Neural control of interlimb oscillations

How do humans and other animals accomplish coordinated movements? How are novel combinations of limb joints rapidly assembled into new behavioral units that move together in in-phase or anti-phase movement patterns during complex movement tasks? A neural central pattern generator (CPG) model simulates data from human bimanual coordination tasks. As in the data, anti-phase oscillations at low frequencies switch to in-phase oscillations at high frequencies, in-phase oscillations occur at both low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, a “seagull effect” of larger errors occurs at intermediate phases, and oscillations slip toward in-phase and anti-phase when driven at intermediate phases. These oscillations and bifurcations are emergent properties of the CPG model in response to volitional inputs. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. When an equal command or GO signal activates both model channels, the model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Received: 22 August 1994 / Accepted in revised form: 13 May 1997     

Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis

Central pattern generators (CPGs) consisting of interacting groups of neurons drive a variety of repetitive, rhythmic behaviors in invertebrates and vertebrates, such as arise in locomotion, respiration, mastication, scratching, and so on. These CPGs are able to generate rhythmic activity in the absence of afferent feedback or rhythmic inputs. However, functionally relevant CPGs must adaptively respond to changing demands, manifested as changes in oscillation period or in relative phase durations in response to variations in non-patterned inputs or drives. Although many half-center CPG models, composed of symmetric units linked by reciprocal inhibition yet varying in their intrinsic cellular properties, have been proposed, the precise oscillatory mechanisms operating in most biological CPGs remain unknown. Using numerical simulations and phase-plane analysis, we comparatively investigated how the intrinsic cellular features incorporated in different CPG models, such as subthreshold activation based on a slowly inactivating persistent sodium current, adaptation based on slowly activating calcium-dependent potassium current, or post-inhibitory rebound excitation, can contribute to the control of oscillation period and phase durations in response to changes in excitatory external drive to one or both half-centers. Our analysis shows that both the sensitivity of oscillation period to alterations of excitatory drive and the degree to which the duration of each phase can be separately controlled depend strongly on the intrinsic cellular mechanisms involved in rhythm generation and phase transitions. In particular, the CPG formed from units incorporating a slowly inactivating persistent sodium current shows the greatest range of oscillation periods and the greatest degree of independence in phase duration control by asymmetric inputs. These results are explained based on geometric analysis of the phase plane structures corresponding to the dynamics for each CPG type, which in particular helps pinpoint the roles of escape and release from synaptic inhibition in the effects we find.     

Periodicity, Mixed-Mode Oscillations, and Quasiperiodicityin a Rhythm-Generating Neural Network

We studied patterns of oscillatory neural activity in the network that generates respiratory rhythm in mammals. When isolated in vitro, this network spontaneously generates an inspiratory-related motor rhythm, with stable amplitude from cycle to cycle. We show that progressively elevating neuronal excitability in vitro causes periodic modulation of this inspiratory rhythm, evoking (in order): mixed-mode oscillations, quasiperiodicity, and ultimately disorganized aperiodic activity. Thus, the respiratory network oscillator follows a well defined sequence of behavioral states characterized by dynamical systems theory, which includes discrete stages of periodic and quasiperiodic amplitude modulation and progresses (according to theory) to aperiodic chaos-like behavior. We also observed periodic, mixed-mode periodic, and quasiperiodic breathing patterns in neonatal rodents and human infants in vivo, suggesting that breathing patterns generated by the intact nervous system reflect deterministic neural activity patterns in the underlying rhythm-generating network.     

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.     

The high number of neurons contributes to the robustness of the locust flight-CPG against parameter variation

 Real pattern-generating networks often consist of more neurons than necessary for the production of a certain rhythm. We investigated the question of whether these neurons contribute to the robustness of a pattern-generating system of using the central pattern generator (CPG) for flight of the locust, generating the deafferented activity pattern of wing elevator and wing depressor motoneurons, as an example of a rhythm-generating system. The neuronal network was reconstructed, based on the known connectivity of the interneurons in the flight CPG, using a biologically orientated network simulator (BioSim 3.0). This simulator allows a physiologically realistic simulation of particular neurons as well as the synaptic connections between them. The flight CPG consists of at least five cyclic loops. The simulation shows that each of them is in principle able to produce a rhythm comparable to the rhythm produced by the whole network, i.e. the ‘deafferented’ flight pattern of elevator and depressor motoneurons. Varying the parameter ‘synaptic strength’ in each of these loops and in the complete system shows that this parameter can be changed within certain ranges without loosing the ability to produce oscillations. These ranges are much smaller in each of the subloops than in the whole network. This result demonstrates that the robustness of the system is increased by supranumerary neurons and connections. Changing the active properties of the simulated neurons so that they are able to produce plateau potentials has no effect on the robustness of the simulated network. Received: 13 April 1994/Accepted in revised form: 15 September 1994     

