Correlations and the encoding of information in the nervous system

Is the information transmitted by an ensemble of neurons determined solely by the number of spikes fired by each cell, or do correlations in the emission of action potentials also play a significant role? We derive a simple formula which enables this question to be answered rigorously for short time–scales. The formula quantifies the corrections to the instantaneous information rate which result from correlations in spike emission between pairs of neurons. The mutual information that the ensemble of neurons conveys about external stimuli can thus be broken down into firing rate and correlation components. This analysis provides fundamental constraints upon the nature of information coding, showing that over short time–scales, correlations cannot dominate information representation, that stimulus–independent correlations may lead to synergy (where the neurons together convey more information than they would if they were considered independently), but that only certain combinations of the different sources of correlation result in significant synergy rather than in redundancy or in negligible effects. This analysis leads to a new quantification procedure which is directly applicable to simultaneous multiple neuron recordings.