Fano factor as a key measure of sensitivity in biological networks
Sensitivity of a biological process is vital for its proper function and regulation. Biological networks in equilibrium display such sensitivity mainly through cooperative binding of ligands to network elements comprised of multiple sites of an oligomeric protein. The classical measure of binding cooperativity is the Hill slope obtained empirically from binding isotherm data, known as the Hill plot. Hill slope value greater (less) than unity indicates positive (negative) cooperativity. In this study, we have shown that the Hill slope is actually a combination of two Fano factors associated with the number of bound and empty sites of the network, respectively. Taking a ladder network capable of showing positive cooperativity only, we have analytically proved that if the variation of Fano factors with fractional saturation of the network is non-linear, the binding is cooperative and if the variation is linear, the binding is non-cooperative with Hill slope equal to unity. Further, through numerical analyses of a linear network that can exhibit both positive and negative cooperativity, it is established that the curves of Fano factor for the positive (negative) cooperative cases reside above (below) the line representing the non-cooperative case. Our results, thus, confirm the role of Fano factor as the crucial measure of sensitivity in biological networks.