Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction.

The single photon response in vertebrate phototransduction is highly reproducible despite a number of random components of the activation cascade, including the random activation site, the random walk of an activated receptor, and its quenching in a random number of steps. Here we use a previously generated and tested spatiotemporal mathematical and computational model to identify possible mechanisms of variability reduction. The model permits one to separate the process into modules, and to analyze their impact separately. We show that the activation cascade is responsible for generation of variability, whereas diffusion of the second messengers is responsible for its suppression. Randomness of the activation site contributes at early times to the coefficient of variation of the photoresponse, whereas the Brownian path of a photoisomerized rhodopsin (Rh*) has a negligible effect. The major driver of variability is the turnoff mechanism of Rh*, which occurs essentially within the first 2-4 phosphorylated states of Rh*. Theoretically increasing the number of steps to quenching does not significantly decrease the corresponding coefficient of variation of the effector, in agreement with the biochemical limitations on the phosphorylated states of the receptor. Diffusion of the second messengers in the cytosol acts as a suppressor of the variability generated by the activation cascade. Calcium feedback has a negligible regulatory effect on the photocurrent variability. A comparative variability analysis has been conducted for the phototransduction in mouse and salamander, including a study of the effects of their anatomical differences such as incisures and photoreceptors geometry on variability generation and suppression.

[1]  E A Dratz,et al.  The molecular mechanism of visual excitation and its relation to the structure and composition of the rod outer segment. , 1987, Annual review of physiology.

[2]  Edward N. Pugh,et al.  From candelas to photoisomerizations in the mouse eye by rhodopsin bleaching in situ and the light-rearing dependence of the major components of the mouse ERG , 2004, Vision Research.

[3]  W. Baehr,et al.  Expression and mutagenesis of mouse rod photoreceptor cGMP phosphodiesterase. , 1994, The Journal of biological chemistry.

[4]  P Bisegna,et al.  Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction. , 2003, Biophysical journal.

[5]  Theodore G. Wensel,et al.  RGS Expression Rate-Limits Recovery of Rod Photoresponses , 2006, Neuron.

[6]  T. Lamb,et al.  Amplification and kinetics of the activation steps in phototransduction. , 1993, Biochimica et biophysica acta.

[7]  F. Rieke,et al.  Mechanisms Regulating Variability of the Single Photon Responses of Mammalian Rod Photoreceptors , 2002, Neuron.

[8]  Wei He,et al.  Slowed recovery of rod photoresponse in mice lacking the GTPase accelerating protein RGS9-1 , 2000, Nature.

[9]  Gordon L Fain,et al.  Measurement of cytoplasmic calcium concentration in the rods of wild‐type and transducin knock‐out mice , 2002, The Journal of physiology.

[10]  K. Hofmann,et al.  Interaction between photoactivated rhodopsin and its kinase: stability and kinetics of complex formation. , 1993, Biochemistry.

[11]  D. Tranchina,et al.  Multiple Steps of Phosphorylation of Activated Rhodopsin Can Account for the Reproducibility of Vertebrate Rod Single-photon Responses , 2003, The Journal of general physiology.

[12]  D. Baylor,et al.  Recoverin Regulates Light-dependent Phosphodiesterase Activity in Retinal Rods , 2004, The Journal of general physiology.

[13]  P. Detwiler,et al.  The calcium feedback signal in the phototransduction cascade of vertebrate rods , 1994, Neuron.

[14]  M. Sowa,et al.  Acceleration of key reactions as a strategy to elucidate the rate-limiting chemistry underlying phototransduction inactivation. , 2003, Investigative ophthalmology & visual science.

[15]  N. Pullen,et al.  Cooperativity during multiple phosphorylations catalyzed by rhodopsin kinase: supporting evidence using synthetic phosphopeptides. , 1993, Biochemistry.

[16]  Jeannie Chen,et al.  Mouse models to study GCAP functions in intact photoreceptors. , 2002, Advances in experimental medicine and biology.

[17]  Krzysztof Palczewski,et al.  Organization of the G Protein-coupled Receptors Rhodopsin and Opsin in Native Membranes* , 2003, Journal of Biological Chemistry.

[18]  Y. Hao,et al.  Apoptosis: final common pathway of photoreceptor death in rd, rds, and rhodopsin mutant mice. , 1993, Neuron.

[19]  S. Lowen The Biophysical Journal , 1960, Nature.

