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Abtout A, Fain G, Reingruber J. Analysis of waveform and amplitude of mouse rod and cone flash responses. J Physiol 2021; 599:3295-3312. [PMID: 33977528 DOI: 10.1113/jp281225] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 04/28/2021] [Indexed: 12/14/2022] Open
Abstract
KEY POINTS Most vertebrate eyes have rod and cone photoreceptors, which use a signal transduction pathway consisting of many biological processes to transform light into an electrical response. We dissect and quantify the contribution of each of these processes to the photoreceptor light response by using a novel method of analysis that provides an analytical solution for the entire time course of the dim-flash light response. We find that the shape of the light response is exclusively controlled by deactivation parameters. Activation parameters scale this shape and alter the response amplitude. We show that the rising phase of the response depends on Ca2+ feedback, and we identify the deactivation parameters that control the recovery phase of the response. We devise new methods to extract values for deactivation and activation parameters from a separate analysis of response shape and response amplitude. ABSTRACT Vertebrate eyes have rod and cone photoreceptors, which use a complex transduction pathway comprising many biological processes to transform the absorption of light into an electrical response. A fundamental question in sensory transduction is how these processes contribute to the response. To study this question, we use a well-accepted phototransduction model, which we analyse with a novel method based on the log transform of the current. We derive an analytical solution that describes the entire time course of the photoreceptor response to dim flashes of light. We use this solution to dissect and quantify the contribution of each process to the response. We find that the entire dim-flash response is proportional to the flash intensity. By normalizing responses to unit amplitude, we define a waveform that is independent of the light intensity and characterizes the invariant shape of dim-flash responses. We show that this waveform is exclusively determined by deactivation rates; activation rates only scale the waveform and affect the amplitude. This analysis corrects a previous assumption that the rising phase is determined entirely by activation rates. We further show that the rising phase depends on Ca2+ feedback to the cyclase, contrary to current belief. We identify the deactivation rates that control the recovery phase of the response, and we devise new methods to extract activation and deactivation rates from an analysis of response shape and response amplitude. In summary, we provide a comprehensive understanding of how the various transduction processes produce the cellular response.
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Affiliation(s)
- Annia Abtout
- Institut de Biologie de l'École Normale Supérieure, Paris, France
| | - Gordon Fain
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California, USA.,Department of Ophthalmology and Stein Eye Institute, University of California, Los Angeles, California, USA
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Photoreceptor phosphodiesterase (PDE6): activation and inactivation mechanisms during visual transduction in rods and cones. Pflugers Arch 2021; 473:1377-1391. [PMID: 33860373 DOI: 10.1007/s00424-021-02562-x] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Revised: 03/27/2021] [Accepted: 03/30/2021] [Indexed: 01/16/2023]
Abstract
Rod and cone photoreceptors of the vertebrate retina utilize cGMP as the primary intracellular messenger for the visual signaling pathway that converts a light stimulus into an electrical response. cGMP metabolism in the signal-transducing photoreceptor outer segment reflects the balance of cGMP synthesis (catalyzed by guanylyl cyclase) and degradation (catalyzed by the photoreceptor phosphodiesterase, PDE6). Upon light stimulation, rapid activation of PDE6 by the heterotrimeric G-protein (transducin) triggers a dramatic drop in cGMP levels that lead to cell hyperpolarization. Following cessation of the light stimulus, the lifetime of activated PDE6 is also precisely regulated by additional processes. This review summarizes recent advances in the structural characterization of the rod and cone PDE6 catalytic and regulatory subunits in the context of previous biochemical studies of the enzymological properties and allosteric regulation of PDE6. Emphasis is given to recent advances in understanding the structural and conformational changes underlying the mechanism by which the activated transducin α-subunit binds to-and relieves inhibition of-PDE6 catalysis that is controlled by its intrinsically disordered, inhibitory γ-subunit. The role of the regulator of G-protein signaling 9-1 (RGS9-1) in regulating the lifetime of the transducin-PDE6 is also briefly covered. The therapeutic potential of pharmacological compounds acting as inhibitors or activators targeting PDE6 is discussed in the context of inherited retinal diseases resulting from mutations in rod and cone PDE6 genes as well as other inherited defects that arise from excessive cGMP accumulation in retinal photoreceptor cells.
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Arshavsky VY, Wensel TG. Timing is everything: GTPase regulation in phototransduction. Invest Ophthalmol Vis Sci 2013; 54:7725-33. [PMID: 24265205 DOI: 10.1167/iovs.13-13281] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
As the molecular mechanisms of vertebrate phototransduction became increasingly clear in the 1980s, a persistent problem was the discrepancy between the slow GTP hydrolysis catalyzed by the phototransduction G protein, transducin, and the much more rapid physiological recovery of photoreceptor cells from light stimuli. Beginning with a report published in 1989, a series of studies revealed that transducin GTPase activity could approach the rate needed to explain physiological recovery kinetics in the presence of one or more factors present in rod outer segment membranes. One by one, these factors were identified, beginning with PDEγ, the inhibitory subunit of the cGMP phosphodiesterase activated by transducin. There followed the discovery of the crucial role played by the regulator of G protein signaling, RGS9, a member of a ubiquitous family of GTPase-accelerating proteins, or GAPs, for heterotrimeric G proteins. Soon after, the G protein β isoform Gβ5 was identified as an obligate partner subunit, followed by the discovery or R9AP, a transmembrane protein that anchors the RGS9 GAP complex to the disk membrane, and is essential for the localization, stability, and activity of this complex in vivo. The physiological importance of all of the members of this complex was made clear first by knockout mouse models, and then by the discovery of a human visual defect, bradyopsia, caused by an inherited deficiency in one of the GAP components. Further insights have been gained by high-resolution crystal structures of subcomplexes, and by extensive mechanistic studies both in vitro and in animal models.
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Affiliation(s)
- Vadim Y Arshavsky
- Albert Eye Research Institute, Duke University, Durham, North Carolina
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Makino CL, Wen XH, Olshevskaya EV, Peshenko IV, Savchenko AB, Dizhoor AM. Enzymatic relay mechanism stimulates cyclic GMP synthesis in rod photoresponse: biochemical and physiological study in guanylyl cyclase activating protein 1 knockout mice. PLoS One 2012; 7:e47637. [PMID: 23082185 PMCID: PMC3474714 DOI: 10.1371/journal.pone.0047637] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Accepted: 09/13/2012] [Indexed: 12/21/2022] Open
Abstract
Regulation of cGMP synthesis by retinal membrane guanylyl cyclase isozymes (RetGC1 and RetGC2) in rod and cone photoreceptors by calcium-sensitive guanylyl cyclase activating proteins (GCAP1 and GCAP2) is one of the key molecular mechanisms affecting the response to light and is involved in congenital retinal diseases. The objective of this study was to identify the physiological sequence of events underlying RetGC activation in vivo, by studying the electrophysiological and biochemical properties of mouse rods in a new genetic model lacking GCAP1. The GCAP1−/− retinas expressed normal levels of RetGC isozymes and other phototransduction proteins, with the exception of GCAP2, whose expression was elevated in a compensatory fashion. RetGC activity in GCAP1−/− retinas became more sensitive to Ca2+ and slightly increased. The bright flash response in electroretinogram (ERG) recordings recovered quickly in GCAP1−/−, as well as in RetGC1−/−GCAP1−/−, and RetGC2−/−GCAP1−/− hybrid rods, indicating that GCAP2 activates both RetGC isozymes in vivo. Individual GCAP1−/− rod responses varied in size and shape, likely reflecting variable endogenous GCAP2 levels between different cells, but single-photon response (SPR) amplitude and time-to-peak were typically increased, while recovery kinetics remained faster than in wild type. Recovery from bright flashes in GCAP1−/− was prominently biphasic, because rare, aberrant SPRs producing the slower tail component were magnified. These data provide strong physiological evidence that rod photoresponse recovery is shaped by the sequential recruitment of RetGC isozyme activation by GCAPs according to the different GCAP sensitivities for Ca2+ and specificities toward RetGC isozymes. GCAP1 is the ‘first-response’ sensor protein that stimulates RetGC1 early in the response and thus limits the SPR amplitude, followed by activation of GCAP2 that adds stimulation of both RetGC1 and RetGC2 to speed-up photoreceptor recovery.
