Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction

A model describing the role of transversal and longitudinal diffusion of cGMP and Ca(2+) in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP and Ca(2+) in the inter-disc spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 microm, consistent with experimental data. This approach represents a tool to analyze point-wise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.     

Cyclic GMP diffusion coefficient in rod photoreceptor outer segments.

Cyclic GMP (cGMP) is the intracellular messenger that mediates phototransduction in retinal rods. As photoisomerizations of rhodopsin molecules are local events, the longitudinal diffusion of cGMP in the rod outer segment should be a contributing factor to the response of the cell to light. We have employed the truncated rod outer segment preparation from bullfrog (Rana catesbeiana) and tiger salamander (Ambystoma tigrinum) to measure the cGMP diffusion coefficient. In this preparation, the distal portion of a rod outer segment was drawn into a suction pipette for measuring membrane current, and the rest of the cell was then sheared off with a glass probe, allowing bath cGMP to diffuse into the outer segment and activate the cGMP-gated channels on the surface membrane. Addition and removal of bath cGMP were fast enough to produce effectively step changes in cGMP concentration at the open end of the outer segment. When cGMP hydrolysis is inhibited by isobutylmethylxanthine (IBMX), the equation for the diffusion of cGMP inside the truncated rod outer segment has a simple analytical solution, which we have used to analyze the rise and decay kinetics of the cGMP-elicited currents. From these measurements we have obtained a cGMP diffusion coefficient of approximately 70 x 10(-8) cm2 s-1 for bullfrog rods and approximately 60 x 10(-8) cm2 s-1 for tiger salamander rods. These values are six to seven times lower than the expected value in aqueous solution. The estimated diffusion coefficient is the same at high (20-1000 microM) and low (5-10 microM) concentrations of cGMP, suggesting no significant effect from buffering over these concentration ranges.     

Longitudinal diffusion in retinal rod and cone outer segment cytoplasm: the consequence of cell structure

Excitation signals spread along photoreceptor outer segments away from the site of photon capture because of longitudinal diffusion of cGMP, a cytoplasmic second messenger. The quantitative features of longitudinal diffusion reflect the anatomical structure of the outer segment, known to be profoundly different in rod and cone photoreceptors. To explore how structural differences affect cytoplasmic diffusion and to assess whether longitudinal diffusion may contribute to the difference in signal transduction between photoreceptor types, we investigated, both theoretically and experimentally, the longitudinal diffusion of small, hydrophilic molecules in outer segments. We developed a new theoretical analysis to explicitly compute the longitudinal diffusion constant, Dl, in terms of outer segment structure. Using time-resolved fluorescence imaging we measured Dl of Alexa488 and lucifer yellow in intact, single cones and validated the theoretical analysis. We used numerical simulations of the theoretical model to investigate cGMP diffusion in outer segments of various species. At a given time interval, cGMP spreads further in rod than in cone outer segments of the same dimensions. Across all species, the spatial spread of cGMP at the peak of the dim light photocurrent is 3-5 microm in rod outer segments, regardless of their absolute size. Similarly the cGMP spatial spread is 0.7-1 microm in cone outer segments, independently of their dimensions.     

Diffusion coefficient of cyclic GMP in salamander rod outer segments estimated with two fluorescent probes.

