Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8–10 Hz with a rostro-caudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%–40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition. Received: 1 April 1997 / Accepted in revised form: 20 March 1998     

Intersegmental coordination in the lamprey: simulations using a network model without segmental boundaries

Swimming in vertebrates such as eel and lamprey involves the coordination of alternating left and right activity in each segment. Forward swimming is achieved by a lag between the onset of activity in consecutive segments rostrocaudally along the spinal cord. The intersegmental phase lag is approximately 1% of the cycle duration per segment and is independent of the swimming frequency. Since the lamprey has approximately 100 spinal segments, at any given time one wave of activity is propagated along the body. Most previous simulations of intersegmental coordination in the lamprey have treated the cord as a chain of coupled oscillators or well-defined segments. Here a network model without segmental boundaries is described which can produce coordinated activity with a phase lag. This ‘continuous’ pattern-generating network is composed of a column of 420 excitatory interneurons (E1 to E420) and 300 inhibitory interneurons (C1 to C300) on each half of the simulated spinal cord. The interneurons are distributed evenly along the simulated spinal cord, and their connectivity is chosen to reflect the behavior of the intact animal and what is known about the length and strength of the synaptic connections. For example, E100 connects to all interneurons between E51 and E149, but at varying synaptic strengths, while E101 connects to all interneurons between E52 and E150. This unsegmented E-C network generates a motor pattern that is sampled by output elements similar to motoneurons (M cells), which are arranged along the cell column so that they receive input from seven E and five C interneurons. The M cells thus represent the summed excitatory and inhibitory input at different points along the simulated spinal cord and can be regarded as representing the ventral root output to the myotomes along the spinal cord. E and C interneurons have five simulated compartments and Hodgkin-Huxley based dynamics. The simulated network produces rhythmic output over a wide range of frequencies (1–11 Hz) with a phase lag constant over most of the length, with the exception of the ‘cut’ ends due to reduced synaptic input. As the inhibitory C interneurons in the simulation have more extensive caudal than rostral projections, the output of the simulation has positive phase lags, as occurs in forward swimming. However, unlike the biological network, phase lags in the simulation increase significantly with burst frequency, from 0.5% to 2.3% over the range of frequencies of the simulation. Local rostral or caudal increases in excitatory drive in the simulated network are sufficient to produce motor patterns with increased or decreased phase lags, respectively. Received: 15 December 1995 / Accepted in revised form: 17 September 1996     

Intersegmental phase lags in the lamprey spinal cord: Experimental confirmation of the existence of a boundary region

A critical feature of the motor pattern generated by the lamprey spinal cord is an intersegmental delay that is constant down the cord and scales with cycle duration. This has been modelled as the output of a chain of coupled oscillators, within a general mathematical framework developed by Kopell and Ermentrout (1986, 1988). The analysis predicts that for asymmetric coupling of equally-activated oscillators, the intersegmental phase lag will be uniform along the chain except in a boundary layer at one end. Here we provide experimental evidence that a boundary layer does occur at the rostral end of an isolated preparation of lamprey spinal cord. In the context of the mathematical analysis, this indicates that ascending coupling is dominant in the control of intersegmental phase lag in the lamprey.     

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     

Mechanisms for lateral turns in lamprey in response to descending unilateral commands: a modeling study

 Straight locomotion in the lamprey is, at the segmental level, characterized by alternating bursts of motor activity with equal duration and spike frequency on the left and the right sides of the body. Lateral turns are characterized by three main changes in this pattern: (1) in the turn cycle, the spike frequency, burst duration, and burst proportion (burst duration/cycle duration) increase on the turning side; (2) the cycle duration increases in both the turn cycle and the succeeding cycle; and (3) in the cycle succeeding the turn cycle, the burst duration increases on the non-turning side (rebound). We investigated mechanisms for the generation of turns in single-segment models of the lamprey locomotor spinal network. Activation of crossing inhibitory neurons proved a sufficient mechanism to explain all three changes in the locomotor rhythm during a fictive turn. Increased activation of these cells inhibits the activity of the opposite side during the prolonged burst of the turn cycle, and slows down the locomotor rhythm. Secondly, this activation of the crossing inhibitory neurons is accompanied by an increased calcium influx into the cells. This gives a suppressed activity on the turning side and a contralateral rebound after the turn, through activation of calcium-dependent potassium channels. Received: 28 June 2000 / Accepted for publication: 10 May 2001     

