Farzan Nadim

Modeling the leech heartbeat elemental oscillator I. Interactions of intrinsic and synaptic currents

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 currentIh 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.

Frequency Regulation of a Slow Rhythm by a Fast Periodic Input

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.

Modeling the leech heartbeat elemental oscillator. II. Exploring the parameter space.

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.

The role of short-term synaptic dynamics in motor control

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.

Neuromodulation of neurons and synapses.

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.

Proprioceptor Regulation of Motor Circuit Activity by Presynaptic Inhibition of a Modulatory Projection Neuron

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.

Membrane Resonance in Bursting Pacemaker Neurons of an Oscillatory Network Is Correlated with Network Frequency

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 ∼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 ICa and the hyperpolarization-activated inward current Ih 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 Ih or ICa. Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.

Membrane Capacitance Measurements Revisited: Dependence of Capacitance Value on Measurement Method in Nonisopotential Neurons

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.

Intercircuit control via rhythmic regulation of projection neuron activity.

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.

Dynamic interaction of oscillatory neurons coupled with reciprocally inhibitory synapses acts to stabilize the rhythm period.

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.