Novel Integrate-and-re-like Model of Repetitive Firing in Cortical Neurons

Cortical neurons convert synaptic inputs arising from thousands of other neurons into a single output spike train. In order to better understand this basic computation, we have derived a simple repetitive ring model from the Hodgkin-Huxley equations. This novel model is related to the conventional integrate-andre model, but uses a time-varying time constant (whose value follows a stereotyped trajectory after each spike) in place of the usual xed time constant. The model, whose parameters can be extracted from as few as two interspike intervals, provides an excellent t to the responses of cortical neurons in vitro to both constant and time-varying inputs. Neurons in the cortex convert the synaptic input generated by thousands of other neurons into an output spike train. Because this transformation is central for cortical computation, an understanding of the computation performed by cortical circuits requires an understanding of this basic inputoutput transformation. Encoding is, at least in principle, well understood. The basic framework for our modern understanding was provided by Hodgkin and Huxley almost fty years ago [Hodgkin and Huxley, 1952]. They showed that spike generation in the axon of the giant squid could be described in terms of just two distinct nonlinear conductance mechanisms: a sodium channel, and a potassium channel. Since that time, hundreds of new channels have been identi ed. Dozens of channels coexist in single cortical neurons, distributed inhomogeneously throughout the dendritic tree. Thus while a description of the squid axon required measurement of the properties of only two channels, and the corresponding one or two dozen parameters, a comparably complete and accurate description of a cortical neuron|a description of each channel, along with its distribution throughout the dendritic tree|would require measurement of thousands of parameters. In practice, such a feat remains beyond the capacity of current experimental techniques. Moreover, even if it were possible, a complete description might be too complex to be of much use. We have therefore pursued a di erent strategy. We have asked what the simplest model is that can account for the ring of cortical cells. Fig. 1 shows typical repetitive ring in a regularring layer 2/3 cortical neuron. Our goal, then, is to derive a simple model of such responses to a constant stimulation, and of the responses to more complex stimuli. Repetitive firing (layer 2/3)