubMed
Numerous modulatory fibers control the output of the pyloric and gastric mill neural networks in the crustacean stomatogastric ganglion (STG). We now describe the first results of intracellular recordings from the axon of one of these input neurons, stomatogastric nerve axon 1 (SNAX 1), close to where it enters the STG. SNAX 1 excites both the pyloric and gastric mill rhythms and is identified on the basis of its synaptic interactions with identified STG neurons. SNAX 1 receives synaptic input from several sources within the STG. As a result of these synaptic inputs, SNAX 1 fires bursts of action potentials that are time-locked to both the pyloric and gastric mill rhythms. The synaptic connections made onto the SNAX axon terminals are likely to play important roles in shaping the impulse activity patterns in these modulatory inputs. Thus, the fibers that modulate the pattern-generating networks in the STG are themselves influenced by elements in these networks, and modulation is a dynamic interaction between input fibers and STG neurons.
Golowasch J and Marder E (1992) Proctolin activates an inward current whose voltage dependence is modified by extracellular Ca2+. J Neurosci 12:810-7. PubMed
The pentapeptide proctolin modulates the activity of the rhythmic pattern generators in the crustacean stomatogastric nervous system. Proctolin strongly excites the lateral pyloric and the inferior cardiac neurons of the stomatogastric ganglion (STG), causing them to fire extended high-frequency bursts of action potentials (Hooper and Marder, 1987; Nusbaum and Marder, 1989a,b). We now report that proctolin depolarizes these cells maximally at membrane potentials close to the threshold for action potential generation. In voltage clamp, proctolin evokes an inward current, carried at least partially by Na+, that shows strong outward rectification. Removal of extracellular Ca2+ markedly increases the amplitude of the proctolin-evoked current and linearizes its current-voltage curve. The properties of the proctolin current make it ideally suited to contribute to the activity-dependent modulation of the pyloric network of the STG.
Golowasch J and Marder E (1992) Ionic currents of the lateral pyloric neuron of the stomatogastric ganglion of the crab. J Neurophysiol 67:318-31. PubMed
1. The lateral pyloric (LP) neuron is an important component of the network that generates the pyloric rhythm of the stomatogastric ganglion (STG) and is a direct target of many modulatory inputs to the STG. Our aim in this and the subsequent two papers is to describe the conductances present in this cell and to understand the role these conductances play in shaping the activity of the neuron. 2. LP neurons were studied in two-electrode voltage clamp (TEVC) in a saline solution containing tetrodotoxin (TTX) and picrotoxin (PTX) to isolate them pharmacologically from presynaptic inputs. 3. We identified six voltage-dependent ionic conductances. These include three outward currents that resemble a delayed rectifier current, a Ca(2+)-activated K+ current and an A-current similar to those seen in many other preparations. LP neurons show three inward currents, a fast TTX-sensitive current, a hyperpolarization-activated inward current, and a Ca2+ current.
Golowasch J, Buchholtz F, Epstein IR and Marder E (1992) Contribution of individual ionic currents to activity of a model stomatogastric ganglion neuron. J Neurophysiol 67:341-9. PubMed
1. The behavior of the mathematical model for the lateral pyloric (LP) neuron of the crustacean stomatogastric ganglion (STG) developed in the previous paper was further studied. 2. The action of proctolin, a neuromodulatory peptide that acts directly on the LP neuron, was modeled. The effect of the proctolin-activated current (iproc) on the model neuron mimics the effects of proctolin on the isolated biological LP neuron. The depolarization and increased frequency of firing seen when iproc is activated are associated with changes in the relative contributions of the delayed rectifier (id) and the Ca(2+)-activated outward current (io(Ca] to the repolarization phase of the action potential. 3. The effects of turning off the A-current (iA) in the model were compared with those obtained by pharmacologically blocking iA in the biological neuron. iA appears to regulate action-potential frequency as well as postinhibitory rebound activity. 4. The role of iA on the rhythmic activity of the cell was studied by modifying several of its parameters while periodically activating a simulated synaptically activated conductance, isyn. 5. The effects of manipulations of the maximal conductances (g) for id and io(Ca) were studied. id strongly influences action-potential frequency, whereas io(Ca) strongly influences action-potential duration. 6. Modifications of the maximal conductance of the inward Ca2+ current (iCa) were compared with the effects of blocking iCa in the real cell. 7. The role of the hyperpolarization-activated inward current (ih) during ongoing rhythmic activity was assessed by periodically activating isyn while modifying ih.
