Models of bursting in single cells typically include two subsystems with different timescales. Variations in one or more slow variables switch the system between a silent and a spiking state. We have developed a model for bursting in the pituitary lactotroph that does not include any slow variable. The model incorporates fast, noninactivating calcium and potassium currents (the spike-generating mechanism), as well as the fast, inactivating A-type potassium current ( I A ). I A is active only briefly at the beginning of a burst, but this brief impulse of I A acts as a burst trigger, injecting the spike trajectory close to an unstable steady state. The spiraling of the trajectory away from the steady state produces a period of low-amplitude spiking typical of lactotrophs. Increasing the conductance of A-type potassium current brings the trajectory closer to the unstable steady state, increasing burst duration. However, this also increases interburst interval, and for larger conductance values, all activity stops. To our knowledge, this is the first example of a physiologically based, single-compartmental model of bursting with no slow subsystem.

The filtering of input signals carried out at synapses is key to the information processing performed by networks of neurons. Two forms of presynaptic depression, vesicle depletion and G-protein inhibition of Ca 2+ channels, can play important roles in the presynaptic processing of information. Using computational models, we demonstrate that these two forms of depression filter information in very different ways. G- protein inhibition acts as a high-pass filter, preferentially transmitting high-frequency input signals to the postsynaptic cell, while vesicle depletion acts as a low-pass filter. We examine how these forms of depression separately and together affect the steady-state postsynaptic responses to trains of stimuli over a range of frequencies. Finally, we demonstrate how differential filtering permits the multiplexing of information within a single impulse train.

We describe a model of synaptic transmitter release and presynaptic facilitation that is based on activation of release sites by single Ca 2+ C microdomains. Facilitation is due to Ca 2+ that remains bound to release sites between impulses. This model is inherently stochastic, but deterministic equations can be derived for the mean release. The number of equations required to describe the mean release is small, so it is practical to use the model with models of neuronal electrical activity to investigate the effects of different input spike patterns on presynaptic facilitation. We use it in conjunction with a model of dopamine-secreting neurons of the basal ganglia to demonstrate that transmitter release is greater when the neuron bursts than when it spikes continuously, due to the greater facilitation generated by the bursting impulse pattern. Finally, a minimal form of the model is described that is coupled to simple models of postsynaptic receptors and passive membrane to compute the postsynaptic voltage response to a train of presynaptic stimuli. This form of the model is appropriate for neural network simulations.