Speed, sensitivity, and stability of the light response in rod and cone photoreceptors: Facts and models

Abstract

The light responses of rod and cone photoreceptors in the vertebrate retina are quantitatively different, yet extremely stable and reproducible because of the extraordinary regulation of the cascade of enzymatic reactions that link photon absorption and visual pigment excitation to the gating of cGMP-gated ion channels in the outer segment plasma membrane. While the molecular scheme of the phototransduction pathway is essentially the same in rods and cones, the enzymes and protein regulators that constitute the pathway are distinct. These enzymes and regulators can differ in the quantitative features of their functions or in concentration if their functions are similar or both can be true. The molecular identity and distinct function of the molecules of the transduction cascade in rods and cones are summarized. The functional significance of these molecular differences is examined with a mathematical model of the signal-transducing enzymatic cascade. Constrained by available electrophysiological, biochemical and biophysical data, the model simulates photocurrents that match well the electrical photoresponses measured in both rods and cones. Using simulation computed with the mathematical model, the time course of light-dependent changes in enzymatic activities and second messenger concentrations in non-mammalian rods and cones are compared side by side.

In the dark, rod and cone photoreceptors of the vertebrate retina sustain a circulating ionic current that flows along the extracellular space from the inner to the outer segment (Hagins et al., 1970). The circulating current is an outward K⁺ ion flux across the inner segment membrane mediated by voltage-gated K⁺ channels (Bader et al., 1982; Hestrin, 1987; Barnes and Hille, 1989; Maricq and Korenbrot, 1990a, b) and an inward Na⁺ and Ca²⁺ ion flux across the outer segment membrane mediated by cyclic nucleotide-gated ion channels (CNG channels) (Fesenko et al., 1985; Yau and Nakatani, 1985a). Light suppresses this current by closing the outer segment CNG channels and, as a consequence, the cell membrane potential hyperpolarizes (Baylor and Fuortes, 1970; Tomita, 1971; Baylor and Hodgkin, 1973; Schwartz, 1973) initiating the process of vision.

The functional features of the light response of rods and cones are well suited to the ecological needs of vertebrate behavior. Thoroughly dark adapted rods yield a detectable signal, a signal larger than their intrinsic noise, when only a single visual pigment molecule is excited by light (Baylor et al., 1979b) while cones yield a detectable signal only when light flashes excite 4 to 10 visual pigment (VP) molecules per cell (Naarendorp et al., 2010; Koenig and Hofer, 2011; Korenbrot, 2012b). Cones adjust their photosensitivity as a function of mean background intensity, and thus can respond to changes over 9 log units of light intensity, the range of illuminance from a clear night sky (2 × 10⁻³ lux) to that by direct sunlight (1.3 × 10⁵ lux) (Wikipedia.org). Rods, however, adapt over a smaller range of light intensities than do cones (Baylor et al., 1984; Fain et al., 1989; Matthews et al., 1990; Schnapf et al., 1990). Indeed, under bright steady illumination the outer segment dark current can be fully suppressed in rods (response saturation), but not in cones (response cannot be saturated) (Jones et al., 1993; Burkhardt, 1994; Kenkre et al., 2005). In cones, extremely intense steady light suppresses the circulating current for only a brief moment and it then recovers to a new steady value, reflecting reopening of the CNG channels. In human cones, for example, when over 90% of the visual pigment (VP) is bleached, the dark current amplitude is only half that measured in the dark (Kenkre et al., 2005) and the same is observed in cones of non-mammalian species (Jones et al., 1993).

Over the first six log units of light intensity above threshold, cones respond with constant contrast. That is, flashes of a given intensity measured as a percentage of the background intensity generate the same amplitude response regardless of the absolute magnitude of the background light (Normann and Werblin, 1974; Normann and Perlman, 1979; Burkhardt and Gottesman, 1987; Burkhardt, 1994). This feature allows cones to respond over about two log units of light intensity centered on the background level, regardless of the absolute background intensity (Burkhardt and Gottesman, 1987; Perlman and Normann, 1998). This is also the range of intensities relative to the mean background level typical of natural scenes (Mante et al., 2005). The time course of the light response is faster in cones than in rods, and can inform of changes in illuminance as frequent as every 100–200 msec, for example, the interval between eye saccades typical in language reading (Blythe et al., 2006). The chromatic range of the cone response, summed over the absorbance spectra of all known cone opsins (with peak absorbance ranging from 360 nm to 630 nm) is well tuned to the solar spectral irradiance on earth’s surface, a spectrum that ranges from 220 nm to 2400 nm with a single peak at 500 nm (Thuilier et al., 2003).

Rod and cone photoresponses differ in any given vertebrate species, yet both are extremely stable and reproducible. This reflects the exceptional regulation of the cascade of enzymatic reactions that link VP excitation by light to the gating of the CNG ion channels. This enzymatic transduction pathway accomplishes the same task in both receptor types but with different speed, photosensitivity and light and dark adaptation features. The extensive biochemical and biophysical information on the transduction pathways in rods and cones can be difficult to reduce into a single coherent view. Mathematical models offer a succinct and precise tool to describe and understand physiological processes based on the function of the molecules that constitute the processes. Starting with the pioneering mathematical models of phototransduction by Tranchina and Sneyd in cones (Sneyd and Tranchina, 1989; Tranchina et al., 1991) and Forti et al. in rods (Forti et al., 1989; Torre et al., 1990), ever improving, coherent models of phototransduction have evolved to include new and refined biochemical and biophysical information. A number of contemporary models have been developed that quantitatively describe the full complement of reactions involved in the phototransduction pathway. Among them are: rods (Pugh and Lamb, 1993; Hamer et al., 2003; Hamer et al., 2005; Caruso et al., 2010; Shen et al., 2010); cones (Reingruber and Holcman, 2008; Soo et al., 2008; Korenbrot, 2012b). These models share many specific features and generally address either rod or cone phototransduction. In this review, we explore quantitative differences and similarities between the biochemical and biophysical reactions of the phototransduction pathways in rods and cones. We compare and contrast the differences and similarities using the same, comprehensive mathematical model of phototransduction (Korenbrot, 2012a). This model evolves from, and incorporates many features common to preceding models and adds recently discovered regulatory events, particularly with respect to feedback control by cytoplasmic Ca²⁺. The efficacy of the model and the functional significance of many of the molecular differences between the rods and cones are verified by matching simulated and experimental photocurrents measured in dark-adapted photoreceptors.

Brief overview of the evolution of the signal transduction pathway of vertebrate photoreceptors

Evolution of the eye can now be traced from ancient multicellular organisms, related to corals and jellyfish, to humans (Schwab, 2011), but evolution of the retinal photoreceptors transduction pathway is not exclusively associated with the eye (reviewed in (Lamb et al., 2009). Rods and cones are but one example of ciliated sensory neurons that use the ancient cGMP (or cAMP) intracellular signal transduction pathway, a pathway associated with CNG ion channels from its very origin (Johnson and Leroux, 2010; Plachetzki et al., 2010). The structural homology of cGMP-gated ion channels and opsins across the genome of many species suggests the cGMP transduction pathway began with CNG ion channel functionally linked to non-opsin G protein coupled receptor protein (GPCR), which only later gained light sensitivity by the evolution of ancestral GPCR into animal opsins (Fredriksson et al., 2003; Plachetzki and Oakley, 2007; Plachetzki et al., 2010). Indeed, an opsin-CNG channel transduction pathway has been found to operate in Hydra, an ancient animal in the same phylum as corals anemones and jellyfishes. In Hydra blocking CNG channel conductance with the drug l-cis diltiazem abolishes a stereotyped light-driven behavior (Plachetzki et al., 2010).

Signal transduction takes place in the outer segment of rods and cones, which are highly evolved non-motile cilia characterized by an axoneme with a centriole-derived basal body and an elaborate intra-ciliary network of microtubulular fibrils that support an intraflagellar transport system (IFT) (reviewed in (Insinna and Besharse, 2008; Sung and Chuang, 2010). In the evolution of animal photoreceptors two classes of cells, ciliary and rhabdomeric, diverged from a common progenitor. These two photoreceptor classes are distinguished by their structure and are each commonly associated with vertebrate and invertebrate species, respectively. However, recent analysis shows that the two classes of photoreceptors are each associated with a distinct class of opsin molecules and transduction pathways rather than animal phyla (Plachetzki et al., 2005); (Arendt, 2003; Fain et al., 2010). Rhabdomeric opsin signaling is expressed in retinal ganglion cells and ciliary opsin signaling in invertebrates (Davies et al., 2010) (Nilsson and Arendt, 2008). The cilia-associated GPCR-CNG channel signaling pathway of vertebrate photoreceptors is found in phylogenetically diverse organisms (Johnson and Leroux, 2010). Particularly well understood are the GPCR-cyclic GMP (or AMP)-CNG ion channel pathways in ciliated sensory neurons of C. elegans (reviewed in (Bargmann, 2006) and ciliated olfactory neurons of vertebrates (reviewed in (Menini, 2010).

Functional consequence of the differences in rod and cone outer segment cytoarchitecture

The cytoarchitecture of the outer segment is very different in non-mammalian rods and cones, although it is less remarkable among mammalian photoreceptors (reviewed in (Borwein, 1981). In cones there is only one membrane, the plasma membrane that folds back and forth forming lamella and also envelopes these lamella over about half their perimeter (Fetter and Corless, 1987). In rods, in contrast, the plasma membrane forms lamella only over a very short length at the base of the outer segment. These lamella then separate from the plasma membrane forming collapsed, closed disks. The plasma membrane envelops the disks over the full length of the outer segment, but the discs remain electrically disconnected from the plasma membrane.

There are some recognized functional consequences of the structural difference between rod and cone outer segments. The optics in intact eyes direct light rays along a nearly straight line from the inner segment to the outer segments and along the outer segment length. VP molecules at the base of the outer segment absorb photons and, therefore, reduce the photon flux available to the VP at the outer segment’s tip, a phenomenon known as self-screening. Because of their taper, there is less self-screening in cones than in rods. Also, the cone outer segment taper, coupled with the specific geometry of the inner segment, improves the optical performance of cone photoreceptor allowing the inner segment to focus light onto the outer segment (Harosi and Novales Flamarique, 2012).

cGMP diffuses along the outer segment length and, therefore, transduction and adaptation signals extend away from the physical site of photon capture (Hemila and Reuter, 1981; Lamb et al., 1981; Matthews, 1986; Gray-Keller et al., 1999). Because of the differences in their cytoarchitecture, cGMP spreads further along the length of a rod than a cone outer segments of the same diameter (Holcman and Korenbrot, 2004). Across all species, the spatial spread of cGMP at the peak of the dim light photocurrent is 3 to 5 μm in rod outer segments, regardless of their absolute size. In cone outer segments and regardless of their absolute dimensions, the cGMP spatial spread of cGMP at the peak of the dim light photocurrent is 0.7 to 1 μm (Holcman and Korenbrot, 2004; Wu et al., 2006).

Rods, but not cones, respond to single excited VP* molecules with remarkable reproducibility (Rieke and Baylor, 1998; Whitlock and Lamb, 1999). This reproducibility is surprising because of the expected stochastic variability in a sequence of events initiated by one molecule (Rh*), but which invokes the activity of many other proteins as well (GRK, PDE, GC etc.). A specific mechanism is necessary to explain the single photon response reproducibility. Two mechanisms have been considered in theoretical detail and they may well coexists since one does not necessarily invalidate the other. In one scheme SPR reproducibility follows from the fact that rhodopsin inactivates through a sequence of transitions, not as a single event (Rieke and Baylor, 1998; Hamer et al., 2003). A second scheme proposes that SPR reproducibility follows from the physical separation of discs from the plasma membrane. The diffusion of the cGMP signal from the disc surface to the plasma membrane creates a spatial homogeneity that erases memory of the spot on the membrane where the stimulus photon was captured and suppresses SPR variability (Caruso et al., 2010).

The signal transduction pathway in rods and cones

VP in rods (rhodopsin) and cones (cone opsin) are members of the family of GPCR proteins (G protein coupled receptors). Their structure consists of 7 transmembrane alpha-helical domains with a bound light absorbing chromophore, 11-cis retinal (Palczewski, 2006; Park et al., 2008). Photon absorption initiates a sequence of conformational changes, each characterized by a distinct absorption spectrum in the visible range; the conversion rate from one state to another is temperature dependent. The conformational state that activates the transduction enzymatic pathway, Meta-II, first appears at room temperature about 1 msec after photon absorption. The sequence and thermal rates of conversion of various VP* photo-intermediates between the dark state and Meta-II are quite similar in rod and cone visual pigments, regardless of their wavelength of maximum absorbance (Imai et al., 1995, Yoshizawa, 1994 #26102; Imai et al., 1997; Vought et al., 1999; Kusnetzow et al., 2001).