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Affiliation(s)
- Clint L. Makino
- Department of Ophthalmology, Massachusetts Eye and Ear Infirmary and Harvard Medical School, Boston, Massachusetts, United States of America
| | - Xiao-Hong Wen
- Department of Ophthalmology, Massachusetts Eye and Ear Infirmary and Harvard Medical School, Boston, Massachusetts, United States of America
| | - Elena V. Olshevskaya
- Department of Basic Sciences and Pennsylvania College of Optometry, Salus University, Elkins Park, Pennsylvania, United States of America
| | - Igor V. Peshenko
- Department of Basic Sciences and Pennsylvania College of Optometry, Salus University, Elkins Park, Pennsylvania, United States of America
| | - Andrey B. Savchenko
- Department of Basic Sciences and Pennsylvania College of Optometry, Salus University, Elkins Park, Pennsylvania, United States of America
| | - Alexander M. Dizhoor
- Department of Basic Sciences and Pennsylvania College of Optometry, Salus University, Elkins Park, Pennsylvania, United States of America
- * E-mail:
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5
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Arshavsky VY, Burns ME. Photoreceptor signaling: supporting vision across a wide range of light intensities. J Biol Chem 2011; 287:1620-6. [PMID: 22074925 DOI: 10.1074/jbc.r111.305243] [Citation(s) in RCA: 148] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
For decades, photoreceptors have been an outstanding model system for elucidating basic principles in sensory transduction and biochemistry and for understanding many facets of neuronal cell biology. In recent years, new knowledge of the kinetics of signaling and the large-scale movements of proteins underlying signaling has led to a deeper appreciation of the photoreceptor's unique challenge in mediating the first steps in vision over a wide range of light intensities.
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Affiliation(s)
- Vadim Y Arshavsky
- Departments of Ophthalmology and Pharmacology, Duke University, Durham, North Carolina 27710, USA.
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6
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Abstract
A fundamental question of cell signaling biology is how faint external signals produce robust physiological responses. One universal mechanism relies on signal amplification via intracellular cascades mediated by heterotrimeric G-proteins. This high amplification system allows retinal rod photoreceptors to detect single photons of light. Although much is now known about the role of the α-subunit of the rod-specific G-protein transducin in phototransduction, the physiological function of the auxiliary βγ-complex in this process remains a mystery. Here, we show that elimination of the transducin γ-subunit drastically reduces signal amplification in intact mouse rods. The consequence is a striking decline in rod visual sensitivity and severe impairment of nocturnal vision. Our findings demonstrate that transducin βγ-complex controls signal amplification of the rod phototransduction cascade and is critical for the ability of rod photoreceptors to function in low light conditions.
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Astakhova LA, Firsov ML, Govardovskii VI. Kinetics of turn-offs of frog rod phototransduction cascade. ACTA ACUST UNITED AC 2009; 132:587-604. [PMID: 18955597 PMCID: PMC2571975 DOI: 10.1085/jgp.200810034] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
The time course of the light-induced activity of phototrandsuction effector enzyme cGMP-phosphodiesterase (PDE) is shaped by kinetics of rhodopsin and transducin shut-offs. The two processes are among the key factors that set the speed and sensitivity of the photoresponse and whose regulation contributes to light adaptation. The aim of this study was to determine time courses of flash-induced PDE activity in frog rods that were dark adapted or subjected to nonsaturating steady background illumination. PDE activity was computed from the responses recorded from solitary rods with the suction pipette technique in Ca2+-clamping solution. A flash applied in the dark-adapted state elicits a wave of PDE activity whose rising and decaying phases have characteristic times near 0.5 and 2 seconds, respectively. Nonsaturating steady background shortens both phases roughly to the same extent. The acceleration may exceed fivefold at the backgrounds that suppress ≈70% of the dark current. The time constant of the process that controls the recovery from super-saturating flashes (so-called dominant time constant) is adaptation independent and, hence, cannot be attributed to either of the processes that shape the main part of the PDE wave. We hypothesize that the dominant time constant in frog rods characterizes arrestin binding to rhodopsin partially inactivated by phosphorylation. A mathematical model of the cascade that considers two-stage rhodopsin quenching and transducin inactivation can mimic experimental PDE activity quite well. The effect of light adaptation on the PDE kinetics can be reproduced in the model by concomitant acceleration on both rhodopsin phosphorylation and transducin turn-off, but not by accelerated arrestin binding. This suggests that not only rhodopsin but also transducin shut-off is under adaptation control.
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Affiliation(s)
- Luba A Astakhova
- Sechenov Institute for Evolutionary Physiology & Biochemistry, Russian Academy of Sciences, 194223 St. Petersburg, Russia
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Zhang XJ, Cahill KB, Elfenbein A, Arshavsky VY, Cote RH. Direct allosteric regulation between the GAF domain and catalytic domain of photoreceptor phosphodiesterase PDE6. J Biol Chem 2008; 283:29699-705. [PMID: 18779324 DOI: 10.1074/jbc.m803948200] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Photoreceptor cGMP phosphodiesterase (PDE6) is the central enzyme in the visual transduction cascade. The PDE6 catalytic subunit contains a catalytic domain and regulatory GAF domains. Unlike most GAF domain-containing cyclic nucleotide phosphodiesterases, little is known about direct allosteric communication of PDE6. In this study, we demonstrate for the first time direct, inter-domain allosteric communication between the GAF and catalytic domains in PDE6. The binding affinity of PDE6 for pharmacological inhibitors or for the C-terminal region of the inhibitory gamma subunit (Pgamma), known to directly inhibit PDE6 catalysis, was increased approximately 2-fold by ligands binding to the GAF domain. Binding of the N-terminal half of Pgamma to the GAF domains suffices to induce this allosteric effect. Allosteric communication between GAF and catalytic domains is reciprocal, in that drug binding to the catalytic domain slowed cGMP dissociation from the GAF domain. Although cGMP hydrolysis was not affected by binding of Pgamma1-60, Pgamma lacking its last seven amino acids decreased the Michaelis constant of PDE6 by 2.5-fold. Pgamma1-60 binding to the GAF domain increased vardenafil but not cGMP affinity, indicating that substrate- and inhibitor-binding sites do not totally overlap. In addition, prolonged incubation of PDE6 with vardenafil or sildenafil (but not 3-isobutyl-1-methylxanthine and zaprinast) induced a distinct conformational change in the catalytic domain without affecting the binding properties of the GAF domains. We conclude that although Pgamma-mediated regulation plays the dominant role in visual excitation, the direct, inter-domain allosteric regulation described in this study may play a feedback role in light adaptational processes during phototransduction.
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Affiliation(s)
- Xiu-Jun Zhang
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham, New Hampshire 03824, USA
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9
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Abstract
Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.
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Affiliation(s)
- H P Snippe
- Department of Neurobiophysics, University of Groningen, Groningen, The Netherlands.
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10
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Bui BV, Fortune B. Origin of electroretinogram amplitude growth during light adaptation in pigmented rats. Vis Neurosci 2006; 23:155-67. [PMID: 16638169 DOI: 10.1017/s0952523806232024] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2004] [Accepted: 02/06/2006] [Indexed: 11/06/2022]
Abstract
We assessed the growth of the rat photopic electroretinogram (ERG) during light adaptation and the mechanisms underlying this process. Full field ERG responses were recorded from anesthetized adult Brown-Norway rats at each minute for 20 min of light adaptation (backgrounds: 1.8, 2.1, 2.4 log scotopic cd m(-2)). The rat photopic b-wave amplitude increased with duration of light adaptation and its width at 33% maximal amplitude narrowed (by approximately 40 ms). These effects peaked 12-15 min after background onset. The narrowing of the b-wave reflected steepening of the b-wave recovery phase, with little change in the rising phase. OP amplitudes grew in proportion to the b-wave. Inhibition of inner retinal responses using TTX resulted in a greater relative growth of b-wave and OP amplitude compared with fellow control eyes, and delayed the change in recovery phase by approximately 5 min. Inhibition of all ionotropic glutamate receptors with CNQX/D-AP7 delayed both rising and recovery phases equally (approximately 12 ms) without altering b-wave width or the time course of adaptation changes. These outcomes suggest that inner retinal light responses are not directly responsible for b-wave amplitude growth, but may contribute to the change in its recovery phase during adaptation. A TTX-sensitive mechanism may help to hasten this process. The cone a-wave was isolated using PDA/L-AP4 or CNQX/L-AP4. A-wave amplitude (35 ms after stimulus onset) also increased with time during light adaptation and reached a maximum (130 +/- 29% above baseline) 12-15 min after background onset. B-wave amplitude growth in fellow control eyes closely followed the course and relative magnitude of cone a-wave amplitude growth. Hence, the increase of the cone response during light adaptation is sufficient to explain b-wave amplitude growth.
