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PubMed2002

Dynamical working memory and timed responses: the role of reverberating loops in the olivo-cerebellar system.

This article explores dynamical properties of the olivo-cerebellar system that arise from the specific wiring of inferior olive (IO), cerebellar cortex, and deep cerebellar nuclei (DCN). We show that the irregularity observed in the firing pattern of the IO neurons is not necessarily produced by noise but can instead be the result of a purely deterministic network effect. We propose that this effect can serve as a dynamical working memory or as a neuronal clock with a characteristic timescale of about 100 ms that is determined by the slow calcium dynamics of IO and DCN neurons. This concept provides a novel explanation of how the cerebellum can solve timing tasks on a timescale that is two orders of magnitude longer than the millisecond timescale usually attributed to neuronal dynamics. One of the key ingredients of our model is the observation that due to postinhibitory rebound, DCN neurons can be driven by GABAergic ("inhibitory") input from cerebellar Purkinje cells. Topographic projections from the DCN to the IO form a closed reverberating loop with an overall synaptic transmission delay of about 100 ms that is in resonance with the intrinsic oscillatory properties of the inferior olive. We use a simple time-discrete model based on McCulloch-Pitts neurons in order to investigate in a first step some of the fundamental properties of a network with delayed reverberating projections. The macroscopic behavior is analyzed by means of a mean-field approximation. Numerical simulations, however, show that the microscopic dynamics has a surprisingly rich structure that does not show up in a mean-field description. We have thus performed extensive numerical experiments in order to quantify the ability of the network to serve as a dynamical working memory and its vulnerability by noise. In a second step, we develop a more realistic conductance-based network model of the inferior olive consisting of about 20 multicompartment neurons that are coupled by gap junctions and receive excitatory and inhibitory synaptic input via AMPA and GABAergic synapses. The simulations show that results for the time-discrete model hold true in a time-continuous description.

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High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model.

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) or the internal segment of the globus pallidus (GPi) has recently been recognized as an important form of intervention for alleviating motor symptoms associated with Parkinson's disease, but the mechanism underlying its effectiveness remains unknown. Using a computational model, this paper considers the hypothesis that DBS works by replacing pathologically rhythmic basal ganglia output with tonic, high frequency firing. In our simulations of parkinsonian conditions, rhythmic inhibition from GPi to the thalamus compromises the ability of thalamocortical relay (TC) cells to respond to depolarizing inputs, such as sensorimotor signals. High frequency stimulation of STN regularizes GPi firing, and this restores TC responsiveness, despite the increased frequency and amplitude of GPi inhibition to thalamus that result. We provide a mathematical phase plane analysis of the mechanisms that determine TC relay capabilities in normal, parkinsonian, and DBS states in a reduced model. This analysis highlights the differences in deinactivation of the low-threshold calcium T -current that we observe in TC cells in these different conditions. Alternative scenarios involving convergence of thalamic signals in the cortex are also discussed, and predictions associated with these results, including the occurrence of rhythmic rebound bursts in certain TC cells in parkinsonian states and their drastic reduction by DBS, are stated. These results demonstrate how DBS could work by increasing firing rates of target cells, rather than shutting them down.

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PubMed1994

Lesion-induced transient suppression of inhibitory function in rat neocortex in vitro.

The structural and functional consequences of a local thermolesion were examined in rat neocortex with electrophysiological in vitro techniques and immunocytochemistry. Age-matched untreated and sham-operated animals served as controls and were analysed in the same way. The lesions consisted of a core of coagulated tissue 2-3 mm in diameter and reached ventrally into the deep cortical layers. After two days reactive astrocytes and after nine days a dense gliosis were observed in the immediate vicinity. Modifications in the intrinsic membrane characteristics and the synaptic network properties were investigated with intra- and extracellular recording techniques after survival times of one to eight days. Neurons recorded in the surrounding of lesions in neocortical slices revealed a significantly more depolarized resting membrane potential and a higher neuronal input resistance. In comparison to cells in control slices, maximal discharge rates to injection of depolarizing current pulses of neurons close to a focal lesion were not significantly altered and intrinsic burst firing was never observed. However, between postlesion days 1 and 5, neurons in the surroundings of lesions showed a transient increase in synaptic excitability. This hyperactivity was most clearly pronounced at a distance of 2-3 mm from the centre of the lesion (i.e. about 1-1.5 mm away from the lesion border) and characterized by long-duration field potential responses and multiphasic long-lasting excitatory postsynaptic potentials to orthodromic stimulation of the afferent input. This lesion-induced hyperexcitability was associated with a significant reduction in the peak conductance of the Cl(-)-dependent fast inhibitory postsynaptic potential and the K(+)-dependent long-latency inhibitory postsynaptic potential, suggesting that the intracortical GABAergic system was functionally impaired. The decrease in synaptic inhibition was associated with prolonged N-methyl-D-aspartate receptor-mediated activity, which could be reversibly blocked by D-amino-phosphonovaleric acid. In addition, neurons recorded in the vicinity of the lesion responded to an orthodromic synaptic stimulus with a long-lasting burst. The lesion-induced disturbance in the balance between the excitatory and inhibitory system may not only have profound influences on the mechanisms of intracortical information processing, but may also lead to the expression of epileptiform activity and long-term functional deficits.

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PubMed1996

Complexity, communication between cells, and identifying the functional components of living systems: some observations.

The concept of 'complexity' has become very important in theoretical biology. It is a many faceted concept and too new and ill defined to have a universally accepted meaning. This review examines the development of this concept from the point of view of its usefulness as a criteria for the study of living systems to see what it has to offer as a new approach. In particular, one definition of complexity has been put forth which has the necessary precision and rigor to be considered as a useful categorization of systems, especially as it pertains to those we call 'living'. This definition, due to Robert Rosen, has been developed in a number of works and involves some deep new concepts about the way we view systems. In particular, it focuses on the way we view the world and actually practice science through the use of the modelling relation. This mathematical object models the process by which we assign meaning to the world we perceive. By using the modelling relation, it is possible to identify the subjective nature of our practices and deal with this issue explicitly. By so doing, it becomes clear that our notion of complexity and especially its most popular manifestations, is in large part a product of the historical processes which lead to the present state of scientific epistemology. In particular, it is a reaction to the reductionist/mechanistic view of nature which can be termed the 'Newtonian Paradigm'. This approach to epistemology has dominated for so that its use as a model has become implicit in most of what we do in and out of science. The alternative to this approach is examined and related to the special definition of complexity given by Rosen. Some historical examples are used to emphasize the dependence of our view of what is complex in a popular sense on the ever changing state of our knowledge. The role of some popular concepts such as chaotic dynamics are examined in this context. The fields of artificial life and related areas are also viewed from the perspective of this rigorous view of complexity and found lacking. The notion that in some way life exists 'at the edge of chaos' is examined from the perspective of the second law of thermodynamics given by Schneider and Kay. Finally, the casual elements in complex systems are explored in relation to complexity. Rosen has shown that a clear difference in causal relations exists between complex and simple systems and that this difference leads to a uniquely useful definition of what we mean by 'living'. Rosen makes it very clear that the class of systems which are complex is a much larger class than those which we call living. For that reason, the focus of this review will be on complexity as a stepping stone towards the deeper question of what makes a system alive.

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