The active VP* state, as long as it exists, repeatedly collides with inactive heterotrimeric G protein molecules. The photoreceptor specific G protein, transducin, exist in the dark as a heterotrimer with bound GDP: Tαβγ-GDP. Upon collision with VP*, an active transducin state, T*, is generated by the exchange of GDP for GTP and dissociation into separate Tα-GTP and a Tβγ subunits (reviewed in (Chen, 2005; Downs et al., 2006; Shichida and Morizumi, 2007). Transducin molecules in rods (GNAT1) and cones (GNAT2) are distinct from each other (Lerea et al., 1986; Lerea et al., 1989). Molecular details of the interaction between Meta-II-rhodopsin and rod-transducin continue to be illuminated through recent studies of protein crystal structure (Noel et al., 1993; Sondek et al., 1994; Sondek et al., 1996; Scheerer et al., 2008; Jastrzebska et al., 2010; Choe et al., 2011). Comparable structural studies do not exist for the cone-specific opsins. Nonetheless, genomic analysis shows that the functional domains in opsin, those that interact with the relevant enzymes of the transduction cascade, are nearly the same in all vertebrate rods and cones (Carleton et al., 2005).

Tα-GTP, for as long as it exists, collides with inactive cGMP-specific phosphodiesterase (PDE6) and generates an active state, PDE*, that catalyzes the hydrolysis of cyclic GMP (Zhang and Cote, 2005; Lugnier, 2006; Conti and Beavo, 2007). Inactive PDE is a tetramer consisting of two catalytic subunits and two inhibitory subunits. The catalytic subunits are distinct in rods (PDEα and PDEβ) and cones (PDEc) (Gillespie and Beavo, 1988; Zhang and Cote, 2005; Muradov et al., 2010). The inhibitory subunits, PDEγ are also different in rods and cones. The enzymatic catalytic rate (k_cat ) and substrate sensitivity (K_m) of each rod PDEα, rod PDEβ and cone PDEc subunits are essentially the same (Muradov et al., 2010). In native rod and cone outer segment membranes, one Tα-GTP molecule effectively relieves PDEγ inhibition at one PDE6 site and this leads to one-half of the maximal PDE activity; two Tα-GTP molecules are necessary to elicit maximal activation (Liu et al., 2009; Muradov et al., 2010). That is, one Tα-GTP activates one of the two catalytic subunits in the holo-PDE dimer and this yields the visual-pigment activated PDE*. PDE* has the enzymatic efficiency (kcat/Km) of one PDE subunit (PDEα or PDEβ or PDEc) because the probability that two Tα-GTP will activate the same PDE multimer and, therefore activate both α and β (in rods) or both c subunits (in cones) is very small.

PDE* hydrolyzes cyclicGMP as long as it remains active. The lifetime of PDE* is controlled by the dynamics of VP* or T* inactivation, depending on photoreceptor type and light-intensity (details below). VP* inactivates because it is phosphorylated by photoreceptor-specific opsin-kinase. Opsin-kinase is a member of the large family of GRK (G-coupled receptor kinase) and two specific homologs have been identified in photoreceptors: GRK1 and GRK7. GRK1 is expressed in all rods, but it is also expressed in cones of some species, for example, mice and rats (Weiss et al., 2001). GRK expression in cones, on the other hand, is heterogeneous. GRK7 is expressed in all cones, except in mice and rat cones, which do not have the GRK7 gene (Hisatomi et al., 1998; Chen et al., 2001; Weiss et al., 2001). In some species, pigs and dogs for example, only GRK7 is expressed in the cones. In most species, however, cones coexpress GRK1 and GRK7: zebrafish, carp (Weiss et al., 2001; Rinner et al., 2005; Tachibanaki et al., 2005; Wada et al., 2006), monkeys and humans (Chen et al., 2001; Weiss et al., 2001).

Both cone and rod VP* have 6 to 7 consensus phosphorylation sites in their cytoplasmic carboxy terminus, depending on species. VP* is progressively less able to activate transducin as the number of sites actually phosphorylated increases (Hurley et al., 1998; Mendez et al., 2000; Kennedy et al., 2004). Phosphorylated-VP*, however, fully ceases to activate transducin only when it interacts with arrestin-1, a protein that binds the cytoplasmic surface of phosphorylated VP* and prevents any further interaction between VP* and transducin (reviewed in (Gross and Burns, 2010; Gurevich et al., 2011). At least two sites on the rhodopsin cytoplasmic carboxy terminus must be phosphorylated to promote arrestin binding, and the functional characteristics of arrestin binding change as the number of phosphorylated sites increases (Vishnivetskiy et al., 2007). Rods and cones express distinct arrestin molecules (Zhu et al., 2002a; Zhu et al., 2002b), and there are two classes of cone arrestin, perhaps in different cone subtypes (Brown et al., 2010; Renninger et al., 2011).

T* inactivates because GTP bound to Tα hydrolyses to GDP, and Tα-GDP re-associates with Tβγ. The intrinsic GTPase activity of Tα-GTP is sluggish and this rate is accelerated by interaction of Tα-GTP with RGS9 (regulator of G protein signaling) {Hε, 1998 #18358}. In fact, Tα-GTP interacts with a multi-protein complex that includes, in addition to RGS9: R9AP (anchoring protein), Gβ5-long, Gβ5-short and γ PDE (Hu and Wensel, 2002; Grant et al., 2006; Wensel, 2008). The molecular identity of the regulators of Tα-GTP appears to be the same in rods and cones (Zhang et al., 2003; Zhang et al., 2006; Wensel, 2008). T* inactivation is rate limited by its catalytic interaction with the “RGS9” multi-protein complex of regulatory proteins (Burns and Pugh, 2010).

To terminate the photoresponse and restore the dark condition, PDE* is inactivated and cGMP is newly synthesized from GTP by membrane-bound guanylate cyclase (GC) (reviewed in (Pugh et al., 1997; Koch et al., 2002). GC activity is Ca-dependent: catalytic activity decreases as Ca²⁺ concentration rises (Lolley and Racz, 1982; Koch and Stryer, 1988; Dizhoor et al., 1994; Koch et al., 2002). Ca-dependence is mediated by the interaction of the membrane-bound GC with soluble, Ca²⁺ binding proteins (Lambrecht and Koch, 1991) named GC-activating proteins (GCAP) (Lambrecht and Koch, 1991; Dizhoor et al., 1995; Gorczyca et al., 1995). GC activity is higher in light than in darkness because illumination lowers cytoplasmic free Ca²⁺ concentration through a well-understood mechanism detailed below.

It is difficult to anticipate the identity of the GC and GCAP protein homologues expressed in any given photoreceptor. Unique GC molecules are expressed in rods (retGCR1 and retGCR2) and cones (retGCC) (Hisatomi et al., 1999; Takemoto et al., 2009). However, the pairing of GCAPs and GCs varies with photoreceptor type and species. In humans, for example, GCAP1, GCAP2, GC1 and GC2 are all expressed in both rods and cones, while GCAP3 is expressed exclusively in cones (Imanishi et al., 2002). Yet neither mice cones (nor rods) express GCAP3 (Imanishi et al., 2002). The cellular expression pattern of GCAPS is even more complex in non-mammals. In zebrafish, for example, there are 6 GCAP isoforms of distinct amino acid composition, including homologues of mammalian GCAP1, 2 and 3, and each cone subtype expresses a particular combination of GCAP molecules (Imanishi et al., 2002; Scholten and Koch, 2011). All GCAPs, nonetheless, are members of the same genomic family: they are myristoylated Ca/Mg-binding proteins of the EF-hand superfamily. GCAPs consist of four EF-hands; one does not bind metals while the other three can bind Ca²⁺ and Mg²⁺. GC activation at low Ca²⁺ and its inhibition at high Ca²⁺ follow a cycle of Ca²⁺/Mg²⁺ exchanges on GCAP. At low Ca²⁺, Mg²⁺ binds three EF-hands and GCAP activates GC. When Ca²⁺ concentration raises, Ca²⁺ replaces Mg²⁺ in one of the three EF hands and this inhibits GC activity (Dizhoor and Hurley, 1999; Dizhoor et al., 2010).

Light- and Ca²⁺-dependent changes in cytoplasmic cGMP concentration are translated into a membrane current through the activity of the cyclic GMP-gated (CNG) ion channels, the only ion channels present in the outer segment plasma membrane (Cook et al., 1989; Karpen et al., 1992). The probability these channels are open or closed is directly controlled by the cytoplasmic cGMP concentration (Haynes et al., 1986; Zimmerman and Baylor, 1986; Matthews, 1987; Haynes and Yau, 1990; Picones and Korenbrot, 1994). Although the principal gating mechanism of cGMP is to change the open-to-close probability, CNG channels exhibit more than one open conductance state and cGMP also changes the absolute conductance of the open channels (Sesti et al., 1994; Bucossi et al., 1997). CNG channels are heteromeric aggregates of α and β subunits (Kaupp and Seifert, 2002; Biel and Michalakis, 2009). Rod channels are assembled from 3 CNGA1 subunits and 1CNGB1 (Weitz et al., 2002; Zheng et al., 2002; Zhong et al., 2002). Recent X-ray structural analysis of analogous regions in the structure of rod and cone channel subunits suggest that cone channels are assembled from 3 CNGA3 subunits and 1CNGB3 subunits (Shuart et al., 2011).

CNG channels are selectively permeable to cations over anions, but also select among mono and divalent cations (Picones and Korenbrot, 1992; Zimmerman and Baylor, 1992; Tanaka and Furman, 1993; Haynes, 1995). The channels are permeable to Ca²⁺ ions, but permeating Ca²⁺ also binds to specific sites in the open pore from which it can be displaced by the transmembrane voltage (Colamartino et al., 1991; Eismann et al., 1994; Haynes, 1995; Picones and Korenbrot, 1995). This complex permeation and binding interaction between Ca²⁺ ions and the channel is physiologically important because it defines the voltage-dependence of the cGMP-gated current (Zimmerman and Baylor, 1992; Wells and Tanaka, 1997; Ohyama et al., 2002). The relative Ca²⁺ to Na⁺ permeability is higher in cone than in rod CNG channels (Frings et al., 1995; Picones and Korenbrot, 1995). Because of this permeability difference, in physiological ionic solutions the fraction of the current carried by Ca²⁺ is about twice as large in cone as in rod CNG channels (Ohyama et al., 2000; Ohyama et al., 2002).

There exists only a single class of active ion transporters in the outer segment plasma membrane, Na⁺/Ca²⁺, K⁺ ion exchangers (Cervetto et al., 1989; Lagnado and McNaughton, 1991; Schnetkamp et al., 1991). These ion carriers transport Ca²⁺ out of the outer segment, against an electromotive force, driven by the thermodynamically favored Na⁺ influx. The Na⁺/Ca²⁺, K⁺ transporters (NCKX) are members of the superfamily of CaCA (Ca²⁺/cation antiporter) transport proteins. Different homologues are expressed in rods (NCKX1) and cones (NCKX2) (reviewed in (Schnetkamp, 2004; Lytton, 2007). The ion transport rate is controlled by the intra and extracellular concentration of each of the transported ions, as well as membrane voltage. The cation dependencies of NCKX1 and NCKX2 (external K⁺, external Na⁺, internal Ca²⁺ ) are very similar to each other (Sheng et al., 2000). In intact photoreceptors under voltage-clamp, Na⁺ and K⁺ concentrations are constant and the transporter rate is controlled only by the changing intracellular Ca²⁺ (Perry and McNaughton, 1993).

Cytoplasmic free Ca²⁺ in the outer segment is controlled by the dynamics of its influx (via CNG channels) and efflux (via the NCKX transporter), combined with the action of cytoplasmic Ca²⁺ buffers (Yau and Nakatani, 1985b; Miller and Korenbrot, 1987; Lagnado et al., 1992). In the dark, the rates of Ca²⁺ inflow and outflow are the same and cytoplasmic free Ca²⁺ concentration is constant. Light causes a decrease in outer segment free Ca²⁺ because illumination reduces Ca²⁺ influx as CNG channels close (Gray-Keller and Detwiler, 1994; Younger et al., 1996; Sampath et al., 1999). Since Na⁺/Ca²⁺,K⁺ exchanger transport is itself controlled by cytoplasmic free Ca²⁺, then as Ca²⁺ concentration decreases so does the transporter-mediated Ca²⁺ efflux. Under steady illumination, therefore, Ca²⁺ efflux soon becomes equal to the reduced influx and a new stationary condition is reached with a new steady, but lower Ca²⁺ concentration.