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Affiliation(s)
- Bang V Bui
- Discoveries in Sight, Devers Eye Institute, Legacy Health System, Portland, Oregon 97232, USA
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Strissel KJ, Lishko PV, Trieu LH, Kennedy MJ, Hurley JB, Arshavsky VY. Recoverin undergoes light-dependent intracellular translocation in rod photoreceptors. J Biol Chem 2005; 280:29250-5. [PMID: 15961391 DOI: 10.1074/jbc.m501789200] [Citation(s) in RCA: 81] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Photoreceptor cells have a remarkable capacity to adapt the sensitivity and speed of their responses to ever changing conditions of ambient illumination. Recent studies have revealed that a major contributor to this adaptation is the phenomenon of light-driven translocation of key signaling proteins into and out of the photoreceptor outer segment, the cellular compartment where phototransduction takes place. So far, only two such proteins, transducin and arrestin, have been established to be involved in this mechanism. To investigate the extent of this phenomenon we examined additional photoreceptor proteins that might undergo light-driven translocation, focusing on three Ca(2+)-binding proteins, recoverin and guanylate cyclase activating proteins 1 (GCAP1) and GCAP2. The changes in the subcellular distribution of each protein were assessed quantitatively using a recently developed technique combining serial tangential sectioning of mouse retinas with Western blot analysis of the proteins in the individual sections. Our major finding is that light causes a significant reduction of recoverin in rod outer segments, accompanied by its redistribution toward rod synaptic terminals. In both cases the majority of recoverin was found in rod inner segments, with approximately 12% present in the outer segments in the dark and less than 2% remaining in that compartment in the light. We suggest that recoverin translocation is adaptive because it may reduce the inhibitory constraint that recoverin imposes on rhodopsin kinase, an enzyme responsible for quenching the photo-excited rhodopsin during the photoresponse. To the contrary, no translocation of rhodopsin kinase itself or either GCAP was identified.
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Affiliation(s)
- Katherine J Strissel
- Department of Ophthalmology, Harvard Medical School and the Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA
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12
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Jarvinen JLP, Lamb TD. Inverted photocurrent responses from amphibian rod photoreceptors: role of membrane voltage in response recovery. J Physiol 2005; 566:455-66. [PMID: 15919708 PMCID: PMC1464743 DOI: 10.1113/jphysiol.2005.090258] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022] Open
Abstract
We recorded photocurrent responses of retinal rods isolated from cane toads Bufo marinus and clawed frogs Xenopus laevis. With the outer segment drawn part way into the suction pipette, presentation of flashes to the base of the outer segment (outside the pipette) elicited a slow inverted response. Stimulation of the same region, with the outer segment drawn fully in, gave a response of conventional polarity. For moderate to bright flashes a fast transient preceded the slow inverted response. Upon bleaching the tip of the outer segment, the slow inverted response was abolished but the fast initial transient remained, and we attribute this fast component to a capacitive current. Experiments employing simultaneous whole-cell patch-clamp and suction pipette recording revealed that both the fast and slow components of the inverted responses were absent in voltage-clamped cells. In current-clamped cells the slow inverted current response was delayed substantially with respect to the voltage response. We present a computational model for the slow component, in which hyperpolarization leads to increased activity of the Na+ -Ca2+, K+ exchanger, hence lowering the cytoplasmic Ca2+ concentration, activating guanylyl cyclase, raising cyclic GMP concentration, opening cyclic nucleotide-gated channels, and increasing circulating current in the unstimulated region. For the measured voltage response to stimulation of the base, we solve these equations to predict the photocurrent in the tip, and obtain an adequate explanation of the inverted responses. Our work suggests a novel role for membrane voltage in accelerating the inactivation phase of the response to light.
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Affiliation(s)
- Jaakko L P Jarvinen
- Physiological Laboratory, University of Cambridge, Downing Street, Cambridge CB2 3EG, UK.
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Solessio E, Mani SS, Cuenca N, Engbretson GA, Barlow RB, Knox BE. Developmental regulation of calcium-dependent feedback in Xenopus rods. ACTA ACUST UNITED AC 2005; 124:569-85. [PMID: 15504902 PMCID: PMC2234010 DOI: 10.1085/jgp.200409162] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
The kinetics of activation and inactivation in the phototransduction pathway of developing Xenopus rods were studied. The gain of the activation steps in transduction (amplification) increased and photoresponses became more rapid as the rods matured from the larval to the adult stage. The time to peak was significantly shorter in adults (1.3 s) than tadpoles (2 s). Moreover, adult rods recovered twice as fast from saturating flashes than did larval rods without changes of the dominant time constant (2.5 s). Guanylate cyclase (GC) activity, determined using IBMX steps, increased in adult rods from ∼1.1 s−1 to 3.7 s−1 5 s after a saturating flash delivering 6,000 photoisomerizations. In larval rods, it increased from 1.8 s−1 to 4.0 s−1 9 s after an equivalent flash. However, the ratio of amplification to the measured dark phosphodiesterase activity was constant. Guanylate cyclase–activating protein (GCAP1) levels and normalized Na+/Ca2+, K+ exchanger currents were increased in adults compared with tadpoles. Together, these results are consistent with the acceleration of the recovery phase in adult rods via developmental regulation of calcium homeostasis. Despite these large changes, the single photon response amplitude was ∼0.6 pA throughout development. Reduction of calcium feedback with BAPTA increased adult single photon response amplitudes threefold and reduced its cutoff frequency to that observed with tadpole rods. Linear mathematical modeling suggests that calcium-dependent feedback can account for the observed differences in the power spectra of larval and adult rods. We conclude that larval Xenopus maximize sensitivity at the expense of slower response kinetics while adults maximize response kinetics at the expense of sensitivity.
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Affiliation(s)
- Eduardo Solessio
- Center for Vision Research, Weiskotten Hall, SUNY Upstate Medical University, 750 East Adams St., Syracuse, NY 13210, USA.
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Peshenko IV, Moiseyev GP, Olshevskaya EV, Dizhoor AM. Factors that determine Ca2+ sensitivity of photoreceptor guanylyl cyclase. Kinetic analysis of the interaction between the Ca2+-bound and the Ca2+-free guanylyl cyclase activating proteins (GCAPs) and recombinant photoreceptor guanylyl cyclase 1 (RetGC-1). Biochemistry 2004; 43:13796-804. [PMID: 15504042 DOI: 10.1021/bi048943m] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We explored the possibility that, in the regulation of an effector enzyme by a Ca(2+)-sensor protein, the actual Ca(2+) sensitivity of the effector enzyme can be determined not only by the affinity of the Ca(2+)-sensor protein for Ca(2+) but also by the relative affinities of its Ca(2+)-bound versus Ca(2+)-free form for the effector enzyme. As a model, we used Ca(2+)-sensitive activation of photoreceptor guanylyl cyclase (RetGC-1) by guanylyl cyclase activating proteins (GCAPs). A substitution Arg(838)Ser in RetGC-1 found in human patients with cone-rod dystrophy is known to shift the Ca(2+) sensitivity of RetGC-1 regulation by GCAP-1 to a higher Ca(2+) range. We find that at physiological concentrations of Mg(2+) this mutation increases the free Ca(2+) concentration required for half-maximal inhibition of the cyclase from 0.27 to 0.61 microM. Similar to rod outer segment cyclase, Ca(2+) sensitivity of recombinant RetGC-1 is strongly affected by Mg(2+), but the shift in Ca(2+) sensitivity for the R838S mutant relative to the wild type is Mg(2+)-independent. We determined the apparent affinity of the wild-type and the mutant RetGC-1 for both Ca(2+)-bound and Ca(2+)-free GCAP-1 and found that the net shift in Ca(2+) sensitivity of the R838S RetGC-1 observed in vitro can arise predominantly from the change in the affinity of the mutant cyclase for the Ca(2+)-free versus Ca(2+)-loaded GCAP-1. Our findings confirm that the dynamic range for RetGC regulation by Ca(2+)/GCAP is determined by both the affinity of GCAP for Ca(2+) and relative affinities of the effector enzyme for the Ca(2+)-free versus Ca(2+)-loaded GCAP.
