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.

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. Additionally, the divergent and convergent neuromodulator actions can be unambiguously synergistic or antagonistic. 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.

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.

SUMMARYNeuronal 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.

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.

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 gL and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase-frequency, selectivity, etc.) in the gL−g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 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 (Ih 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.

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 gastropyloricmusclestretchreceptor(GPR)neuron,regulatesthegastricmill(chewing)motorrhythm.Previousworkshowedthatrhythmically 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 stomatogastric 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.

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 Ϫ50 to Ϫ60 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 M 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. Key words: graded synaptic transmission; pyloric network; central pattern generation; oscillations; synaptic depression; inhibitionMost rhythmic movements are produced by central patterngenerating circuits (Marder and C alabrese, 1996). In many cases, the rhythmic movements are produced over a significant frequency range without appreciable alteration of the fundamental phase relationships or the character of the movement; e.g., an animal is allowed to breathe or to walk at different rates, slowly or quickly. Because circuit dynamics depend on both synaptic and intrinsic properties, it is interesting to ask how these dynamics are affected by changes in network frequency. In this paper we present the effects of frequency on the graded synaptic transmission between neurons of the pyloric circuit of the spiny lobster Panulirus interruptus.The pyloric network of the stomatogastric ganglion (STG) of P. interruptus is one of the best understood pattern-generating circuits. The connectivity among these neurons and their intrinsic membrane properties have been determined (Selverston and Miller, 1980;Eisen and Marder, 1982; Miller and Selverston, 1982a,b). Both in vivo and in vitro studies in a variety of crustacean species have shown that the triphasic pyloric rhythm operates over a frequency range from ϳ0.1 to ϳ2.5 Hz (Ayers and Selverston, 1979;Rezer and Moulins, 1983;Eisen and Marder, 1984;T urrigiano and Heinzel, 1992; Hooper, 1997a,b). One of the essential puzzles is how the pyloric rhythm can produce approximately the same motor pattern over such a wide frequency range. One possibility is that time-dependent changes in functional synaptic strength, such as facilitation and depression, play a critical role in maintaining network phase relationships as the frequency changes. This th...