Flexibility in the patterning and control of axial locomotor networks in lamprey

In lower vertebrates, locomotor burst generators for axial muscles generally produce unitary bursts that alternate between the two sides of the body. In lamprey, a lower vertebrate, locomotor activity in the axial ventral roots of the isolated spinal cord can exhibit flexibility in the timings of bursts to dorsally-located myotomal muscle fibers versus ventrally-located myotomal muscle fibers. These episodes of decreased synchrony can occur spontaneously, especially in the rostral spinal cord where the propagating body waves of swimming originate. Application of serotonin, an endogenous spinal neurotransmitter known to presynaptically inhibit excitatory synapses in lamprey, can promote decreased synchrony of dorsal-ventral bursting. These observations suggest the possible existence of dorsal and ventral locomotor networks with modifiable coupling strength between them. Intracellular recordings of motoneurons during locomotor activity provide some support for this model. Pairs of motoneurons innervating myotomal muscle fibers of similar ipsilateral dorsoventral location tend to have higher correlations of fast synaptic activity during fictive locomotion than do pairs of motoneurons innervating myotomes of different ipsilateral dorsoventral locations, suggesting their control by different populations of premotor interneurons. Further, these different motoneuron pools receive different patterns of excitatory and inhibitory inputs from individual reticulospinal neurons, conveyed in part by different sets of premotor interneurons. Perhaps, then, the locomotor network of the lamprey is not simply a unitary burst generator on each side of the spinal cord that activates all ipsilateral body muscles simultaneously. Instead, the burst generator on each side may comprise at least two coupled burst generators, one controlling motoneurons innervating dorsal body muscles and one controlling motoneurons innervating ventral body muscles. The coupling strength between these two ipsilateral burst generators may be modifiable and weakening when greater swimming maneuverability is required. Variable coupling of intrasegmental burst generators in the lamprey may be a precursor to the variable coupling of burst generators observed in the control of locomotion in the joints of limbed vertebrates.     

Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey

Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-d-aspartate (NMDA) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations. The bursting mechanism relies on intracellular accumulation of calcium that activates Ca²⁺-dependent K⁺. The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry following the action potential, Ca_AP pool, and the other represents the calcium inflow through the NMDA channels, Ca_NMDA pool. The Ca²⁺-dependent K⁺ activated by these two calcium pools are referred to as K_CaAP and K_CaNMDA, respectively, and their relative conductances are modulated and increase with the background activation of the network. When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of 0.5–5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA. When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal strength, this kind of network is capable of reproducing several experimental observations such as those occurring during strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst intervals at different levels of the spinal cord. Received: 29 September 1998 Accepted in Revised Form: 26 March 1999     

Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey

Factors contributing to the production of a phase lag along chains of oscillatory networks consisting of Hodgkin-Huxley type neurons are analyzed by means of simulations. Simplified network configurations are explored consisting of the basic building blocks of the spinal central pattern generator (CPG) generating swimming in the lamprey. It consists of reciprocally coupled crossed inhibitory C interneurons and ipsilateral excitatory E interneurons that activate C neurons and other E neurons. Oscillatory activity in the model network can, in the simplest case, be produced by a pair of reciprocally coupled C interneurons oscillating through an escape mechanism. Different levels of tonic excitation drive the network over a wide burst frequency range. In this type of network, powerful frequency-regulating factors are the effective inhibition produced by the active side, in combination with the tendency of the inactive side to escape from the inhibition. These two mechanisms can be affected by several factors, e.g. spike frequency adaptation (calcium-dependent K(+) channels), N-methyl-D-aspartate membrane properties as well as presence of low-voltage activated calcium channels. A rostrocaudal phase lag can be produced either by extending the contralateral inhibitory projections or the ipsilateral excitatory projections relatively more in the caudal than the rostral direction, since both an increased inhibition and a phasic excitation slow down the receiving network. The phase lag becomes decreased if the length of the intersegmental projections is increased or if the projections are extended symmetrically in both the rostral and the caudal directions. The simulations indicate that the conditions in the ends of an oscillator chain may significantly affect sign, magnitude and constancy of the phase lag. Also, with short and relatively weak intersegmental connections, the network remains robust against perturbations as well as intrinsic frequency differences along the chain. The phase lag (percentage of cycle duration) increases, however, with burst frequency also when the coupling strength is comparatively weak. The results are discussed and compared with previous "phase pulling" models as well as relaxation oscillators.     

