The Biophysical Basis of Firing Variability in Cortical Neurons - Computational Neuroscience: A Comprehensive Approach - page 163

is c where g w ( t ) is Gaussian white noise, and the standard deviation of τ / 2, and

c is a constant.
This generates stationary noise. However, real channel noise is usually not sta-
tionary: for example, transmitter-activated channels have transition rates which de-
pend on the changing transmitter concentration, and voltage-activated channels have
voltage-dependent transition rates. To account for such nonstationarity with high
accuracy, it is necessary to use stochastic simulations of populations of channels,
modelling the state transitions of all channels in each population [9, 55]. One may
also use an OU process which is nonstationary in to approximate the stochas-

tic Hodgkin-Huxley system [19]. However, since as described later, a great deal of
spike-time variance is generated by noise in a limited band of membrane potential -
around threshold - then a stationary OU noise source or sources may be a reasonably
accurate yet simple model for predicting firing variability. An OU process is also a
good model for synaptic noise, composed of large numbers of small, identical EPSPs
or IPSPs which have a fast onset and decay exponentially and whose arrival times
are a Poisson process [1].

and

6.5 Integration of a transient input by cortical neu-

rons

Cortical neurons fire in response to fast-fluctuating stimuli with much more precision
(i.e., with reproducibly-timed action potentials in an ensemble of identical trials),
than in response to constant stimuli [41]. In cortical neurons, precision has been
found to improve as the frequency of sinusoidal stimulation is increased up to about
25 Hz [44]. In Aplysia neurons, it has been demonstrated that the precision depends
on the presence of frequencies close to the preferred firing frequency of the cell at the
mean level of current [32], an effect which is probably general to many neurons. It
is clear that in an ensemble of responses to a complex fluctuating stimulus, a strong
fluctuation forces coherence across trials by compelling the cell to spike, putting it in
a particular dynamical state within a tightly-delimited interval of time. Most of the
influence of the preceding history is lost. This is because voltage-gated channels are
forced into an activated dynamical state, and the temporarily high conductance of the
neuronal membrane allows a high rate of dissipation, or leak of charge stored on the
membrane capacitance. In this section, I will discuss the variability of response of a
cortical neuron during a single large input fluctuation, from the moment of complete
coherence at the beginning of the fluctuation, until the input has decayed sufficiently
that the cell is silent. This discussion is based on [48].
Figure 6.4 shows the response of a pyramidal cell to a burst of excitatory synaptic
conductance, an exponentially-decaying transient in the rate of arrival of excitatory
synaptic conductances. The conductance stimulus is delivered using the technique of
conductance injection, or dynamic clamp [49, 53]. This technique is ideal for inves-