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Affiliation(s)
- Igor V Peshenko
- The Hafter Research Laboratory, Pennsylvania College of Optometry, Elkins Park, Pennsylvania 19027-1598, USA
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15
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Kennedy MJ, Dunn FA, Hurley JB. Visual pigment phosphorylation but not transducin translocation can contribute to light adaptation in zebrafish cones. Neuron 2004; 41:915-28. [PMID: 15046724 DOI: 10.1016/s0896-6273(04)00086-8] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2003] [Revised: 12/22/2003] [Accepted: 02/03/2004] [Indexed: 11/20/2022]
Abstract
The ability of cone photoreceptors to adapt to light is extraordinary. In this study we evaluated two biochemical processes, visual pigment phosphorylation and transducin translocation, for their ability to contribute to light adaptation in zebrafish cones. Since cytoplasmic Ca2+ regulates light adaptation, the sensitivities of these processes to both light and Ca2+ were examined. Cytoplasmic Ca2+ regulates the sites of light-stimulated phosphorylation. Unexpectedly, we found that Ca2+ also regulates the extent of phosphorylation of unbleached cone pigments. Immunocytochemical analyses revealed that neither light nor cytoplasmic Ca2+ influences the localization of transducin in zebrafish cones.
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Affiliation(s)
- Matthew J Kennedy
- Department of Biochemistry, Box 357350, University of Washington, Seattle, WA 98195, USA
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Peshenko IV, Dizhoor AM. Guanylyl cyclase-activating proteins (GCAPs) are Ca2+/Mg2+ sensors: implications for photoreceptor guanylyl cyclase (RetGC) regulation in mammalian photoreceptors. J Biol Chem 2004; 279:16903-6. [PMID: 14993224 DOI: 10.1074/jbc.c400065200] [Citation(s) in RCA: 83] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Guanylyl cyclase-activating proteins (GCAP) are EF-hand Ca(2+)-binding proteins that activate photoreceptor guanylyl cyclase (RetGC) in the absence of Ca(2+) and inhibit RetGC in a Ca(2+)-sensitive manner. The reported data for the RetGC inhibition by Ca(2+)/GCAPs in vitro are in disagreement with the free Ca(2+) levels found in mammalian photoreceptors (Woodruff, M. L., Sampath, A. P., Matthews, H. R., Krasnoperova, N. V., Lem, J., and Fain, G. L. (2002) J. Physiol. (Lond.) 542, 843-854). We have found that binding of Mg(2+) dramatically affects both Ca(2+)-dependent conformational changes in GCAP-1 and Ca(2+) sensitivity of RetGC regulation by GCAP-1 and GCAP-2. Lowering free Mg(2+) concentrations ([Mg](f)) from 5.0 mm to 0.5 mm decreases the free Ca(2+) concentration required for half-maximal inhibition of RetGC ([Ca]((1/2))) by recombinant GCAP-1 and GCAP-2 from 1.3 and 0.2 microm to 0.16 and 0.03 microm, respectively. A similar effect of Mg(2+) on Ca(2+) sensitivity of RetGC by endogenous GCAPs was observed in mouse retina. Analysis of the [Ca]((1/2)) changes as a function of [Mg](f) in mouse retina shows that the [Ca]((1/2)) becomes consistent with the range of 23-250 nm free Ca(2+) found in mouse photoreceptors only if the [Mg](f) in the photoreceptors is near 1 mm. Our data demonstrate that GCAPs are Ca(2+)/Mg(2+) sensor proteins. While Ca(2+) binding is essential for cyclase activation and inhibition, Mg(2+) binding to GCAPs is critical for setting the actual dynamic range of RetGC regulation by GCAPs at physiological levels of free Ca(2+).
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Affiliation(s)
- Igor V Peshenko
- Hafter Research Laboratory, Pennsylvania College of Optometry, Elkins Park, Pennsylvania 19027
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17
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Calvert PD, Makino CL. The time course of light adaptation in vertebrate retinal rods. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2003; 514:37-60. [PMID: 12596914 DOI: 10.1007/978-1-4615-0121-3_3] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
The photoresponse of a rod wanes over time in steady illumination, as light loses its efficacy in generating the response. Such desensitization is adaptive because it extends the range of ambient light levels over which the rod signals changes in light intensity by several orders of magnitude. Adaptation begins to unfold rapidly after the onset of light with a time constant of approximately 1 s, causing the rod's sensitivity to steady light to decrease by nearly two log units. Thereafter, a much slower phase of adaptation evolves with a time constant of 9 s. During this phase the rod's sensitivity decreases by an additional log unit. Both phases are dependent upon the light-induced fall in intracellular Ca2+. The fast phase of light adaptation can be attributed to Ca2+ feedback processes regulating the lifetime ofphotoactivated rhodopsin, cGMP synthesis and sensitivity of the cGMP-gated channel to cGMP. Although the mechanism(s) of the slow phase is not yet known, it appears to include further regulation of the lifetime of photoactivated rhodopsin.
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Affiliation(s)
- Peter D Calvert
- Department of Ophthalmology, Harvard Medical School and the Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA.
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18
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Koch KW. Target recognition of guanylate cyclase by guanylate cyclase-activating proteins. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2003; 514:349-60. [PMID: 12596932 DOI: 10.1007/978-1-4615-0121-3_21] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/01/2023]
Abstract
Guanylate cyclase-activating proteins (GCAPs) control the activity of membrane bound guanylate cyclases in vertebrate photoreceptor cells. They form a permanent complex with guanylate cyclase 1 (ROS-GC1) at low and high Ca2+-concentrations. Five different target regions of GCAP-1 have been identified in ROS-GC1 at rather distant sites. These findings could indicate a multipoint attachment site for GCAP-1 or, alternatively, the presence of transient binding sites with short contact to GCAP-1. In addition some data are consistent with the operation of one or more transducer units, that represent regulatory regions without being direct binding sites. A permanent ROS-GC1/GCAP-1 complex is physiologically significant, since it allows a very short response time of cyclase activity when the intracellular Ca2+-concentration changes. Thereby, activation of cyclase participates in speeding up the recovery of the photoresponse after illumination and restores the circulating dark current.
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Affiliation(s)
- Karl-Wilhelm Koch
- Institut für Biologische Informationsverarbeitung 1, Forschungszentrum Jülich, D-52425 Jülich, Germany.
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19
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Abstract
In retinal rods, Ca(2+) exerts negative feedback control on cGMP synthesis by guanylate cyclase (GC). This feedback loop was disrupted in mouse rods lacking guanylate cyclase activating proteins GCAP1 and GCAP2 (GCAPs(-/-)). Comparison of the behavior of wild-type and GCAPs(-/-) rods allowed us to investigate the role of the feedback loop in normal rod function. We have found that regulation of GC is apparently the only Ca(2+) feedback loop operating during the single photon response. Analysis of the rods' light responses and cellular dark noise suggests that GC normally responds to light-driven changes in [Ca(2+)] rapidly and highly cooperatively. Rapid feedback to GC speeds the rod's temporal responsiveness and improves its signal-to-noise ratio by minimizing fluctuations in cGMP.
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Affiliation(s)
- Marie E Burns
- Department of Neurobiology, Stanford University Medical Center, Stanford, CA 94305, USA.
