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JH Parkes, PA Liebman; How the Eye Can Turn Exponental Decays Into a Gaussian Distribution . Invest. Ophthalmol. Vis. Sci. 2002;43(13):1422.
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Purpose: Vertebrate rods respond to single photons with high reproducibility, generating a Gaussian distribution of electrical responses, or quantum bumps (Baylor, Lamb, and Yau, 1979). This ruled out, as the terminating event, a single stochastic event that would necessarily yield an exponentially decaying response, and all biochemical reactions are essentially of this type. We wanted to see how a Gaussian response could be generated from exponential decays. Methods: Random activations of G protein, with one or more random phosphorylations and terminated by a final arrestin binding were simulated using a Monte Carlo method. Results: As the number of phosphorylations required to deactivate rhodopsin increases, the resulting distribution increasingly resembles a Gaussian (Figure). View OriginalDownload SlideView OriginalDownload Slide The shape of these distributions does not depend on the relative frequencies of G protein activations and phosphorylations, but is a consequence solely of the fact that the specified number of random events must occur for deactivation. However, the distributions all have too great a frequency at the high end. Some limitation is needed in the number of G proteins that can be activated. An absolute limit of about 350 G proteins per R* gives the distribution a symmetric Gaussian shape. Equally, a reduction in the density of inactive G proteins in the immediate vicinity of the R* to some lower steady state level can be sufficient. Conclusion: Deactivation of rhodopsin is the only step in visual excitation that presents this problem since there is only one active R* molecule. Because there are so many of them, G proteins and PDEs may individually exhibit stochastic deactivation without affecting the Gaussian shape of the light response.
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