Fano Factor as the Key Measure of Sensitivity in Biological Networks

Sensitivity is a crucial feature for proper function and regulation of biological processes. Cooperative protein-ligand binding, which can be described as transitions in biological networks, is a fundamental mechanism for such sensitivity. The phenomenological sensitivity measure is the empirical Hill slope. However, a measure of sensitivity directly related to network dynamics at the cellular level is still lacking. In this study, using discrete-state stochastic analysis of seminal ligand-binding networks, we establish that the Fano factor is a crucial measure of sensitivity. Nonlinear variation of the Fano factor with fractional saturation of the network gives the criterion of cooperativity, with noncooperative binding producing a linear trend. The positive (negative) deviation of the Fano factor curve from linearity indicates positive (negative) cooperativity. Finally, the ratio of Fano factor values in cooperative and noncooperative binding becomes equal to the Hill slope, affirming its role as the essential measure of sensitivity in biological networks.