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20
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Paglia MJ, Mou H, Cote RH. Regulation of photoreceptor phosphodiesterase (PDE6) by phosphorylation of its inhibitory gamma subunit re-evaluated. J Biol Chem 2002; 277:5017-23. [PMID: 11741972 DOI: 10.1074/jbc.m106328200] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Phosphorylation of the inhibitory gamma subunit (Pgamma) of rod cGMP phosphodiesterase (PDE6) has been reported to turn off visual excitation without the requirement for inactivation of the photoreceptor G-protein transducin. We evaluated the significance of Pgamma phosphorylation for PDE6 regulation by preparing Pgamma stoichiometrically phosphorylated at Thr(22) or at Thr(35). Phosphorylation of Pgamma at either residue caused a minor decrease--not the previously reported increase--in the ability of Pgamma to inhibit catalysis at the active site of purified PDE6 catalytic dimers. Likewise, Pgamma phosphorylation had little effect on its potency to inhibit transducin-activated PDE6 depleted of its endogenous Pgamma subunits. The strength of Pgamma interaction with the regulatory GAF domain of PDE6 was reduced severalfold upon Pgamma phosphorylation at Thr(22) (but not Thr(35)), as judged by allosteric changes in cGMP binding to these noncatalytic sites on the enzyme (Mou, H., and Cote, R. H. (2001) J. Biol. Chem. 276, 27527-27534). In contrast, the effects of Pgamma phosphorylation on its interactions with activated transducin were much more pronounced. Phosphorylation of Pgamma at either Thr(22) or Thr(35) greatly diminished its ability to bind activated transducin, consistent with earlier work. In situ phosphorylation of Pgamma by endogenous rod outer segment kinases was enhanced severalfold upon light activation, but only approximately 10% of the endogenous Pgamma was phosphorylated. This is attributed to Pgamma being a poor substrate for protein kinases when associated with the PDE6 holoenzyme. We conclude that, contrary to previous reports, Pgamma phosphorylation at either Thr(22) or Thr(35) modestly weakens its direct interactions with PDE6. However, Pgamma phosphorylation subsequent to its dissociation from PDE6 is likely to abolish its binding to activated transducin and may serve to make phosphorylated Pgamma available to regulate other signal transduction pathways (e.g. mitogen-activated protein kinase; Wan, K. F., Sambi, B. S., Frame, M., Tate, R., and Pyne, N. J. (2001) J. Biol. Chem. 276, 37802-37808) in photoreceptor cells.
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Affiliation(s)
- Michael J Paglia
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham, New Hampshire 03824-2617, USA
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21
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Abstract
Vertebrate rod photoreceptors adjust their sensitivity as they adapt during exposure to steady light. Light adaptation prevents the rod from saturating and significantly extends its dynamic range. We examined the time course of the onset of light adaptation in bullfrog rods and compared it with the projected onset of feedback reactions thought to underlie light adaptation on the molecular level. We found that adaptation developed in two distinct temporal phases: (1) a fast phase that operated within seconds after the onset of illumination, which is consistent with most previous reports of a 1-2-s time constant for the onset of adaptation; and (2) a slow phase that engaged over tens of seconds of continuous illumination. The fast phase desensitized the rods as much as 80-fold, and was observed at every light intensity tested. The slow phase was observed only at light intensities that suppressed more than half of the dark current. It provided an additional sensitivity loss of up to 40-fold before the rod saturated. Thus, rods achieved a total degree of adaptation of approximately 3,000-fold. Although the fast adaptation is likely to originate from the well characterized Ca(2+)-dependent feedback mechanisms regulating the activities of several phototransduction cascade components, the molecular mechanism underlying slow adaptation is unclear. We tested the hypothesis that the slow adaptation phase is mediated by cGMP dissociation from noncatalytic binding sites on the cGMP phosphodiesterase, which has been shown to reduce the lifetime of activated phosphodiesterase in vitro. Although cGMP dissociated from the noncatalytic binding sites in intact rods with kinetics approximating that for the slow adaptation phase, this hypothesis was ruled out because the intensity of light required for cGMP dissociation far exceeded that required to evoke the slow phase. Other possible mechanisms are discussed.
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Affiliation(s)
- Peter D Calvert
- Department of Ophthalmology, Harvard Medical School, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA.
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22
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Affiliation(s)
- James B Hurley
- Department of Biochemistry, University of Washington, Seattle, WA 91895, USA
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23
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Balasubramanian N, Levay K, Keren-Raifman T, Faurobert E, Slepak VZ. Phosphorylation of the regulator of G protein signaling RGS9-1 by protein kinase A is a potential mechanism of light- and Ca2+-mediated regulation of G protein function in photoreceptors. Biochemistry 2001; 40:12619-27. [PMID: 11601986 DOI: 10.1021/bi015624b] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In vertebrate photoreceptors, photoexcited rhodopsin interacts with the G protein transducin, causing it to bind GTP and stimulate the enzyme cGMP phosphodiesterase. The rapid termination of the active state of this pathway is dependent upon a photoreceptor-specific regulator of G protein signaling RGS9-1 that serves as a GTPase activating protein (GAP) for transducin. Here, we show that, in preparations of photoreceptor outer segments (OS), RGS9-1 is readily phosphorylated by an endogenous Ser/Thr protein kinase. Protein kinase C and MAP kinase inhibitors reduced labeling by about 30%, while CDK5 and CaMK II inhibitors had no effect. cAMP-dependent protein kinase (PKA) inhibitor H89 reduced RGS9-1 labeling by more than 90%, while dibutyryl-cAMP stimulated it 3-fold, implicating PKA as the major kinase responsible for RGS9-1 phosphorylation in OS. RGS9-1 belongs to an RGS subfamily also including RGS6, RGS7, and RGS11, which exist as heterodimers with the G protein beta subunit Gbeta5. Phosphorylated RGS9-1 remains associated with Gbeta5L, a photoreceptor-specific splice form, which itself was not phosphorylated. RGS9-1 immunoprecipitated from OS was in vitro phosphorylated by exogenous PKA. The PKA catalytic subunit could also phosphorylate recombinant RGS9-1, and mutational analysis localized phosphorylation sites to Ser(427) and Ser(428). Substitution of these residues for Glu, to mimic phosphorylation, resulted in a reduction of the GAP activity of RGS9-1. In OS, RGS9-1 phosphorylation required the presence of free Ca(2+) ions and was inhibited by light, suggesting that RGS9-1 phosphorylation could be one of the mechanisms mediating a stronger photoresponse in dark-adapted cells.
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Affiliation(s)
- N Balasubramanian
- Department of Molecular and Cellular Pharmacology and Neuroscience Program, University of Miami School of Medicine, Miami, Florida 33136, USA
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24
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Matthews HR, Cornwall M, Crouch R. Prolongation of actions of Ca2+ early in phototransduction by 9-demethylretinal. J Gen Physiol 2001; 118:377-90. [PMID: 11585850 PMCID: PMC2233701 DOI: 10.1085/jgp.118.4.377] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
During adaptation Ca2+ acts on a step early in phototransduction, which is normally available for only a brief period after excitation. To investigate the identity of this step, we studied the effect of the light-induced decline in intracellular Ca2+ concentration on the response to a bright flash in normal rods, and in rods bleached and regenerated with 11-cis 9-demethylretinal, which forms a photopigment with a prolonged photoactivated lifetime. Changes in cytoplasmic Ca2+ were opposed by rapid superfusion of the outer segment with a 0Na+/0Ca2+ solution designed to minimize Ca2+ fluxes across the surface membrane. After regeneration of a bleached rod with 9-demethlyretinal, the response in Ringer's to a 440-nm bright flash was prolonged in comparison with the unbleached control, and the response remained in saturation for 10-15s. If the dynamic fall in Ca2+i induced by the flash was delayed by stepping the outer segment to 0Na+/0Ca2+ solution just before the flash and returning it to Ringer's shortly before recovery, then the response saturation was prolonged further, increasing linearly by 0.41 +/- 0.01 of the time spent in this solution. In contrast, even long exposures to 0Na+/0Ca2+ solution of rods containing native photopigment evoked only a modest response prolongation on the return to Ringer's. Furthermore, if the rod was preexposed to steady subsaturating light, thereby reducing the cytoplasmic calcium concentration, then the prolongation of the bright flash response evoked by 0Na+/0Ca2+ solution was reduced in a graded manner with increasing background intensity. These results indicate that altering the chromophore of rhodopsin prolongs the time course of the Ca2+-dependent step early in the transduction cascade so that it dominates response recovery, and suggest that it is associated with photopigment quenching by phosphorylation.