The light-dependent change in cytoplasmic Ca²⁺ controls the function of several molecules in the transduction pathway: the enzymatic velocity of GC and GRK, the cGMP-sensitivity of CNG channels and the transport rate of the Na⁺/Ca²⁺,K⁺ exchanger. Except for the ion exchanger, Ca²⁺ control is mediated by the function of soluble, Ca²⁺-binding proteins that interact with the target protein. For GC, it is the GCAP proteins. For GRK it is recoverin (Kawamura et al., 1996; Sato and Kawamura, 1997; Tachibanaki et al., 2005). Recoverin is a myristoylated protein, member of the EF-hand superfamily (Gorodovikova et al., 1994; Kawamura et al., 1996; Kawamura and Tachibanaki, 2002); (Flaherty et al., 1993; Weiergraber et al., 2003). Recoverin has 4 EF hands, of which two bind Ca²⁺ each with different apparent affinity. At high Ca²⁺, recoverin binds to GRK and is physically trapped between opsin and the kinase, thus preventing GRK from phosphorylating the VP (Ames et al., 2006). At low Ca²⁺, recoverin does not bind to GRK and the enzyme can act on VP*.

The cGMP dependence of rod and cone CNG channel activity is Ca²⁺ dependent: the cGMP concentration that opens a given fraction of the channels is lowered as Ca²⁺ concentration decreases (Nakatani et al., 1995a; Sagoo and Lagnado, 1996; Rebrik et al., 2000; Rebrik and Korenbrot, 2004). This Ca-dependent modulation of ligand sensitivity depends on the interaction between the CNG channel protein and a Ca²⁺ binding, soluble modulator protein. The channel modulator in rods is calmodulin (Hsu and Molday, 1994; Gordon et al., 1995; Bauer, 1996), and CNG-modulin, a newly discovered protein in non-mammalian cones (Rebrik et al., 2012a). Search is underway for a mammalian homolog of CNG-modulin.

Animal models and methods to investigate rod and cone transduction pathways

To focus on quantitative details, rather than generalities, we review in detail the transduction pathway underlying flash responses of rods in tiger salamander (Ambystoma tigrinum) and single cones in striped bass (Morone saxitilis) as models of all rods and cones. References quoted are limited, in as much as possible, to these two species, even when comparable information exists for photoreceptors in other species. Electrophysiological and biophysical data in these two photoreceptors are rich, but biochemical data are not. On the other hand, extensive biochemical research has been conducted in rods of other amphibian (toad Buffo and frog Rana) and cones of other fish (carp Cyprinus and zebrafish Danio). Biochemical data measured in mammals are used only when not available for non-mammalian species to avoid unjustified parametric values. The need to mix data gathered in different species may well lead to some errors and approximations, but the rod cone differences are so remarkable that errors that will likely be corrected in the future are unlikely to change profoundly our current view.

Transduction signals have been measured in rods and cones of several mammals (Tamura et al., 1989; Nakatani et al., 1991; Zhang et al., 2003), including primates and humans (Baylor et al., 1984; Schnapf et al., 1990; Kraft et al., 1993; Schneeweis and Schnapf, 1999). The opportunity to create genetically modified rod and cone photoreceptors has also fomented studies in mice as animal models (Fu and Yau, 2007). It turns out, however, that mammalian and non-mammalian rods are rather similar in their transduction characteristics, once differences in temperature and the Q10 of enzymatic activities are accounted for (Baylor et al., 1983; Lamb, 1984). The features of cone photosignals, on the other hand, are far more diverse across species and can differ even within the same species depending on the opsin molecule they express. In striped bass, for example, there are single and twin cones that express different opsins, λmax 542 nm and 605 nm respectively, and the receptors differ in photosensitivity, in the waveform of their photocurrents and their light-adaptation features (Miller and Korenbrot, 1993a 25379).

Several voltage- and ligand-gated ion channels are present in the plasma membrane of rod and cone inner segments (rods: (Bader et al., 1982; Corey et al., 1984; Hestrin, 1987), cones(Maricq and Korenbrot, 1988, 1990a, b; Tatsukawa et al., 2005; Liu et al., 2006). The activity of these channels serves to control the photoreceptor membrane voltage and determines the features of their synaptic signal. The activity of these channels must be distinguished from that of the light-driven CNG channels, an objective met by measuring photocurrents under voltage clamp. Photocurrent kinetics are accurately measured in rods, even in the absence of voltage-clamp, with the use of suction electrodes that record outer segment currents excluding the inner segment (Baylor et al., 1979a). This technique is appropriate because the outer segment membrane capacitance is small (8.6 ± 1.3 pF in tiger salamander) (Miller and Korenbrot, 1994), and under physiological ionic solutions rod cGMP-dependent current amplitude is voltage-independent over the voltage range measured between darkness and light (−30 mV to −60 mV) (Baylor and Nunn, 1986; Miller and Korenbrot, 1994). The tiger salamander rod photocurrents shown here were measured under voltage clamp in the whole-cell mode using tight-seal electrodes in the “perforated” patch configuration (Horn and Marty, 1988; Miller and Korenbrot, 1994).

Accurate current kinetics in bass cones can only be measured under voltage clamp because the outer segment plasma membrane capacitance is large (58.1 ± 13.2 pF (Miller and Korenbrot, 1993b). Bass single cone photocurrents shown here were measured under voltage clamp in the whole-cell mode (Korenbrot, 2012a). However, the method suffers because of the loss of outer segment regulatory proteins by diffusion into the electrode lumen (Rebrik and Korenbrot, 1998, 2004). Photocurrents shown here were stable because they were recorded within 7–8 minutes after first attaining the whole cell mode (7–8 minutes).

Dark current noise and the thermal stability of visual pigments

The amplitude of the outer segment dark current (Table 1) is only 2–5% percent of the maximum possible value of this current in both rods and cones (Hestrin and Korenbrot, 1987; Cameron and Pugh, 1990; Rebrik and Korenbrot, 1998). Because the maximum probability of CNG channels being in their open state is about 87%, the full extent of the photocurrent reflects controlled changes in the probability of CNG channels being open between a few percent (in the dark) and zero. Although this makes the overall magnitude of the photocurrent small, it makes it extremely reliable: The statistical variance in the probability of channel opening, that is, the uncertainty that the channel is in fact open with the desired probability is least in the extremes, when the probability is either very small or very large (Picones and Korenbrot, 1994; Alvarez et al., 2002).

Table 1.

Model parameter values that best simulate dark current in rods and cones^a

	Parameters	Units	b Cones	c Rods
CNG ion channel	Idark	pA	27.3 ± 10.5	70.1 ± 18.9
	cGMPdark	μM	d27.9 ± 14.2	10.9 ± 1.6
PDE	dark VPDE	μM/sec	e6.5 ± 1.48	4.26 ± 1.0
	Km	μM	f26	10
	εdark	μM/sec	g12.6 ± 0.9	8.2 ± 1.9
GC	darkVGC	μM/sec	h6.5 ± 1.48	4.26 ± 1.0
Ca2+ influx	${{}^{in}J}_{Ca}^{\mathit{dark}}$	μM/sec	i 15 ± 5.8	16.3 ± 4.3
	Pf		j0.34	0.14
Ca2+ efflux	${{}^{\mathit{out}}J}_{Ca}^{\mathit{dark}}$	μM/sec	k15 ± 5.8	16.3 ± 4.3
Free [Ca2+]		μM	l0.4	0.6

^aValues listed are referred to as “statistical”. They were measured experimentally in each and every one of the cells under investigation and the results averaged.

^bStriped bass single cones, mean ± SD, N=18.

^cTiger salamander rods, mean ± SD, N=20.

^dComputed from the circulating dark current (Text equations (1.1) and (1.2). Imax=2500 pA in cones (Rebrik et al., 2000), 1500 pA in rods (Hestrin and Korenbrot, 1987).

^eComputed from the rate of dark current change when PDE or GC are suddenly and completely blocked, using text equations (1.1), (1.2) and the cytoplasmic free cGMP in the dark. The values listed are the mean of experimental measurements in intact tiger salamander rods (Hodgkin and Nunn, 1988; Koutalos et al., 1995b) and bass cones (Holcman and Korenbrot, 2005).

^fExperimental data. In rods (Dumke et al., 1994b; Leskov et al., 2000; Muradov et al., 2010). In cones (Gillespie and Beavo, 1988; Muradov et al., 2010).

^gFrom text equation (1.3).

^hIn darkness, GC and PDE enzymatic activities are the same.

ⁱComputed from the circulating dark current. Text equation (1.6).

^jExperimental data for both rods and cones (Ohyama et al., 2000).

^kIn darkness Ca²⁺ influx and efflux rate are the same.

^lAssigned from experimental data. Rods (Gray-Keller and Detwiler, 1994; Younger et al., 1996). Cones (Sampath et al., 1999).

The amplitude of the dark current is not constant but fluctuates about a mean value. This statistical variance is referred to as current noise and is characterized by the amplitude and frequency of the fluctuations. The amplitude of dark current noise is critically important to determine photoreceptor light threshold: A light signal is detectable only if its amplitude exceeds that of the dark current noise. Photoreceptor dark current noise is caused by three different phenomena: 1) variance in the probability of open-to-close transitions of the CNG channel, 2) fluctuations in the enzymatic activity of phopsphodiesterase, and 3) spontaneous thermal activation of the VP. Noise due to channel stochastic behavior is of little physiological consequence because it is minimized, as discussed above, and it contributes to current noise only at frequencies much higher than the frequency of the photoresponse (Rieke and Baylor, 1996; Holcman and Korenbrot, 2005).

PDE enzymatic activity in the dark fluctuates about its mean value, causing variance in the cytoplasmic cGMP concentration. The current noise thus generated is continuous in time and its power spectrum is different from that of the light-dependent signal (Rieke and Baylor, 1996, 2000; Holcman and Korenbrot, 2005). In rods, the rms amplitude of the PDE-generated current noise is small (~0.035 pA) (Baylor et al., 1980; Rieke and Baylor, 1996), much smaller than that of signals generated by excitation of a single rhodopsin molecule (~1 pA), which makes the single rhodopsin response (SRR) readily detectable (Baylor et al., 1979b; Yau et al., 1979b).

The membrane current signal generated by VP thermal bleaching is indistinguishable from that generated by light-activated VP*. In rods, therefore, dark current noise arises from the sum of the small continuous component due to fluctuating PDE activity, and discrete large events that arise from rhodopsin thermal bleaching (Baylor et al., 1980). The difference between SRR generated by heat and those generated by light is only in their frequency. Light events, of course, occur at a frequency determined by the rate of photon delivery (Whitlock and Lamb, 1999; Doan et al., 2006). The rate of thermal events is determined by temperature and the number of rhodopsin molecules per rod. In toad rods at room temperature, for example, 1 Rh (out of 3x10⁹) is bleached by heat every 50 sec (Yau et al., 1979a; Baylor et al., 1980; Vu et al., 1997).

The thermal stability of VP reflects the strength of the bond between the 11-cis-retinal chromophore and the opsin protein. Whether the VP is expressed in rods or cones, thermal stability decreases as the wavelength of maximum absorbance shifts from blue to red (Luo et al., 2011). In green cones, opsin (543 nm) is nearly as stable as rhodopsin (520 nm), but the estimated single opsin response is rather small (~0.08 pA in bass cones), much smaller than the PDE-generated current noise amplitude (~0.28 pA) (Rieke and Baylor, 2000; Holcman and Korenbrot, 2005). In green cones, hence, the dominant source of dark current noise is the fluctuation in PDE activity. Furthermore, it can be expected that a signal will be detected above noise only when at least 3 to 4 VP molecules are excited simultaneously (Holcman and Korenbrot, 2005). Indeed, the signal threshold in bass green cones is the simultaneous absorption of 4–7 photons (Korenbrot, 2012b).

Because red opsin is so much less stable than green or blue opsin (Luo et al., 2011), VP thermal activation is the dominant source of dark noise in red-sensitive cones (Rieke and Baylor, 2000; Sampath and Baylor, 2002). The red cone dark current noise is larger in amplitude than that of green cones; hence, red cones can be expected to be less photosensitive than green ones. In striped bass, for example, one class of red-sensitive twin cones are 40 times less light sensitive than the green cones (Miller and Korenbrot, 1993a). An elegant demonstration of the relation between opsin absorbance maximum and dark current noise and photosensitivity are experimental studies of Xenopus rods transformed to express human red cone opsin. The photoresponses are rod-like in waveform indicating cone opsin can commandeer the rod transduction enzymes, but they are less sensitive and much noisier than wild type rods indicating dark current noise and sensitivity are determined by the relatively unstable red cone opsin (Kefalov et al., 2003). Qualitatively similar findings have been made in transgenic mice rod photoreceptors expressing the green-sensitive cone opsin, except the cone opsin in these transgenic rods is much less stable than expected (Sakurai et al., 2007).