Experiments on the central pattern generator for swimming in amphibian embryos

The central nervous system of paralysed Xenopus laevis embryos can generate a motor output pattern suitable for swimming locomotion. By recording motor root activity in paralysed embryos with transected nervous systems we have shown that: (a) the spinal cord is capable of swimming pattern generation; (b) swimming pattern generator capability in the hindbrain and spinal cord is distributed; (c) caudal hindbrain is necessary for sustained swimming output after discrete stimulation. By recording similarly from embryos whose central nervous system was divided longitudinally into left and right sides, we have shown that: (a) each side can generate rhythmic motor output with cycle periods like those in swimming; (b) during this activity cycle period increases within an episode, and there is the usual rostrocaudal delay found in swimming; (c) this activity is influenced by sensory stimuli in the same way as swimming activity; (d) normal phase coupling of the left and right sides can be established by the ventral commissure in the spinal cord. We conclude that interactions between the antagonistic (left and right) motor systems are not necessary for swimming rhythm generation and present a model for swimming pattern generation where autonomous rhythm generators on each side of the nervous system drive the motoneurons. Alternation is achieved by reciprocal inhibition, and activity is initiated and maintained by tonic excitation from the hindbrain.     

Traveling-wave pattern generator controls movement and organization of sensory feedback in a spinal cord model

 A traveling wave in a two-dimensional spinal cord model constitutes a stable pattern generator for quadruped gaits. In the context of the somatotopic organization of the spinal cord, this pattern generator is sufficient to generate stable locomotive limb trajectories. The elastic properties of muscles alone, providing linear negative feedback, are sufficient to stabilize stance and locomotion in the presence of perturbative forces. We further show that such a pattern generator is capable of organizing sensory processing in the spinal cord. A single-layer perceptron was trained to associate the sensory feedback from the limb (coding force, length, and change of length for each muscle) with the two-dimensional activity profile of the traveling wave. This resulted in a well-defined spatial organization of the connections within the spinal network along a rostrocaudal axis. The spinal network driven by peripheral afferents alone supported autonomous locomotion in the positive feedback mode, whereas in the negative feedback mode stance was stabilized in response to perturbations. Systematic variation of a parameter representing the effect of gamma-motor neurons on muscle spindle activity in our model led to a corresponding shift of limb position during stance and locomotion, resulting in a systematic displacement alteration of foot positions. Received: 30 July 2001 / Accepted in revised form: 17 April 2002 Correspondence to: A. Kaske (e-mails: alexander.kaske@mtc.ki.se, alexander.kaske@vglab.com)     

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.     

Calcium imaging of network function in the developing spinal cord

We have used calcium imaging to visualize the spatiotemporal organization of activity generated by in vitro spinal cord preparations of the developing chick embryo and the neonatal mouse. During each episode of spontaneous activity, we found that chick spinal neurons were activated rhythmically and synchronously throughout the transverse extent of the spinal cord. At the onset of a spontaneous episode, optical activity originated in the ventrolateral part of the cord. Back-labeling of spinal interneurons with calcium dyes suggested that this ventrolateral initiation was mediated by activation of a class of interneurons, located dorsomedial to the motor nucleus, that receive direct monosynaptic input from motoneurons. Studies of locomotor-like activity in the anterior lumbar segments of the neonatal mouse cord revealed the existence of a rostrocaudal wave in the oscillatory component of each cycle of rhythmic motoneuron activity. This finding raises the possibility that the activation of mammalian motoneurons during locomotion may share some of the same rostrocaudally organized mechanisms that evolved to control swimming in fishes.     