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Affiliation(s)
- Hugh R. Matthews
- Physiological Laboratory, University of Cambridge, Downing Street, Cambridge CB2 3EG, United Kingdom
| | - M.C. Cornwall
- Department of Physiology, Boston University Medical School, Boston, MA 02215
| | - R.K. Crouch
- Department of Ophthalmology, Medical University of South Carolina, Charleston, SC 29401
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25
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Mou H, Cote RH. The Catalytic and GAF Domains of the Rod cGMP Phosphodiesterase (PDE6) Heterodimer Are Regulated by Distinct Regions of Its Inhibitory γ Subunit. J Biol Chem 2001; 276:27527-34. [PMID: 11375400 DOI: 10.1074/jbc.m103316200] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
The central effector of visual transduction in retinal rod photoreceptors, cGMP phosphodiesterase (PDE6), is a catalytic heterodimer (alphabeta) to which low molecular weight inhibitory gamma subunits bind to form the nonactivated PDE holoenzyme (alphabetagamma(2)). Although it is known that gamma binds tightly to alphabeta, the binding affinity for each gamma subunit to alphabeta, the domains on gamma that interact with alphabeta, and the allosteric interactions between gamma and the regulatory and catalytic regions on alphabeta are not well understood. We show here that the gamma subunit binds to two distinct sites on the catalytic alphabeta dimer (K(D)(1) < 1 pm, K(D)(2) = 3 pm) when the regulatory GAF domains of bovine rod PDE6 are occupied by cGMP. Binding heterogeneity of gamma to alphabeta is absent when cAMP occupies the noncatalytic sites. Two major domains on gamma can interact independently with alphabeta with the N-terminal half of gamma binding with 50-fold greater affinity than its C-terminal, inhibitory region. The N-terminal half of gamma is responsible for the positive cooperativity between gamma and cGMP binding sites on alphabeta but has no effect on catalytic activity. Using synthetic peptides, we identified regions of the amino acid sequence of gamma that bind to alphabeta, restore high affinity cGMP binding to low affinity noncatalytic sites, and retard cGMP exchange with both noncatalytic sites. Subunit heterogeneity, multiple sites of gamma interaction with alphabeta, and positive cooperativity of gamma with the GAF domains are all likely to contribute to precisely controlling the activation and inactivation kinetics of PDE6 during visual transduction in rod photoreceptors.
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Affiliation(s)
- H Mou
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham, New Hampshire 03824-2617, USA
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26
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Calvert PD, Govardovskii VI, Krasnoperova N, Anderson RE, Lem J, Makino CL. Membrane protein diffusion sets the speed of rod phototransduction. Nature 2001; 411:90-4. [PMID: 11333983 DOI: 10.1038/35075083] [Citation(s) in RCA: 141] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Retinal rods signal the activation of a single receptor molecule by a photon. To ensure efficient photon capture, rods maintain about 109 copies of rhodopsin densely packed into membranous disks. But a high packing density of rhodopsin may impede other steps in phototransduction that take place on the disk membrane, by restricting the lateral movement of, and hence the rate of encounters between, the molecules involved. Although it has been suggested that lateral diffusion of proteins on the membrane sets the rate of onset of the photoresponse, it was later argued that the subsequent processing of the complexes was the main determinant of this rate. The effects of protein density on response shut-off have not been reported. Here we show that a roughly 50% reduction in protein crowding achieved by the hemizygous knockout of rhodopsin in transgenic mice accelerates the rising phases and recoveries of flash responses by about 1.7-fold in vivo. Thus, in rods the rates of both response onset and recovery are set by the diffusional encounter frequency between proteins on the disk membrane.
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Affiliation(s)
- P D Calvert
- Department of Ophthalmology, Harvard Medical School and the Massachusetts Eye and Ear Infirmary, Boston, Massachusetts 02114, USA.
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27
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Abstract
When light is absorbed within the outer segment of a vertebrate photoreceptor, the conformation of the photopigment rhodopsin is altered to produce an activated photoproduct called metarhodopsin II or Rh(*). Rh(*) initiates a transduction cascade similar to that for metabotropic synaptic receptors and many hormones; the Rh(*) activates a heterotrimeric G protein, which in turn stimulates an effector enzyme, a cyclic nucleotide phosphodiesterase. The phosphodiesterase then hydrolyzes cGMP, and the decrease in the concentration of free cGMP reduces the probability of opening of channels in the outer segment plasma membrane, producing the electrical response of the cell. Photoreceptor transduction can be modulated by changes in the mean light level. This process, called light adaptation (or background adaptation), maintains the working range of the transduction cascade within a physiologically useful region of light intensities. There is increasing evidence that the second messenger responsible for the modulation of the transduction cascade during background adaptation is primarily, if not exclusively, Ca(2+), whose intracellular free concentration is decreased by illumination. The change in free Ca(2+) is believed to have a variety of effects on the transduction mechanism, including modulation of the rate of the guanylyl cyclase and rhodopsin kinase, alteration of the gain of the transduction cascade, and regulation of the affinity of the outer segment channels for cGMP. The sensitivity of the photoreceptor is also reduced by previous exposure to light bright enough to bleach a substantial fraction of the photopigment in the outer segment. This form of desensitization, called bleaching adaptation (the recovery from which is known as dark adaptation), seems largely to be due to an activation of the transduction cascade by some form of bleached pigment. The bleached pigment appears to activate the G protein transducin directly, although with a gain less than Rh(*). The resulting decrease in intracellular Ca(2+) then modulates the transduction cascade, by a mechanism very similar to the one responsible for altering sensitivity during background adaptation.
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Affiliation(s)
- G L Fain
- Department of Physiological Science, University of California, Los Angeles, California 90095-1527, USA.
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28
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Hamer RD. Analysis of Ca++-dependent gain changes in PDE activation in vertebrate rod phototransduction. Mol Vis 2000; 6:265-86. [PMID: 11139649 PMCID: PMC1482459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023] Open
Abstract
PURPOSE Recent biochemical and physiological data point to the existence of one or more Ca++-mediated feedback mechanisms modulating gain at stages early in the vertebrate phototransduction cascade, i.e., prior to activation of cGMP-phosphodiesterase (PDE). The present study is a computational analysis that combines quantitative optimization to key data with a qualitative evaluation of each candidate model's ability to capture "signature" features of representative rod responses obtained under a broad range of dark- (DA) and light-adapted (LA) conditions. The primary data motivating the analyses were the two-flash data of Murnick & Lamb. These data exhibited strikingly nonlinear behavior: the period of complete photocurrent saturation (Tsat) in response to a Test flash was reduced substantially when preceded by a less-intense saturating Pre-flash. Depending on the delay between Pre- and Test flashes, the change in Tsat (DTsat) could exceed the magnitude of the delay, and could be reduced by as much as approximately 50%, corresponding to a large reduction in gain by a factor of 10-15. The overall goal of the study was to evaluate what model structure(s) were commensurate with both the Murnick & Lamb data and the salient qualitative features of rod responses obtained under a broad range of DA and LA conditions. METHODS Three candidate models were quantitatively optimized to the Murnick & Lamb saturated toad rod flash responses and, simultaneously, to a set of sub-saturated flash responses. Using the parameters from these optimizations, each candidate model was then used to simulate a suite of DA and LA responses. RESULTS The analyses showed that: (1) Within the context of a model with Ca++ feedback onto rhodopsin (R*) lifetime (tR), the salient features of the Murnick & Lamb data can only be accounted for if the rate-limiting step is not the Ca++-sensitive step in the early cascade reactions, i.e., if PDE* lifetime, and not tR, is rate-limiting. (2) With tR rate-limiting, the model cannot account for DTsat exceeding the delay. (3) The Ca++-dependent reduction in tR required to effect the large gain is incommensurate with the empirical dynamics of dim-flash responses. (4) Regardless of which reaction is rate-limiting, a model using solely modulation of R* lifetime puts strong constraints on the domain of biochemical parameters commensurate with the large gain changes Murnick & Lamb observed. (5) The analyses show that, in principle, the Murnick & Lamb data can be accounted for when tR is both rate-limiting and Ca++-sensitive if, in addition to the feedback onto tR, there is an earlier, stronger Ca++ feedback that does not affect R* inactivation kinetics (e.g., gain at R* activation or transducin (T*) activation). (6) Ca++-modulation of R* activation or T* activation as the sole early gain mechanism can also account for the Murnick & Lamb data, but fails to predict the data of Matthews, and can thus be rejected along with any model of comparable form. CONCLUSIONS The results imply that the Murnick & Lamb data per se are insufficient to rule out rate-limitation by (Ca++-sensitive) R* lifetime; evaluation of a broader set of responses is required. The analyses illustrate the importance of evaluating candidate models in relation to sets of data obtained under the broadest possible range of DA and LA conditions. The analyses are aided by the presence of reproducible signature, qualitative features in the data since these tend to constrain the domain of acceptable model structures and/or parameter sets. Some implications for vertebrate photoreceptor light-adaptation are discussed.
