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A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rall-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the(More)
Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major(More)
We examine some simple mathematical models which have been recently employed to predict the evolution of population dynamical systems involving virus particles. They include: (1) A general two-component antibody-viral system; (2) A simplified two-component model for HIV-1 dynamics (3) An HIV-1 three-component model including virions and (4) A four-component(More)
The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions(More)
An analytical approach is presented for determining the response of a neuron or of the activity in a network of connected neurons, represented by systems of nonlinear ordinary stochastic differential equations—the Fitzhugh-Nagumo system with Gaussian white noise current. For a single neuron, five equations hold for the first- and second-order central(More)
Ca(2+) currents in neurons and muscle cells have been classified as being one of 5 types, of which four, L, N, P/Q and R were said to be high threshold and one, T, was designated low threshold. This review focuses on quantitative aspects of L-type currents. L-type channels are now distinguished according to their structure as one of four main subtypes(More)
Stein's model for a neuron receiving randomly arriving post-synaptic potentials is studied from an analytic viewpoint, using some recent results in the theory of first passage times for temporally homogeneous Markov processes. The case when the only input is excitatory can be treated exactly. It is shown that the moments of the firing time are guaranteed to(More)
Neuronal spike trains from both single and multi-unit recordings often contain patterns such as doublets and triplets of spikes that precisely replicate themselves at a later time. The presence of such precisely replicating patterns can still be detected when the tolerance on interval replication is shortened to a fraction of a millisecond. In this context(More)