Realistic synaptic inputs for model neural networks

An expressionis derived relating the input current for a single neuron in a neural network to the firing rates of exutatory and ithbrtory mputr synapsing on lite dendrrtic tree of the neuron. Any dendritic geometry and any pattem of synap tic connections c m be treated using the tecldques presented. The input aments calctdllated. combmned with known k n g rate functrons, d l o w the eRects of synaptic conductance dmnges along dendritic cables to be rncluded in a meamfield deswrp tmn of network beliaviour. The shunting effects of mhibitory synaptic conductances provide a solution to tlie ltigh firing rate problem i n neutral network models 1. I n t r o d n c t i o n Neural network models are often based on a mean-field approach [l] that uses known properties of single neurons to predict the behaviour of large neuronal populations In such models, the average firing rates of excitatory and inhibitory neurons are used to describe the activity of the population. The basic equations of mean-field theory relate these average rates to the rate of firing of a single neuron expressed as a function of its input current The equations become a dosed system when the input current IS expressed in turn as a function of the average firing rates for the population In a laboratory setting, the rate of singleneuron firing for various input currents can be measured by injecting current directly iuto the soma through a microelectrode. However, to use this firing rate in a network setting, we need to know the amount of current flowing into the soma from synaptic inputs as a function of the firing rates of presynaptic excitatory and inhibitory neurons. This information is much more difficult to obtain. In neural network models, the input current is generally taken to be a h e a r function of the excitatory and inhibitory input firing rates. This approximation leaves out several essential features of real synaptic inputs and real dendritic trees. The arrival of an action potential at a presynaptic terminal results in a change in the membrane conductance on the postsynzptic side. The total synaptic conductance due to many synaptic inputs is an approxiinately linear function of the input firing rate, but this does not imply that injected current is linear in the firing rate. Even for quite low input firing rates, the synaptic conductance may be comparable …