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.     

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 currentI _h 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.     

A Model of a Segmental Oscillator in the Leech Heartbeat Neuronal Network

We modeled a segmental oscillator of the timing network that paces the heartbeat of the leech. This model represents a network of six heart interneurons that comprise the basic rhythm-generating network within a single ganglion. This model builds on a previous two cell model (Nadim et al., 1995) by incorporating modifications of intrinsic and synaptic currents based on the results of a realistic waveform voltage-clamp study (Olsen and Calabrese, 1996). Due to these modifications, the new model behaves more similarly to the biological system than the previous model. For example, the slow-wave oscillation of membrane potential that underlies bursting is similar in form and amplitude to that of the biological system. Furthermore, the new model with its expanded architecture demonstrates how coordinating interneurons contribute to the oscillations within a single ganglion, in addition to their role of intersegmental coordination.     

A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity

A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.’s (J Comput Neurosci 10:281–302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.     

Frequency-dependent coupling between rhythmically active neurons in the leech.

The heart excitor (HE) cells, a set of rhythmically active motor neurons, drive the heartbeat of the medicinal leech. Their activity is gated by inhibitory input from a network of interneurons, but that influence may be modified locally by electrotonic coupling between the HE cells. In this paper I analyze that electrotonic coupling by applying direct current and alternating current signals, and compare the results with predictions based on linear cable theory. The electrotonic junction itself appears to be conventional, but because of the membrane properties of the HE cells, the coupling strength depends upon both the frequency and polarity of the signal and the phase of heartbeat cycle when the signal is applied.     

Leydig neuron activity modulates heartbeat in the medicinal leech

1. Leydig neurons fire spontaneously at low rates (less than 4 Hz), but their activity increases with mechanical stimulation or electrical stimulation of mechanosensory neurons. These conditions also cause acceleration of bursting in heart motor neurons. 2. The firing rate of Leydig cells was found to regulate heart rate in chains of isolated ganglia. When Leydig neurons were made to fire action potentials at relatively high frequencies (ca. 5-10 Hz), however, heart motor neurons ceased bursting and were either silenced or fired erratically. 3. Firing of Leydig neurons at high rates caused bilateral heart interneurons of ganglia 3 or 4 to fire tonically rather than in their normal alternating bursts Tonic firing of these heart interneurons accounts for the prolonged barrages of ipsps recorded in heart motor neurons and the disruption of their normal cyclic activity. 4. Preventing spontaneous activity of Leydig neurons with injected currents in isolated ganglia caused deceleration of the heartbeat rhythm but did not halt oscillation. 5. Electrical stimulation of peripheral nerve roots with Leydig neuron activity suppressed in isolated ganglia caused acceleration of heart rate.     

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Centrally patterned rhythmic activity integrated by a peripheral circuit linking multiple oscillators

The central pattern generator for heartbeat in the medicinal leech, Hirudo generates rhythmic activity conveyed by heart excitor motor neurons in segments 3-18 to coordinate the bilateral tubular hearts and side vessels. We focus on behavior and the influence of previously un-described peripheral nerve circuitry. Extracellular recordings from the valve junction (VJ) where afferent vessels join the heart tube were combined with optical recording of contractions. Action potential bursts at VJs occurred in advance of heart tube and afferent vessel contractions. Transections of nerves were performed to reduce the output of the central pattern generator reaching the heart tube. Muscle contractions persisted but with a less regular rhythm despite normal central pattern generator rhythmicity. With no connections between the central pattern generator and heart tube, a much slower rhythm became manifest. Heart excitor neuron recordings showed that peripheral activity might contribute to the disruption of centrally entrained contractions. In the model presented, peripheral activity would normally modify the activity actually reaching the muscle. We also propose that the fundamental efferent unit is not a single heart excitor neuron, but rather is a functionally defined unit of about three adjacent motor neurons and the peripheral assembly of coupled peripheral oscillators.     

