Heartbeat control in the medicinal leech: A model system for understanding the origin,coordination, and modulation of rhythmic motor patterns

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 oscillator 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. © 1995 John Wiley & Sons, Inc.     

Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord

The segmental locomotor network in the lamprey spinal cord was simulated on a computer using a connectionist-type neural network. The cells of the network were identical except for their excitatory levels and their synaptic connections. The synaptic connections used were based on previous experimental work. It was demonstrated that the connectivity of the circuit is capable of generating oscillatory activity with the appropriate phase relations among the cells. Intersegmental coordination was explored by coupling two identical segmental networks using only the cells of the network. Each of the possible couplings of a bilateral pair of cells in one oscillator with a bilateral pair of cells in the other oscillator produced stable phase locking of the two oscillators. The degree of phase difference was dependent upon synaptic weight, and the operating range of synaptic weights varied among the pairs of connections. The coupling was tested using several criteria from experimental work on the lamprey spinal cord. Coupling schemes involving several pairs of connecting cells were found which 1) achieved steadystate phase locking within a single cycle, 2) exhibited constant phase differences over a wide range of cycle periods, and 3) maintained stable phase locking in spite of large differences in the intrinsic frequencies of the two oscillators. It is concluded that the synaptic connectivity plays a large role in producing oscillations in this network and that it is not necessary to postulate a separate set of coordinating neurons between oscillators in order to achieve appropriate phase coupling.     

Intersegmental coordinating system of the lamprey central pattern generator for locomotion

Summary In the lamprey,Ichthyomyzon unicuspis, the wave of activity required for normal swimming movements can be generated by a central pattern generator (CPG) residing in the spinal cord. A constant phase coupling between spinal segments can be organized by intersegmental coordinating neurons intrinsic to the cord. The rostral and caudal segmental oscillators of the CPG have different preferred frequencies when separated from each other. Therefore the system must maintain the segmental oscillators of the locomotor CPG at a single common frequency and with the proper relative timing. Using selective lesions and a split-bath, it is demonstrated that the coordinating system is comprised of at least 3 subsystems, short-axon systems in the lateral and medial tracts and a long axon system in the lateral tracts. Each alone can sustain relatively stable coordinated activity.Abbreviations CPG central pattern generator - NMDA N-methyl-D-aspartate - VR ventral root     

Conditioned reflex: detector and command neuron

Conditioned reflex is characterized by plasticity resulting in a bilateral selective input-output linking. In simple nervous systems, input stimuli are represented by selective detectors connected with command neurons through plastic synapses strengthened during associative learning and weakened during extinction. The process of associative learning is due to temporal coincidence of excitation in both detector and command neurons. Short-term memory within a plastic synapses is mediated by phosphorilation of postsynaptic receptor molecules not requiring protein synthesis. Long-term synaptic memory parallels expression of immediate early genes that mediates structural gene expression and protein synthesis. A simple detector-command neuron association becomes more complex in the course of evolution. Input mechanism is supplemented with predetector interneurons preceding detectors. Detector selectively tuned to specific input stimulus is converging on a command neuron constitute selectivity mechanism for conditioned reflexes to complex stimuli. The complication also concerns the output mechanisms. Command neurons become more specialized, and an additional link of premotor interneurons is incorporated between command neurons and motor neurons. Via synapses, the command neurons can produce excitation in a particular set of premotor neurons controlling a specific set of motor neurons responsible for behavioral act configuration. Specialization of command neurons in combination with premotor neuron structures increases the variability of outputs. Conditioned reflexes with more complex inputs and more flexible outputs determine the diversity of acquired behaviors.     

Neuronal Network Models of Phase Separation Between Limb CPGs of Digging Sand Crabs

Ordinary differential equations are used to model a peculiar motor behaviour in the anomuran decapod crustacean Emerita analoga. Little is known about the neural circuitry that permits E. analoga to control the phase relationships between movements of the fourth legs and pair of uropods as it digs into sand, so mathematical models might aid in identifying features of the neural structures involved. The geometric arrangement of segmental ganglia controlling the movements of each limb provides an intuitive framework for modelling. Specifically, due to the rhythmic nature of movement, the network controlling the fourth legs and uropods is viewed as three coupled identical oscillators, one dedicated to the control of each fourth leg and one for the pair of uropods, which always move in bilateral synchrony. Systems of Morris–Lecar equations describe the voltage and ion channel dynamics of neurons. Each central pattern generator for a limb is first modelled as a single neuron and then, more realistically as a multi-neuron oscillator. This process results in high-dimensional systems of equations that are difficult to analyse. In either case, reduction to phase equations by averaging yields a two-dimensional system of equations where variables describe only each oscillator’s phase along its limit cycle. The behaviour observed in the reduced equations approximates that of the original system. Results suggest that the phase response function in the two dimensional system, together with minimal input from asymmetric bilateral coupling parameters, is sufficient to account for the observed behaviour.     

