Models Of Neurophysiological Systems

Neurological Disorders And Stroke

Investigators

Linked publications, trials & patents

Abstract

This project is designed to use mathematical and computational methods to develop models based on experimental data of the morphology and function of individual dendrites, whole neurons, and neuron networks. During FY2002 we completed development of a model approach that can successfully reproduce the complex three-dimensional morphology of cat spinal motoneurons using just two parameters. The result suggests that the direction in which a dendritic branch projects away from a branching point depends in part on the direction of its parent branch and in part on the radial direction of the branch point away from the cell soma. In FY2003 we developed a method to measure quantitatively the natural meander of dendritic branches and a computer algorithm that reproduces this natural meander quite accurately. Neither of these aspects had been done before. We have begun to develop methods to quantitative the three-dimensional distribution of natural dendrites in space. This is a very difficult theoretical issue but it is necessary to solve it in order to provide a complete mathematical description of the morphology of mammalian neurons. Such parsimonious descriptions have proven valuable in revealing the biological constraints under which neurons form and are maintained. A second sub-project concerns development of a mathematical model of the effects of beta innervation of muscle spindles in mammals. Muscle spindles contain specialized small intrafusal muscle fibers that are innervated by two types of gamma motoneurons (called static and dynamic) that do not receive direct excitatory feedback from group Ia muscle spindle afferents. However, many muscle spindles also receive so-called beta innervation from motoneurons that also innervate the large extrafusal skeletal muscle fibers that form the main bulk of muscles and also receive powerful group Ia excitation. Beta motoneurons form a positive feedback system but the system is highly complex and inaccessible to experimentation. The possible functional consequences of positive beta-loop feedback are best explored by quantitative modeling and this study is the first to our knowledge to attempt this. Building on a simple model of the muscle spindle stretch receptor reported earlier, we have developed a computational model of the complete stretch reflex system, including a mixed population of 280 alpha and beta motoneurons and their muscle units with properties of the three known motor unit types, plus 60 muscle spindles that receive both beta and gamma fusimotor drive, in order to examine how various levels of recruitment of the population affect force production with and without beta loops feedback. The simulation results indicate that the beta feedback loop can produce substantial increments in force output during slow ramp stretches as well as sinusoidal stretches, depending in complex ways on the initial level of excitation to the motoneuron pool and the presence or absence of superimposed gamma fusimotor bias.