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Basal ganglia (BG) constitute a network of seven deep brain nuclei involved in a variety of crucial brain functions including: action selection, action gating, reward based learning, motor preparation, timing, etc. In spite of the immense amount of data available today, researchers continue to wonder how a single deep brain circuit performs such a bewildering range of functions. Computational models of BG have focused on individual functions and fail to give an integrative picture of BG function. A major breakthrough in our understanding of BG function is perhaps the insight that activities of mesencephalic dopaminergic cells represent some form of 'reward' to the organism. This insight enabled application of tools from 'reinforcement learning,' a branch of machine learning, in the study of BG function. Nevertheless, in spite of these bright spots, we are far from the goal of arriving at a comprehensive understanding of these 'mysterious nuclei.' A comprehensive knowledge of BG function has the potential to radically alter treatment and management of a variety of BG-related neurological disorders (Parkinson's disease, Huntington's chorea, etc.) and neuropsychiatric disorders (schizophrenia, obsessive compulsive disorder, etc.) also. In this article, we review the existing modeling literature on BG and hypothesize an integrative picture of the function of these nuclei.

In an earlier study, we suggested that adaptive gap junctions (GJs) might be a basis of cardiac memory, a phenomenon which refers to persistent electrophysiological response of the heart to external pacing. Later, it was also shown that the proposed mechanism of adaptation of GJs is consistent with known electrophysiology of GJs. In the present article, we show that a pair of cardiac cell models coupled by dynamic, voltage-sensitive GJs exhibits bistable behavior under certain conditions. Three kinds of cell pairs are considered: (1) a Noble-Noble cell pair that represents adjacent cells in Purkinje network, (2) a pair of DiFranceso-Noble cells that represents adjacent SA nodal cells, and (3) a model of Noble cell coupled to Luo-Rudy cell model, which represents an interacting pair of a Purkinje fiber and a ventricular myocyte. Bistability is demonstrated in all the three cases. We suggest that this bistability might be an underlying factor behind cardiac memory. Focused analysis of a pair of Noble cell models showed that bistability is obtained only when the properties of GJs "match" with the properties of the pair of cells that is coupled by the GJs. This novel notion of match between GJs and cardiac cell types might give an insight into specialized distributions of various connexin proteins in cardiac tissue.

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit "flips" in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous-a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy.

The phenomenon of systematic recruitment of motor units with increasing demand load is usually explained by the size principle. Though this principle successfully explains the gain-related aspects of muscle force generation, it does not address the need for desynchronization of motor unit activities in order to produce a smooth tension profile at the level of whole muscle, while individual muscle fibers are "twitching." We propose an oscillator model of motor neurons in which a pool of motor neurons fires a bundle of muscle fibers. Although individual muscle fibers have a complicated tension profile, the tension produced by the entire bundle is regulated and follows a command signal accurately. This is shown to be possible because of uncorrelated activity produced by local inhibitory connections among motor neurons. Connections that produce synchronized oscillations result in uncontrolled contractions of the muscle. These results seem to suggest that while synchronized activity indicates pathology and disease, desynchronized activity is the precondition for normal muscle function. Physiological evidence for the proposed theory of motor unit synchronization is presented.