Modeling a Neural Oscillator that Paces Heartbeat in the Medicinal Leech

SYNOPSIS. Heartbeat in the medicinal leech is paced by a neuraloscillator comprising two elemental oscillators whose activityis coordinated intersegmental coordinating fibers. The elementaloscillators each consist of a bilateral pair of heart interneuronslinked by reciprocal inhibitory synapses. The activity cycleof each elemental oscillator consists of alternating burstsof action potentials (plateau/burst phase) and periods inhibition(inactive phase). Oscillation ensues in the reciprocally inhibitorypairs because each neuron is able to escape from the inhibitionits contralateral partner and thus move on to the plateau/burstphase. We have identified and described membrane currents thatcontribute to oscillation and studied graded synaptic transmissionbetween the neurons, using discontinuous current clamp and switchingsingle electrode voltage clamp techniques. A hyperpolarization-activatedinward current, Ih, plays a major role in escape from inhibition,and Ca²⁺ currents produce plateau potentials that support burstformation and mediate graded synaptic transmission. To consolidate our knowledge and guide future research, we haveconstructed a first generation computer model of a neural oscillatorbased on reciprocal inhibition, using Hodgkin-Huxley equationsand a synaptic transfer model, derived from our biophysicalstudies, with Nodus software (De Schutter, 1989). This modelhas confirmed an important role for I_h in sustaining oscillationand has implicated a similarly important role for outward currents(particularly I_A), which remain to be studied. Neural oscillatorsbased on reciprocal inhibition appear to be ubiquitous, andour studies, biophysical and computational, provide insightsinto how they may operate.     

Activity pattern of an oscillatory network after synaptic block in the leech central nervous system

The activity of heart interneurons (HN cells) and heart motor neurons in the central nervous system of the medicinal leech was recorded intracellularly from their cell bodies in the third and fourth segmental ganglion (G3 and G4, respectively). Reciprocal inhibitory synaptic transmission between HN cells in the G3 was blocked by photoinactivation of neuropil glial cells in the same ganglion. The block disrupted the alternating rhythmic spike activity of HN cells in the G3 in isolated G3s but not in chains of G3 and G4. In the latter case, the rhythmic spike pattern of HN cells in the G3 appears to originate in the G4 because, for example, severing one connective between the G3 and G4 silenced the ipsilateral heart interneuron in the G3, whereas its contralateral homologue remained rhythmically active. Simultaneous recordings from HN cells in the G3 and G4 suggest that the latter may serve to coordinate the rhythmic activity of HN cells in the G3, when synaptic interaction between HN cells in the G3 is blocked. This study reveals a considerable capacity of the neural network controlling the heart beat to compensate for the impairment of synapses within one ganglion. Accepted: 8 August 1997     

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, _Leak; a persistent K current, _K2; and of a persistent Na+ current, _P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of _Leak, _K2, and _P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.     

Neural Control of Interappendage Phase During Locomotion

Interappendage phasing of crayfish swimmeret movements dependsupon a central nervous system network of command, oscillator,and coordinating neurons. The command neurons serve to set thegeneral excitation level in each of the segmental oscillators.The oscillator neurons in each hemi-ganglion generate the rhythmicalternations of powerstroke and returnstroke motor neuron activity.The coordinating neurons transmit the precise timing informationabout the state of one oscillator to other oscillators. Thisinformation can serve to advance or to delay the motor burstsdriven by the other oscillators. Which effect is observed dependsupon the arrival time of the coordinating neuron discharge withinthe cycle period of the modulated oscillator. This type of modulationleads to the prediction that a stable interappendage phase canresult from situations where there is not a fixed excitabilitygradient among the segmental oscillators. This prediction hasbeen verified using a cut command neuron preparation.     

Mechanisms of gamma oscillations in the hippocampus of the behaving rat

Gamma frequency oscillations (30-100 Hz) have been suggested to underlie various cognitive and motor functions. Here, we examine the generation of gamma oscillation currents in the hippocampus, using two-dimensional, 96-site silicon probes. Two gamma generators were identified, one in the dentate gyrus and another in the CA3-CA1 regions. The coupling strength between the two oscillators varied during both theta and nontheta states. Both pyramidal cells and interneurons were phase-locked to gamma waves. Anatomical connectivity, rather than physical distance, determined the coupling strength of the oscillating neurons. CA3 pyramidal neurons discharged CA3 and CA1 interneurons at latencies indicative of monosynaptic connections. Intrahippocampal gamma oscillation emerges in the CA3 recurrent system, which entrains the CA1 region via its interneurons.     