Outer segment circulating current and biochemical activity in the dark

Rod photoreceptors in the dark consume more energy than they do in the light calculated as the rate of ATP hydrolysis per sec (Okawa et al., 2008). This because sustenance of the circulating dark current requires the activity of ATP-dependent Na⁺ pumps located in the inner segment plasma membrane (Hagins et al., 1970). Because in rods light fully suppresses the dark current more energy is consumed in the dark than the light. In cones, on the other hand, energy consumption in the dark is essentially the same as rods, but energy consumption remains high in the light because the circulating current is never suppressed, even at light levels that bleach over 95% of the VP (Jones et al., 1993; Kenkre et al., 2005).

Cytoplasmic cGMP concentration in the dark

Values presented in the following sections, whether experimentally measured or taken from the literature, are specified in as much as possible for tiger salamander rods (or other non-mammalian rods) and striped bass single cones (or other non-mammalian cones). For convenience, however, they are referred to as rod or cone values, respectively. Citations also are not comprehensive, but limited to the non-mammalian rods and cones, if possible, and bass and tiger salamander photoreceptors preferably.

The amplitude of the outer segment dark current is a direct measure of the standing cytoplasmic free cGMP concentration. For both rods and cones, the relationship between current amplitude and cGMP concentration is experimentally known, therefore, dark cytoplasmic cGMP concentration can be calculated for any photoreceptor by measuring its dark current.

In both rods and cones the cGMP dependence of current amplitude is given by the Hill equation (reviewed in (Yau and Baylor, 1989):

$$\frac{I(\mathit{cGMP},Ca)}{I_{\mathit{max}}}=\frac{{[\mathit{cGMP}]}^{n_{\mathit{CNG}}}}{{[\mathit{cGMP}]}^{n_{\mathit{CNG}}}+K_{\mathit{cGMP}}{(Ca)}^{n_{\mathit{CNG}}}}$$ (1.1)

where I _{(cGMP, Ca )} is outer segment membrane current, I_max is its maximum possible value, [cGMP] is cGMP concentration, n_CNG is a dimensionless parameter that denotes the cooperativity of cGMP in gating the CNG channels, and K_cGMP(Ca) is the cGMP concentration at which current is half its maximum value.

The value of K_cGMP is invariant when measured in membrane fragments detached from salamander rod or bass cone outer segments (Picones and Korenbrot, 1992; Sagoo and Lagnado, 1996; Hackos and Korenbrot, 1997), but it is Ca-dependent in intact photoreceptors (Nakatani et al., 1995a; Sagoo and Lagnado, 1996; Rebrik et al., 2000). The quantitative features of this modulation are one of the most significant physiological differences between receptor types. In rods the modulation is small in extent and occurs only at very low Ca²⁺ concentration, whereas in cones it is much larger in extent and its Ca²⁺ sensitivity overlaps the concentration range of the lightdependent changes in outer segment free Ca²⁺. In both bass cones and salamander rods the dependence of K_cGMP(Ca) on Ca²⁺ is well described by:

$$K_{\mathit{cGMP}}(Ca)={{}^{min}K}_{\mathit{cGMP}}+({{}^{max}K}_{\mathit{cGMP}}-{{}^{min}K}_{\mathit{cGMP}})\frac{Ca}{Ca+{{}^{\mathit{CNG}}K}_{Ca}}$$ (1.2)

where ^min K_cGMP and ^max K_cGMP are minimum and maximum values of K_cGMP(Ca), Ca is cytoplasmic free Ca²⁺ concentration and ^CNG K_Ca is the Ca²⁺ concentration at which $K_{\mathit{cGMP}}={{}^{min}K}_{\mathit{cGMP}}+\frac{{{}^{max}K}_{\mathit{cGMP}}-{{}^{min}K}_{\mathit{cGMP}}}{2}$. On average in bass single cones the values of ^min K_cGMP and ^maxK_cGMP are 105 μM and 316 μM, respectively, and ^CNG K_Ca is 0.86 μM (Rebrik and Korenbrot, 1998; Rebrik et al., 2000). In contrast, in salamander rods ^min K_cGMP and ^max K_cGMP are 28 μM and 37 μM, respectively, and ^CNGK_Ca is 0.055 μM (Sagoo and Lagnado, 1996). The dependence is on a 1.4 power of Ca²⁺. The same values are reported for frog rods (Nakatani et al., 1995b). Mean measured values of dark current amplitude and the inferred dark cyclic GMP concentrations are listed in Table 1.

cGMP metabolic flux in the dark

cGMP concentration in the dark is high because the nucleotide is continuously synthesized by GC. The concentration is constant because the rate of synthesis is equal and opposite the rate of hydrolysis by PDE active in darkness.

PDE enzymatic activity follows Michaelis-Menten kinetics and its Km is known in both rods (Leskov et al., 2000; Muradov et al., 2010) and cones (Gillespie and Beavo, 1988; Huang et al., 2004).

$${{}^{\mathit{dark}}V}_{\mathit{PDE}}={\epsilon }_{\mathit{dark}}\frac{{[\mathit{cGMP}]}_{\mathit{dark}}}{{[\mathit{cGMP}]}_{\mathit{dark}}+{{}^{\mathit{cGMP}}K}_m}$$ (1.3)

where ^darkV_PDE is the PDE catalytic activity in the dark, [cGMP]_dark is the free cytoplasmic cGMP concentration and ^cGMPK_m is the Michaelis-Menten constant.

$${\epsilon }_{\mathit{dark}}=\frac{k_{\mathit{cat}}{}^{\mathit{dark}}N\ast }{{LV}_{OS}}$$ (1.4)

k_cat is the enzymatic turnover rate per molecule, N * is the number of active PDE* in darkness, L is Avogadro’s number, V_OS is outer segment volume.

GC enzymatic activity is Ca²⁺-dependent in both rods (Lolley and Racz, 1982; Koch and Stryer, 1988) and cones (Takemoto et al., 2009) and given in the dark by:

$${{}^{\mathit{dark}}V}_{GC}=\left(\frac{V_{GC}^{max}}{1+{\left(\frac{{}^{\mathit{dark}}Ca}{K_{Ca}}\right)}^n}\right)$$ (1.5)

where ^darkV_GC is the GC catalytic velocity in darkness, $V_{GC}^{max}$ is the maximum enzyme activity, ^darkCa is the cytoplasmic free Ca²⁺ concentration in the dark, K_Ca is the Ca²⁺ concentration at which the enzyme activity is half its maximum value and n is a dimensionless parameter that denotes cooperativity.

In the analysis detailed here, we assigned ^darkCa to be 0.4 μM in the bass cones and 0.6 μM in the salamander rods. These are near the mean values of free Ca²⁺ concentration measured in other non-mammalian rods (Korenbrot and Miller, 1989; Gray-Keller and Detwiler, 1994; McCarthy et al., 1994) and cones (Sampath et al., 1999; Leung et al., 2007) at circulating dark currents comparable to those of the bass cones and salamander rods.

^darkV_GC and ^darkV_PDE are experimentally known for bass cones and tiger salamander rods. In the dark, when these photoreceptors are suddenly exposed to a membrane permeable PDE inhibitor, the circulating dark current increases in amplitude reflecting net cGMP synthesis by GC no longer opposed by the blocked PDE activity (Holcman and Korenbrot, 2005) (Hodgkin and Nunn, 1988). The rate of dark current change upon pharmacological block of PDE is a direct measure of the dark GC catalytic activity. The same enzymatic rates are measured for PDE and GC when the respective counter balancing enzyme is blocked (Hodgkin and Nunn, 1988). From the experimentally measured changes in dark current upon suppression of one enzyme or the other, we computed PDE enzymatic activity in the dark. To this end, we first converted the rate of current change to a rate of cGMP concentration change using text equation (1.1), enzymatic activity was then computed based on this rate, and the dark cGMP concentration known from dark current amplitude measured immediately before the pharmacological perturbation (Table 1). ε_dark was thus known for each cell from experimental data, without the need to know the ^darkN * value.

Ca²⁺ influx and efflux in the dark

Ca²⁺ influx, is a constant fraction of the outer segment inward dark current, and is given by (in μM/sec when the current is measured in pA).

$${{}^{in}J}_{Ca}=\frac{I_{OS}{P}_f{10}^6}{{\mathit{zFV}}_{OS}{B}_{\mathit{uff}(Ca)}}$$ (1.6)

where I_OS (pA) is the outer segment membrane current current, P_f is the fraction of the dark current carried by Ca²⁺, z is Ca²⁺ valence, F is Faraday’s constant, V_os is the outer segment cytoplasmic volume and B_{uff (Ca )} is the cytoplasmic Ca²⁺ buffering capacity, defined below. P_f is significantly higher in cone than rod CNG channels (Ohyama et al., 2000; Ohyama et al., 2002)(Table 1). The Ca²⁺ influx in the dark is the solution of this equation when the outer segment current is the dark circulating current.

Ca²⁺ efflux, is mediated by the Na⁺/Ca²⁺, K⁺ exchanger. The exchanger transport rate is controlled by the intra and extracellular concentrations of Ca²⁺, Na⁺ and K⁺ as well as membrane voltage (Sheng et al., 2000); (Perry and McNaughton, 1993). Assuming light does not change the Na⁺ and K⁺ concentrations and under voltage-clamp, the exchanger-mediated Ca²⁺ efflux is controlled by cytoplasmic Ca²⁺ and given (in μM/sec) by:

$${{}^{\mathit{out}}J}_{Ca}=\frac{2{{}^{\mathit{out}}I}_{\mathit{NCKX}}^{max}{10}^6}{{\mathit{zFV}}_{OS}{B}_{\mathit{uff}(Ca)}}\left[\frac{Ca}{Ca+K_{Ca}^{\mathit{exc}}}\right]$$ (1.7)

where $I_{\mathit{NCKX}}^{max}$ (in pA) is the maximum exchanger current and other terms are the same as in text equation (1.6). The term in the square parenthesis is the Ca²⁺ dependence of the Na⁺/Ca²⁺ K⁺ exchanger transport rate where Ca is free cytoplasmic Ca2+ in the dark is and $K_{Ca}^{\mathit{exc}}$ is the Ca²⁺ concentration at which the transport rate is half its maximum value. Ca²⁺ efflux in the dark is the solution of this equation when Ca²⁺ is the cytoplasmic free Ca²⁺ in the dark.

Cytoplasmic Ca²⁺ buffer capacity, is a feature of all biological cells, but the quantitative characteristics of this function are known in detail in relatively few instances (reviewed in (Neher, 1995). The only study available on the subject in photoreceptors is in tiger salamander rods, an investigation that suggests there exist two instantaneous buffer systems, one of high affinity and low capacity that operates below 1 μM free Ca²⁺ and another of low affinity and high capacity that operates at higher Ca²⁺ levels (Lagnado et al., 1992). If buffer systems in cones are similar to those rods, and assuming buffer molecules instantaneously bind Ca²⁺ at single sites with conventional equilibrium kinetics, it can be stated that in both receptor types (Lagnado et al. 1992):

$${Ca}_{\mathit{TotB}}=\frac{C_{HA}Ca}{Ca+K_{HA}}+(B+1)Ca$$ (1.8)

where Ca is the free ion concentration, Ca_TotB is the total Ca²⁺ (free plus buffer bound), C_HA is the total concentration of the high affinity buffer of Michaelis-Menten constant K_HA and B is the buffer capacity of the low affinity buffer.

Ca²⁺ buffering capacity is the ratio of bound to free Ca²⁺, a parameter frequently assigned a single value, but which, in fact, is a function of Ca²⁺, the derivative of equation (1.8) (Berlin et al., 1994; Neher, 1995)

$$\mathit{Buff}(Ca)=\frac{{\mathit{dCa}}_{\mathit{TotB}}}{\mathit{dCa}}=\frac{C_{HA}{K}_{HA}}{{(Ca+K_{HA})}^2}+B+1$$ (1.9)

Biophysical and biochemical processes in the light

Following is a mathematical narrative of the reactions in the light transduction pathway of salamander rods and bass single cones. The majority of the reactions and their mathematical representation are part of and consistent with recent models (Hamer, 2000; Hamer et al., 2005; Soo et al., 2008; Burns and Pugh, 2009; Shen et al., 2010; Korenbrot, 2012b; Reingruber and Holcman, 2008 ). The model used here enriches previous ones because it incorporates the known quantitative characteristics of all Ca²⁺-dependent reactions in both rods and cones: GC enzymatic activity, GRK enzymatic activity, CNG channels ligand sensitivity, and Na⁺/Ca²⁺ K⁺ transport rate. The model serves as a tool to compare rod and cone transduction pathways in detail.