Experiments have demonstrated that single photoisomerizations in amphibian and primate rods can cause the suppression of 3-5% of the dark circulating current at the response peak (Baylor, D. A., T. D. Lamb, and K. W. Yau. 1979. J. Physiol. (Lond.). 288:613-634; Baylor, D. A., B. J. Nunn, and J. L. Schnapf. 1984. J. Physiol. (Lond.). 357:575-607). These results indicate that the change in [cGMP] effected by a single isomerization must spread longitudinally over at least the corresponding fractional length of the outer segment. The effective longitudinal diffusion coefficient, Dx, of cGMP is thus an important determinant of rod sensitivity. We report here measurements of the effective longitudinal diffusion coefficients, Dx, of two fluorescently labeled molecules: 5/6-carboxyfluorescein and 8-(fluoresceinyl)thioguanosine 3',5'-cyclic monophosphate, introduced into detached outer segments via whole-cell patch electrodes. For these compounds, the average time for equilibration of the entire outer segment with the patch pipette was approximately 6 min. Fluorescence images of rods were analyzed with a one-dimensional diffusion model that included limitations on transfer between the electrode and outer segment and the effects of intracellular binding of the dyes. The analyses yielded estimates of Dx of 1.9 and 1.0 microns 2.s-1 for the two dyes. It is shown that these results place an upper limit on Dx for cGMP of 11 microns2.s-1. The actual value of Dx for cGMP in the rod will depend on the degree of intracellular binding of cGMP. Estimates of the effective buffering power for cGMP in the rod at rest range from two to six (Lamb and Pugh, 1992; Cote and Brunnock, 1993). When combined with these estimates, our results predict that for cGMP itself, Dx falls within the range of 1.4-5.5 microns 2.s-1.     

Time course and Ca(2+) dependence of sensitivity modulation in cyclic GMP-gated currents of intact cone photoreceptors

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.     

Electrical and adaptive properties of rod photoreceptors in bufo marinus. II. Effects of cyclic nucleotides and protaglandins

Substances known to alter cyclic nucleotide levels in cells were applied to the isolated toad retina and effects on rod electrical and adaptive behavior were studied. The retina was continually superfused in control ringer’s or ringer’s containing one or a combination of drugs, and rod activity was recorded intracellularly. Superfusion with cGMP, Bu(2)GMP, isobutylmethylxanthine (IBMX; a phosphodiesterase inhibitor), or PGF(2α) (a prostaglandin) caused effects in rods that closely match those observed when extracellular Ca(2+) levels were lowered. For example, short exposures (up to 6 min) of the retina to these substances caused depolarization of the membrane potential, increase in response amplitudes, and some changes in waveform; but under dark-adapted or partially light-adapted conditions receptor sensitivity was virtually unaffected. That is, the position of the V-log I curve on the intensity axis was determined by the prevailing light level, not by drug level. These drugs, like lowered extracellular Ca(2+), also decreased the period of receptor saturation after a bright-adapting flash, resulting in an acceleration of the onset of membrane and sensitivity recovery during dark adaptation.

Long-term (6-15 min) exposure of a dark-adapted retina to 5 mM IBMX or a combination of IBMX and cGMP caused a loss of response amplitude and a desensitization of the rods that was similar to that observed in rods after a long-term low Ca(2+) (10(-9)M) treatment. Application of high (3.2 mM) Ca(2+) to the retina blocked the effects of applied Bu(2)cGMP. PGE(1) superfusion mimicked the effects of increasing extracellular Ca(2+). The results show that increased cGMP and lowered Ca(2+) produce similar alterations in the electrical activity of rods. These findings suggest that Ca(2+) and cGMP are interrelated messengers. We speculate that low Ca(2+) may lead to increased intracellular cGMP, and/or that applied cGMP, and/or that applied cGMP may lower cytosol Ca(2+), perhaps by stimulating Ca(2+)- ATPase pumps in the outer segment.

     

Diffusion coefficient of the cyclic GMP analog 8-(fluoresceinyl)thioguanosine 3'',5'' cyclic monophosphate in the salamander rod outer segment.

