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Applied Math Seminar CALCIUM DYNAMICS IN DENDRITIC SPINES AND SPINE MOTILITY |
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A dendritic spine is a cell-like structure located on a dendrite of a neuron. It conducts calcium ions from the synapse to the dendrite. A dendritic spine can contain anywhere between a few and up to thousands of calcium ions at a time. Internal calcium is known to bring about fast contractions of dendritic spines (twitching) after a burst, an action potential, or a back-propagating action potential. In this paper, we propose an explanation of the cause and effect of the twitching and its role in the functioning of the spine as a conductor of calcium. We model the spine as a machine powered by the calcium it conducts and we describe its moving parts. The latter are proteins that are involved in the conduction process. These proteins are found inside the dendritic spine and their spatial distribution can be measured. We propose a molecular model of calcium dynamics in a dendritic spine, which shows that the rapid calcium motility in the spine is due to the concerted contraction of certain proteins that bind calcium. The contraction induces a stream of the cytoplasmic fluid in the direction of the dendritic shaft, thus speeding up the time course of spinal calcium dynamics, relative to pure diffusion. According to the proposed model, the diffusive motion of the calcium ions is described by a system of Langevin equations, coupled to the hydrodynamical fluid flow field induced by contraction of proteins. These contractions occur when enough calcium binds to specific protein molecules inside the spine. By following the random ionic trajectories, we compute the distribution of calcium exit time from the spine, the evolution of concentration of calcium bound to specific proteins, the relative number of ions pumped out, compared to the number of ions that leave at the dendritic shaft, and so on. A computer simulation of this model of calcium dynamics in a dendritic spine was run with any the number of calcium ions varying from one or two, up to the hundreds. The simulation indicates that spine motility can be explained by the basic rules of chemical reaction rate theory at the molecular level . Analysis of the simulation data reveals two time periods in the calcium dynamics. In the first period calcium motion is driven by a hydrodynamical push, while there are no push effects in the second, when ionic motion is mainly diffusion in a domain with obstacles. A biological conclusion is that the role of rapid motility in dendritic spines is to increase the efficiency of calcium conduction to the dendrite and to speed up the emptying of the spine. |