Computational reconstitution of spine calcium transients from individual proteins.

We have built a stochastic model in the program MCell that simulates Ca(2+) transients in spines from the principal molecular components believed to control Ca(2+) entry and exit. Proteins, with their kinetic models, are located within two segments of dendrites containing 88 intact spines, centered in a fully reconstructed 6 × 6 × 5 µm(3) cube of hippocampal neuropil. Protein components include AMPA- and NMDA-type glutamate receptors, L- and R-type voltage-dependent Ca(2+) channels, Na(+)/Ca(2+) exchangers, plasma membrane Ca(2+) ATPases, smooth endoplasmic reticulum Ca(2+) ATPases, immobile Ca(2+) buffers, and calbindin. Kinetic models for each protein were taken from published studies of the isolated proteins in vitro. For simulation of electrical stimuli, the time course of voltage changes in the dendritic spine was generated with the desired stimulus in the program NEURON. Voltage-dependent parameters were then continuously re-adjusted during simulations in MCell to reproduce the effects of the stimulus. Nine parameters of the model were optimized within realistic experimental limits by a process that compared results of simulations to published data. We find that simulations in the optimized model reproduce the timing and amplitude of Ca(2+) transients measured experimentally in intact neurons. Thus, we demonstrate that the characteristics of individual isolated proteins determined in vitro can accurately reproduce the dynamics of experimentally measured Ca(2+) transients in spines. The model will provide a test bed for exploring the roles of additional proteins that regulate Ca(2+) influx into spines and for studying the behavior of protein targets in the spine that are regulated by Ca(2+) influx.

Computational modeling of three-dimensional electrodiffusion in biological systems: application to the node of Ranvier.

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical results for computed action potentials agree well with cable model predictions for large clusters of voltage-gated ion channels. At smaller channel clusters, however, the three-dimensional electrodiffusion predictions diverge from the cable model predictions and show a broadening of the action potential, indicating a significant effect due to each channel's own local electric field. The node of Ranvier complex is an elaborate organization of membrane-bound aqueous compartments, and the model presented here represents what we believe is a significant first step in simulating electrophysiological events with combined realistic structural and physiological data.

Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines.

The entry of calcium into dendritic spines can trigger a sequence of biochemical reactions that begins with the activation of calmodulin (CaM) and ends with long-term changes to synaptic strengths. The degree of activation of CaM can depend on highly local elevations in the concentration of calcium and the duration of transient increases in calcium concentration. Accurate measurement of these local changes in calcium is difficult because the spaces are so small and the numbers of molecules are so low. We have therefore developed a Monte Carlo model of intracellular calcium dynamics within the spine that included calcium binding proteins, calcium transporters and ion channels activated by voltage and glutamate binding. The model reproduced optical recordings using calcium indicator dyes and showed that without the dye the free intracellular calcium concentration transient was much higher than predicted from the fluorescent signal. Excitatory postsynaptic potentials induced large, long-lasting calcium gradients across the postsynaptic density, which activated CaM. When glutamate was released at the synapse 10 ms before an action potential occurred, simulating activity patterns that strengthen hippocampal synapses, the calcium gradient and activation of CaM in the postsynaptic density were much greater than when the order was reversed, a condition that decreases synaptic strengths, suggesting a possible mechanism underlying the induction of long-term changes in synaptic strength. The spatial and temporal mechanisms for selectivity in CaM activation demonstrated here could be used in other signaling pathways.