Cyclic GMP (cGMP) is the intracellular messenger mediating phototransduction in retinal rods, with its longitudinal diffusion in the rod outer segment (ROS) likely to be a factor in determining light sensitivity. From the kinetics of cGMP-activated currents in the truncated ROS of the salamander (Ambystoma tigrinum), the cGMP diffusion coefficient was previously estimated to be approximately 60 x 10(-8) cm2 s-1. On the other hand, fluorescence measurements in intact salamander ROS using 8-(fluoresceinyl)thioguanosine 3',5'-cyclic monophosphate (Fl-cGMP) led to a diffusion coefficient for this compound of 1 x 10(-8) cm2 s-1; after corrections for differences in size and in binding to cellular components between cGMP and Fl-cGMP, this gave an upper limit of 11 x 10(-8) cm2 s-1 for the cGMP diffusion coefficient. To properly compare the two sets of measurements, we have examined the diffusion of Fl-cGMP in the truncated ROS. From the kinetics of Fl-cGMP-activated currents, we have obtained a diffusion coefficient of 3 x 10(-8) cm2 s-1 for this analog; the cGMP diffusion coefficient measured from the same truncated ROSs was approximately 80 x 10(-8) cm2 s-1. Thus, a factor of 27 appears appropriate for correcting differences in size and intracellular binding between cGMP and Fl-cGMP. Application of this correction factor to the Fl-cGMP diffusion coefficient measurements by Olson and Pugh (1993) gives a cGMP diffusion coefficient of approximately 30 x 10(-8) cm2 s-1, in reasonable agreement with the value measured from the truncated ROS.     

p19 detected in the rat retina and pineal gland is a guanylyl cyclase-activating protein (GCAP)

The Ca(2+)-dependent activation of retina-specific guanylyl cyclase (retGC) is mediated by guanylyl cyclase-activating proteins (GCAPs). Here we report for the first time detection of a 19 kDa protein (p19) with GCAP properties in extracts of rat retina and pineal gland. Both extracts stimulate synthesis of cGMP in rod outer segment (ROS) membranes at low (30 nM) but not at high (1 microM) concentrations of Ca(2+). At low Ca(2+), immunoaffinity purified p19 activates guanylyl cyclase(s) in bovine ROS and rat retinal membranes. Moreover, p19 is recognized by antibodies against bovine GCAP1 and, similarly to other GCAPs, exhibits a Ca(2+)-dependent electrophoretic mobility shift.     

Recoverin and rhodopsin kinase activity in detergent-resistant membrane rafts from rod outer segments

Cholesterol-rich membranes or detergent-resistant membranes (DRMs) have recently been isolated from bovine rod outer segments and were shown to contain several signaling proteins such as, for example, transducin and its effector, cGMP-phosphodiesterase PDE6. Here we report the presence of rhodopsin kinase and recoverin in DRMs that were isolated in either light or dark conditions at high and low Ca2+ concentrations. Inhibition of rhodopsin kinase activity by recoverin was more effective in DRMs than in the initial rod outer segment membranes. Furthermore, the Ca2+ sensitivity of rhodopsin kinase inhibition in DRMs was shifted to lower free Ca2+ concentration in comparison with the initial rod outer segment membranes (IC50=0.76 microm in DRMs and 1.91 microm in rod outer segments). We relate this effect to the high cholesterol content of DRMs because manipulating the cholesterol content of rod outer segment membranes by methyl-beta-cyclodextrin yielded a similar shift of the Ca2+-dependent dose-response curve of rhodopsin kinase inhibition. Furthermore, a high cholesterol content in the membranes also increased the ratio of the membrane-bound form of recoverin to its cytoplasmic free form. These data suggest that the Ca2+-dependent feedback loop that involves recoverin is spatially heterogeneous in the rod cell.     