Neuromodulation via conditional release of endocannabinoids in the spinal locomotor network

Endocannabinoids act as retrograde signals to modulate synaptic transmission. Little is known, however, about their significance in integrated network activity underlying motor behavior. We have examined the physiological effects of endocannabinoids in a neuronal network underlying locomotor behavior using the isolated lamprey spinal cord. Our results show that endocannabinoids are released during locomotor activity and participate in setting the baseline burst rate. They are released in response to mGluR1 activation and act as retrograde messengers. This conditional release of endocannabinoids can transform motoneurons and crossing interneurons into modulatory neurons by enabling them to regulate their inhibitory synaptic inputs and thus contribute to the modulation of the locomotor burst frequency. These results provide evidence that endocannabinoid retrograde signaling occurs within the locomotor network and contributes to motor pattern generation and regulation in the spinal cord.     

Studies on the excitability of the central program generator in the spinal cord of the terrapin Pseudemys scripta elegans

We present observations on the multicyclic scratch reflex in spinal terrapins as produced by electrical stimuli applied to the shell at the specific regions at which a mechanical stimulus produces the reflex. EMGs and hip and knee movements are recorded. The responses to the electrical stimuli are similar to the responses to mechanical stimuli. There is a three phase EMG pattern (Stein and Grossman, 1980), to which the movement pattern is related (Bakker and Crowe, 1982). A response may consist of a series of up to 25 movement cycles with a total time course of up to about 30 sec. The initial cycles of a response are relatively fast (less than 1 sec), but the cycles at the expiration of the response may have a duration of 2-3 sec. A single electrical stimulus pulse is often insufficient to trigger a series response. Instead, a weak EMG burst of a few tenths of a second duration, together with a slight movement, is often seen. However, a second pulse can set the cycle series in motion even after an interval of 40 sec between the pulses. A further booster stimulus pulse given while a reflex response is taking place can increase the speed of the movement. If the booster pulse is given just after cessation of reflex activity it can restart the activity, but this second cycle series is often shorter than the first one. The results indicate that the excitability of the central program generator is not constant. Long duration changes in the excitability are produced within the spinal cord.     

Different modes of swimming of the carp, Cyprinus carpio L.

An electromyographical study has been made of carp swimming muscles at various points along the body length during sustained and burst locomotion. During sustained swimming, red muscles show a constant time lag between activation of anterior and posterior segments which is practically independent of the speed of locomotion. In contrast, anterior and posterior homolateral segments are activated simultaneously during bursts of rapid movement. This pattern of co-ordination between body segments differs from that reported for other species.     

Collaterals and Bifurcations of Axons of Spinal Cord Motoneurons of the Lamprey <Emphasis Type="Italic">Lampetra fluviatilis</Emphasis>

Structure of central projections of the motoneuron axons of the spinal cord of the lamprey Lampetra fluviatilis was studied using labeling with horseradish peroxidase in vitro. Axons of the lamprey spinal cord motoneurons were found to have collaterals terminating in ventral columns of the white matter, in which they establish contacts with dendrites of adjacent motoneurons, which can be considered as a substrate of the intermotoneuron interaction. Some axons of motoneurons give bifurcations to two equal branches connected with two neighboring ventral roots, which seems to facilitate propagation of rhythmic activity of locomotor generator in the rostro caudal direction for providing continuous wave of contraction of myotome muscles in the course of undulating movement.     

Computer simulation of the segmental neural network generating locomotion in lamprey by using populations of network interneurons

Realistic computer simulations of the experimentally established local spinal cord neural network generating swimming in the lamprey have been performed. Populations of network interneurons were used in which cellular properties, like cell size and membrane conductance including voltage dependent ion channels were randomly distributed around experimentally obtained mean values, as were synaptic conductances (kainate/AMPA, NMDA, glycine) and delays. This population model displayed more robust burst activity over a wider frequency range than the more simple subsample model used previously, and the pattern of interneuronal activity was appropriate. The strength of the reciprocal inhibition played a very important role in the regulation of burst frequency, and just by changing the inhibitory bias the entire physiological range could be covered. At the lower frequency range of bursting the segmental excitatory interneurons provide stability as does the activation of voltage dependent NMDA receptors. Spike frequency adaptation by means of summation of afterhyperpolarization (AHP) serves as a major burst terminating factor, and at lower rates the membrane properties conferred by the NMDA receptor activation. The lateral interneurons were not of critical importance for the burst termination. They may, however, be of particular importance for inducing a rapid burst termination during for instance steering and righting reactions. Several cellular factors combine to provide a secure and stable motor pattern in the entire frequency range.     

