This project is designed to use mathematical and computational methods to develop models of individual dendrites, neurons, and neuron networks are based on experimental data and that can reveal fundamental insights into the operation of the biological systems under investigation. Three projects have been studied during FY1998, all of which used models systems developed in Mathematica. The first deals with why neuronal dendrites branch. We conclude that dendrites branch extensively because they must invade source regions for innervation in order to resemble natural neurons. The volume elements within 150 microns of the branches of simulated dendrites were each weighted by the calculated electrotonic connectivity to the soma of the nearest dendrite segment. This coupling-weighted external volume was summed and divided by the internal dendrite volume, assumed to be a cost function, to give the """"""""coupled volume ratio"""""""" (CVR). Four parameters - ratios of each daughter to parent diameters, branch length, branch direction - were adjusted in a search algorithm to generate dendrites with maximum CVRs. Optimal values of the four parameters produced dendrites that resembled those in the target set of 60 dendrites from reconstructed cat motoneurons. The resemblance of optimized dendrites to natural ones was greatest for radii of influence between 100 and 200 microns. We conclude: 1) that the ratio of external coupled volume to internal dendrite volume is a realistic figure of merit for neurons; and 2) that motoneuron dendrites come close to optimal shapes for this figure of merit. The second project arose from discussions with Dr. Michael O'Donovan about whether regenerative spread of activity in a simulated three dimensional array of point neurons interconnected by purely excitatory synapses would resemble the spatiotemporal patterns of activity observed in his experimental preparations. A cubic array of 27,000 cells with local excitatory connections was developed. For each cell, a synaptically weighted sum of firing rates in the net caused a decaying depolarization and firing at a rate proportional to excess above threshold. After threshold stimulation by a pattern of depolarization, total net activity declined and then grew as the pattern of activity consolidated to a centroid which became the nucleus of regenerative growth. The five variables: stimulus pattern, strength and reach of connections, and firing threshold and gain were interchangeable; plots of the time course of total activity near threshold could be predicted from the value of a particular combination of these variables. Future simulations will include a stochastic ramp of excitation and will evaluate longer time courses. The third project involves animations of neuronal interactions in a model of the basic circuit that produces rhythmic respiration that is based on experiments of Dr. Jeffrey Smith. The dynamic behavior of up to 20 interconnected neurons with data-based properties and connections were visualized into computed videos, with excitatory and inhibitory action in the cells modeled as different colored deformations in a flexible sheet and synaptic traffic seen as colored areas flowing from cell to cell. These movies permit visualization of the synchronization of independent oscillators as their interconnection strength increases, as well as the sequence of synaptic flows and membrane dynamics among the five cell types that shape the time course of respiration.
| Maltenfort, Mitchell G; Burke, R E (2003) Spindle model responsive to mixed fusimotor inputs and testable predictions of beta feedback effects. J Neurophysiol 89:2797-809 |
| Burke, R E (2000) Comparison of alternative designs for reducing complex neurons to equivalent cables. J Comput Neurosci 9:31-47 |