Spontaneous synchronization of coupled circadian oscillators

In mammals, the circadian pacemaker, which controls daily rhythms, is located in the suprachiasmatic nucleus (SCN). Circadian oscillations are generated in individual SCN neurons by a molecular regulatory network. Cells oscillate with periods ranging from 20 to 28 h, but at the tissue level, SCN neurons display significant synchrony, suggesting a robust intercellular coupling in which neurotransmitters are assumed to play a crucial role. We present a dynamical model for the coupling of a population of circadian oscillators in the SCN. The cellular oscillator, a three-variable model, describes the core negative feedback loop of the circadian clock. The coupling mechanism is incorporated through the global level of neurotransmitter concentration. Global coupling is efficient to synchronize a population of 10,000 cells. Synchronized cells can be entrained by a 24-h light-dark cycle. Simulations of the interaction between two populations representing two regions of the SCN show that the driven population can be phase-leading. Experimentally testable predictions are: 1), phases of individual cells are governed by their intrinsic periods; and 2), efficient synchronization is achieved when the average neurotransmitter concentration would dampen individual oscillators. However, due to the global neurotransmitter oscillation, cells are effectively synchronized.     

Hippocampal rhythm generation: Gamma-related theta-frequency resonance in CA3 interneurons

 During different behavioral states different population activities are present in the hippocampal formation. These activities are not independent: sharp waves often occur together with high-frequency ripples, and gamma-frequency activity is usually superimposed on theta oscillations. There is both experimental and theoretical evidence supporting the notion that gamma oscillation is generated intrahippocampally, but there is no generally accepted view about the origin of theta waves. Precise timing of population bursts of pyramidal cells may be due to a synchronized external drive. Membrane potential oscillations recorded in the septum are unlikely to fulfill this purpose because they are not coherent enough. We investigated the prospects of an intrahippocampal mechanism supplying pyramidal cells with theta frequency periodic inhibition, by studying a model of a network of hippocampal inhibitory interneurons. As shown previously, interneurons are capable of generating synchronized gamma-frequency action potential oscillations. Exciting the neurons by periodic current injection, the system could either be entrained in an oscillation with the frequency of the inducing current or exhibit in-phase periodic changes at the frequency of single cell (and network) activity. Simulations that used spatially inhomogeneous stimulus currents showed anti-phase frequency changes across cells, which resulted in a periodic decrease in the synchrony of the network. As this periodic change in synchrony occurred in the theta frequency range, our network should be able to exhibit the theta-frequency weakening of inhibition of pyramidal cells, thus offering a possible mechanism for intrahippocampal theta generation. Received: 23 February 2000 / Accepted in revised form: 30 June 2000     

Hormone‐mediated modulation of the electromotor CPG in pulse‐type weakly electric fish. Commonalities and differences across species

Like stomatogastric activity in crustaceans, vocalization in teleosts and frogs, and locomotion in mammals, the electric organ discharge (EOD) of weakly electric fish is a rhythmic and stereotyped electromotor pattern. The EOD, which functions in both perception and communication, is controlled by a two‐layered central pattern generator (CPG), the electromotor CPG, which modifies its basal output in response to environmental and social challenges. Despite major anatomo‐functional commonalities in the electromotor CPG across electric fish species, we show that Gymnotus omarorum and Brachyhypopomus gauderio have evolved divergent neural processes to transiently modify the CPG outputs through descending fast neurotransmitter inputs to generate communication signals. We also present two examples of electric behavioral displays in which it is possible to separately analyze the effects of neuropeptides (mid‐term modulation) and gonadal steroid hormones (long‐term modulation) upon the CPG. First, the nonbreeding territorial aggression of G. omarorum has been an advantageous model to analyze the status‐dependent modulation of the excitability of CPG neuronal components by vasotocin. Second, the seasonal and sexually dimorphic courtship signals of B. gauderio have been useful to understand the effects of sex steroids on the responses to glutamatergic inputs in the CPG. Overall, the electromotor CPG functions in a regime that safeguards the EOD waveform. However, prepacemaker influences and hormonal modulation enable an enormous versatility and allows the EOD to adapt its functional state in a species‐, sex‐, and social context‐specific manners.     