[20]  Y. Tsukamoto The number, depth and elongation of disc incisures in the retinal rod of Rana catesbeiana. , 1987, Experimental eye research.

[21]  Fred Rieke,et al.  Origin and Functional Impact of Dark Noise in Retinal Cones , 2000, Neuron.

[22]  Daniele Andreucci,et al.  Modeling the role of incisures in vertebrate phototransduction. , 2006, Biophysical journal.

[23]  P. Schnetkamp Optical measurements of Na-Ca-K exchange currents in intact outer segments isolated from bovine retinal rods , 1991, The Journal of general physiology.

[24]  P. Bisegna,et al.  Homogenization and concentration of capacity in the rod outer segment with incisures , 2006 .

[25]  Y. Hao,et al.  Apoptosis: Final common pathway of photoreceptor death in rd, rds, and mutant mice , 1993, Neuron.

[26]  M. S. Eckmiller,et al.  Microtubules in a rod-specific cytoskeleton associated with outer segment incisures , 2000, Visual Neuroscience.

[27]  C. Makino,et al.  Enhanced Shutoff of Phototransduction in Transgenic Mice Expressing Palmitoylation-deficient Rhodopsin*♦ , 2005, Journal of Biological Chemistry.

[28]  Fred Rieke,et al.  Multiple Phosphorylation Sites Confer Reproducibility of the Rod's Single-Photon Responses , 2006, Science.

[29]  S. W. Hall,et al.  Phosphodiesterase activation by photoexcited rhodopsin is quenched when rhodopsin is phosphorylated and binds the intrinsic 48-kDa protein of rod outer segments. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[30]  D. Baylor,et al.  Responses of retinal rods to single photons. , 1979, The Journal of physiology.

[31]  P. Schnetkamp Cation selectivity of and cation binding to the cGMP-dependent channel in bovine rod outer segment membranes , 1990, The Journal of general physiology.

[32]  D. Holcman,et al.  Longitudinal diffusion in retinal rod and cone outer segment cytoplasm: the consequence of cell structure. , 2004, Biophysical journal.

[33]  Anirvan M. Sengupta,et al.  Engineering aspects of enzymatic signal transduction: photoreceptors in the retina. , 2000, Biophysical journal.

[34]  Vsevolod V. Gurevich,et al.  Each rhodopsin molecule binds its own arrestin , 2007, Proceedings of the National Academy of Sciences.

[35]  R L Sidman,et al.  Morphological, physiological, and biochemical changes in rhodopsin knockout mice. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[36]  A. Engel,et al.  Rhodopsin Signaling and Organization in Heterozygote Rhodopsin Knockout Mice* , 2004, Journal of Biological Chemistry.

[37]  W. G. Owen,et al.  Free calcium concentrations in bullfrog rods determined in the presence of multiple forms of Fura-2. , 1994, Biophysical journal.

[38]  T. Lamb,et al.  Variability in the Time Course of Single Photon Responses from Toad Rods Termination of Rhodopsin’s Activity , 1999, Neuron.

[39]  B. Sakitt Counting every quantum , 1972, The Journal of physiology.

[40]  Marie E. Burns,et al.  Rapid and Reproducible Deactivation of Rhodopsin Requires Multiple Phosphorylation Sites , 2000, Neuron.

[41]  Marie E. Burns,et al.  Dynamics of Cyclic GMP Synthesis in Retinal Rods , 2002, Neuron.

[42]  F. Lottspeich,et al.  Primary structure and functional expression of the Na/Ca,K‐exchanger from bovine rod photoreceptors. , 1992, The EMBO journal.

[43]  V. Arshavsky,et al.  Structure and function of the visual arrestin oligomer , 2007, The EMBO journal.

[44]  Edward N. Pugh,et al.  Chapter 5 Phototransduction in vertebrate rods and cones: Molecular mechanisms of amplification, recovery and light adaptation , 2000 .

[45]  D. Hood,et al.  Phototransduction in human cones measured using the a-wave of the ERG , 1995, Vision Research.

[46]  Marie E Burns,et al.  Prolonged Photoresponses and Defective Adaptation in Rods of Gβ5-/- Mice , 2003, The Journal of Neuroscience.

[47]  P. D. Calvert,et al.  Membrane protein diffusion sets the speed of rod phototransduction , 2001, Nature.

