Synaptic Currents, Neuromodulation and Kinetic Models Kinetic Models of Synaptic Currents 1 1 Introduction
Synaptic interactions are essential to neural network models of all levels of complexity. Synaptic interactions in \realistic" network models pose a particular challenge, since the aim is not to only to capture the essence of synaptic mechanisms, but also to do so in a computationally eecient manner to facilitate simulations of large networks. In this paper, we review several types of models which address these goals. Synaptic currents are mediated by ion channels activated by neurotransmitter released from presynaptic terminals. Kinetic models are a powerful formalism for the description of channel behavior, and are therefore well-suited to the description of synaptic interactions, both traditional and neuromodulatory. Although full representation of the molecular details of the synapse generally requires highly complex kinetic models, we focus on simpler kinetic models which are very eecient to compute. We show how these models capture the time courses of several types of synaptic responses as well as the important phenomena of summation, saturation and desensitization. For neural models that do not include action potentials, synaptic currents are typically modeled as a direct function of the some presynaptic activity measure. In the simplest case, synaptic interactions are described by a sigmoid function, and presynaptic activity is interpreted as the average ring rate of the aaerent neuron. Alternatively, the postsynaptic currents can be described by a rst-order diierential equation in which one term depends on the presynaptic membrane potential through a sigmoid function (Wang and Rinzel, 1992). Another possibility is to interpret the activity level as the fraction of neurons active per unit of time, thus representing the interaction between neural populations rather than single neurons (Wilson and Cowan, 1973). For spiking neurons, a popular model of postsynaptic currents (PSC's) is the alpha function r(t ? t 0) = (t ? t 0) 1 expp?(t ? t 0)== 1 ] (1) (Rall, 1967), where r(t) resembles the time course of experimentally-recorded postsy-naptic potentials (PSP's) with a time constant 1. The alpha function and its double-exponential generalization can be used to approximate most synaptic currents with a small number of parameters and, if implemented properly, at low computation and stor-2 age requirements (Srinivasan and Chiel, 1993). Other types of template function were also proposed for spiking neurons (Tsodyks et al., 1990; Traub and Miles, 1991). The disadvantages of the alpha-function, or related approaches, include the lack of correspondence to a plausible biophysical mechanism and the absence of a …