Principle of neuronal organization of defensive reflexes in mollusks

Spontaneous and evoked synaptic activity of command neurons for the defensive response of spiracle closing were studied by simultaneous intracellular recording of activity of several identified CNS neurons in snails. Comparison of monosynaptic EPSPs in command neurons evoked by discharges of presynaptic neurons with spontaneous synaptic potentials indicated that the central organization of the defensive reflex is in the form of a two-layered neuron net in which each neuron of the afferent layer possesses a local receptive field, but which overlaps with other afferent neurons. Each neuron of the afferent layer is connected with each neuron of the efferent layer by monosynaptic excitatory connections that differ in efficiency (maximal only with one neuron of the efferent layer). Both receptive fields of neurons of the afferent layer and "fields of efficiency of synaptic connections" are distributed according to the normal law. As a result of this organization the neuron net acquires a new quality: The action of different stimuli leads to the appearance of differently located "spatial excitation profiles" of efferent layer neurons even when this action of the stimulus occurs not at the center of the receptive field.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 16, No. 1, pp. 26–34, January-February, 1984.     

Fine structure of the brain and brain nerves ofOikopleura dioica (Urochordata,Appendicularia)

Summary Each second brain nerve consists of only one single fibre terminating at two different types of touch receptors in the oral region. The two nerves are the dendrites of two perikarya in the forebrain and are the master neurons for ciliary reversal in the stigmata, which is a two-neuron reflex. By axoaxonal synapses they control one motor neuron in the midbrain, i.e. the command neuron for ciliary reversal in both rings. This cell sends one axon branch in each third nerve to the cilia cells. In the left nerve this fibre is closely associated with a coarsely granulated accessory fibre, which apparently regulates the ciliary beat. The third nerves also contain one fibre each from another motor neuron in the hindbrain. These fibres make synaptic contacts at some specialized epidermal cells in the lateral trunk behind the ciliary rings. A few previously unknown nerves in the dorsal forebrain innervate epidermal cells. It is likely that the complicated epidermal motor innervation regulates the secretory activity of the oikoplasts or of the epidermal cells in constructing a new house, including the necessary complicated filters and food trapping mechanisms.     

Fault tolerance in the cardiac ganglion of the lobster

Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results. Received: 2 April 1998 / Accepted in revised form: 2 July 1998     

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.     

Synchronization in a neural network of phase oscillators with the central element

A neural network model is considered which is designed as a system of phase oscillators and contains the central oscillator and peripheral oscillators which interact via the central oscillator. The regime of partial synchronization was studied when current frequencies of the central oscillator and one group of peripheral oscillators are near to each other while current frequencies of other peripheral oscillators are far from being synchronized with the central oscillator. Approximation formulas for the average frequency of the central oscillator in the regime of partial synchronization are derived, and results of computation experiments are presented which characterize the accuracy of the approximation.     

Phase plane description of crayfish swimmeret oscillator

Crayfish swimmeret system shows rhythmic, coordinated behavior when the command fibers are stimulated chronically by electrical pulses, and the oscillating frequency becomes faster with increasing stimulus frequency. This behavior is organized by the distributed neural oscillators in the abdominal ganglia. We investigated the dynamics of the neural oscillators which are controlled by command fibers. Phase resetting experiment technique was used for this purpose; a temporary cessation of commanding pulses, which was regarded as suppressive perturbation for the neural oscillator, was applied to the chronically stimulated oscillator, and phase transition curves (PTCs) were measured. For the short cessation of command pulses, type 1 PTCs were obtained. With increasing cessation length, the PTC shifted downward, and finally changed into type 0. We also measured PTCs for temporarily increased stimulus frequency, which was an excitatory perturbation for the neural oscillator and increased the frequency of the oscillation transiently. For the short excitatory perturbation, the PTCs were also type 1 and shifted upward. PTCs changed their shapes from type 1 into type 0, as increasing the perturbation length. These shapes of the PTCs contain important information about the properties of the neural oscillator. Analyzing these PTCs, we present a phase plane diagram which describes the character of the command control of the neural oscillator.     

