Correlated Neuronal Activity: High- and Low-Level Views - Computational Neuroscience: A Comprehensive Approach - page 353

g E (t)

¬ m

m

2 t

2 s

corr

g E

Time lag

¬ m + s

¬ m − s

Figure 12.4
Parameterization of a continuous conductance trace. The top graph represents the to-
tal synaptic conductance generated by excitatory spikes driving a postsynaptic neu-
ron. This conductance can be characterized statistically by its mean m, standard
deviation s, and correlation time t corr . The left histogram is the distribution of con-
ductance values of the top trace. The histogram on the right is its autocorrelation
function. The width of the peak is parameterized by t corr . The bottom graph shows a
binary variable that approximates the continuous trace. The binary function has the
same mean, standard deviation and correlation time as the original function [69].

to some extent, combine both types of firing modes.

12.6 A simple, quantitative model

Now we discuss a simple model for which the responses to correlated input can be
calculated analytically [69]. The first step is to describe its input.

12.6.1 Parameterizing the input

The input to a neuron consists of two sets of spike trains, ones that are excitatory
and others that are inhibitory. What are the total synaptic conductances generated
by these spikes? How can they be characterized? An example generated through
a computer simulation is shown in Figure 12.4. The top trace represents the total
excitatory conductance g E (

t ) produced by the constant bombardment of excitatory