Ca2+ fluxes and channel regulation in rods of the albino rat

By use of microelectrodes, changes in the receptor current and the Ca2+ concentration were measured in the rod layer of the rat retina after stimulation by flashes or steady light. Thereby light induced Ca2+ sources, and sinks along a rod were determined in dependence of time. Thus, the Ca2+ fluxes across the plasma membrane of a mammalian rod could be studied in detail. By light stimulation, Ca2+ sources are evoked along the outer segment only. Immediately after a saturating flash, a maximum of Ca2+ efflux is observed which decays exponentially with tau = 0.3 s at 37 degrees C (4.2 s at 23 degrees C). During regeneration of the dark current, the outer segment acts as a Ca2+ sink, indicating a restoration of the Ca(2+)-depleted outer segment. These findings agree with earlier reports on amphibian rods. Further experiments showed that the peak Ca2+ efflux and tau are temperature dependent. The peak amplitude also depends on the external Ca2+ concentration. In contrast to the reports on amphibian rods, only a part of the Ca2+ ions extruded from the outer segment is directly restored. Surprisingly, during steady light the Ca2+ efflux approaches a permanent residual value. Therefore, in course of a photoresponse, Ca2+ must be liberated irreversibly from internal Ca2+ stores. There is certain evidence that the inner segment acts as a Ca2+ store. Our results show that the Ca2+ fraction of the ions carrying the dark current is proportional to the extracellular Ca2+ concentration. This indicates that the Ca2+ permeability of the plasma membrane of the rod outer segment is independent of the Ca2+ concentration.     

Characterization of guanylate cyclase activity in single retinal rod outer segments

cGMP mediates vertebrate phototransduction by directly gating cationic channels on the plasma membrane of the photoreceptor outer segment. This second messenger is produced by a guanylate cyclase and hydrolyzed by a light-activated cGMP-phosphodiesterase. Both of these enzyme activities are Ca2+ sensitive, the guanylate cyclase activity being inhibited and the light-activated phosphodiesterase being enhanced by Ca2+. Changes in these activities due to a light-induced decrease in intracellular Ca2+ are involved in the adaptation of photoreceptors to background light. We describe here experiments to characterize the guanylate cyclase activity and its modulation by Ca2+ using a truncated rod outer segment preparation, in order to evaluate the enzyme's role in light adaptation. The outer segment of a tiger salamander rod was drawn into a suction pipette to allow recording of membrane current, and the remainder of the cell was sheared off with a probe to allow internal dialysis. The cGMP-gated channels on the surface membrane were used to monitor conversion of GTP, supplied from the bath, into cGMP by the guanylate cyclase in the outer segment. At nominal 0 Ca2+, the cyclase activity had a Km of 250 microM MgGTP and a Vmax of 25 microM cGMP s-1 in the presence of 1.6 mM free Mg2+; in the presence of 0.5 mM free Mg2+, the Km was 310 microM MgGTP and the Vmax was 17 microM cGMP s-1. The stimulation by Mg2+ had an EC50 of 0.2 mM Mg2+ for MgGTP at 0.5 mM. Ca2+ inhibited the cyclase activity. In a K+ intracellular solution, with 0.5 mM free Mg2+ and 2.0 mM GTP, the cyclase activity was 13 microM cGMP s-1 at nominal 0 Ca2+; Ca2+ decreased this activity with a IC50 of approximately 90 nM and a Hill coefficient of approximately 2.0.     

Calcium feedback and sensitivity regulation in primate rods.

Membrane current was recorded from a single primate rod with a suction pipette while the cell was bath perfused with solutions maintained at a temperature of approximately 38 degrees C. A transient inward current was observed at the onset of bright illumination after briefly exposing the outer segment in darkness to Ringer's (Locke) solution containing 3-isobutyl-1-methylxanthine (IBMX), an inhibitor of cGMP phosphodiesterase. After briefly removing external Na+ from around the outer segment in darkness, a similar current was observed upon Na+ restoration in bright light. By analogy to amphibian rods, this inward current was interpreted to represent the activity of an electrogenic Na(+)-dependent Ca2+ efflux, which under physiological conditions in the light is expected to reduce the free Ca2+ in the outer segment and provide negative feedback (the "Ca2+ feedback") to the phototransduction process. The exchange current had a saturated amplitude of up to approximately 5 pA and a decline time course that appeared to have more than one exponential component. In the absence of the Ca2+ feedback, made possible by removing the Ca2+ influx and efflux at the outer segment using a 0 Na(+)-0 Ca2+ external solution, the response of a rod to a dim flash was two to three times larger and had a longer time to peak than in physiological solution. These changes can be approximately accounted for by a simple model describing the Ca2+ feedback in primate rods. The dark hydrolytic rate for cGMP was estimated to be 1.2 s-1. The incremental hydrolytic rate, beta*(t), activated by one photoisomerization was approximately 0.09 s-1 at its peak, with a time-integrated activity, integral of beta*(t)dt, of approximately 0.033, both numbers being derived assuming spatial homogeneity in the outer segment. Finally, we have found that primate rods adapt to light in much the same way as amphibian and other mammalian rods, such as showing a Weber-Fechner relation between flash sensitivity and background light. The Ca2+ feedback model we have constructed can also explain this feature reasonably well.     

