Abstract
The single photon response (SPR) in vertebrate photoreceptors is inherently variable due to several stochastic events in the phototransduction cascade, the main one being the shutoff of photoactivated rhodopsin. Deactivation is driven by a random number of steps, each of random duration with final quenching occurring after a random delay. Nevertheless, variability of the SPR is relatively low, making the signal highly reliable. Several biophysical and mathematical mechanisms contributing to variability suppression have been examined by the authors. Here we investigate the contribution of local depletion of cGMP by PDE*, the non linear dependence of the photocurrent on cGMP, Ca2+ feedback by making use of a fully space resolved (FSR) mathematical model, applied to two species (mouse and salamander), by varying the cGMP diffusion rate severalfold and rod outer segment diameter by an order of magnitude, and by introducing new, more refined, and time dependent variability functionals. Globally well stirred (GWS) models, and to a lesser extent transversally well stirred models (TWS), underestimate the role of nonlinearities and local cGMP depletion in quenching the variability of the circulating current with respect to fully space resolved models (FSR). These distortions minimize the true extent to which SPR is stabilized by locality in cGMP depletion, nonlinear effects linking cGMP to current, and Ca2+ feedback arising from the physical separation of E* from the ion channels located on the outer shell, and the diffusion of these second messengers in the cytoplasm.
Highlights
Vertebrate rod photoreceptors accurately detect light and reliably discriminate differences at exceedingly low levels of illumination
Variability of cGMP depletion inherited from E gets deamplified by the nonlinear dependence of ion channel activity on [cGMP], by Eq 9. Between these two steps is the redistribution of cGMP, as it diffuses centrally from the outer shell, dampening the randomness of cGMP at the outer shell
The phototransduction cascades in these two types of photoreceptors are quite different, yet one thing they share is multiple layers of photopigment-containing membranes
Summary
Vertebrate rod photoreceptors accurately detect light and reliably discriminate differences at exceedingly low levels of illumination. Active rhodopsin R can be localized anywhere on the rod outer segment disc membrane (Fig 1), and it continues random diffusion in the membrane, encountering and activating a variable number of transducin G-protein (T) molecules by facilitating the exchange of GDP bound to inactive heterotrimeric transducin for GTP. The relatively small changes in [cGMP] that occur during the SPR invite a further simplification, linearization of the relation between [cGMP] and ion channel activity ([15, 16]) We disprove such approaches by providing numerical evidence that the full 3-dimensional structure of the ROS and the local nature of the cascade activation-deactivation and nonlinearities in the effects of second messengers, play key roles in suppressing variability. We discuss what information is provided by different functionals that evolve over time and use them to show how variability is distorted by reducing spatial resolution and by linearization of second messenger effects
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