Formal analysis of resonance entrainment by central pattern generator

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback.     

TEMPORAL PATTERN OF LH SECRETION: REGULATION BY MULTIPLE ULTRADIAN OSCILLATORS VERSUS A SINGLE CIRCADIAN OSCILLATOR

The possibility that the 24h rhythm output is the composite expression of ultradian oscillators of varying periodicities was examined by assessing the effect of external continuously or pulsed (20-minute) Gonadotropinreleasing hormone (GnRH) infusions on in vitro luteinizing hormone (LH) release patterns from female mouse pituitaries during 38h study spans. Applying stepwise analyses (spectral, cosine fit, best-fit curve, and peak detection analyses) revealed the waveform shape of LH release output patterns over time is composed of several ultradian oscillations of different periods. The results further substantiated previous observations indicating the pituitary functions as an autonomous clock. The GnRH oscillator functions as a pulse generator and amplitude regulator, but it is not the oscillator that drives the ultradian LH release rhythms. At different stages of the estrus cycle, the effect of GnRH on the expression of ultradian periodicities varies, resulting in the modification of their amplitudes but not their periods. The functional output from the system of ultradian oscillators may superimpose a “circadian or infradian phenotype” on the observed secretion pattern. An “amplitude control” hypothesis is proposed: The temporal pattern of LH release is governed by several oscillators that function in conjunction with one another and are regulated by an amplitude-controlled mechanism. Simulated models show that such a mechanism results in better adaptive response to environmental requirements than does a single circadian oscillator. (Chronobiology International, 18(3), 399–412, 2001)     

Temporal pattern of LH secretion: regulation by multiple ultradian oscillators versus a single circadian oscillator

The possibility that the 24h rhythm output is the composite expression of ultradian oscillators of varying periodicities was examined by assessing the effect of external continuously or pulsed (20-minute) Gonadotropinreleasing hormone (GnRH) infusions on in vitro luteinizing hormone (LH) release patterns from female mouse pituitaries during 38h study spans. Applying stepwise analyses (spectral, cosine fit, best-fit curve, and peak detection analyses) revealed the waveform shape of LH release output patterns over time is composed of several ultradian oscillations of different periods. The results further substantiated previous observations indicating the pituitary functions as an autonomous clock. The GnRH oscillator functions as a pulse generator and amplitude regulator, but it is not the oscillator that drives the ultradian LH release rhythms. At different stages of the estrus cycle, the effect of GnRH on the expression of ultradian periodicities varies, resulting in the modification of their amplitudes but not their periods. The functional output from the system of ultradian oscillators may superimpose a “circadian or infradian phenotype” on the observed secretion pattern. An “amplitude control” hypothesis is proposed: The temporal pattern of LH release is governed by several oscillators that function in conjunction with one another and are regulated by an amplitude-controlled mechanism. Simulated models show that such a mechanism results in better adaptive response to environmental requirements than does a single circadian oscillator. (Chronobiology International, 18(3), 399-412, 2001)     

Transmitter-dependent involvement of the respiratory interneurons in the locomotor rhythm in the pulmonate mollusc Lymnaea

Pedal cell RPeD1 of the pond snail L. stagnalis becomes involved in a central rhythm identified as an activity of the central pattern generator (CPG) for locomotion. The RPeD1 rhythm developed as driven by a synaptic input in isolated CNS preparations treated with 0.05 mM serotonin (5HT) or 0.1 mM 5-hydroxytryptophan (5HTP). The 5HT-induced co-ordinated rhythmic activity was retained by each of two pedal ganglia after complete isolation thus suggesting that the respective CPG lies entirely within the pedal portion of the CNS and is paired. The findings suggest that the RPeD1 switching from one network to another represents a neurotransmitter-dependent phenomenon.     

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

Systems-level modeling of neuronal circuits for leech swimming

This paper describes a mathematical model of the neuronal central pattern generator (CPG) that controls the rhythmic body motion of the swimming leech. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG. We show through numerical simulations that the values of a few parameters can be estimated within physiologically reasonable ranges to achieve good fit of the data with respect to the phase, amplitude, and period. This parameter estimation leads to predictions regarding the synaptic coupling strength and intrinsic period gradient along the nerve cord, the latter of which agrees qualitatively with experimental observations.     