Coordinated network functioning in the spinal cord: An evolutionary perspective

The successful achievement of harmonious locomotor movement results from the integrated operation of all body segments. Here, we will review current knowledge on the functional organization of spinal networks involved in mammalian locomotion. Attention will not simply be restricted to hindlimb muscle control, but by also considering the necessarily coordinated activation of trunk and forelimb muscles, we will try to demonstrate that while there has been a progressive increase in locomotor system complexity during evolution, many basic organizational features have been preserved across the spectrum from lower vertebrates through to humans. Concerning the organization of axial neuronal networks that control trunk muscles, it has been found across the vertebrate range that during locomotor movement a motor wave travels longitudinally in the spinal cord via the coupling of rhythmic segmental networks. For hindlimb activation it has been found in all species studied that the rostral lumbar segments contain the key elements for pattern generation. We also showed that rhythmic arm movements are under the control of cervical forelimb generators in quadrupeds as well as in human. Finally, it is highlighted that the coordination of quadrupedal movements during locomotion derives principally from an asymmetrical coordinating influence occurring in the caudo-rostral direction from the lumbar hindlimb networks.     

Hypergravity susceptibility of ventral root activity during fictive swimming in tadpoles (Xenopus laevis)

1. Fictive swimming is an experimental model to study early motor development. As vestibular activity also affects the development of spinal motor projections, the present study focused on the question whether in Xenopus laevis tadpoles, the rhythmic activity of spinal ventral roots (VR) during fictive swimming revealed age-dependent modifications after hypergravity exposure. In addition, developmental characteristics for various features of fictive swimming between stages 37/38 and 47 were determined. Parameters of interest were duration of fictive swimming episodes, burst duration, burst frequency (i.e., cycle length), and rostrocaudal delay. 2. Ventral root recordings were performed between developmental stage 37/38, which is directly after hatching and stage 47 when the hind limb buds appear. The location of recording electrodes extended from myotome 4 to 17. 3. Hypergravity exposure by 3 g-centrifugation lasted 9 to 11 days. It started when embryos had just terminated gastrulation (stage 11/19-group), when first rhythmical activity in the ventral roots appeared (stage 24/27-group), and immediately after hatching (stage 37/41-group). Ventral root recordings were taken for 8 days after termination of 3 g-exposure. 4. Between stage 37/38 (hatching) and stage 47 (hind limb bud stage) burst duration, cycle length and rostrocaudal delay recorded between the 10th and 14th postotic myotome increased while episode duration decreased significantly. In tadpoles between stage 37 and 43, the rostrocaudal delay in the proximal tail part was as long as in older tadpoles while in caudal tail parts, it was shorter. During this period of development, there was also an age-dependent progression of burst extension in the proximal tail area that could not be observed between the 10th and 14th myotome. 6. After termination of the 3 g-exposure, the mean burst duration of VR activity increased significantly (p < 0.01) when 3 g-exposure started shortly after gastrulation but not when it started thereafter. Other parameters for VR activity such as cycle length, rostrocaudal delay and episode duration were not affected by this level of hypergravity. 7. It is postulated that (i) functional separation of subunits responsible for intersegmental motor coordination starts shortly after hatching of young tadpoles; and that (ii) gravity exerts a trophic influence on the development of the vestibulospinal system during different periods of embryonic development leading to the formation of more rigid neuronal networks earlier in the spinal than in the ocular projections.     

Mathematical models for the swimming pattern of a lamprey

A significant characteristic in a swimming pattern of a lamprey is the generation of a constant phase lag along its body in spite of the wide range of undulation frequencies. In this paper, we discuss a mathematical treatment for coupled oscillators with time-delayed interaction and propose a model for the central pattern generator (CPG) of a lamprey to account for the generation of a constant phase relation, with consideration of the signal conduction time. From this model, it is suggested that the desired phase relation can be produced by long ascending connections from the tail to the neck region of the CPG.