Topographic motor projections in the limb imposed by LIM homeodomain protein regulation of ephrin-A:EphA interactions

The formation of topographic neural maps relies on the coordinate assignment of neuronal cell body position and axonal trajectory. The projection of motor neurons of the lateral motor column (LMC) along the dorsoventral axis of the limb mesenchyme constitutes a simple topographic map that is organized in a binary manner. We show that LIM homeodomain proteins establish motor neuron topography by coordinating the mediolateral settling position of motor neurons within the LMC with the dorsoventral selection of axon pathways in the limb. These topographic projections are established, in part, through LIM homeodomain protein control of EphA receptors and ephrin-A ligands in motor neurons and limb mesenchymal cells.     

Interaction of coupled nonlinear oscillators having different intrinsic resting levels

The interaction among coupled oscillators is governed by oscillator properties (intrinsic frequency and amplitude) and coupling mechanisms. This study considers another oscillator property, the intrinsic resting level, and evaluates its role in governing oscillator interactions. The results of computer experiments on a chain of either three or five bidirectionally coupled nonlinear oscillators, suggest that an intrinsic resting level gradient, if present, is one of the factors governing the interaction between coupled oscillators. If there is no intrinsic frequency gradient, then an intrinsic resting level gradient is sufficient to produce many features of interaction among coupled oscillators. If both intrinsic frequency and intrinsic resting level gradients are present, then both of them determine the manner in which the coupled oscillators interact with each other.     

Auditory input to motor neurons of the dorsal longitudinal flight muscles in a noctuid moth (Barathra brassicae L.)

Summary Motor neurons innervating the dorsal longitudinal muscles of a noctuid moth receive synaptic input activated by auditory stimuli. Each ear of a noctuid moth contains two auditory neurons that are sensitive to ultrasound (Fig. 1). The ears function as bat detectors. Five pairs of large motor neurons and three pairs of small motor neurons found in the pterothoracic ganglia innervate the dorsal longitudinal (depressor) muscles of the mesothorax (Figs. 2 to 5). In non-flying preparations the motor neurons receive no oscillatory synaptic input. Synaptic input to a cell resulting from ultrasonic stimulation is consistent and can be either depolarizing or hyperpolarizing (Figs. 6 to 9). Quiescent neurons only rarely fire a spike in response to auditory inputs. Motor neurons in flying preparations receive oscillatory synaptic drive from the flight pattern generator and usually fire a spike for each wingbeat cycle (Figs. 10 to 12). Ultrasonic stimulation can provide augmented synaptic drive causing a neuron to fire two spikes per wingbeat cycle thus increasing flight vigor (Fig. 11). The same stimulus presented on another occasion can also inhibit spiking in the same motor neuron, but the rhythmic drive remains (Fig. 12). Thus, when the flight oscillator is running auditory stimuli can modulate neuronal responses in different ways depending on some unknown state of the nervous system. Sound intensity is the only stimulus parameter essential for activating the auditory pathway to these motor neurons. The intensity must be sufficient to excite two or three auditory neurons. The significance of these responses in relation to avoidance behavior to bats is discussed.     

Intersegmental Coordination: Lessons from Modeling Systems of Coupled Non-Linear Oscillators

SYNOPSIS. Intersegmental coordination of both vertebrates andinvertebrates is poorly understood primarily because so littleis known about the substrate of the neural underpinnings andhow the elements interact to produce the complex timing relationshipsrequired by the organism. We describe here a systems approachcombining experimental and theoretical treatment of the lampreylocomotor central pattern generator. The central pattern generatoris viewed as a chain of coupled non-linear oscillators correspondingto segmental burst generators. We analyze various coupling schemesin terms of their ability to produce a stable traveling wavesimilar to that seen in the isolated spinal cord and the intactanimal. The role of long coordinating neurons is particularlydiscussed.     

