Synthesis of generalized algorithms for the fast computation of synaptic conductances with Markov kinetic models in large network simulations

Markov kinetic models constitute a powerful framework to analyze patch-clamp data from single-channel recordings and model the dynamics of ion conductances and synaptic transmission between neurons. In particular, the accurate simulation of a large number of synaptic inputs in wide-scale network models may result in a computationally highly demanding process. We present a generalized consolidating algorithm to simulate efficiently a large number of synaptic inputs of the same kind (excitatory or inhibitory), converging on an isopotential compartment, independently modeling each synaptic current by a generic n-state Markov model characterized by piece-wise constant transition probabilities. We extend our findings to a class of simplified phenomenological descriptions of synaptic transmission that incorporate higher-order dynamics, such as short-term facilitation, depression, and synaptic plasticity.