The firing reliability and precision of an isopotential membrane patch consisting of a realistically large number of ion channels is investigated using a stochastic Hodgkin-Huxley (HH) model. In sharp contrast to the deterministic HH model, the biophysically inspired stochastic model reproduces qualitatively the different reliability and precision characteristics of spike firing in response to DC and fluctuating current input in neocortical neurons, as reported by Mainen & Sejnowski (1995). For DC inputs, spike timing is highly unreliable; the reliability and precision are significantly increased for fluctuating current input. This behavior is critically determined by the relatively small number of excitable channels that are opened near threshold for spike firing rather than by the total number of channels that exist in the membrane patch. Channel fluctuations, together with the inherent bistability in the HH equations, give rise to three additional experimentally observed phenomena: subthreshold oscillations in the membrane voltage for DC input, “spontaneous” spikes for subthreshold inputs, and “missing” spikes for suprathreshold inputs. We suggest that the noise inherent in the operation of ion channels enables neurons to act as “smart” encoders. Slowly varying, uncorrelated inputs are coded with low reliability and accuracy and, hence, the information about such inputs is encoded almost exclusively by the spike rate. On the other hand, correlated presynaptic activity produces sharp fluctuations in the input to the postsynaptic cell, which are then encoded with high reliability and accuracy. In this case, information about the input exists in the exact timing of the spikes. We conclude that channel stochasticity should be considered in realistic models of neurons.

Neurons in the mammalian CNS receive 10 4 -10 5 synaptic inputs onto their dendritic tree. Each of these inputs may fire spontaneously at a rate of a few spikes per second. Consequently, the cell is bombarded by several hundred synapses in each and every millisecond. An extreme example is the cerebellar Purkinje cell (PC) receiving approximately 100,000 excitatory synapses from the parallel fibers (p.f.s) onto dendritic spines covering the thin dendritic branchlets. What is the effect of the p.f.s activity on the integrative capabilities of the PC? This question is explored theoretically using analytical cable models as well as compartmental models of a morphologically and physiologically characterized PC from the guinea pig cerebellum. The input of individual p.f.s was modeled as a transient conductance change, peaking at 0.4 nS with a rise time of 0.3 msec and a reversal potential of +60 mV relative to rest. We found that already at a firing frequency of a few spikes per second the membrane conductance is several times larger than the membrane conductance in the absence of synaptic activity. As a result, the cable properties of the PC significantly change; the most sensitive parameters are the system time constant (τ 0 ) and the steady-state attenuation factor from dendritic terminal to soma. The implication is that the cable properties of central neurons in freely behaving animals are different from those measured in slice preparation or in anesthetized animals, where most of the synaptic inputs are inactive. We conclude that, because of the large conductance increase produced by the background activity of the p.f.s, the activity of the PC will be altered from this background level either when the p.f.s change their firing frequency for a period of several tens of milliseconds or when a large population of the p.f.s fires during a narrow time window.