V. B. Kazantsev

Self-referential phase reset based on inferior olive oscillator dynamics

The olivo-cerebellar network is a key neuronal circuit that provides high-level motor control in the vertebrate CNS. Functionally, its network dynamics is organized around the oscillatory membrane potential properties of inferior olive (IO) neurons and their electrotonic connectivity. Because IO action potentials are generated at the peaks of the quasisinusoidal membrane potential oscillations, their temporal firing properties are defined by the IO rhythmicity. Excitatory inputs to these neurons can produce oscillatory phase shifts without modifying the amplitude or frequency of the oscillations, allowing well defined time-shift modulation of action potential generation. Moreover, the resulting phase is defined only by the amplitude and duration of the reset stimulus and is independent of the original oscillatory phase when the stimulus was delivered. This reset property, henceforth referred to as selfreferential phase reset, results in the generation of organized clusters of electrically coupled cells that oscillate in phase and are controlled by inhibitory feedback loops through the cerebellar nuclei and the cerebellar cortex. These clusters provide a dynamical representation of arbitrary motor intention patterns that are further mapped to the motor execution system. Being supplied with sensory inputs, the olivo-cerebellar network is capable of rearranging the clusters during the process of movement execution. Accordingly, the phase of the IO oscillators can be rapidly reset to a desired phase independently of the history of phase evolution. The goal of this article is to show how this selfreferential phase reset may be implemented into a motor control system by using a biologically based mathematical model.

Olivo-cerebellar cluster-based universal control system.

The olivo-cerebellar network plays a key role in the organization of vertebrate motor control. The oscillatory properties of inferior olive (IO) neurons have been shown to provide timing signals for motor coordination in which spatio-temporal coherent oscillatory neuronal clusters control movement dynamics. Based on the neuronal connectivity and electrophysiology of the olivo-cerebellar network we have developed a general-purpose control approach, which we refer to as a universal control system (UCS), capable of dealing with a large number of actuator parameters in real time. In this UCS, the imposed goal and the resultant feedback from the actuators specify system properties. The goal is realized through implementing an architecture that can regulate a large number of parameters simultaneously by providing stimuli-modulated spatio-temporal cluster dynamics.

Spiking signatures of spontaneous activity bursts in hippocampal cultures

Dense dissociated hippocampal cultures are known to generate spontaneous bursting electrical activity which can be recorded by multielectrode arrays. We have analyzed spatio-temporal profiles of the distribution of spikes in the bursts recorded after 2 weeks in vitro. We have found a statistically significant similarity between the spiking patterns in sequential bursting events, we refer to these spiking patterns as spiking signatures. Such spiking signatures may appear in different parts of the bursts, including the activation patterns – the first spike times in the bursts, and deactivation patterns – the last spike times in the bursts. Moreover, these patterns may display apparent time scaling, e.g., they may be replayed in the subsequent bursts at different speeds, while preserving the spiking order. We discuss how such properties of the bursts may be associated with the formation of repeatable signaling pathways in cultured networks in vitro.

Modeling inferior olive neuron dynamics

A model for the study of the dynamic properties of inferior olive neuron is presented. The model, a dynamical system, comprises two autonomous components of minimal complexity that are capable of reproducing the large gamut of experimentally observed inferior olive neuron dynamics. The two autonomous parts are responsible for largely different aspects of the dynamic profile of the model. These include subthreshold oscillations and different modes (high and low threshold) of action potential generation.

Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability

We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible neural network is described introducing different kinds of coupling between neurons.

Spiking dynamics of interacting oscillatory neurons

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.

Homoclinic orbits and solitary waves in a one-dimensional array of Chua's circuits

The possible propagation of solitary waves in a one-dimensional array of inductively coupled Chuas circuits is considered. We show that in the long-wave limit, the problem can be reduced to the analysis of the homoclinic orbits of a dynamical system described by three coupled nonlinear ordinary differential equations modeling the individual dynamics of a single Chuas circuit. Analytical, numerical, and experimental results concerning the bifurcations associated with the appearance of homoclinic orbits and thus with the propagation of solitary waves are provided. >

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons.

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.

MUTUAL SYNCHRONIZATION OF TWO LATTICES OF BISTABLE ELEMENTS

Abstract The interaction of two coupled lattice dynamical systems of bistable elements is investigated. In particular, we give the critical value of the coupling strength and related variables for the mutual synchronization of regular and chaotic states.

Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators

The phase dynamics of a pair of spiking neural oscillators coupled by a unidirectional nonlinear connection has been studied. The synchronization effect with the controlled relative phase of spikes has been obtained for various coupling strengths and depolarization parameters. It has been found that the phase value is determined by the difference between the depolarization levels of neurons and is independent of the synaptic coupling strength. The synchronization mechanism has been studied by means of the construction and analysis of one-dimensional phase maps. The phase locking effect for spikes has been interpreted in application to the synaptic plasticity in neurobiology.