Modeling Calcium Dynamics in Dendritic Spines

Source abstract

Dendritic spines are microstructures located on dendrites of neurons, where calcium can be compartmentalized. They are usually the postsynaptic parts of synapses and may contain anywhere from a few up to thousands of calcium ions at a time. Initiated by an action potential, a back-propagating action potential, or a synaptic stimulation, calcium ions enter spines and are known to bring about their fast contractions (twitching), which in turn affect calcium dynamics. In this paper, we propose a coarse-grained reaction-diffusion (RD) model of a Langevin simulation of calcium dynamics with twitching and relate the biochemical changes induced by calcium to structural changes occurring at the spine level. The RD equations model the contraction of proteins as chemical events and serve to describe how changes in spine structure affect calcium signaling. Calcium ions induce contraction of actin-myosin-type proteins and produce a flow of the cytoplasmic fluid in the direction of the dendritic shaft, thus speeding up the time course of calcium dynamics in the spine, relative to pure diffusion. Experimental and simulation results reveal two time periods in spine calcium dynamics. Simulations [D. Holcman, Z. Schuss, and E. Korkotian, Biophysical Journal, 87 (2004), pp. 81--91] show that in the first period, calcium motion is mainly driven by the hydrodynamics, while in the second period it is diffusion. The coarse-grained RD model also gives this result, and the analysis reveals how the two time constants depend on spine geometry. The model's prediction, that there are not two time periods in the diffusion of inert molecules in the spine, has been verified experimentally.