Sensitivity Transformation For Vertebrate Vision

The visual response to a flash given in the dark is known to saturate according to the Michaelis-Menten relationship. Nevertheless, the incremental response from increasing levels of mean luminance tends to follow a Weber-Fechner relationship well into the saturation range determined from the Michaelis-Menten results. This sensitivity transformation from Michaelis-Menten to Weber-Fechner is an important characteristic of light adaptation in the vertebrate retina. Recent studies concerning the role of calcium in photoreceptor adaptation have shown that the relaxation from peak to plateau in the response of isolated photoreceptors was absent under conditions in which adaptation was blocked. Comparing the pronounced relaxation from peak to plateau in turtle horizontal cells with the absence of such relaxation in the catfish response, we noted also that turtle incremental sensitivity shows a Weber-Fechner relationship while catfish incremental sensitivity more closely follows the local slope of the Michaelis-Menten relation. Based on these observations, we have obtained an expression to relate the relaxation from peak to plateau with the sensitivity transformation. We assume that adaptation shifts the half-maximum point of the Michaelis-Menten curve so that the light response relaxes to a plateau value equal to a specified fraction phi of the peak response. We show that this manipulation alone results in a transformation from Michaelis-Menten kinetics to Weber-Fechner sensitivity.