[48]  G. Fain,et al.  Bleached Pigment Produces a Maintained Decrease in Outer Segment Ca2+ in Salamander Rods , 1998, The Journal of general physiology.

[49]  F. Rieke,et al.  Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction. , 2005, Systems biology.

[50]  J B Hurley,et al.  Abnormal photoresponses and light-induced apoptosis in rods lacking rhodopsin kinase. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Vsevolod V Gurevich,et al.  Regulation of Arrestin Binding by Rhodopsin Phosphorylation Level* , 2007, Journal of Biological Chemistry.

[52]  Denis A. Baylor,et al.  Prolonged photoresponses in transgenic mouse rods lacking arrestin , 1997, Nature.

[53]  M. Lavail,et al.  Rods and cones in the mouse retina. II. Autoradiographic analysis of cell generation using tritiated thymidine , 1979, The Journal of comparative neurology.

[54]  D. Baylor,et al.  Role of guanylate cyclase-activating proteins (GCAPs) in setting the flash sensitivity of rod photoreceptors , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[55]  G. Fain,et al.  Opsin activation of transduction in the rods of dark‐reared Rpe65 knockout mice , 2005, The Journal of physiology.

[56]  U Wilden,et al.  Duration and amplitude of the light-induced cGMP hydrolysis in vertebrate photoreceptors are regulated by multiple phosphorylation of rhodopsin and by arrestin binding. , 1995, Biochemistry.

[57]  P. Detwiler,et al.  Longitudinal spread of second messenger signals in isolated rod outer segments of lizards , 1999, The Journal of physiology.

[58]  J H Parkes,et al.  Phosphorylation modulates the affinity of light-activated rhodopsin for G protein and arrestin. , 2000, Biochemistry.

[59]  P. Mcnaughton,et al.  Calcium homeostasis in the outer segments of retinal rods from the tiger salamander. , 1992, The Journal of physiology.

[60]  D. Baylor,et al.  Two components of electrical dark noise in toad retinal rod outer segments. , 1980, The Journal of physiology.

[61]  Daniele Andreucci,et al.  Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction , 2003 .

[62]  J Honerkamp,et al.  Stochastic simulation of the transducin GTPase cycle. , 1996, Biophysical journal.

[63]  H. W. Veen,et al.  Handbook of Biological Physics , 1996 .

[64]  A. Engel,et al.  Atomic-force microscopy: Rhodopsin dimers in native disc membranes , 2003, Nature.

[65]  D. Baylor,et al.  The photocurrent, noise and spectral sensitivity of rods of the monkey Macaca fascicularis. , 1984, The Journal of physiology.

[66]  P. Liebman,et al.  Kinetic studies suggest that light-activated cyclic GMP phosphodiesterase is a complex with G-protein subunits. , 1986, Biochemistry.

[67]  D. Baylor,et al.  The membrane current of single rod outer segments , 1979, Vision Research.

[68]  P. Schnetkamp,et al.  Unidirectional Na+, Ca2+, and K+ fluxes through the bovine rod outer segment Na-Ca-K exchanger. , 1991, The Journal of biological chemistry.

[69]  T. Lamb,et al.  Cyclic GMP and calcium: The internal messengers of excitation and adaptation in vertebrate photoreceptors , 1990, Vision Research.

[70]  D. Baylor,et al.  Molecular origin of continuous dark noise in rod photoreceptors. , 1996, Biophysical journal.

[71]  J. Hurley,et al.  Light-Dependent Redistribution of Arrestin in Vertebrate Rods Is an Energy-Independent Process Governed by Protein-Protein Interactions , 2005, Neuron.

[72]  P. Schnetkamp Na-Ca or Na-Ca-K exchange in rod photoreceptors. , 1989, Progress in biophysics and molecular biology.

[73]  D. Papermaster,et al.  Cone lamellae and red and green rod outer segment disks contain a large intrinsic membrane protein on their margins: An ultrastructural immunocytochemical study of frog retinas , 1982, Vision Research.

[74]  David J. Baylor,et al.  Mechanisms of rhodopsin inactivation in vivo as revealed by a COOH-terminal truncation mutant , 1995, Science.

[75]  A. Cohen The ultrastructure of the rods of the mouse retina. , 1960, The American journal of anatomy.

[76]  M. Adamian,et al.  Cytoskeletal specializations at the rod photoreceptor distal tip , 1991, The Journal of comparative neurology.

