Computer Simulations of Synaptic Signaling

We are studying the biochemical signaling cascades that are triggered by calcium influx into the postsynaptic spine, and that regulate adaptive changes in the synaptic machinery. Our tools to study the function of the highly interconnected biochemical pathways include both biochemical experiments and computer simulations. Our goal is to create simulations that will generate testable predictions about the flow of protein phosphorylation events in spines and dendrites, under conditions of calcium influx that cause changes in synaptic strength.
 
Data for "Realistic" Simulations

Most of the major molecules forming the signaling machinery at the postsynaptic membrane of dendritic spines have now been characterized by our lab and others [1, 2]. To build realistic simulations it is necessary to determine the relative stoichiometry of the molecules whose functions will be simulated.

We are using quantitative western blots of proteins in the postsynaptic density fraction and in synaptosome to estimate the relative numbers of the molecules of interest, for example we are determining the ratios of subunits of the NMDA receptor to PSD-95 and to subunits of CaM kinase II. We can then calculate average numbers of each molecule present in the major anatomical classes of spines of pyramidal neurons in area CA1 of the hippocampus [3], based on information about glutamate receptor currents and about spine geometry found in the literature.  The biochemical measurements and calculations serve two purposes. They give us a more precise view of the likely predominance of certain pathways, based on the relative number of interplaying signaling molecules, and they provide starting parameters for computer simulations of the signaling cascades at the postsynaptic site of glutamatergic synapses, following influx of calcium.

Computer Simulations

In order to numerically simulate the entry of Ca ions into the spine, its diffusion, and the biochemical reactions triggered by the Ca influx, we use MCell: (http://www.mcell.cnl.salk.edu) ,a software package for stochastic simulation of biochemical processes in vivo.  MCell was originally developed to model the events at the neuromuscular junction: acetylcholine release, diffusion, binding to acetylcholine receptors and the nicotinic acetylcholine channel kinetics [3,4]. However, in collaboration with the MCell group at the Salk Institute, we are extending it so that it can be used for modeling of other biochemical processes.

Contrary to the traditional numerical approach, in which a system of partial differential reaction-diffusion equations is solved numerically, MCell uses the Monte-Carlo approach to simulate diffusion of individual molecules (ions) and their reactions in an arbitrarily shaped space. It requires the number and positions of all molecules, diffusion constants, binding and unbinding constants for all reactions and a description of the geometry where the process that is simulated takes place.

Diffusion is performed in MCell as a random walk. During one time step each diffusing molecule moves in a randomly chosen direction and travels a distance that is randomly chosen from the theoretical diffusion distribution for the given diffusion coefficient of the molecule and the time step. Therefore, contrary to the majority of random walk algorithms, MCell does not use a lattice for diffusion.

Reactions are also treated as stochastic events. The probability that two individual molecules bind is calculated from the binding rate. Only the molecules that come close enough during diffusion, as determined by the ray tracing algorithm, can possibly bind. Dissociation probability is determined from the dissociation rate.  Virtually any geometry within which diffusion and reaction take place can be specified, which gives MCell a significant advantage in simulation of in vivo processes over the traditional approaches based on partial differential equations.

We are presently deriving models for the kinetics of activation of CaM kinase II, and devising in vitro experiments with purified CaM kinase II to test the models at levels of calcium and calmodulin that the enzyme is likely to encounter near the postsynaptic membrane.  In this way, we will determine the appropriate reaction rates and probabilities to incorporate into a model of the spine synapse.  Eventually, we will devise experiments to test predictions of our models for activation of CaM kinase II, and its modulation, in living neurons.

References:

[1] Kennedy M.B. (2000) Signal-Processing Machines at the Postsynaptic Density. Science 290: 750-754

[2] Sheng, M. (2001) Molecular organization of the postsynaptic specialization. Proceedings of the National Academy of Sciences 98: 7058-7061

[3] Harris K.M., Jensen., and Tsao B. (1992) Three-dimensional structure of dendritic spines and synapses in rat hippocampus (CA1) at postnatal day 15 and adult ages: implications for the maturation of synaptic physiology and long-term potentiation. Journal of Neuroscience 12: 2685-2705

[4] Bartol TM Jr., Land BR, Salpeter EE, Salpeter MM (1991) Monte Carlo simulation of miniature endplate current generation in the vertebrate neuromuscular junction. Biophysics Journal  59: 1290-1307

[5] Stiles, J.R., Bartol, T.M., Salpeter, M.M, Salpeter, E.E., and Sejnowski, T.J., (2000) Synaptic variability: new insights from reconstructions and Monte Carlo simulations with MCell. In Synapses, W.M. Cowan, C.F. Stevens, and T.C. Suddhof, eds. (Baltimore, Johns Hopkins Univ. Press), 681-731.