Elucidating the link between binding statistics and Shannon information in biological cooperative networks

Cooperative response is ubiquitous and vital for regulatory control and ultra-sensitivity in various cellular biophysical processes. Ligands, acting as signaling molecules, carry information which is transmitted through the elements of the biochemical network during binding processes. In this work, we address a fundamental issue regarding the link between the information content of the various states of the binding network and the observable binding statistics. Two seminal models of cooperativity, viz ., the Koshland-Nemethy-Filmer (KNF) network and the Monod-Wyman-Changeux (MWC) network are considered for this purpsoe which are solved using the chemical master equation approach. Our results establish that the variation of Shannon information associated with the network states has a generic form related to the average binding number. Further, the logarithmic sensitivity of the slope of Shannon information is shown to be related to the Hill slope in terms of the variance of the binding number distributions.

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