CTCF regulates ataxin-7 expression through promotion of a convergently transcribed, antisense noncoding RNA

Neural networks in the spinal cord control two basic features of locomotor movements: rhythm generation and pattern generation. Rhythm generation is generally considered to be dependent on glutamatergic excitatory neurons. Pattern generation involves neural circuits controlling left-right alternation, which has been described in great detail, and flexor-extensor alternation, which remains poorly understood. Here, we use a mouse model in which glutamatergic neurotransmission has been ablated in the locomotor region of the spinal cord. The isolated in?vitro spinal cord from these mice produces locomotor-like activity-when stimulated with neuroactive substances-with prominent flexor-extensor alternation. Under these conditions, unlike in control mice, networks of inhibitory interneurons generate the rhythmic activity. In the absence of glutamatergic synaptic transmission, the flexor-extensor alternation appears to be generated by Ia inhibitory interneurons, which mediate reciprocal inhibition from muscle proprioceptors to antagonist motor neurons. Our study defines a minimal inhibitory network that is needed to produce flexor-extensor alternation during locomotion.     

Neural mechanism for generating and switching motor patterns of rhythmic movements of ovipositor valves in the cricket

In adult female crickets (Gryllus bimaculatus), rhythmic movements of ovipositor valves are produced by contractions of a set of ovipositor muscles that mediate egg-laying behavior. Recordings from implanted wire electrodes in the ovipositor muscles of freely moving crickets revealed sequential changes in the temporal pattern of motor activity that corresponded to shifts between behavioral steps: penetration of the ovipositor into a substrate, deposition of eggs, and withdrawal of the ovipositor from the substrate. We aimed in this study to illustrate the neuronal organization producing these motor patterns and the pattern-switching mechanism during the behavioral sequence. Firstly, we obtained intracellular recordings in tethered preparations, and identified 12 types of interneurons that were involved in the rhythmic activity of the ovipositor muscles. These interneurons fell into two classes: ‘initiator interneurons’ in which excitation preceded the rhythmic contractions of ovipositor muscles, and ‘oscillator interneurons’ in which the rhythmic oscillation and spike bursting occurred in sync with the oviposition motor rhythm. One of the oscillator interneurons exhibited different depolarization patterns in the penetration and deposition motor rhythms. It is likely that some of the oscillator interneurons are involved in producing different oviposition motor patterns. Secondly, we analyzed oviposition motor patterns when the mecahnosensory hairs located on the inside surface of the dorsal ovipositor valves were removed. In deafferented preparations, the sequential change from deposition to withdrawal did not occur. Therefore, the switching from deposition pattern to withdrawal pattern is signaled by the hair sensilla that detect the passage of an egg just before it is expelled.     

Sprouting and connectivity of embryonic leech heart excitor (HE) motor neurons in the absence of their peripheral target

The rhythmic pumping of the hearts in the medicinal leech,Hirudo medicinalis, is neurogenic and mediated by a defined circuit involving identified interneurons in a central pattern generator (CPG) and segmentally iterated motor neurons that drive the heart muscle. During early embryogenesis, presumptive heart excitor (HE) motor neurons extend many axon branches into the body wall; they later innervate the heart while retracting the supernumerary peripheral axons, and only much later in development receive synaptic input from the central pattern generator (Jellies, Kopp and Bledsoe (1992)J. Exp. Biol., 170, 71–92.)- In this study, HE motor neurons were deprived of an early interaction with the heart by surgical ablation of a circumscribed portion of body wall including the heart primordium. Anatomical and electrophysiological data were obtained using intracellular techniques to examine the hypothesis that peripheral interactions with the developing heart provide instructive cues for the final differentiation of these neurons. Target-deprived HE motor neurons continued to extend multiple axons in ventral, lateral and dorsal body wall throughout late embryonic and into postembryonic stages and they extended anomalous axons within the CNS. This resembles the early embryonic growth of HE motor neurons before heart tube differentiation. Furthermore, HE motor neurons deprived of heart contact exhibited tonic activity similar to the situation during early development before they are contacted by the CPG interneurons. In contrast, sham-operated and contralateral HE motor neurons oscillated normally. These results suggest that heart tube contact is specifically required for at least some aspects of HE development and provide a framework in which to identify cell-cell interactions that are involved in matching neurons and targets to generate behaviorally relevant neural circuits.     