[77]  P. Schnetkamp NaCa or NaCaK exchange in rod photoreceptors , 1989 .

[78]  G. Fain,et al.  Early receptor current of wild‐type and transducin knockout mice: photosensitivity and light‐induced Ca2+ release , 2004, The Journal of physiology.

[79]  E N Pugh,et al.  A quantitative account of the activation steps involved in phototransduction in amphibian photoreceptors. , 1992, The Journal of physiology.

[80]  U Wilden,et al.  Light-dependent phosphorylation of rhodopsin: number of phosphorylation sites. , 1982, Biochemistry.

[81]  K. Koch,et al.  Ca2+-dependent control of rhodopsin phosphorylation: recoverin and rhodopsin kinase. , 2002, Advances in experimental medicine and biology.

[82]  D. Baylor,et al.  Origin of reproducibility in the responses of retinal rods to single photons. , 1998, Biophysical journal.

[83]  S. Hecht,et al.  ENERGY, QUANTA, AND VISION , 1942, The Journal of general physiology.

[84]  Marie E. Burns,et al.  Novel Form of Adaptation in Mouse Retinal Rods Speeds Recovery of Phototransduction , 2003, The Journal of general physiology.

[85]  A. Milam,et al.  Rhodopsin Phosphorylation and Dephosphorylation in Vivo(*) , 1995, The Journal of Biological Chemistry.

[86]  E. Pugh Variability in Single Photon Responses A Cut in the Gordian Knot of Rod Phototransduction? , 1999, Neuron.

[87]  E. Pugh,et al.  Diffusion coefficient of cyclic GMP in salamander rod outer segments estimated with two fluorescent probes. , 1993, Biophysical journal.

[88]  T. Lamb,et al.  The Role of Steady Phosphodiesterase Activity in the Kinetics and Sensitivity of the Light-Adapted Salamander Rod Photoresponse , 2000, The Journal of general physiology.

[89]  E. N. Pugh,et al.  The control of phosphodiesterase in rod disk membranes: Kinetics, possible mechanisms and significance for vision , 1979, Vision Research.

[90]  M. Lavail,et al.  Rods and cones in the mouse retina. I. Structural analysis using light and electron microscopy , 1979, The Journal of comparative neurology.

[91]  E. Pugh,et al.  The kinetics of inactivation of the rod phototransduction cascade with constant Ca2+i , 1996, The Journal of general physiology.

[92]  Donald L. Miller,et al.  Cytoplasmic free calcium concentration in dark-adapted retinal rod outer segments , 1989, Vision Research.

[93]  T. Lamb,et al.  The Gain of Rod Phototransduction Reconciliation of Biochemical and Electrophysiological Measurements , 2000, Neuron.

[94]  N. Engheta,et al.  Kinetics of Recovery of the Dark-adapted Salamander Rod Photoresponse , 1998, The Journal of general physiology.

[95]  D. Baylor,et al.  Single-photon detection by rod cells of the retina , 1998 .

[96]  D. Baylor,et al.  Role for the target enzyme in deactivation of photoreceptor G protein in vivo. , 1998, Science.

[97]  R. Payne,et al.  The concentration of cytosolic free calcium in vertebrate rod outer segments measured with fura-2 , 1988, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[98]  E. Pugh,et al.  Photoreceptor Guanylate Cyclases: A Review , 1997, Bioscience reports.

[99]  M. Sokolov,et al.  Arrestin Translocation Is Induced at a Critical Threshold of Visual Signaling and Is Superstoichiometric to Bleached Rhodopsin , 2006, The Journal of Neuroscience.

[100]  Y. Koutalos,et al.  Cyclic GMP diffusion coefficient in rod photoreceptor outer segments. , 1995, Biophysical journal.

[101]  Anirvan M. Sengupta,et al.  G-protein-coupled enzyme cascades have intrinsic properties that improve signal localization and fidelity. , 2005, Biophysical journal.

[102]  K. Donner,et al.  Low retinal noise in animals with low body temperature allows high visual sensitivity , 1988, Nature.

[103]  E. Pugh,et al.  Recovery phase of the murine rod photoresponse reconstructed from electroretinographic recordings , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[104]  B. Litman,et al.  Isolation and identification of the phosphorylated species of rhodopsin. , 1984, Biochemistry.

[105]  Yiannis Koutalos,et al.  Calcium diffusion coefficient in rod photoreceptor outer segments. , 2002, Biophysical journal.