Regulation of cGMP levels by guanylate cyclase in truncated frog rod outer segments

Cyclic GMP is the second messenger in phototransduction and regulates the photoreceptor current. In the present work, we tried to understand the regulation mechanism of cytoplasmic cGMP levels in frog photoreceptors by measuring the photoreceptor current using a truncated rod outer segment (tROS) preparation. Since exogenously applied substance diffuses into tROS from the truncated end, we could examine the biochemical reactions relating to the cGMP metabolism by manipulating the cytoplasmic chemical condition. In tROS, exogenously applied GTP produced a dark current whose amplitude was half-maximal at approximately 0.4 mM GTP. The conductance for this current was suppressed by light in a fashion similar to when it is activated by cGMP. In addition, no current was produced in the absence of Mg2+, which is known to be necessary for the guanylate cyclase activity. These results indicate that guanylate cyclase was present in tROS and synthesized cGMP from exogenously applied GTP. The enzyme activity was distributed throughout the rod outer segment. The amount of synthesized cGMP increased as the cytoplasmic Ca2+ concentration of tROS decreased, which indicated the activation of guanylate cyclase at low Ca2+ concentrations. Half-maximal effect of Ca2+ was observed at approximately 100 nM. tROS contained the proteins involved in the phototransduction mechanism and therefore, we could examine the regulation of the light response waveform by Ca2+. At low Ca2+ concentrations, the time course of the light response was speeded up probably because cGMP recovery was facilitated by activation of the cyclase. Then, if the cytoplasmic Ca2+ concentration of a photoreceptor decreases during light stimulation, the Ca2+ decrease may explain the acceleration of the light response during light adaptation. In tROS, however, we did observe an acceleration during repetitive light flashes when the cytoplasmic Ca2+ concentration increased during the stimulation. This result suggests the presence of an additional light-dependent mechanism that is responsible for the acceleration of the light response during light adaptation.     

Role of secondary phosphoinositide messengers in storage of Ca2+ ions in retinal rod microsomes

The influence of guanosine-5'-triphosphate and secondary messengers forming in rod outer segment membranes during light-stimulated hydrolysis of phosphoinositides on the ATP-dependent Ca(2+)-uptake in microsomes of the retinal rod inner segment was studied. The water-soluble cytoplasmic components of the retinal rod outer segment were shown to be capable of stimulating the Ca(2+)-pump of endoplasmic reticulum after light illumination. This process is likely to proceed with the participation of 1,2-diacylglycerol localized in microsome membrane.     

Regulation of photoreceptor membrane guanylyl cyclases by guanylyl cyclase activator proteins

