  A key problem in computational neuroscience is to find simple, tractable
models that are nevertheless flexible enough to capture the response properties
of real neurons. Here we examine the capabilities of recurrent point process
models known as Poisson generalized linear models (GLMs). These models are
defined by a set of linear filters, a point nonlinearity, and conditionally
Poisson spiking. They have desirable statistical properties for fitting and
have been widely used to analyze spike trains from electrophysiological
recordings. However, the dynamical repertoire of GLMs has not been
systematically compared to that of real neurons. Here we show that GLMs can
reproduce a comprehensive suite of canonical neural response behaviors,
including tonic and phasic spiking, bursting, spike rate adaptation, type I and
type II excitation, and two forms of bistability. GLMs can also capture
stimulus-dependent changes in spike timing precision and reliability that mimic
those observed in real neurons, and can exhibit varying degrees of
stochasticity, from virtually deterministic responses to greater-than-Poisson
variability. These results show that Poisson GLMs can exhibit a wide range of
dynamic spiking behaviors found in real neurons, making them well suited for
qualitative dynamical as well as quantitative statistical studies of
single-neuron and population response properties.