Time course of visual pigment activation and inactivation

The number and rate of delivery of photons define the rate of visual pigment activation into a state, VP*, that interacts with transducin to initiate the phototransduction process. VP* inactivates because opsin is phosphorylated by G protein-coupled receptor kinase (GRK) (Chen et al., 1995; Baylor and Burns, 1998). Complete and reproducible rhodopsin inactivation requires multiple phosphorylation of each molecule (Mendez et al., 2000). The time course of VP* inactivation is complex because GRK catalytic rate depend on the state of VP* phosphorylation: the rate of phosphorylation of additional sites depends on the number of sites already phosphorylated (Hurley et al., 1998).

The number of physiologically relevant VP* phosphorylation sites is controversial (Hamer et al., 2003; Caruso et al., 2010). Based on certain experimental results (Doan et al., 2006) discussed further below, we adopted 6 as the number of relevant phosphorylation sites. Because the efficiency of transducin activation decays rapidly as each site is phosphorylated (decays by about a factor of 2 for each added phosphate (Gibson et al., 2000), whether 4, 5 or 6 sites are phosphorylated is of relatively little consequence in the waveform of the rod or cone photocurrent simulations. Arrestin can only bind to phosphorylated VP* and only after arrestin binding are VP* and its phosphorylated products completely unable to activate transducin (Gross and Burns, 2010).

GRK adds phosphates one at a time at a rate γ_nPi, which depends on n_Pi the number of phosphorylated sites. Each phosphorylated state of VP* is identified as ${VP}_{n_{Pi}}^{\ast }$. where 0 ≥ ·· n_Pi ·· ≤ 6. Arrestin binds to phosphorylated VP* with rate μ_nPi and quenches the ability of VP* to activate transducin. Therefore, the rate of change of the number of VP* molecules with n_Pi phosphorylated sites is given by:

$$\frac{{\mathit{dVP}}_0^{\ast }(t)}{dt}=\mathit{Phot}(t)-{\gamma }_0{VP}_0^{\ast }(t)$$ (2.1)

$$\frac{{\mathit{dVP}}_1^{\ast }(t)}{dt}={\gamma }_0{VP}_0^{\ast }(t)-({\gamma }_1+{\mu }_1){VP}_1^{\ast }(t)$$ (2.2)

$$\begin{array}{c}·\\ ·\\ \frac{{\mathit{dVP}}_{n_{P_i}}^{\ast }(t)}{dt}={\gamma }_{n_{Pi}-1}{VP}_{b_{Pi}-1}^{\ast }(t)-({\gamma }_{n_{Pi}}+{\mu }_{n_{Pi}})V{P}_{n_{Pi}}(t)\end{array}$$ (2.3)

where Phot(t) is the number of VP* molecules produced by stimulus photons, γ_nPi is the rate of phosphorylation of VP* with n_Pi phosphorylated sites and μ_nPi is the rate of arrestin-dependent quenching of phosphorylated-VP*.

The rate of VP* phosphorylation, γ_nPi, decreases exponentially as the number of phosphorylated sites increases:

$${\gamma }_{(n_{Pi}+1)}={\gamma }_{n_{Pi}}{e}^{-\omega \gamma }$$ (2.4)

where ω_γ is a constant. μ_nPi is assumed to increase linearly with the number of phosphorylated sites n_Pi. This is a simplification since experimental data shows at least two sites must be phosphorylated before arrestin binds phosphorylated Rh*.

$${\mu }_{n_{Pi}}=n_{Pi}{\mu }_0$$ (2.5)

The GRK catalytic activity is Ca²⁺-dependent. The Ca²⁺ dependence of cone VP* phosphorylation rate is given by (our fit to the descriptive data) (Sato and Kawamura, 1997):

$${\gamma }_0={\gamma }_{\mathit{max}}\left(0.1+0.9\left(\frac{1}{1+\frac{Ca}{{{}^{\gamma }K}_{Ca}}}\right)\right)$$ (2.6)

where γ_max is the maximum possible value of this rate and ^γK_Ca is the Ca²⁺ concentration at which γ₀ = 0.55γ_max.

Time course of PDE activation and inactivation

VP* interacts with the G-protein transducin and generates T* (Tα-GTP), an activated form of the G-protein. Ψ_nPi is a rate gain that specifies the number of T molecules activated per sec by one VP*, a value that declines with the number of phosphorylated sites in VP. The affinity between of VP* and T declines exponentially with approximately 2-fold decrease per phosphorylation (Gibson et al. 2000). Thus:

$${\mathrm{\Psi }}_{(n_{Pi}+1)}={\mathrm{\Psi }}_{n_{Pi}}{e}^{-{\omega }_{\mathit{act}}}$$ (2.7)

Where, again, n_Pi is the number of phosphorylated sites, between 0 and 6, and ω_act =0.69 is the rate of exponential decay, an experimentally known value (Gibson et al., 2000).

One T* activates one PDE subunit in the PDE holo-enzyme to produce light-activated PDE*. PDE* inactivates at a rate α_PDE, which is the same as the rate at which T* disappears. The time course of PDE* existence, therefore, is given:

$$\frac{\mathit{dPDE}\ast (VP\ast ,t)}{dt}=\mathrm{\sum }{\mathrm{\Psi }}_{n_{Pi}}{VP}_{n_{Pi}}^{\ast }-{\alpha }_{\mathit{PDE}}{\mathit{PDE}}^{\ast }(t)$$ (2.8)

T* disappearance requires its interaction with a multi-protein complex that includes: RGS9, R9AP, Gβ5L and γPDE (reviewed in (Wensel, 2008). The best present model of this complex interaction posits that T* and PDE* form a single T*-PDE* molecular unit that interacts with a second molecular unit, composed of a multi-protein assembly of regulatory enzymes referred to as “RGS9” (reviewed in (Burns and Pugh, 2010). The RGS9 complex catalytically facilitates the conversion of the T*-PDE* unit into inactive T and PDE states. Inactivation of T*, hence, reflects two kinetic processes: the catalytic action of the “RGS9” complex and the intrinsic transducin GTPase activity. Either could be rate limiting. Which is the rate limiting event has been tested experimentally by investigating the effects of varying RGS9 concentration in transgenic mice rods (Burns and Pugh, 2009). Because the rate of photocurrent inactivation in rods changes with RGS9 concentration (Burns and Pugh, 2009), it has been proposed that in rods the rate limiting event is the rate of formation of the T*-PDE*-“RGS9” multimer and not the rate of GTPase hydrolysis characteristic of Tα-GTP. That is, the rate of formation of the T*-PDE*-“RGS9” complex is slower than the rate of GTP hydrolysis and, therefore, it is the event that determines the speed of PDE* (and T*) disappearance (reviewed in (Burns and Pugh, 2010). Comparable experiments are not yet been conducted in cones, but the same model will be applied.

Time course of light-dependent changes in cytoplasmic Ca²⁺ and GC activity

The rate of activation and inactivation of GC activity faithfully tracks the light-dependent changes in cytoplasmic free Ca²⁺. To define the time course of changes in GC activity, therefore, the time course of changes in cytoplasmic free Ca²⁺ must be described.

Ca²⁺ concentration changes when the outer segment Ca²⁺ influx and efflux are not the same. That is,

$$\frac{\mathit{dCa}(t)}{dt}={{}^{in}J}_{Ca}-{{}^{\mathit{out}}J}_{Ca}$$ (2.9)

From text equations (1.6) and (1.7)

$$\frac{\mathit{dCa}(t)}{dt}=\frac{I(t)P_f{10}^6-2^{\mathit{out}}{I}_{\mathit{NCKX}}^{max}\left(Ca/\left(Ca+K_{Ca}^{\mathit{exc}}\right)\right){10}^6}{{\mathit{zFV}}_{\mathit{COS}}\mathit{Buff}(Ca)}$$ (2.10)

Integration of text equation (2.10), yields the time course of free Ca²⁺ concentration change, Ca(t). The time course of GC activity changes is given by:

$$V_{GC}=(Ca(t))=\left(\frac{V_{GC}^{max}}{1+{\left(\frac{Ca(t)}{{{}^{GC}K}_{Ca}}\right)}^{n_{GC}}}\right)$$ (2.11)

where V_GC (Ca(t)) is the Ca²⁺-dependent GC activity, $V_{GC}^{max}$ is the maximum possible value of this activity, Ca(t) is free cytoplasmic Ca2+, and ^GCK_Ca is the Ca²⁺ concentration at which the enzyme activity is half its maximum value. n_GC is a dimensionless parameter that denotes cooperativity.

Time course of light-dependent changes in cytoplasmic cGMP concentration

The light-dependent rate of cGMP hydrolysis is determined by PDE* catalytic activity, ^lightV_PDE, where:

$${{}^{\mathit{light}}V}_{\mathit{PDF}}({VP}^{\ast },\mathit{cGMP})={\epsilon }_{\mathit{sub}}{\mathit{PDE}}^{\ast }\frac{\mathit{cGMP}(t)}{\mathit{cGMP}(t)+{{}^{\mathit{cGMP}}K}_m}$$ (2.12)

PDE* is the number of light-activated PDE molecules (the integral of equation (2.8)), cGMP is the nucleotide concentration, ^cGMPK_m is the PDE Michaelis-Menten constant for cGMP and

$${\epsilon }_{\mathit{sub}}=\frac{k_{\mathit{cat}}}{{LV}_{OS}}$$ (2.13)

k_cat (sec⁻¹) is the enzymatic turnover rate per PDE*. L is Avogadro’s number and V_OS is the photoreceptor outer segment cytoplasmic volume (half the geometrical volume).

The rate at which a metabolite is produced (or destroyed) during a bioprocess is calculated from its metabolic flux ((Goldberg et al., 1983; Ames et al., 1986)). Metabolic flux is a flux balance analysis used to determine the rate at which a metabolite is. cGMP metabolic flux, the net rate of change of cGMP in the course of a light-elicited response is given by the difference between its rate of synthesis by GC and hydrolysis by PDE.

$$\frac{\mathit{dcGMP}({VP}^{\ast },Ca,\mathit{cGMP})}{dt}=(V_{GC}(Ca(t))-({{}^{\mathit{dark}}V}_{\mathit{PDF}}+{{}^{\mathit{dark}}V}_{\mathit{PDF}}({VP}^{\ast },\mathit{cGMP}))$$ (2.14)

cGMP-gated, Ca-modulated membrane current

The simultaneous changes in free Ca²⁺ (integral of text equation (2.10) ) and cGMP concentrations (integral of text equation (2.14) are then used to compute the light-dependent changes in circulating outer segment current (equations (1.1) and (1.2)).

Flash photocurrent sensitivity and kinetics

Figure 1 illustrates changes in the circulating outer segment current caused by flash illumination of a dark adapted tiger salamander rod and a striped bass single cone. Currents were measured at room temperature under voltage clamp, by convention the holding current was defined as zero and the suppression of the inward current shown as an upward change (the photocurrent). The data in Figure 1 illustrate the archetypical differences in the transduction signal of dark-adapted rods and cones.

Figure 1.

Photocurrents measured at room temperature under voltage clamp in dark-adapted tiger salamander rods (holding voltage −30 mV) and striped bass single cones (holding voltage −40 mV). For the rod, 20 msec flashes delivered at time zero excited 13, 27, 53, 146, 307 and 614 rhodopsin molecule (λmax 520 nm) (Miller and Korenbrot, 1994). For the cone, 10 msec flashes delivered at time zero excited 35, 89, 178, 355, 892, 1780 and 3552 green opsin molecules (λmax 542 nm) (Korenbrot, 2012b).

In both rods and cones, the peak amplitude of the signal is a function of intensity well described by an exponential saturation function (Lamb et al., 1981):

$$I({VP}^{\ast })=\text{I}\mathit{peak}(1-exp(-{VP}^{\ast }/k))$$ (2.15)

where Ipeak is the maximum value of the photocurrent peak amplitude, VP* is light intensity expressed as the number of excited VP molecules in the cell and k is an adjustable parameter (σ=ln2k is the light intensity at which current amplitude is half its maximum value). Mean Ipeak and σ values for salamander rods and bass cones are listed in Table 2. The light response is faster in cones than rods, made evident by the shorter time to the photocurrent peak amplitude (Table 2).

Table 2.

Flash photosensitivity of dark adapted photoreceptors

	Single cones striped bass				Rods tiger salamander
	Ipeak	σ	Threshold	Time to peak	Ipeak	σ	Threshold	Time to peak
	pA	VP*	VP*	msec	pA	VP*	VP*	msec
Mean	26.2	245.3	9.9	96.6	71	73	b1	1192.4
SEM	2.4	25.6	0.8	3.4	6.5	4.1		58.3
Cell count (N)	15	15	15	15	9	17		11
Minimum	16.5	101.9	4.6	70	40	43		865
Maximum	43.6	452.1	16.6	115	107	156		1531

Optimized fit of model simulations to experimental data

The mathematical model of the phototransduction pathway can simulate photocurrents, but such exercise is useful only to the extent that values of the many parameters in the model are not all freely adjusted, but constrained by known biochemical and biophysical facts. Such constraints make matching simulated and experimental data less capricious, and validate using the model as a quantitative tool to evaluate the significance of known rod cone differences. The model, however, should be taken as a work in progress and not complete; it is a shorthand representation of what we know now, but it cannot predict what may yet be discovered.

