Fast Calculation of Synaptic Conductances

Abstract

The drawback of these solutions is that one must keep track of the times of occurrences of each spike that initiated the synaptic potentials, and recalculate each exponential in the summation at each time step. This creates a large storage and computational overhead. Since both these equations represent the impulse response of a second-order differential equation, another approach is to numerically integrate additional differential equations for each synapse in the network (Wilson and Bower 1989). We have developed an improved method for computing synaptic conductances that separates equations 1 and 2 into two components: one that is a function of the current time of the simulation and one that accumulates the contributions of previous spike events to the synaptic conductance. We demonstrate that this method requires only the storage of two running sums and the time constants for each synapse, and that it is mathematically equivalent to equations 1 and 2. We will then demonstrate that it is also faster for a given level of precision than numerically integrating differential equations for each synapse. We will first describe our algorithm for equation 1, and then for equation 2.