Buchholtz F, Golowasch J, Epstein IR and Marder E (1992) Mathematical model of an identified stomatogastric ganglion neuron. J Neurophysiol 67:332-40. PubMed
1. The ionic currents in the lateral pyloric (LP) cell of the stomatogastric ganglion (STG) described in the preceding paper of the rock crab Cancer borealis were fit with a set of differential equations that describe their voltage, time, and Ca2+ dependence. The voltage-dependent currents modeled are a delayed rectifier-like current, id; a Ca(2+)-activated outward current, io(Ca); a transient A-like current, iA; a Ca2+ current, iCa; an inwardly rectifying current, ih; and a fast tetrodotoxin (TTX)-sensitive Na+ current, iNa. 2. A single-compartment, isopotential model of the LP cell was constructed from the six voltage-dependent currents, a voltage-independent leak current il, a Ca2+ buffering system, and the membrane capacitance. 3. The behavior of the model LP neuron was compared with that of the biological neuron by simulating physiological experiments carried out in both voltage-clamp and current-clamp modes. The model and biological neurons show similar action-potential shapes, durations, steady-state current-voltage (I-V) curves, and respond to injected current in a comparable way.
Golowasch J, Núñez H and Yáñez J (1991) La victoria del pingüino antártico en la isla Ardley: Ventaja física o mayor agresividad? Bol Mus Nac Hist Nat Chile 42:97-103.
Golowasch J, Kumar W and Marder E (1990) Membrane currents in rhythmic neurons. In: Crustacean Systems in Neurobiology (Wiese K, ed). Birkhäuser, Basel. SpringerLink
Hooper SL, O'Neil MB, Wagner R, Ewer J, Golowasch J and Marder E (1986) The innervation of the pyloric region of the crab, Cancer borealis: homologous muscles in decapod species are differently innervated. J Comp Physiol A 159:227-40. PubMed
The muscles of the pyloric region of the stomach of the crab, Cancer borealis, are innervated by motorneurons found in the stomatogastric ganglion (STG). Electrophysiological recording and stimulating techniques were used to study the detailed pattern of innervation of the pyloric region muscles. Although there are two Pyloric Dilator (PD) motorneurons in lobsters, previous work reported four PD motorneurons in the crab STG (Dando et al. 1974; Hermann 1979a, b). We now find that only two of the crab PD neurons innervate muscles homologous to those innervated by the PD neurons in the lobster, Panulirus interruptus. The remaining two PD neurons innervate muscles that are innervated by pyloric (PY) neurons in P. interruptus. The innervation patterns of the Lateral Pyloric (LP), Ventricular Dilator (VD), Inferior Cardiac (IC), and PY neurons were also determined and compared with those previously reported in lobsters. Responses of the muscles of the pyloric region to the neurotransmitters, acetylcholine (ACh) and glutamate, were determined by application of exogenous cholinergic agonists and glutamate. The effect of the cholinergic antagonist, curare, on the amplitude of the excitatory junctional potentials (EJPs) evoked by stimulation of the pyloric motor nerves was measured. These experiments suggest that the differences in innervation pattern of the pyloric muscles seen in crab and lobsters are also associated with a change in the neurotransmitter active on these muscles. Possible implications of these findings for phylogenetic relations of decapod crustaceans and for the evolution of neural circuits are discussed.
Golowasch J, Kirkwood A and Miller C (1986) Allosteric effects of Mg2+ on the gating of Ca2+-activated K+ channels from mammalian skeletal muscle. J Exp Biol 124:5-13. PubMed
Ca2+-activated K+ channels from rat muscle transverse tubule membranes were inserted into planar phospholipid bilayers, and the activation of these channels by Ca2+ was studied. On the cytoplasmic side of the channel, calcium ions (in the range 10-100 mumol l-1) increase the opening probability of the channel in a graded way. This 'activation curve' is sigmoid, with an average Hill coefficient of about 2. Magnesium ions, in the range 1-10 mmol l-1, increase the apparent affinity of the channel for Ca2+ and greatly enhance the sigmoidicity of the Ca2+ activation curve. In the presence of 10 mmol l-1 Mg2+, the Hill coefficient for Ca2+ activation is about 4.5. This effect depends upon Mg2+ concentration but not upon applied voltage. Mg2+ is effective only when added to the cytoplasmic side of the channel. The results argue that this high-conductance, Ca2+-activated K+ channel contains at least six Ca2+-binding sites involved in the activation process.
Paris-Zinsmeister VA, Valencia J and Golowasch J (1984) Procedures and methodologies for obtaining tissue samples from the pygoscelid penguins of Antarctica. Antarctic J US 14:155-158. PDF
Golowasch J, Kalin M, Villagrán C and Armesto J (1982) Características demográficas de una población de Nothofagus obliqua (Mirb.) Blume var. macrocarpa dc. en el Cerro El Roble (33o lat. S) en Chile. Bol Mus Nac Hist Nat Chile 39:37-44.