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

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding.