TY - JOUR

T1 - A population density approach that facilitates large-scale modeling of neural networks

T2 - Extension to slow inhibitory synapses

AU - Nykamp, Duane Q.

AU - Tranchina, Daniel

PY - 2001/3

Y1 - 2001/3

N2 - A previously developed method for efficiently simulating complex networks of integrate-and-fire neurons was specialized to the case in which the neurons have fast unitary postsynaptic conductances. However, inhibitory synaptic conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that cannot be captured with neurons that have only fast synapses. We thus extend the model to include slow inhibitory synapses. In this model, neurons are grouped into large populations of similar neurons. For each population, we calculate the evolution of a probability density function (PDF), which describes the distribution of neurons over state-space. The population firing rate is given by the flux of probability across the threshold voltage for firing 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 increases 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 independent of its voltage, we derive a reduction to a one-dimensional PDF and avoid increasing the computational complexity of the problem. We demonstrate that although this assumption is not strictly valid, the results of the reduced model are surprisingly accurate.

AB - A previously developed method for efficiently simulating complex networks of integrate-and-fire neurons was specialized to the case in which the neurons have fast unitary postsynaptic conductances. However, inhibitory synaptic conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that cannot be captured with neurons that have only fast synapses. We thus extend the model to include slow inhibitory synapses. In this model, neurons are grouped into large populations of similar neurons. For each population, we calculate the evolution of a probability density function (PDF), which describes the distribution of neurons over state-space. The population firing rate is given by the flux of probability across the threshold voltage for firing 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 increases 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 independent of its voltage, we derive a reduction to a one-dimensional PDF and avoid increasing the computational complexity of the problem. We demonstrate that although this assumption is not strictly valid, the results of the reduced model are surprisingly accurate.

UR - http://www.scopus.com/inward/record.url?scp=0035289566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035289566&partnerID=8YFLogxK

U2 - 10.1162/089976601300014448

DO - 10.1162/089976601300014448

M3 - Article

C2 - 11244554

AN - SCOPUS:0035289566

VL - 13

SP - 511

EP - 546

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 3

ER -