Selection of parametric values

To fit simulated to experimental data we divide model parameters into three categories: Invariant, Statistical, and Adjustable. “Invariant” parameters are selected from the available literature and their values are kept the same for all cells and all simulations. “Statistical” parameters are experimentally measured in each cell under analysis. “Adjustable” parameters are adjusted to optimize the fit between simulated and experimental currents in each cell under study. Adjustments were made with computer-assistance to fit simulated to experimental data by least square minimization (Raphson-Newton, tolerance=0.001). The values of adjustable parameters are not arbitrary; their initial values were constrained, whenever possible, by experimentally known values. Tables 3 and 4 list parametric values arrived at through simulations and footnotes cite the constraining experimental facts.

Table 3.

Model parameter values that best simulate flash photocurrents in dark adapted bass single cones^a

	Parameters	Category	Units	Cone 1		Cone 2		Cone 3
VP*	Intensity	Statistical	VP*	167	17,443	174	17,136	173	7,720
GRK	γmax	Adjustable	μM/sec	100	65	100	70	105	68
	μ0	Invariant	μM/sec	0.5
	ωγ	Invariant		0.1
T*	Ψ0	Adjustable	1/sec	b230		215		230
	ωact	Invariant		c0.69
PDE*	εsub	Adjustable	μM/sec per molecule	d0.185		0.323		0.416
	αPDE	Adjustable	1/sec	17.4	47	7	19	14	28
GC	$V_{GC}^{max}$	Invariant	μM/sec	e110.5
	GCKCa	Invariant	μM	0.1
	nGC	Invariant		2
Ca2+ influx	inJCa	Statistical	μM/sec	25.3		37.5		17
	Pf	Invariant		f0.34
Ca2+ buffer	KHA	Adjustable	μM	g0.030		0.044		0.091
	C HA	Adjustable	μM	21.4		4.6		66
	B	Adjustable		10.6		7		15
Ca2+ efflux	$J_{Ca}^{max}$	Statistical	pA	h4		3.23		7.63
	$K_{Ca}^{\mathit{exc}}$	Adjustable	μM	0.025		0.005		0.025

^aValues of parameters first used to compute dark current are not repeated here. They have the same values listed in Table 1.

^bExperimental value is unknown in cones.

^cValue from experimental data (Gibson et al., 2000). Experimental data available only for rhodopsin

^dText equation (2.13).

^eExperimental value assigned from experimental measurements in truncated carp cones (Vmax = 140 uM/sec, (Takemoto et al., 2009)).

^fExperimental value (Ohyama et al., 2000)

^gExperimental mean values in aequorin-loaded rods are K_HA < 0.7 μM, C_HA 37 μM and B 16 (Lagnado et al., 1992). Experimental values are unknown in cones.

^hWith these values the computed mean time constant of Ca²⁺ clearance from bass cone outer segment when all CNG channels are suddenly closed is 40.0 ± 15.4 msec, similar to the experimental value of 43 ± 9.8 msec in the tiger salamander cone (Sampath et al, 1999)

Table 4.

Model parameter values that best simulated flash photocurrents in dark adapted tiger salamander rods^a

	Parameters	Category	Units	Rod 1		Rod 2		Rod 3
VP*	Intensity	Statistical	VP*	53	3509	53	3509	53	3509
GRK	γmax	Adjustable	μM/sec	3.03		2.7	3.0	2.9
	μ0	Invariant	μM/sec	0.5
	ωγ	Invariant		0.1
T*	Ψ0	Adjustable	1/sec	b73		80		62
	ωact	Invariant		c0.69
PDE*	εsub	Invariant	μM/sec per molecule	d0.0083
	kcat		1/sec	e5*103
	αPDE	Adjustable	1/sec	f0.59		1.0	0.83	0.89	0.78
GC	$V_{GC}^{max}$	Adjustable	μM/sec	g26.1		26.2		26.4
	GCKCa	Invariant	μM	0.2
	nGC	Invariant		1.5
Ca2+ influx	inJ Ca	Statistical	μM/sec	19.5		16.8		13.1
	Pf	Invariant		h0.14
Ca2+ buffer	KHA	Adjustable	μM	i0.056
	CH	Adjustable	μM	5		8.5		8
	B	Adjustable		1		1		2
Ca2+ efflux max	$J_{Ca}^{max}$	Statistical	pA	18.3		18.5		18.74
	$K_{Ca}^{\mathit{exc}}$	Invariant	μM	j 1.6

^aValues of parameters first used to compute dark current are not repeated here. They have the same values listed in Table 1.

^bΨ₀ experimental mean value in rods is ~100 sec⁻¹ (Leskov et al., 2000).

^cExperimental data (Gibson et al., 2000).

^dThe ε_sub value superficially appears to be 10-fold higher than the β_sub value experimentally measured by Leskov et al. (2000) and frequently quoted. However, both values reflect the same PDE hydrolytic activity, k_cat, they are simply defined in different units.

^eAssigned k_cat value measured in biochemical assays’ [ (Dumke et al., 1994a; D’Amours and Cote, 1999; Zhang et al., 2003; Muradov et al., 2009). ε_sub is calculated from this assigned value and the salamander rod outer segment cytoplasmic volume (1 pL)

^fSimilar to experimental time constant measured in truncated toad rod outer segments (~ 2 ec)(Rieke and Baylor, 1998)

^gThe same parameter has the value 13 μM/sec in truncated frog rods (Koutalos et al., 1995a) and 29 μM/sec in truncated carp rods (Takemoto et al., 2009)

^hExperimental value (Ohyama et al., 2000).

ⁱExperimental mean values are K_HA ≪ 0.7 μM, C_HA 37 μM and B 16 (Lagnado et al., 1992).

^jAssigned from the experimentally known value (Lagnado et al., 1992; Sheng et al., 2000).

Simulations were particularly sensitive to the following adjustable parameters: 1) The features of the Na⁺/Ca²⁺K⁺ exchanger transport, $I_{\mathit{NCKX}}^{max}$ and $K_{Ca}^{\mathit{exc}}$ (text equation (1.7)). They were constrained by demanding their value be the same in the dark and the light for the same cell, by their ability to match the known light-dependent changes in cytoplasmic free Ca²⁺ concentration (Gray-Keller et al., 1999; Sampath et al., 1999), as well as biochemical data on the ionic dependence of the exchanger function (Lagnado et al., 1992; Sheng et al., 2000). 2) The features of cytoplasmic Ca²⁺ buffers (text equation (1.8)). They were constrained by demanding their value be the same in the dark and the light and their initial values consistent with data available for Ca²⁺ buffering in rod outer segments (Lagnado et al., 1992). 3) The relative contributions of VP* phosphorylation γ (text equation (2.1)) and PDE inactivation rate α_PDE (text equation (2.8)) to the control of the time course of PDE* inactivation (text equation (2.8) ).

Experimental and model-simulated flash photocurrents in dark-adapted rods and cones

Photocurrents elicited by light flashes of varying intensity in a dark-adapted bass single cone are illustrated in Figure 2. Shown are both experimental and simulated photocurrents optimally fit to the experimental data. Values of the model parameters used in the simulations are presented in Table 3, cone 1. The range of quality of fit between model and experimental data is shown in Figure 3, using 2 additional cones. Parametric values in these simulations are also presented in Table 3, cones 2 and 3.

Figure 2.

Experimental (noisy, black traces) and simulated (noiseless, red traces) photocurrents measured under voltage-clamp at −40 mV in a dark adapted bass single cone. Photocurrents were elicited by 10 msec light flashes of intensity: 36, 71, 167, 356, 710, 1744, 3561, 7106 and 17443 VP*. For the cell Ipeak=22.2 pA and σ=170 VP*.

Figure 3.

Experimental (noisy, black traces) and simulated (noiseless, red traces) photocurrents measured in different dark adapted bass single cones. A and B were measured in one cell (Ipeak=19.1 pA and σ=195 VP*). C and D in another (Ipeak=42 pA and σ=112 VP*). Flash intensities tested were A 174 and 1747 VP*, B 17743 VP*, C 173 and 808 VP* and D 7720 VP* in. The values of the parameters used to compute the simulated data are listed in Table 3. At intensities above amplitude saturation (panels B and D) simulations fit experimental data only if PDE* inactivation was rate limited by VP* phosphorylation and this rate was slower than that during non-saturating responses (Table 3). The simulations illustrated in blue are computed without adjusting γ_max, maintaining the value used to fit the dim light responses.

Figures 4 and 5 illustrate experimental and simulated photocurrents elicited by flashes presented to 3 different dark-adapted tiger salamander rods. The parametric values used to compute the simulated photocurrents in the Figures are listed in Table 4. Table 5 presents side by side the mean ± SD of parametric values inferred from successful analytical simulations measured in 18 cones and 9 rods.

Figure 4.

Experimental (noisy, black traces) and simulated (noiseless, red traces) photocurrents measured under voltage-clamp at −30 mV in a dark adapted tiger salamander rod. Photocurrents were elicited by 20 msec light flashes of intensity: 13, 27, 53, 147, 307, 614 and 3509 VP*. Ipeak=72 pA, σ=62 Rh*.

Figure 5.

Experimental (noisy, black traces) and simulated (noiseless, red traces) photocurrents measured in different dark-adapted tiger salamander rods. A and B were measured in one cell (Ipeak=74 pA and σ=59 Rh*) C and D in another (Ipeak=73 pA and σ=85.8 Rh*). Flash intensities tested were: A 13 and 53 VP*, B 5871 VP*; C 13 and 53 VP* and D 3509 VP*. The values of the parameters used to compute the simulated data are listed in Table 4.

Table 5.

Summary comparison of model parameter values in rods and cones

	Parameters	Units	a Cone	b Rod
CNG channels	min KcG	μM	120.6 ± 9.3	28 ± 6
	maxKcG	μM	316 ± 43	37 ± 8
	KCa	μM	0.863 ± 0.051	0.055 ± 0.013
	nCNG		2.5	2.3
GRK	γmax	μM/sec	See Figure 9	See Figure 9
	μ0	μM/sec	0.5
	ωγ		0.1
T	Ψ 0	1/sec	231 ± 19	85 ± 17
	ωact		0.69
PDE	εsub	μM/sec	c0.334 ± 0.091	0.00837
	kcat	1/sec	10 × 103	5 × 103
	αPDE	1/sec	See Figure 9	See Figure 9
GC	$V_{GC}^{max}$	μM/sec	110.5	25.9 ± 2.9
	GCKCa	μM	0.1	0.2
	nGC		2	1.5
Ca2+ influx	Pf		0.34	0.14
Ca2+ buffer	KHA	μM	0.052 ± 0.025	0.056 ± 0.017
	CHA	μM	20.9 ± 12.9	7.3 ± 2.9
	B		11.5 ± 3.9	1.2 ± 0.4
Ca2+ efflux	$I_{\mathit{NCKX}}^{max}$	pA	4.87 ±1.88	18.2 ± 4.8
	$K_{Ca}^{\mathit{exc}}$	μM	h0.019 ± 0.009	1.6

^aStriped bass single cones, mean ± SD, N=18

^bTiger salamander rods, mean ± SD, N=9

Simulated photocurrents fit experimental data well except for the small, nearly exponential component observed as photocurrent amplitude approaches its maximum (saturated) amplitude. This component is generated by the electrogenic activity of the Na⁺/Ca²⁺K⁺ exchanger (Nakatani and Yau, 1989; Perry and McNaughton, 1991). Although simulations illustrated here do not explicitly display this component, it is an implicit constituent of all model simulations. The time course of this electrogenic current reflects the dynamics of the light-dependent change in free cytoplasmic Ca²⁺, and is given (in pA) by $I_{\mathit{NCKX}}^{max}Ca/Ca+K_{Ca}^{\mathit{exc}}$ (from equation (1.7)). Therefore, the accuracy of the model to simulate free Ca²⁺ dynamic is also reflected in the accuracy with which the computed NCKX electrogenic current fits experimental data. Figure 6 illustrates the electrogenic NCKX current measured in a bass single cone and the computed NCKX exchanger current. To emphasize, the model computations were fit to the photocurrents measured in this cone at various light intensities, not specifically to the NCKX current. The simulated NCKX current is simply one of the components of the phototransduction process. The quality of the fit between computed and experimental data is very good and attests to the strength of the model computations.

Figure 6.

Photocurrents in striped bass isolated single cones. A. Voltage-clamped photocurrents measured at −40 mV at room temperature. 10 msec duration flashes of 540 nm light were delivered at time zero. Intensity of the flashes tested was (in VP*): 175, 705, 4121, 18578 and 74648 respectively. At intensities sufficient to saturate photocurrent amplitude, the current approached saturation along a time course described by a single exponential process (blue tracing), of initial amplitude 2 pA and time constant τ_NCKX = 45 msec.