Neural Generation of the Peristaltic and Non-Peristaltic Heartbeat Coordination Modes in the Leech, Hirudo Medicinalis

The bilateral paired heart tubes of the leech Hirudo medicinalisare controlled, via excitatory synapses, by a set of bilaterallypaired segmental heart motor neurons (HE cells) which are inturn controlled, via inhibitory synapses, by a set of bilaterallypaired segmental heart interneurons (HN cells). The HE cellsproduce rhythmic impulse bursts because their inherent steadydischarge is periodically inhibited by the HN cells, most ofwhich produce impulse bursts endogenously. The known synapticinteractions among the HN cells and HE cells can account wellfor the observed behavior of the hearts. The HE cells are coordinatedby the HN cells such that the segmental heart tube sectionson one side constrict in a caudorostral sequence (peristalsis),while the segmental heart tube sections on the other side constrictnearly synchronously (non-peristalsis). This difference in thecoordination modes of the two hearts is not permanent; reciprocalcoordination mode transitions occur every 10–50 heartbeatcycles. Only one member of HN(5) cell pair (the HN cells ofthe fifth segmental ganglion) is rhythmically active at a time,the other being completely inactive. By coordinating the frontand rear HN cells the active HN(5) cell produces non-peristalsisipsilaterally and peristalsis contralaterally. Reciprocal changesin the activity-inactivity pattern of the HN(5) cell pair areresponsible for the reciprocal changes in the coordination mode.     

Neural mechanisms generating the leech swimming rhythm: Swim-initiator neurons excite the network of swim oscillator neurons

Summary This paper describes newly identified excitatory connections linking the segmentally iterated swim-initiator interneurons with the network of oscillator neurons that generates the leech swimming rhythm. Apparently monosynaptic excitatory chemical connections are made from one class of swim-initiator neurons (cells 204/205) to several members of the swim oscillator network, including cells 28, 115 and, as described by Weeks (1982c), cell 208. A second class of swim-initiator neurons, cells 21 and 61, also excites this subset of the oscillator neurons.The unpaired swim oscillator neuron, cell 208, also chemically excites cells 28 and 115, apparently directly. Thus, in addition to its role as a member of the swim oscillator, the excitatory output from cell 208 to the swim oscillator adds to that provided by the swim-initiator neurons.The results of this paper enlarge the subset of identified swim oscillator neurons synaptically excited by the swim-initiator neurons. These newly described targets of the swim-initiators strengthen the hypotheses that: 1) the swim-initiator neurons supply much of the tonic excitatory drive responsible for activation and maintenance of the swim central motor program, and 2) the two classes of swim-initiators, cells 204/205 and cells 21/61, act synergistically to initiate and maintain swimming.Abbreviations EPSP excitatory postsynaptic potential - IPSP inhibitory postsynaptic potential - CNS central nervous system     

Gates and oscillators: a network model of the brain clock

The suprachiasmatic nuclei (SCN) control circadian oscillations of physiology and behavior. Measurements of electrical activity and of gene expression indicate that these heterogeneous structures are composed of both rhythmic and nonrhythmic cells. A fundamental question with regard to the organization of the circadian system is how the SCN achieve a coherent output while their constituent independent cellular oscillators express a wide range of periods. Previously, the consensus output of individual oscillators had been attributed to coupling among cells. The authors propose a model that incorporates nonrhythmic "gate" cells and rhythmic oscillator cells with a wide range of periods, that neither requires nor excludes a role for interoscillator coupling. The gate provides daily input to oscillator cells and is in turn regulated (directly or indirectly) by the oscillator cells. In the authors' model, individual oscillators with initial random phases are able to self-assemble so as to maintain cohesive rhythmic output. In this view, SCN circuits are important for self-sustained oscillation, and their network properties distinguish these nuclei from other tissues that rhythmically express clock genes. The model explains how individual SCN cells oscillate independently and yet work together to produce a coherent rhythm.     

Ionic currents, transmitters and models of motor pattern generators

Recent work, combining direct study of ion channels and synapses with pharmacological manipulations and realistic computer simulations, has deepened our understanding of how motor circuits produce rhythmic outputs. In several preparations, both the roles of some key ionic currents in circuit operation and the mechanisms by which circuit operation may be modulated have been identified.