Local inhibitor of the crayfish telson-flexor motor giant neurons: morphology and physiology

The motor circuits that control telson flexion in the crayfish (Procambarus clarkii) include a curiously arranged sub-circuit: a premotor 'command' neuron excites a motor neuron via a trisynaptic pathway, but also inhibits (and prevents firing of) the motor neuron via a shorter latency pathway (Kramer et al. 1981 a). The premotor and motor neurons in this circuit have been previously identified (Kramer et al. 1981 a; Dumont and Wine 1985a, b; see Fig. 1). We have now identified a local interneuron that inhibits the motor neurons. The cell we studied is called the 'C' cell because of its distinctive structure (Figs. 2, 3). A single pair of bilaterally homologous C-cells was found in the last (6th) abdominal ganglion. The C-cells are invariably dye coupled to one another following injections of lucifer yellow into either one of them, and are frequently dye coupled to smaller axons in the 2nd, 3rd, and 6th nerves. In addition, some of the extensive branches of the C-cell extend out into the 6th nerve, where they are in close proximity to the axons of the motor neurons they inhibit (Fig. 3). Two kinds of evidence established that the C-cell directly inhibits the motor neurons. First, when simultaneous recordings were made from the C-cell and the motor neurons, spikes in the C-cell, no matter how evoked, were invariably followed, within 1.5 ms, by depolarizing IPSPs in the motor neuron (Fig. 6). Second, when the C-cell was hyperpolarized so that it could not fire, that same IPSP in the motor neuron was abolished (Fig. 6). The inhibitory pathway to the motor neurons must be fired at short latency in order to prevent firing caused by the trisynaptic excitatory input (Fig. 1). The C-cells were fired at short latency (less than 3 ms) by impulses in either of the escape command cells (Fig. 4), and at even shorter latency by impulses in the Segmental Giant of the 6th ganglion (SG6) (Fig. 5). It has been established elsewhere that the SGs are a major output pathway of the escape command cells; our results suggest that they may be the pathway for command-evoked firing of the C-cell. The C-cells are also excited by two descending, non-giant, flexion premotor neurons, called I2 and I3 (Fig. 5). The EPSPs from a single I2 or I3 impulse were subthreshold, but temporal and spatial summation of EPSPs from the non-giant pathway sometimes fired the C-cells.(ABSTRACT TRUNCATED AT 400 WORDS)     

Control of multistability in ring circuits of oscillators

The essential dynamics of some biological central pattern generators (CPGs) can be captured by a model consisting of N neurons connected in a ring. These circuits, like many oscillatory nonlinear circuits of sufficient complexity, are capable of multistability, that is, of generating different firing patterns distinguished by the phasic relationships between the firing in each circuit element (neuron). Moreover, a shift in firing pattern can be induced by a transient perturbation. A systematic approach, based on phase-response curve (PRC) theory, was used to determine the optimum timing for perturbations that induce a shift in the firing pattern. The first step was to visualize the solution space of the ring circuit, including the attractive basins for each stable firing pattern; this was possible using the relative phase of N−1 oscillators, with respect to an arbitrarily selected reference oscillator, as coordinate axes. The trajectories in this phase space were determined using an iterative mapping based only on the PRCs of the uncoupled component oscillators; this algorithm was called a circuit emulator. For an accurate mapping of the attractive basin of each pattern exhibited by the ring circuit, the emulator had to take into account the effect of a perturbation or input on the timing of two bursts following the onset of the perturbation, rather than just one. The visualization of the attractive basins for rings of two, three, and four oscillators enabled the accurate prediction of the amounts of phase resetting applied to up to N−1 oscillators within a cycle that would induce a transition from any pattern to any another pattern. Finally, the timing and synaptic characterization of an input called the switch signal was adjusted to produce the desired amount of phase resetting. Received: 29 May 1998 / Accepted in revised form: 18 September 1998     

An oscillator theory of motor unit recruitment

The phenomenon of systematic recruitment of motor units with increasing demand load is usually explained by the size principle. Though this principle successfully explains the gain-related aspects of muscle force generation, it does not address the need for desynchronization of motor unit activities in order to produce a smooth tension profile at the level of whole muscle, while individual muscle fibers are "twitching." We propose an oscillator model of motor neurons in which a pool of motor neurons fires a bundle of muscle fibers. Although individual muscle fibers have a complicated tension profile, the tension produced by the entire bundle is regulated and follows a command signal accurately. This is shown to be possible because of uncorrelated activity produced by local inhibitory connections among motor neurons. Connections that produce synchronized oscillations result in uncontrolled contractions of the muscle. These results seem to suggest that while synchronized activity indicates pathology and disease, desynchronized activity is the precondition for normal muscle function. Physiological evidence for the proposed theory of motor unit synchronization is presented.     

Coping with variability in small neuronal networks

Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.