Signal transmission through a metabolic cycle follows the compression hypothesis or a weak Weber's law

Biological signal transduction often involves a metabolic cycle in which the flux at one point is driven by the input signal and the concentration of one of the metabolites of the cycle serves as the output signal. A kinetic analysis of such a metabolic cycle is made under an assumption that the law of mass action applies. The resultant kinetic model can produce a response that overshoots, quickens, and eventually saturates as the input intensity is increased. The possible model behavior ranges parametrically from non-adaptive (compression hypothesis) to weakly adaptive (limited Weber's law).