A molecular basis for Weber's law

A mathematical model is presented that obeys a strong form of Weber's law--over a range of adapting and stimulus intensities, equal contrast stimuli evoke identical responses. To account for the strong Weber's law, the adaptive stage in the proposed model employs a "delayed" reverse reaction along with a power-law input. It is suggested that this Weber's law mechanism is responsible for a slow, voltage-uncorrelated component of adaptation in the vertebrate photoreceptor. A plausible biochemical mechanism is the G-protein cycle with phosphorylation of photoactivated photopigment (and binding of arrestin to the phosphorylated photopigment) as the adaptive process. In an Appendix, features of the general model and implications of a specific biochemical model are examined by computer simulation.