A population density approach that facilitates large-scale modeling of neural networks: Extension to slow inhibitory synapses

A previously developed method for efficiently simulating complex networks o f integrate-and-fire neurons was specialized to the case in which the neuro ns have fast unitary postsynaptic conductances. However, inhibitory synapti c conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that can not be captured with neurons that have only fast synapses. We thus extend t he model to include slow inhibitory synapses. In this model, neurons are gr ouped into large populations of similar neurons. For each population, we ca lculate the evolution of a probability density function (PDF), which descri bes the distribution of neurons over state-space. The population firing rat e is given by the flux of probability across the threshold voltage for firi ng an action potential. In the case of fast synaptic conductances, the PDF was one-dimensional, as the state of a neuron was completely determined by its transmembrane voltage. An exact extension to slow inhibitory synapses i ncreases the dimension of the PDF to two or three, as the state of a neuron now includes the state of its inhibitory synaptic conductance. However, by assuming that the expected value of a neuron's inhibitory conductance is i ndependent of its voltage, we derive a reduction to a one-dimensional PDF a nd avoid increasing the computational complexity of the problem. We demonst rate that although this assumption is not strictly valid, the results of th e reduced model are surprisingly accurate.