Guanylyl cyclase (GC) plays a central role in the responses of vertebrate rod and cone photoreceptors to light. cGMP is an internal messenger molecule of vertebrate phototransduction. Light stimulates hydrolysis of cGMP, causing the closure of cGMP-dependent cation channels in the plasma membranes of photoreceptor outer segments. Light also lowers the concentration of intracellular free Ca(2+) and by doing so it stimulates resynthesis of cGMP by guanylyl cyclase. The guanylyl cyclases that couple Ca(2+) to cGMP synthesis in photoreceptors are members of a family of transmembrane guanylyl cyclases that includes atrial natriuretic peptide receptors and the heat-stable enterotoxin receptor. The photoreceptor membrane guanylyl cyclases, RetGC-1 and RetGC-2 (also referred to as GC-E and GC-F), are regulated intracellularly by two Ca(2+)-binding proteins, GCAP-1 and GCAP-2. GCAPs bind Ca(2+) at three functional EF-hand structures. Several lines of biochemical evidence suggest that guanylyl cyclase activator proteins (GCAPs) bind constitutively to an intracellular domain of RetGCs. In the absence of Ca(2+) GCAP stimulates and in the presence of Ca(2+) it inhibits cyclase activity. Proper functioning of RetGC and GCAP is necessary not only for normal photoresponses but also for photoreceptor viability since mutations in RetGC and in GCAP cause photoreceptor degeneration.     

All-trans retinol in rod photoreceptor outer segments moves unrestrictedly by passive diffusion

The visual pigment protein of vertebrate rod photoreceptors, rhodopsin, contains an 11-cis retinyl moiety that is isomerized to all-trans upon light absorption. Subsequently, all-trans retinal is released from the protein and reduced to all-trans retinol, the first step in the recycling of rhodopsin's chromophore group through the series of reactions that constitute the visual cycle. The concentration of all-trans retinol in photoreceptor outer segments can be monitored from its fluorescence. We have used two-photon excitation (720 nm) of retinol fluorescence and fluorescence recovery after photobleaching to characterize the mobility of all-trans retinol in frog photoreceptor outer segments. Retinol produced after rhodopsin bleaching moved laterally in the disk membrane bilayer with an apparent diffusion coefficient of 2.5 +/- 0.3 micro m(2) s(-1). The diffusion coefficient of exogenously added retinol was 3.2 +/- 0.5 micro m(2) s(-1). These diffusion coefficients are in close agreement with those reported for lipids, suggesting that retinol is not tightly bound to protein sites that would be diffusing much more slowly in the plane of the membrane. In agreement with this interpretation, a fluorescent-labeled C-16 fatty acid diffused laterally with a similar diffusion coefficient, 2.2 +/- 0.2 micro m(2) s(-1). Retinol also moved along the length of the rod outer segment, with an apparent diffusion coefficient of 0.07 +/- 0.01 micro m(2) s(-1), again suggesting that it is not tightly bound to proteins that would confine it to the disks. The axial diffusion coefficient of exogenously added retinol was 0.05 +/- 0.01 micro m(2) s(-1). In agreement with passive diffusion, the rate of axial movement was inversely proportional to the square of the length of the rod outer segment. Diffusion of retinol on the plasma membrane of the outer segment can readily account for the measured value of the axial diffusion coefficient, as the plasma membrane comprises approximately 1% of the total outer-segment membrane. The values of both the lateral and axial diffusion coefficients are consistent with most of the all-trans retinol in the outer segments moving unrestricted and not being bound to carrier proteins. Therefore, and in contrast to other steps of the visual cycle, there does not appear to be any specialized processing for all-trans retinol within the rod outer segment.     

Effect of light and calcium on cyclic GMP synthesis in rod outer segments of toad retina

The rod outer segments of toad retina contain a guanylate cyclase activity of about 3 +/- 1 nmol of cGMP formed/min per mg protein. In darkness this value is largely independent of the Ca2+ concentration, although it is enhanced by light upon lowering the Ca2+ concentration from 10(-5) to 10(-8) M. The activating effect of light on cyclase at low Ca2+ concentrations is enlarged upon increasing the light intensity. With a flash of light bleaching 7 X 10(-2) percent of rhodopsin, cyclase activity increased by a factor of 30 when Ca2+ levels dropped from 10(-5) to 10(-8) M. In view of recent observations that shortly after a flash of light the calcium activity inside the photoreceptor cell decreases, it seems likely that Ca2+ plays a regulatory role on cGMP metabolism in visual excitation.     