An inter-segmental network model and its use in elucidating gait-switches in the stick insect

Animal locomotion requires highly coordinated working of the segmental neuronal networks that control the limb movements. Experiments have shown that sensory signals originating from the extremities play a pivotal role in controlling locomotion patterns by acting on central networks. Based on the results from stick insect locomotion, we constructed an inter-segmental model comprising local networks for all three legs, i.e. for the pro-, meso- and meta-thorax, their inter-connections and the main sensory inputs modifying their activities. In the model, the local networks are uniform, and each of them consists of a central pattern generator (CPG) providing the rhythmic oscillation for the protractor-retractor motor systems, the corresponding motoneurons (MNs), and local inhibitory interneurons (IINs) between the CPGs and the MNs. Between segments, the CPGs are connected cyclically by both excitatory and inhibitory pathways that are modulated by the aforementioned sensory inputs. Simulations done with our network model showed that it was capable of reproducing basic patterns of locomotion such as those occurring during tri- and tetrapod gaits. The model further revealed a number of elementary neuronal processes (e.g. synaptic inhibition, or changing the synaptic drive at specific neurons) that in the simulations were necessary, and in their entirety sufficient, to bring about a transition from one type of gait to another. The main result of this simulation study is that exactly the same mechanism underlies the transition between the two types of gait irrespective of the direction of the change. Moreover, the model suggests that the majority of these processes can be attributed to direct sensory influences, and changes are required only in centrally controlled synaptic drives to the CPGs.     

Perisomatic feedback inhibition underlies cholinergically induced fast network oscillations in the rat hippocampus in vitro

Gamma frequency network oscillations are assumed to be important in cognitive processes, including hippocampal memory operations, but the precise functions of these oscillations remain unknown. Here, we examine the cellular and network mechanisms underlying carbachol-induced fast network oscillations in the hippocampus in vitro, which closely resemble hippocampal gamma oscillations in the behaving rat. Using a combination of planar multielectrode array recordings, imaging with voltage-sensitive dyes, and recordings from single hippocampal neurons within the CA3 gamma generator, active current sinks and sources were localized to the stratum pyramidale. These proximal currents were driven by phase-locked rhythmic inhibitory inputs to pyramidal cells from identified perisomatic-targeting interneurons. AMPA receptor-mediated recurrent excitation was necessary for the synchronization of interneuronal discharge, which strongly supports a synaptic feedback model for the generation of hippocampal gamma oscillations.     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

Multimodal distribution and discontinuous variation in period of interacting oscillators in the crustacean stomatogastric nervous system

Summary In the stomatogastric ganglion (STG) of Homarus gammarus, pacemaker neurons of the pyloric central pattern generator are entrained by a network oscillator (CPO) contained in the commissural ganglion. A consequence of CPO's influence is that the spontaneous pyloric period can take one of several absolute values, most commonly displaying a bimodal distribution. These discrete values correspond to different coordination modes with the CPO rhythm. Moreover, the oscillation period of pyloric pacemaker neurons varies discontinuously with their membrane potential. This behavior persists when the mean pyloric period is modified by different perfusion salines but disappears when the STG is disconnected from the anterior ganglia. Under these conditions, pyloric pacemaker neurons are deprived of CPO inputs and behave like independent oscillators whose period varies continuously as a function of the membrane potential. The modulatory pyloric suppressor neurons (PS), which are known to decrease the oscillatory capabilities of the pyloric pacemakers, can change the coordination mode between these neurons and the CPO. PS can provoke discontinuous variations in the pyloric period as a function of their firing frequency. Finally, the nonlinear behavior of the pyloric pattern generator described in Homarus also occurs in Jasus lalandii, in which the existence of a CPO has not yet been demonstrated.Abbreviations AB anterior burster neuron - ASW artificial seawater - COG commissural ganglion - CP commissural pyloric neuron - CPG central pattern generator - CPO commissural pyloric oscillator - IC inferior cardiac neuron - ivn inferior ventricular nerve - LP lateral pyloric neuron - OG esophageal ganglion - PD pyloric dilator neuron - PDn pyloric dilator nerve - PS pyloric suppressor neuron - son superior esophageal nerve - PY pylonic neuron - STG stomatogastric ganglion - stn stomatogastric nerve - vlvn ventral branch of the lateral ventricular nerve Maître de conférence à l'U.E.R. de Médecine et de Pharmacie, 2 rue Dr Marcland, 87025 Limoges Cedex, France.