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Affiliation(s)
- R D Hamer
- Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA.
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29
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Norton AW, D'Amours MR, Grazio HJ, Hebert TL, Cote RH. Mechanism of transducin activation of frog rod photoreceptor phosphodiesterase. Allosteric interactiona between the inhibitory gamma subunit and the noncatalytic cGMP-binding sites. J Biol Chem 2000; 275:38611-9. [PMID: 10993884 DOI: 10.1074/jbc.m004606200] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
The rod photoreceptor phosphodiesterase (PDE) is unique among all known vertebrate PDE families for several reasons. It is a catalytic heterodimer (alphabeta); it is directly activated by a G-protein, transducin; and its active sites are regulated by inhibitory gamma subunits. Rod PDE binds cGMP at two noncatalytic sites on the alphabeta dimer, but their function is unclear. We show that transducin activation of frog rod PDE introduces functional heterogeneity to both the noncatalytic and catalytic sites. Upon PDE activation, one noncatalytic site is converted from a high affinity to low affinity state, whereas the second binding site undergoes modest decreases in binding. Addition of gamma to transducin-activated PDE can restore high affinity binding as well as reducing cGMP exchange kinetics at both sites. A strong correlation exists between cGMP binding and gamma binding to activated PDE; dissociation of bound cGMP accompanies gamma dissociation from PDE, whereas addition of either cGMP or gamma to alphabeta dimers can restore high affinity binding of the other molecule. At the active site, transducin can activate PDE to about one-half the turnover number for catalytic alphabeta dimers completely lacking bound gamma subunit. These results suggest a mechanism in which transducin interacts primarily with one PDE catalytic subunit, releasing its full catalytic activity as well as inducing rapid cGMP dissociation from one noncatalytic site. The state of occupancy of the noncatalytic sites on PDE determines whether gamma remains bound to activated PDE or dissociates from the holoenzyme, and may be relevant to light adaptation in photoreceptor cells.
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Affiliation(s)
- A W Norton
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham, New Hampshire 03824-3544, USA
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30
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Francis SH, Turko IV, Corbin JD. Cyclic nucleotide phosphodiesterases: relating structure and function. PROGRESS IN NUCLEIC ACID RESEARCH AND MOLECULAR BIOLOGY 2000; 65:1-52. [PMID: 11008484 DOI: 10.1016/s0079-6603(00)65001-8] [Citation(s) in RCA: 289] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Cyclic nucleotide phosphodiesterases (PDEs) comprise a superfamily of metallophosphohydrolases that specifically cleave the 3',5'-cyclic phosphate moiety of cAMP and/or cGMP to produce the corresponding 5'-nucleotide. PDEs are critical determinants for modulation of cellular levels of cAMP and/or cGMP by many stimuli. Eleven families of PDEs with varying selectivities for cAMP or cGMP have been identified in mammalian tissues. Within these families, multiple isoforms are expressed either as products of different genes or as products of the same gene through alternative splicing. Regulation of PDEs is important for controlling myriad physiological functions, including the visual response, smooth muscle relaxation, platelet aggregation, fluid homeostasis, immune responses, and cardiac contractility. PDEs are critically involved in feedback control of cellular cAMP and cGMP levels. Activities of the various PDEs are highly regulated by a panoply of processes, including phosphorylation events, interaction with small molecules such as cGMP or phosphatidic acid, subcellular localization, and association with specific protein partners. The PDE superfamily continues to be a major target for pharmacological intervention in a number of medically important maladies.
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Affiliation(s)
- S H Francis
- Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232, USA
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31
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Rebrik TI, Kotelnikova EA, Korenbrot JI. Time course and Ca(2+) dependence of sensitivity modulation in cyclic GMP-gated currents of intact cone photoreceptors. J Gen Physiol 2000; 116:521-34. [PMID: 11004202 PMCID: PMC2230625 DOI: 10.1085/jgp.116.4.521] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
We determined the Ca(2+) dependence and time course of the modulation of ligand sensitivity in cGMP-gated currents of intact cone photoreceptors. In electro-permeabilized single cones isolated from striped bass, we measured outer segment current amplitude as a function of cGMP or 8Br-cGMP concentrations in the presence of various Ca(2+) levels. The dependence of current amplitude on nucleotide concentration is well described by the Hill function with values of K(1/2), the ligand concentration that half-saturates current, that, in turn, depend on Ca(2+). K(1/2) increases as Ca(2+) rises, and this dependence is well described by a modified Michaelis-Menten function, indicating that modulation arises from the interaction of Ca(2+) with a single site without apparent cooperativity. (Ca)K(m), the Michaelis-Menten constant for Ca(2+) concentration is 857 +/- 68 nM for cGMP and 863 +/- 51 for 8Br-cGMP. In single cones under whole-cell voltage clamp, we simultaneously measured changes in membrane current and outer segment free Ca(2+) caused by sudden Ca(2+) sequestration attained by uncaging diazo-2. In the presence of constant 8Br-cGMP, 15 micro, Ca(2+) concentration decrease was complete within 50 ms and membrane conductance was enhanced 2.33 +/- 0.95-fold with a mean time to peak of 1.25 +/- 0.23 s. We developed a model that assumes channel modulation is a pseudo-first-order process kinetically limited by free Ca(2+). Based on the experimentally measured changes in Ca(2+) concentration, model simulations match experimental data well by assigning the pseudo-first-order time constant a mean value of 0.40 +/- 0.14 s. Thus, Ca(2+)-dependent ligand modulation occurs over the concentration range of the normal, dark-adapted cone. Its time course suggests that its functional effects are important in the recovery of the cone photoresponse to a flash of light and during the response to steps of light, when cones adapt.
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Affiliation(s)
- Tatiana I. Rebrik
- Department of Physiology, School of Medicine, University of California at San Francisco, San Francisco, California 94143
| | - Ekaterina A. Kotelnikova
- Department of Physiology, School of Medicine, University of California at San Francisco, San Francisco, California 94143
| | - Juan I. Korenbrot
- Department of Physiology, School of Medicine, University of California at San Francisco, San Francisco, California 94143
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Cote RH. Kinetics and regulation of cGMP binding to noncatalytic binding sites on photoreceptor phosphodiesterase. Methods Enzymol 2000; 315:646-72. [PMID: 10736732 DOI: 10.1016/s0076-6879(00)15873-2] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Affiliation(s)
- R H Cote
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham 03824-3544, USA
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Pugh E, Lamb T. Chapter 5 Phototransduction in vertebrate rods and cones: Molecular mechanisms of amplification, recovery and light adaptation. HANDBOOK OF BIOLOGICAL PHYSICS 2000. [DOI: 10.1016/s1383-8121(00)80008-1] [Citation(s) in RCA: 112] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Hamer RD. Computational analysis of vertebrate phototransduction: combined quantitative and qualitative modeling of dark- and light-adapted responses in amphibian rods. Vis Neurosci 2000; 17:679-99. [PMID: 11153649 PMCID: PMC1482460 DOI: 10.1017/s0952523800175030] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We evaluated the generality of two models of vertebrate phototransduction. The approach was to quantitatively optimize each model to the full waveform of high-quality, dark-adapted (DA), salamander rod flash responses. With the optimal parameters, each model was then used to account for signature, qualitative features of rod responses from three experimental paradigms (stimulus/response, "S/R suite"): (1) step responses; (2) the intensity dependence of the period of photocurrent saturation (Tsat vs. ln(I)); and (3) light-adapted (LA) incremental flash sensitivity as a function of background intensity. The first model was the recent successful model of Nikonov et al. (1998). The second model replaced the instantaneous Ca2+ buffering used in the Nikonov et al. model with a dynamic buffer. The results showed that, in the absence of the dynamic Ca2+ buffer, the Nikonov et al. model does not have sufficient flexibility to provide a good fit to the flash responses, and, using the same parameters, reproduce the salient features of the S/R suite--critical features at step onset and offset are absent; the Tsat function has too shallow a slope; and the model cannot generate the empirically observed I-range of Weber-Fechner LA behavior. Some features could be recovered by changing parameters, but only at the expense of the fit to the reference (Ref) data. When the dynamic buffer is added, the model is able to achieve an acceptable fit to the Ref data while reproducing several features of the S/R suite, including an empirically observed Tsat function, and an extended range of LA flash sensitivity adhering to Weber's law. The overall improved behavior of the model with a dynamic Ca2+ buffer indicates that it is an important mechanism to include in a working model of phototransduction, and that, despite the slow kinetics of amphibian rods, Ca2+ buffering should not be simulated as an instantaneous process. However, neither model was able to capture all the features with the same parameters yielding the optimal fit to the Ref data. In addition, neither model could maintain a good fit to the Ref data when five key biochemical parameters were held at their current known values. Moreover, even after optimization, a number of important parameters remained outside their empirical estimates. We conclude that other mechanisms will need to be added, including additional Ca2+-feedback mechanisms. The present research illustrates the importance of a hybrid qualitative/quantitative approach to model development, and the limitations of modeling restricted sets of data.