B and C. Experimental and simulated data activated by 18578 VP*, selected from panel A. B. Experimental (noisy, black trace) and simulated (noiseless, red trace) photocurrents. C. Experimental photocurrent (noisy, black traces) and the electrogenic Na⁺/Ca²⁺, K⁺ exchanger current, I_NCKX (noiseless blue line) in an expanded view near photocurrent amplitude saturation. I_NCKX is as an explicit component of the simulated photocurrent that best fit the experimental current, as shown in B. I_NCKX is outward, but its display is inverted and offset to overlap with the photocurrent: its goes from a high value of 1.4 pA in the dark to zero, when photocurrent amplitude saturates.

Side by side comparison of the molecular events in the phototransduction pathway of rods and cones

Successful photocurrent simulations constrained by experimental facts allow side-by-side comparison of the molecular events that underlie phototransduction in rods and cones, evaluation of the significance of their differences and similarities, and assessment of important information gaps. To compare and contrast the dynamics of various molecular events in rods and cones a sequence of figures illustrates computed functions that depict the time course and amplitude of several molecular events which contribute to the simulated photocurrents illustrated for cone 1 (Figure 2) and rod 1 (Figure 4). For the cone and rod, the signals illustrated were elicited by flashes of intensity near the σ value of each photoreceptor or just above the amplitude-saturating intensity.

Visual pigment activation and inactivation: VP kinase activity and the regulatory role of Recoverin and Arrestin

The rate of VP* activation in rods and cones is determined by the number and delivery rate of stimulus photons. The time constant of formation of VP* (Meta-II) is very nearly the same for rod and cone opsins regardless of the wavelength of their absorbance maximum (Imai et al., 1995; Imai et al., 1997; Vought et al., 1999; Kusnetzow et al., 2001). For example, at room temperature, it is about 10 ms in chicken green opsin (λmax 508 nm) and 30 ms in chicken rhodopsin (λmax 503 nm) (Imai et al., 1995). In contrast, the rate of Meta-II decay is much faster in cones than rods. In VP detergent solutions, for example, the time constant of disappearance is 7 s in chicken green opsin but 210 s in chicken rhodopsin (Imai et al., 1995). Thus, Meta-II lifetime can be expected to be much shorter in cones than rods. The kinetic differences measured in detergent solutions are not necessarily the same as the opsin photodynamics in intact membranes. In micro-spectrophotometric studies with intact goldfish cones and rods, however, hydrolysis of the linkage between opsin and the bleached chromophore (all-trans 3-dehydroretinal) at room temperature has a half-time of about 5 sec in cones and about two orders of magnitude slower in rods (Golobokova and Govardovskii, 2006). In both rods and cones, and for light levels that do not bleach a significant fraction of the VP, photochemical decay of MetaII is slow, much too slow to explain photocurrent recovery, and other mechanisms are responsible for the inactivation of the VP* state. Nevertheless, as we document below, the lifetime of the VP* “active state” is, indeed, much shorter in intact cones than in rods.

From simulations, the time constant of VP* inactivation at near σ light intensity was 0.8–1.2 sec in rods and 0.03–0.04 sec in cones. Experimental studies in truncated toad rods at comparable intensities measure this time constant to be 2–2.5 sec (Rieke and Baylor, 1998). This very large rod-cone difference is explained by the biochemical properties of the opsin kinase function in the two receptor types. Comparing data from fish rods and cones, VP*-kinase catalytic rate per molecule is higher in cones ( ~5 Pi on VP*/GRK sec) than rods ( ~0.5 Pi on VP*/GRK sec) and the enzyme concentrations are also 10-fold higher in cones than rods,~0.04 GRK/VP and ~ 0.004 GRK/VP respectively (Tachibanaki et al., 2005). Consistent with biochemical facts, model simulations show VP*-kinase catalytic velocity in bass cones is about 25 times larger than that in salamander rods (Tables 3, 4 and 5. Figure 7B).

Figure 7.

Simulated time course of existence of excited visual pigment molecules (VP*) generated by flash stimulation. Panel A illustrates the number of VP* molecules in cone1 ( ) and rod1 ( ) in response to flashes near the intensity that half-saturates the photocurrent amplitude, 167 VP* in the cone and 53 VP* in the rod. Panel B illustrates the response to flashes that saturate the photocurrent amplitude, 7106 VP* in the cone and 3509 VP* in the rod. The inset in panel B illustrates the magnitude and time course of VP kinase catalytic activity in response to the bright flash stimulus.

In the process of inactivation, VP* is phosphorylated multiple times and the maximum VP-kinase activity increases as the cytoplasmic Ca²⁺ concentration declines. The Ca²⁺-dependence of GRK activity in the simulations was assigned the features known from biochemical measurements in rods (Kawamura, 1999), comparable experimental data is unavailable for cones. Model simulations were successful under the assumption that the Ca²⁺ sensitivity of rod and cone VP*-kinase (mediated by Recoverin) is the same.

The number of VP* sites phosphorylated in the course of the photoresponse in intact rods or cones is controversial. Biochemical evidence indicates that up to 4 sites can be phosphorylated in intact fish cone opsin (Kennedy et al., 2004). We adopted 6 as the number of physiologically relevant phosphorylation sites because of recent compelling results in mice rods: the reproducibility of single photon responses in transgenic rods matches that of the wild type rod only when 6, and no less than 6, phosphorylation sites are available in the rhodopsin molecules (Doan et al., 2006). Theoretical simulations of the reproducibility of single photon responses in toad rods also match experimental data when rhodopsin is assumed to be phosphorylated at 6 different sites (Hamer et al., 2003), although theoretical exception has been expressed (Caruso et al., 2010).

The model assumes the rate of quenching of phosphorylated-VP* by Arrestin is the same in rods and cones. This assumption is consistent with biochemical investigations in fish retina which show that inhibitory effects of Arrestin on rod and cone GRK are indistinguishable (Arinobu et al., 2010).

Gain in Transducin activation

The gain rate between VP* and the activation of transducin is known from experiments in toad rods to be ~150 T*/VP*sec (Leskov et al., 2000). This was the initial value assigned in the rod photocurrent simulations (Tables 4 and 5). The same parameter has not been experimentally measured in cones, but the T*/VP* rate gain arrived at through the successful cone simulations was a few-fold larger in cones than rods (Tables 3 and 5). The initial rate of rise of the photocurrent continues to increase with light intensity well after photocurrent amplitude is saturated and it reaches a maximum value only when a significant fraction of the VP is bleached (Cobbs and Pugh, 1987; Hestrin and Korenbrot, 1990). In the limit of bright light stimuli, when the initial rate of rise is near its maximum value, the value of this maximum initial rate of rise reflects the rate of PDE* activation (Cobbs and Pugh, 1987). Experimentally, the initial rate of rise of the photocurrent activated by flashes that bleach several percent of the VP are indistinguishable in cones from rods (Cobbs and Pugh, 1987; Hestrin and Korenbrot, 1990), consistent with the conclusion that the maximum stoichiometric rates of T* and PDE* activation are similar in the two photoreceptor types.

The electrophysiological and simulation studies may also help understand the mechanisms behind the finding that replacing rod transducin with cone transducin lowers the photosensitivity of transgenic mice rods mice when compared with wild type (Chen et al., 2010a). The loss in the gain between light intensity and photocurrent amplitude is unlikely to reflect a difference in the VP* to T* gain rate. More likely, lifetime of the T* state of cone transducin is shorter than that of rod transducin in the mouse rod because of differences in the interactions between T* and the “RGS9” protein complex that inactivates T* (Wensel, 2008; Burns and Pugh, 2010).

The efficiency of T* activation by VP* decreases exponentially with the number of phosphorylated sites; experiments show that activation efficiency of transducin by rhodopsin declines by half with every added Pi in rods (Gibson et al., 2000). The relationship between T* activation and the state of VP*phosphorylation is unknown for cones, but simulations were successful under the assumption that it is the same as in rods (Tables 3, 4 and 5).

PDE* activation and inactivation

A particularly informative illustration of the differences in the phototransduction pathway of rods and cones is presented in Figure 8. Shown are simulations of the light-dependent changes in PDE and GC enzymatic activities in rods and cones at dim and bright light stimulation. The principal output of the transduction cascade, an initial decrease in cGMP concentration and its subsequent recovery, arises from the imbalance in the activities of the two enzymes. Initially PDE velocity exceeds that of GC and then GC exceeds the PDE velocity. The changes in enzyme activity are extremely stable and reproducible, and the dynamics of these changes define the waveform and sensitivity of the cGMP concentration change and, therefore, the waveform and light-dependence of the photocurrent. The rate of PDE* inactivation is much faster in cones than rods (Figure 8) (Tables 3 and 4).

Figure 8.

Simulated time course of activation and inactivation of PDE* ( ) and GC (▪ ▪ ▪ ▪ ) in response to flash stimulation. Panel A illustrates enzymatic activity in response to flashes near the intensity that half-saturates the photocurrent amplitude, 167 VP* in cone 1 ( ) 53 VP* in rods 1 ( ). Panel B illustrates the response to flashes that saturate the photocurrent amplitude, 7106 VP* in the cone and 3509 VP* in the rod.

The inactivation of PDE* reflects two sequential, but distinct processes: 1) inactivation of VP* by phosphorylation and 2) disappearance of T*. But, what are the dynamics of the contribution of the two reactions to the overall control of PDE* inactivation? This question can be answered with some confidence only with respect to photocurrents elicited by bright flashes, those that saturate the photocurrent amplitude. Pepperberg et al ((Pepperberg et al., 1992) proposed that under these conditions, one and only one biochemical reaction is the slowest one and its rate dominates the rate of PDE* inactivation. Electrophysiological experiments in salamander rods show that the dominant rate constant in the amplitude-saturated light response is Ca²⁺-independent and, therefore, it was identified as the rate of T* disappearance (Nikonov et al., 1998). In contrast, experiments in tiger salamander cones find the dominant rate constant that controls the duration of amplitude-saturated photocurrents is Ca²⁺-dependent and, therefore, the rate of VP* phosphorylation was identified as the rate-limiting reaction (Matthews and Sampath, 2010). Indeed, rod photocurrent simulations were successful under the assignment that T* disappearance controlled the termination of the photocurrent (Figures 4 and 5). Also, in cones experimental amplitude-saturated photocurrents could be fit only by adjusting the rate of VP* phosphorylation (Figures 2 and 3) (Korenbrot, 2012).

Photocurrent recovery at less than amplitude saturating intensities is complex because it is not controlled by a single, dominant rate constant. In fact, in rods it is not controlled by the inactivation of PDE* alone, but by a combination of the rate of PDE* inactivation and GC activation by the changing cytoplasmic Ca²⁺. Simulations such as those in Figure 8 visualize the plausible contribution of the various biochemical reactions. Recent work in intact frog rods suggests that when light-dependent Ca²⁺ concentration changes are prevented, the kinetics of the recorded dim light photocurrent cannot be unambiguously attributed to either VP* phosphorylation or T* disappearance and both contribute to the control of the photocurrent time course (Astakhova et al., 2008). However, there is a difference between rods and cones. In cones, experimental and modeling considerations suggest the kinetics of photocurrent recovery, even at low light intensities, are dominated by the dynamics of PDE* inactivation and not GC activation by Ca²⁺ (Hamer and Tyler, 1995; Korenbrot and Rebrik, 2002). Indeed, at intensities that do not saturate photocurrent amplitude, good fits between simulated and experimental data in cones can only be obtained by assigning T* disappearance as the dominant rate constant (Korenbrot, 2012) (Figure 8).

Another important difference between rods and cones is apparent in the features of their response light that bleaches a significant fraction of the VP, a condition not investigated in the present analysis. At pigment bleaching-light levels, rods saturate and cease to respond to light. In cones, in contrast, even if light bleaches over 90% of the VP the resulting photocurrent will be at saturating amplitude for several seconds, but, nonetheless it will terminate with CNG channels reopening and the circulating outer segment current returning to its dark value (Estevez et al., 2006). Photocurrent recovery from saturation, just as with much dimmer lights, reflects inactivation of PDE*. However, at light levels that bleach a large percentage of VP* (above ~25%) PDE* inactivation is not rate limited by enzymatic processes (neither VP* phosphorylation nor T* disappearance), but by the thermal decay of the MetaII photoproduct. MetaII decay culminates in the separation of the all-trans chromophore from the cone opsin protein. Once MetaII decays, PDE is restored to its dark state and the cone will respond to light that excites the remaining 10 % dark VP, but, of course, with much, much less photosensitivity (Estevez et al., 2006).

