Input-output characteristics.

<p>Top row: Protocol used to investigate the response of the neuronal population with a given excitatory synaptic weight distribution to a sudden perturbation in its synaptic input. a) Input rate as a function of time. For the first 500 ms, the cumulative synaptic input rate is varied between 500 and 1,000 Hz, expressed as a fraction of the 1,000 Hz base input rate (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4" target="_blank">Methods</a>: Input-Output curves). The population evolves according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e029" target="_blank">equation (3)</a> for a -function distribution of synaptic weights. At 500 ms, the input firing rate instantaneously returns to the base rate of 1000 Hz. b) Output firing rate as a function of time for . The peak output rate attained provides a measure of how strongly the system responds to sudden changes in its input rate. c) Zooming in onto the transient response in (b). The smaller the difference in input rate, the quicker the response of the network, with less overshoot. Bottom row: Quantifying response to sudden changes in input rate. d) Peak output firing rate for different fractions of the base input rate as a function of base input rate for . e) Difference in the peak output firing rate normalized by the difference between input rates, when the input is instantaneously changed from 1/2 the base rate to the full base rate. Normalized differences in output rates for different synaptic weight distributions are plotted as a function of the full input base rate. Heavier-tailed distributions result in lesser overshoot. f) Semi-log plot of the steady state output firing rate as a function of the input firing rate, for different synaptic distributions with the inclusion of short-term synaptic depression. Onset of saturation for very high effective synaptic input rates is evident. Note the greater response of the heavier-tailed power-law and bimodal distributions for lower input firing rates, leading to higher dynamical range.