Calcium dependence of the activation and inactivation kinetics of the light-activated phosphodiesterase of retinal rods

The Ca2+ dependence of the kinetics and light sensitivity of light-activated phosphodiesterase was studied with a pH assay in toad and bovine rod disk membranes (RDM), and in a reconstituted system containing GTP-binding protein, phosphodiesterase and rhodopsin kinase. Three statistics, peak hydrolytic velocity, turnoff time, and time to peak velocity, were measured. ATP decreased phosphodiesterase light sensitivity nearly 10-fold and accelerated the dim-flash kinetics of cGMP hydrolysis when compared to those with GTP alone. CA2+ reversed all of the effects of ATP, Ca2+ increased peak velocity, turnoff time, and time to peak velocity, to the values obtained with GTP alone. The Ca2+ dependence of peak velocity and turnoff time can be characterized as hyperbolic saturation functions with a K0.5 for Ca2+ of 1.0-1.5 mM in toad RDM. In bovine RDM the Ca2+ dependence of peak velocity and turnoff time has a K0.5 of 0.1 mM Ca2+. The Ca2+ dependence in the reconstituted system is similar to that in bovine RDM for peak velocity (K0.5 = 0.1 mM Ca2+) but differs for turnoff time (K0.5 = 2.5 mM Ca2+). We tested the hypothesis that a soluble modulator, normally required to confer submicromolar Ca2+ sensitivity, was too dilute in our assay by comparing data obtained at one RDM concentration with those obtained at 10-fold higher RDM, and therefore a constituent protein, concentration. We observe no difference and present a formal analysis of these data that excludes the hypothesis that the soluble modulator binds its target protein with Kd less than 5 microM. The lack of submicromolar Ca2+ dependence of any of the steps in the cGMP cascade that underlie cGMP phosphodiesterase activation and inactivation in vitro argues against Ca2+ regulation of these steps having a significant role in the light adaptation of the intact rod.     

Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction

Rod photoreceptors are activated by light through activation of a cascade that includes the G protein-coupled receptor rhodopsin, the G protein transducin, its effector cyclic guanosine monophosphate (cGMP) phosphodiesterase and the second messengers cGMP and Ca2+. Signalling is localised to the particular rod outer segment disc, which is activated by absorption of a single photon. Modelling of this cascade has previously been performed mostly by assumption of a well-stirred cytoplasm. We recently published the first fully spatially resolved model that captures the local nature of light activation. The model reduces the complex geometry of the cell to a simpler one using the mathematical theories of homogenisation and concentrated capacity. The model shows that, upon activation of a single rhodopsin, changes of the second messengers cGMP and Ca2+ are local about the particular activated disc. In the current work, the homogenised model is computationally compared with the full, non-homogenised one, set in the original geometry of the rod outer segment. It is found to have an accuracy of 0.03% compared with the full model in computing the integral response and a 5200-fold reduction in computation time. The model can reconstruct the radial time-profiles of cGMP and Ca2+ in the interdiscal spaces adjacent to the activated discs. Cellular electrical responses are localised near the activation sites, and multiple photons sufficiently far apart produce essentially independent responses. This leads to a computational analysis of the notion and estimate of 'spread' and the optimum distribution of activated sites that maximises the response. Biological insights arising from the spatio-temporal model include a quantification of how variability in the response to dim light is affected by the distance between the outer segment discs capturing photons. The model is thus a simulation tool for biologists to predict the effect of various factors influencing the timing, spread and control mechanisms of this G protein-coupled, receptor-mediated cascade. It permits ease of simulation experiments across a range of conditions, for example, clamping the concentration of calcium, with results matching analogous experimental results. In addition, the model accommodates differing geometries of rod outer segments from different vertebrate species. Thus it represents a building block towards a predictive model of visual transduction.