Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns. Author Summary: Neurons use electrical impulses called action potentials to transmit signals from their cell body to their axon terminals, where the impulses trigger release of neurotransmitter. Initiation of an action potential is determined by the balance of currents through ion channels in a neuron's membrane. Although it is well established that membrane ion channels randomly fluctuate between open and closed states, most models of action potentials account for the average current through these channels but not for the current fluctuations caused by this stochastic opening and closing. Here, we examine the consequences of stochastic ion channel gating for stellate neurons found in the entorhinal cortex. The intrinsic properties of these neurons cause characteristic clustered patterns of spiking. We find that in a model of a single stellate neuron that is constrained by previous experimental data clustered action potential patterns are produced only when the model accounts for the random opening and closing of individual ion channels. This stochastic model provides an example of a general mechanism for patterning of neuronal activity and may help to explain the patterns of spikes fired by entorhinal neurons that encode spatial location in behaving animals.