Computational analyses of intracellular signalling provide an overlying framework in which the previous three lines of experimental investigation are consolidated.

We are developing a detailed quantitative model of the postsynaptic signaling system that encompasses:

1.   biophysical measurements of the binding constants between proteins,

2.   diffusion and translocation of proteins, and

3.   intracellular geometric constraints,

all confined in the boundary established by the postsynaptic spine.

A tenet of our computational efforts is that intracellular signaling cannot be accurately represented with ordinary differential equation approaches. The laws of mass action cannot accurately represent the behavior of a small number of reactants in a compartment like the postsynaptic spine. Additionally, the intracellular space is neither homogenous nor well mixed. Accurately capturing these features requires novel computational strategies.

A present focus is the construction and validation of a general purpose Monte Carlo simulator capable of incorporating diffusion and chemical reactions in inhomogeneous media.

A non-lattice constrained Monte Carlo approach has been developed and validated by comparison of results to solutions of the classical diffusion equation (Figure 1). We have used this simulator to investigate the diffusion of a reactant in inhomogeneous media.                                                                                                               Figure 1.  Click to enlarge.

Figure 2 illustrates an aspect of some recent simulations.  Shown is an electron micrograph of a spine in the CA1 region of the rat hippocampus provided as part of an on-going collaboration with Dr. Mark Ellisman's group at USCD.   The goal of these simulations was to provide a sense for Ca2+ -saturated CaM 's range of action in the absence and presence of RC3, a protein whose only known function is to bind CaM. 

We artificially started from a point source of fully Ca2+ -saturated CaM in the center of the spine volume. To calculate the range of action we used previously acquired values for the diffusion rate of CaM (obtained using multi-photon fluorescence correlation spectroscopy) and for the rate(s) at which Ca2+

dissociates (determined by stopped-flow fluorescence techniques).

In the absence of RC3, the range of action of Ca2+ -saturated CaM increases with the Ca2+ concentration and reaches a maximum value of 120 nm (indicated by the large gray circle) at Ca2+ concentrations of more than 10 mM.   In the presence of RC3, the range of action of Ca2+ -saturated CaM is significantly reduced (represented by smaller white circle) due to RC3's capacity to increase Ca2+                  Figure 2.  Click to enlarge.

dissociation from CaM.  These results suggest that RC3 acts as a filter so that

Ca2+ simply passes through the cytoplasm of an RC3-rich region without interacting with CaM.

These results describing RC3's effects on CaM 's range of action will certainly be altered by the inclusion in the simulation of Ca2+ -CaM -dependent targets such as CaMKII or calcineurin. These proteins all bind to CaM and produce complex patterns of competition for their activation, and these interactions will further limit the range of action of CaM.