Vladimir I. Makarenko

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.

Subthreshold membrane potential oscillations in inferior olive neurons are dynamically regulated by P/Q- and T-type calcium channels: a study in mutant mice.

The role of P/Q‐ and T‐type calcium channels in the rhythmic oscillatory behaviour of inferior olive (IO) neurons was investigated in mutant mice. Mice lacking either the CaV2.1 gene of the pore‐forming α1A subunit for P/Q‐type calcium channel, or the CaV3.1 gene of the pore‐forming α1G subunit for T‐type calcium channel were used. In vitro intracellular recording from IO neurons reveals that the amplitude and frequency of sinusoidal subthreshold oscillations (SSTOs) were reduced in the CaV2.1−/− mice. In the CaV3.1−/− mice, IO neurons also showed altered patterns of SSTOs and the probability of SSTO generation was significantly lower (15%, 5 of 34 neurons) than that of wild‐type (78%, 31 of 40 neurons) or CaV2.1−/− mice (73%, 22 of 30 neurons). In addition, the low‐threshold calcium spike and the sustained endogenous oscillation following rebound potentials were absent in IO neurons from CaV3.1−/− mice. Moreover, the phase‐reset dynamics of oscillatory properties of single neurons and neuronal clusters in IO were remarkably altered in both CaV2.1−/− and CaV3.1−/− mice. These results suggest that both α1A P/Q‐ and α1G T‐type calcium channels are required for the dynamic control of neuronal oscillations in the IO. These findings were supported by results from a mathematical IO neuronal model that incorporated T and P/Q channel kinetics.

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.

On the Amazing Olivocerebellar System

Abstract: Over the last four decades elegant sets of a single‐cell studies, originating from various research groups, have contributed significantly to our understanding of olivary and cerebellar physiology. Nevertheless questions relating to the dynamic properties of olivocerebellar network, as a system, remain unsolved. We may be reaching the limits of what can be learned using the single‐cell recordings. Further research on this subject may require study of the spatiotemporal activity profiles of ensemble neuronal activity. This paper summarizes results obtained using voltage‐sensitive dye imaging in inferior olive slices, and the use of mathematical modeling to address such activity profiles.

The olivo-cerebellar circuit as a universal motor control system

The olivo-cerebellar system is one of the central networks organizing movement coordination in vertebrates. This system consists of three main anatomical structures: the inferior olive (IO), the cerebellar nuclei, and the cerebellar cortex. Over the last four decades studies in many laboratories have contributed significantly to our understanding of the electrophysiology of IO and cerebellar neurons. However, addressing the dynamic properties of olivo-cerebellar network requires information beyond the limits attainable using single cell recordings. Research at the neuronal network level is presently being implemented in order to determine the spatiotemporal activity profiles of ensemble neuronal activity using optical imaging of voltage-sensitive dye signals. We summarize here results of such type of study using the in vitro IO slices. The dynamic characteristic of the system is addressed using the imaging results as well as mathematical modeling of the network, as a heuristic tool. A computer-based control system based on such biological findings is outlined.

A new approach to the analysis of multidimensional neuronal activity: Markov random fields

How can information hidden in a spatial configuration of neuronal activity be addressed? The Markov Random Field method for the analysis of the spatial component of a multidimensional neuronal process is introduced and after simulations is applied to experimental data on rat at olivocerebellar activity. Using this method it was determined, for the first time, that the activity demonstrates dynamic coupling and may have different fine spatial substructures. The results obtained support the view that the inferior olive serves as a movement organizing centre that controls motor activity by means of spatially as well as temporally organized patterns of coherent activity. Copyright 1997 Elsevier Science Ltd.

Clustering behavior in a three-layer system mimicking olivo-cerebellar dynamics

A model is presented that simulates the process of neuronal synchronization, formation of coherent activity clusters and their dynamic reorganization in the olivo-cerebellar system. Three coupled 2D lattices dealing with the main cellular groups in this neuronal circuit are used to model the dynamics of the excitatory feedforward loop linking the inferior olive (IO) neurons to the cerebellar nuclei (CN) via collateral axons that also proceed to terminate as climbing fiber afferents to Purkinje cells (PC). Inhibitory feedback from the CN-lattice fosters decoupling of units in a vicinity of a given IO neuron. It is shown that noise-sustained oscillations in the IO-lattice are capable to synchronize and generate coherent firing clusters in the layer accounting for the excitable collateral axons. The model also provides phase resetting of the oscillations in the IO-lattices with transient silent behavior. It is also shown that the CN-IO feedback leads to transient patterns of couplings in the IO and to a dynamic control of the size of clusters.