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Affiliation(s)
- R D Hamer
- Smith-Kettlewell Eye Research Institute, San Francisco, CA 94115, USA.
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Jonas EA, Buchanan J, Kaczmarek LK. Prolonged activation of mitochondrial conductances during synaptic transmission. Science 1999; 286:1347-50. [PMID: 10558987 DOI: 10.1126/science.286.5443.1347] [Citation(s) in RCA: 63] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Although ion channels have been detected in mitochondria, scientists have not been able to record ion transport in mitochondria of intact cells. A variation of the patch clamp technique was used to record ion channel activity from intracellular organelles in the presynaptic terminal of the squid. Electron microscopy indicated that mitochondria are numerous in this terminal and are the only organelles compatible with the tips of the pipettes. Before synaptic stimulation, channel activity was infrequent and its conductance was small, although large conductances ( approximately 0.5 to 2.5 nanosiemens) could be detected occasionally. During a train of action potentials, the conductance of the mitochondrial membrane increased up to 60-fold. The conductance increased after a delay of several hundred milliseconds and continued to increase after stimulation had stopped. Recovery occurred over tens of seconds.
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Affiliation(s)
- E A Jonas
- Department of Pharmacology, Yale University School of Medicine, New Haven, CT 06520, USA
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Abstract
An important recent advance in the understanding of vertebrate photoreceptor light adaptation has come from the discovery that as many as eight distinct molecular mechanisms may be involved, and the realization that one of the principal mechanisms is not dependent on calcium. Quantitative analysis of these mechanisms is providing new insights into the nature of rod photoreceptor light adaptation.
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Affiliation(s)
- E N Pugh
- FM Kirby Center for Molecular Ophthalmology, Department of Ophthalmology, Institute of Neurological Sciences, Stellar-Chance Laboratories, University of Pennsylvania, 422 Curie Boulevard, Philadelphia, Pennsylvania 19104-6069, USA.
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Mou H, Grazio HJ, Cook TA, Beavo JA, Cote RH. cGMP binding to noncatalytic sites on mammalian rod photoreceptor phosphodiesterase is regulated by binding of its gamma and delta subunits. J Biol Chem 1999; 274:18813-20. [PMID: 10373499 DOI: 10.1074/jbc.274.26.18813] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
The binding of cGMP to the noncatalytic sites on two isoforms of the phosphodiesterase (PDE) from mammalian rod outer segments has been characterized to evaluate their role in regulating PDE during phototransduction. Nonactivated, membrane-associated PDE (PDE-M, alpha beta gamma2) has one exchangeable site for cGMP binding; endogenous cGMP remains nonexchangeable at the second site. Non-activated, soluble PDE (PDE-S, alpha beta gamma2 delta) can release and bind cGMP at both noncatalytic sites; the delta subunit is likely responsible for this difference in cGMP exchange rates. Removal of the delta and/or gamma subunits yields a catalytic alphabeta dimer with identical catalytic and binding properties for both PDE-M and PDE-S as follows: high affinity cGMP binding is abolished at one site (KD >1 microM); cGMP binding affinity at the second site (KD approximately 60 nM) is reduced 3-4-fold compared with the nonactivated enzyme; the kinetics of cGMP exchange to activated PDE-M and PDE-S are accelerated to similar extents. The properties of nonactivated PDE can be restored upon addition of gamma subunit. Occupancy of the noncatalytic sites by cGMP may modulate the interaction of the gamma subunit with the alphabeta dimer and thereby regulate cytoplasmic cGMP concentration and the lifetime of activated PDE during visual transduction in photoreceptor cells.
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Affiliation(s)
- H Mou
- Department of Biochemistry and Molecular Biology, University of New Hampshire, Durham, New Hampshire 03824, USA
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Tsang SH, Burns ME, Calvert PD, Gouras P, Baylor DA, Goff SP, Arshavsky VY. Role for the target enzyme in deactivation of photoreceptor G protein in vivo. Science 1998; 282:117-21. [PMID: 9756475 DOI: 10.1126/science.282.5386.117] [Citation(s) in RCA: 159] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Heterotrimeric guanosine 5'-triphosphate (GTP)-binding proteins (G proteins) are deactivated by hydrolysis of the GTP that they bind when activated by transmembrane receptors. Transducin, the G protein that relays visual excitation from rhodopsin to the cyclic guanosine 3',5'-monophosphate phosphodiesterase (PDE) in retinal photoreceptors, must be deactivated for the light response to recover. A point mutation in the gamma subunit of PDE impaired transducin-PDE interactions and slowed the recovery rate of the flash response in transgenic mouse rods. These results indicate that the normal deactivation of transducin in vivo requires the G protein to interact with its target enzyme.
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Affiliation(s)
- S H Tsang
- Edward S. Harkness Eye Institute and Department of Biochemistry and Molecular Biophysics, Columbia University, College of Physicians and Surgeons, New York, NY 10032, USA
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Nikonov S, Engheta N, Pugh EN. Kinetics of recovery of the dark-adapted salamander rod photoresponse. J Gen Physiol 1998; 111:7-37. [PMID: 9417132 PMCID: PMC1887775 DOI: 10.1085/jgp.111.1.7] [Citation(s) in RCA: 104] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/1997] [Accepted: 10/29/1997] [Indexed: 02/05/2023] Open
Abstract
The kinetics of the dark-adapted salamander rod photocurrent response to flashes producing from 10 to 10(5) photoisomerizations (Phi) were investigated in normal Ringer's solution, and in a choline solution that clamps calcium near its resting level. For saturating intensities ranging from approximately 10(2) to 10(4) Phi, the recovery phases of the responses in choline were nearly invariant in form. Responses in Ringer's were similarly invariant for saturating intensities from approximately 10(3) to 10(4) Phi. In both solutions, recoveries to flashes in these intensity ranges translated on the time axis a constant amount (tauc) per e-fold increment in flash intensity, and exhibited exponentially decaying "tail phases" with time constant tauc. The difference in recovery half-times for responses in choline and Ringer's to the same saturating flash was 5-7 s. Above approximately 10(4) Phi, recoveries in both solutions were systematically slower, and translation invariance broke down. Theoretical analysis of the translation-invariant responses established that tauc must represent the time constant of inactivation of the disc-associated cascade intermediate (R*, G*, or PDE*) having the longest lifetime, and that the cGMP hydrolysis and cGMP-channel activation reactions are such as to conserve this time constant. Theoretical analysis also demonstrated that the 5-7-s shift in recovery half-times between responses in Ringer's and in choline is largely (4-6 s) accounted for by the calcium-dependent activation of guanylyl cyclase, with the residual (1-2 s) likely caused by an effect of calcium on an intermediate with a nondominant time constant. Analytical expressions for the dim-flash response in calcium clamp and Ringer's are derived, and it is shown that the difference in the responses under the two conditions can be accounted for quantitatively by cyclase activation. Application of these expressions yields an estimate of the calcium buffering capacity of the rod at rest of approximately 20, much lower than previous estimates.
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Affiliation(s)
- S Nikonov
- Department of Psychology, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Affiliation(s)
- D Tranchina
- Department of Biology, Courant Institute of Mathematical Sciences, and Center for Neural Science, New York University, New York 10003, USA
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