Statistical test of linearity of photoreceptor transduction process: Limulus passes, others fail

We present the results of a theoretical analysis of a completely general linear chain model for transduction in photoreceptors from which we have derived a statistical test for the intrinsic linearity of the single-photon transduction process. By linearity we mean comprising first-order chemical reactions only. We show results of our own measurements in Limulus ventral photoreceptors that pass this linearity test, suggesting that the single-photon transduction in Limulus may be a simple chain of first-order biochemical reactions (plus possible diffusional processes). However, we also demonstrate that published data show the existence of strong nonlinearities in the single-photon responses of toad and perhaps also of locust. Such nonlinearities are not difficult to construct from existing biochemical notions (feedback, cooperativity), but all but one [Kramer, L. (1975) Biophys. Struct. Mech. 1,239-257] of the published analytical models of the single-photon process have been linear. The test we have used is the distribution of "areas" (time integrals of conductance changes) of single-photon responses or "bumps." Reasonable molecular linear chain models do not allow distributions very sharply peaked at non-zero values. Such peaked distributions are seen in toad and locust but not in Limulus.