Models Of Neurophysiological Systems

Neurological Disorders And Stroke

Investigators

Linked publications & trials

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 of this study 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. The latter finding suggests either constraints on lateral dendritic expansion from surrounding structures or perhaps some repulsing influence of the soma on the tree as a whole. These alternatives are not mutually exclusive. We have also developed a simple algorithm that reproduces the natural meander of motoneuron dendrites, which has fractal characteristics. A second 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 innervate both intrafusal fibers and the large extrafusal skeletal muscle fibers that form the main bulk of muscles. We showed some years ago that beta (skeletofusimotor) motoneurons receive the same powerful group Ia excitation as alpha motoneurons that innervate exclusively the extrafusal muscle fibers. To complicate matters further, fusimotor effects on muscle spindle afferents differ depending on whether the beta motoneurons innervate fast or slow twitch extrafusal fibers (static or dynamic effects, respectively). Because the system is so complex and inaccessible to experimentation, the currently unknown functional consequences of positive beta-loop feedback are best explored by quantitative modeling. This study is the first to our knowledge to attempt this. We first developed a muscle spindle model that allows innervation by multiple fusimotor axons and used this to simulate a wide variety of input drive combinations and muscle movements, with and without feeding a portion of the simulated afferent firing to the simulated beta motoneurons (i.e., opening and closing the beta feedback loop). The results suggest that certain combinations of gamma and beta spindle drive can indeed have significant effects on group Ia spindle afferent firing, particularly during alternating imposed muscle stretch and lengthening. The model is being extended to include simulations of a mixed population of alpha and beta motoneurons, plus their muscle units, to examine how various levels of recruitment of the population affect force production with and without beta loops feedback. Finally, we continue to accumulate quantitative data on the morphology of motoneurons in the neonatal mouse spinal cord, labeled intracellularly with Biocytin or by retrograde transport of flourescent tracers. Biocytin-filled cells are completely reconstructed and the data are analyzed quantitatively using methods developed in LNLC and by a group at the Krasnow Institute of George Mason University. The fluoresent tracing material is being examined by confocal microscopy to examine the range of sizes in motoneurons at different postnatal ages, as well as the spacing between them. The data will form part of an extensive data base being developed at the Krasnow Institute as part of the Human Brain Project that is designed to permit scientists anywhere to access and analyze morphological data on many types of neurons.