The functional role of the rate of T* disappearance on the time course of rod photocurrents has been explored in studies of the consequence of overexpressing RGS9 in transgenic mice. Experimentally it was found that overexpression of RGS9, but not of GRK, accelerates photoresponse recovery (Krispel et al., 2006). These results affirm that in rods and at all intensities T* disappearance is slower than VP* phosphorylation and is the dominant rate constant. Further investigation has also shown that the turn-off rate of the rod photocurrent accelerates as RGS9 concentration increases (Burns and Pugh, 2009). These experimental findings have been explained by a conceptual model that posits T* and PDE* form a complex, T*/PDE*, that interacts with a second complex formed by the assembly of regulatory proteins RGS9, R9AP and Gβ5L and referred to simply as “RGS9”. According to this model, “RGS9” catalyzes the conversion of the T*/PDE* complex to inactive PDE with Michaelis-Menten kinetics (reviewed in (Burns and Pugh, 2010). Because of the Michaelis-Menten kinetic behavior, then, the velocity of conversion of T*/PDE* to inactive PDE conversion (and T* disappearance) is determined by the product of “RGS9” concentration and its catalytic activity (its k_cat/K_m value), thus explaining the observed dependence of photocurrent turn-off kinetics on RGS9 concentration.

The Burns-Pugh (2009) model offer an insightful explanation for the observed fact that PDE* inactivation is much quicker in cones than rods (Figure 8) (Tables 3, 4 and 5). The same RGS9 molecule is expressed in rods and cones, but its concentration is much higher in cones than rods (RGS9 to VP mole ratio is ~1:62 in cones and ~1:610 in rods) (Zhang et al., 2003). Hence, the difference in PDE* inactivation rate, between rods and cones can be explained by their difference in RGS9 concentration and can be expected to be about 10 times faster in cones than rods, just as inferred from the simulations (Table 5).

Rods and cones differ not only in the molecular mechanism underlying PDE inactivation, but also in the light-sensitivity of the inactivation reactions. As inferred from model simulations, α_PDE and γ_max in rods are essentially light independent over all intensities tested (Figure 9). In cones, however, both parameters are expected to be light dependent over the intensity range tested (Figure 9).

Figure 9.

Light-dependence of the simulated rate of PDE inactivation α_PDE ( ) and VP kinase maximum activity γ_max (●) in cone 1 ( ) and rod 1 ( ). Shown are the mean ± SD. The continuous lines that join data points are drawn by eye.

Calcium-dependent GC activity

In simulations, GC catalytic activity was assigned similar Ca²⁺-dependence in rods and cones taken from data in the rod biochemical literature (Lolley and Racz, 1982; Koch and Stryer, 1988) because comparable data is not available for cones. On the other hand, Vmax was inferred from the simulations. However, there was little freedom in this adjustment: it was constrained both by the fact that total enzymatic activity in the dark was known and by the requirement that the Vmax applied in dark and light. The values arrived at indicate the maximum GC activity in cones is about 5-fold higher than in rods. Moreover the absolute mean values of GC Vmax (Table 5) are similar to those measured in truncated carp rods and cone outer segments (Takemoto et al., 2009).

Time course of light-dependent changes in cytoplasmic free Ca²⁺

Figure 9 illustrates the simulated changes in free Ca²⁺ underlying the photocurrents of rod 1 and cone 1. The data are selected to compare Ca²⁺ changes at intensities that cause approximately the same fractional change in membrane current, when the peak photocurrent is about half the saturating photocurrent amplitude and at intensities that just saturate photocurrent amplitude. The Ca²⁺ changes are much faster in cones than in rods, as has been long recognized (Korenbrot and Rebrik, 2002). At saturation, Ca²⁺ reaches its lowest concentration in about 1.2 sec in rods, but only 0.13 sec in cones. Ca²⁺ recovers with an approximately exponential time course of 2.7 sec time constant in rods, but only 0.45 sec in cones. In addition, for the same proportional change in current, Ca²⁺ is reduced by nearly 20% in rods, but about 70% in cones. The simulated light-dependent changes in outer segment free Ca²⁺ are similar to those measured experimentally (in rods (Gray-Keller and Detwiler, 1994; Younger et al., 1996); in cones: (Sampath et al., 1999; Leung et al., 2007).

Differences in the kinetics of light-dependent Ca²⁺ concentration changes between rods and cones arise from differences in each of the molecular processes that control outer segment free Ca²⁺. The Ca²⁺ permeability is higher in cone than rod channels (Picones and Korenbrot, 1995; Dzeja et al., 1999), and at the same membrane current about twice as many Ca²⁺ ions enter the cone as the rod outer segment (Ohyama et al., 2000; Ohyama et al., 2002) (Table 5). Ca²⁺ efflux rate, the dominant component of the Ca²⁺ recovery at the end of the photoresponse is much slower in rods than cones. To fit simulated to experimental data in rods, we defined the Ca²⁺ -dependence of the Na⁺/Ca²⁺,K⁺ exchanger, $K_{Ca}^{\mathit{exc}}$ (text equation (1.7)), to be invariant and with a value 1.6 μM based on experimental fact (Lagnado et al., 1992). However, when the same value was assigned in cone simulations, it was impossible to fit experimental data: the rate of Ca²⁺ efflux was much too slow. Successful fits were obtained only by assigning this variable a much lower value (Tables 3, 5), which yields a much higher Ca²⁺ transport rate at physiological free Ca²⁺ concentrations. This is contrary to the reported finding that the ionic-dependence of recombinant cone and rod exchangers are similar to each other (Sheng et al., 2000). However, it must be remembered that there are several splice variants of the exchanger molecule in bass cones (Paillart et al., 2007) and in the intact cell the exchanger forms a tight complex with the CNG channels (Bauer, 2002; Kang et al., 2003). It is possible the exchanger in an intact photoreceptor has different functional properties than the cloned exchanger. There is also the remarkable report than cones in transgenic mice that do not express the canonical NCKX2 exchanger appear to function normally, at least as evaluated with the electroretinogram (Li et al., 2006). The functional characteristics of the NCKX exchanger in an intact cone need to be characterized, much as they have been in rods (Lagnado et al., 1992).

Ca²⁺ buffer

Based on experimental findings in rods simulations assume both rods and cones have two cytoplasmic buffer systems one of high and one of low affinity (Lagnado et al., 1992). Initial values of buffer concentration and affinity were based on the available experimental data (Lagnado et al., 1992). The buffers capacity and dissociation constant inferred from the simulations were calculated through computer-aided fit of simulated to experimental data. Ca²⁺ buffer capacity may well be different in the two receptor types: the affinity constant of the low affinity buffer is not that different in rods and cones, but its concentration is 2- to 4-fold higher in cones than rods. In addition, the buffer capacity of the low affinity buffer is higher in cones than rods (Tables 2, 3, 4). The accuracy of these values is difficult to ascertain because experimental characterization of the buffers exists only for tiger salamander rods and it was conducted with what is by now a technically limited tool surpassed in current technology. This information void needs to be filled.

Ca-dependent modulation of CNG channel ligand sensitivity

The probability of CNG channels being open is controlled by cGMP, but modulated by Ca²⁺. The cGMP sensitivity of channel activity is higher at low Ca²⁺ concentrations. Because of quantitative differences in the extent and Ca²⁺-dependence of this modulation, in intact photoreceptors, cGMP alone controls CNG channel activity in rods, but in cones it is controlled by both cGMP and Ca²⁺. Simulations shown in Figure 11 illustrate the physiological importance of this difference. As we expect, in the normal cone 1 and rod 1 a flash near σ intensity causes a decrease in cGMP, a decrease in cytoplasmic free Ca²⁺ Ca²⁺ and a reduction in the inward outer segment current. These changes are stable and reproducible. When Ca²⁺ control of channel activity is removed in the simulations (a computational knock out), there is little consequence in the rod response (Figure 11B). In stark contrast, when Ca²⁺ control of channel activity is removed in the cone every component of the photoresponse is affected and the photocurrent is larger and unstable. If Ca²⁺ modulation were not present, the responses in cones would be more sensitive, slower and would oscillate as they return to their dark state (additional details in (Korenbrot, 2012). Recent experiments in transgenic mice rods indeed affirm that obstructing the Ca-dependent CNG channel modulation is of little, if any, functional consequence (Chen et al., 2010b).

Figure 11.

Simulated changes in photocurrent, cytoplasmic cGMP concentration and cytoplasmic free Ca²⁺ generated by flash stimulation. Panel A illustrates the responses in cone1 to a flash 167 VP* in intensity, Panel B illustrates the responses in rod 1 to a 53 VP* intensity flash. In each panel are illustrated the responses in a normal photoreceptor ( ) and those in a model in which Ca²⁺-dependent modulation of CNG channel ligand sensitivity is absent ( ).

Conclusions and future directions

The molecular scheme of the phototransduction pathway is essentially the same in rods and cones, but the quantitative details of the function of each of the biochemical and biophysical processes in this pathway differ in the two receptor types. A mathematical representation of the currently accepted phototransduction pathway, constrained whenever possible by experimental values measured in biochemical assays or in the intact photoreceptor, proved remarkably successful in simulating experimental photocurrents. The model allowed side by side comparison of the dynamics of the molecular events of phototransduction in rods and cones. However, the model is simply a convenient tool to assemble and compare data available to date and to point out gaps in our information. Just as other models before, it would be reasonable to expect that the information will be improved and details of the model superseded as newer and better data becomes available.

It is remarkable that evolutionary pressures have succeeded in yielding such different end point-performance from transduction pathways qualitatively so very similar. Examination of Figures 7, 8, 9, and the Tables demonstrate evolutionary success reflects several different strategic choices: 1) genomically-related proteins perform similar functions but with very different quantitative features (GRK for example). 2) proteins of near identical function are expressed at different concentration (RGS9 for example). 3) proteins of similar structure and function are under very different regulation (CNG channels for example).

Cytoplasmic Ca²⁺ acts as a powerful feedback regulator in both rods and cones. Just as in all other cells where Ca²⁺ acts as a second messenger, cytoplasmic buffers are critical in defining the spatial and temporal features of the Ca²⁺ signal. The properties and identity of these buffers, however, are only known for rods and not at all for cones. Future experimental work must address this serious shortcoming, especially in view of the availability of new tools to carry out this task.

Phototransduction occurs even in the absence of light-dependent changes in cytoplasmic Ca²⁺ in both rods and cones, but the functional features of such signals are far different from those measured under normal conditions (Nakatani and Yau, 1988; Fain et al., 1989; Matthews et al., 1990). What is gained by Ca-dependent controls is not the difference between transduction and the failure to transduce, but the ability to regulate the molecular events underlying phototransduction. The regulatory function of Ca²⁺ in phototransduction is a feedback control mechanism because the output of phototransduction, a decrease in cytoplasmic Ca²⁺, influences the events that lead to the change in Ca²⁺ in the first place. It is a negative feedback because the output is fed back in such a way as to partially oppose the input. Signal stability is a serious challenge in the design of engineering systems that are controlled through negative feedback. The simulations show that Ca²⁺-feedback signals are stable in rods when CNG channel activity is controlled by cGMP alone. Control of channel activity by both cGMP and Ca²⁺ has evolved to attain well-controlled and stable photoresponses that meet the imperatives of time course, sensitivity, and light adaptation that sustain the cone transduction function, far different as they are from the rod transduction function.

We reviewed in detail the response of the phototransduction pathway to flash stimuli, a convenient experimental paradigm, but rarely a condition in typical visually driven behavior. The response to steps of light and to flashes superimposed on steps of varying intensity (light adaptation), of course, depend on the same mechanisms as the flash response, but additional changes in the dynamics of some of the molecules of the transduction pathway must also be invoked. It is clear that Ca²⁺ plays an important role in light adaptation, but other molecular processes have also been identified, for example, changes in PDE* lifetime (in rods (Nikonov et al., 2000), in cones (Soo et al., 2008); (Korenbrot, 2012a) and modulation of the ligand sensitivity of the CNG channels in cones (Rebrik et al., 2012b). Future research needs to discover all the molecular events of light adaptation in the detail in which it is now possible to describe the dark-adapted response. When these details are fully resolved, however, the general message will likely be the same as can be said of the differences in the dark adapted response. Physiological differences between any two cells, rods from cones or cones subtypes from each other, do not arise from the function of any one protein alone or any one regulatory process alone, but from aggregated changes in the system of reactions that constitute the transduction pathway as a whole.

Figure 10.

Simulated time course of changes in cytoplasmic free Ca²⁺ concentration) generated by flash stimulation. Panels A and B illustrates the changes in cone 1 ( ) and rod 1 ( ) in response to flashes near the intensity that half-saturates the photocurrent amplitude, 167 VP* in the cone and 53 VP* in the rod. Same data are displayed with two different time scales to highlight differences in time course between rods and cones.