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* Laboratory of Biomedical Engineering, Helsinki University of Technology, Helsinki, Finland; and Department of Biosciences, University of Helsinki, Finland
Correspondence: Address reprint requests to Petri Ala-Laurila, Dept. of Physiology and Biophysics, Boston University School of Medicine, 715 Albany St., Boston, MA 02118-2526 USA. Tel.: 617-638-5336; Fax: 617-638-4273; E-mail: pal{at}iki.fi.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE MODELRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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; Barlow, 1956; Aho et al., 1988; Donner, 1992). Thermal activations of the rod visual pigment are very sparse, but can be studied by the electrical signals they generate in the photoreceptor cell. Discrete "bumps" in the receptor current of single rods, recorded, e.g., by the suction-pipette technique, report single-molecule events in a population of >109 rhodopsins. Thus, Baylor et al. (1980, 1984) were first able to show that the rate constant for thermal activation of toad and macaque rhodopsin (
10–11 s–1 at 37°C) was of the right magnitude to account for the intrinsic "dark light" invoked to explain the statistics of light detection by dark-adapted humans (Barlow, 1956; cf. Hecht et al., 1942).
Baylor et al. (1980) determined the Arrhenius activation energy of the thermal process from the temperature dependence of the rate constant in toad rhodopsin, obtaining 22 kcal/mol. This is only about half of the energy needed for activation by light (Lythgoe and Quilliam, 1938; St.George, 1952; Cooper, 1979; Barlow et al., 1993). Because there can be no reasonable doubt that the discrete dark events in the rod current do arise from spontaneous activation of single molecules of visual pigment (cf. Firsov et al., 2002), the current interpretation of this discrepancy is that the photic and thermal modes of activation follow different pathways, the activation energies of which bear no necessary relation.
This view, however, fails to address the striking and biologically important empirical relation between spectral and thermal properties of visual pigments. There is a significant inverse correlation between the dark-event rate and the wavelength of maximum absorbance (
max) (Donner et al., 1990; Firsov and Govardovskii, 1990; Fyhrquist, 1999; see Figs. 2 and 3 below). The correlation is qualitatively consistent with the hypothesis that a pigment maximally sensitive to long-wavelength light (i.e., low-energy photons) has a comparatively low-energy barrier for activation and thus a high probability for thermal activation, whereas short-wavelength sensitive pigments have a higher activation energy and are therefore thermally more stable (de Vries, 1949; Barlow, 1957).
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max and thermal noise remains a mystery. To resolve this conflict, we propose a new model, drawing on insights already expressed by St. George (1952) and Lewis (1955). The crucial point is that the thermal behavior of a complex molecule (rhodopsin, or even the 11-cis retinaldehyde chromophore) must be described by Hinshelwood (1933) rather than Boltzmann statistics. This is because thermal activation of a molecule composed of many atoms may be supported by the energy present in a large number of vibrational modes, in addition to the kinetic energy in the relative motion of molecules (translational degrees of freedom). Arrhenius-type estimates for the thermal activation energy will decisively depend on how many modes are assumed to be involved, i.e., on the complexity of the activation process. The estimates of Baylor et al. (1980) for toad rhodopsin and subsequent estimates for other visual pigments (e.g., Matthews, 1984) rely on the arbitrary assumption that the activation process is a very simple one, involving only two (translational) degrees of freedom (n = 2). This undermines the evidence for a large difference between the energies of activation by heat and by light.
Here we test the model under the assumption that the thermal activation energy of each pigment has the same value as its photoactivation energy, this being the simplest possible alternative to the current notion that the two are very different. Some justification for assuming that they may be at least rather close comes from recent work suggesting that the gap between the minimum of the excited-state and the maximum of the ground-state energy surfaces for chromophore isomerization could be as small as 5–6 kcal/mol (Mathies, 1999).
When thermal and photic activation energies are set equal, the model predicts the temperature dependence of dark-event rates observed by Baylor et al. (1980) if the number of vibrational modes involved in the thermal activation process is 39. Most importantly, with the same number of vibrational modes, the model gives a good fit to the collected data on max versus light-like thermal noise in rods as well as in cones. The model by no means requires that thermal and photic activation energies be identical, but they must show some correlation, and we suggest there are good reasons to expect they do (see Discussion).
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THE MODEL |
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0 (Ea = hc/0). Stiles (1948) proposed that the reason why spectral sensitivity exhibits no sharp drop at 0 is that photon energy may be supplemented by thermal energy of the visual pigment molecule. If a photon at > 0 encounters a molecule that can contribute enough thermal energy (
hc(1/0 – 1/) to the process, activation may occur. He assumed that the Boltzmann distribution gives the relevant probabilities for encountering visual-pigment molecules at given thermal energy levels. The fraction of molecules with thermal energy greater than some value E is then
 | (1) |
Obviously, the fraction with at least the energy E = hc(1/0 – 1/) needed to supplement a photon of wavelength > 0 decreases proportionally to exp(1/). This would explain the fact that the final slope of absorbance spectra at very long wavelengths, plotted on logarithmic ordinates against wavenumber (1/), approximates a straight line (Stiles, 1948).
Lewis (1955) noted that spectra are in fact gently concave in the wavenumber domain of interest. He pointed out that for a complex molecule with many vibrational modes (many degrees of freedom), the fraction of molecules with thermal energy >E is given by an expression derived by Hinshelwood (1933):
 | (2) |
, 2003); thus the number of modes involved is m + 1 or n/2 depending on notation. For values of n > 2, this produces spectra with gently accelerating slope in the domain 1/ < 1/0. At any given temperature T and for any energy limit E, the Hinshelwood distribution (Eq. 2) yields a larger fraction of molecules that have thermal energy >E than does the Boltzmann distribution (Eq. 1). Lewis showed that the shape of spectra is best described with n-values between 8 and 14. It is to be expected, however, that the number depend on the reaction considered. The smaller the required thermal supplement to the photon energy, the fewer modes are likely to be involved. St. George (1952) notes: "As to the portion of the molecule that is involved in activation, the increase in n toward longer wavelengths fits the idea that an increasingly larger part of the molecule comes into play as the thermal component of the activation energy becomes larger." The limiting case is activation by thermal energy alone.
The total (maximal) number of quadratic energy terms of a molecule, the number of "internal degrees of freedom," is given by:
 | (3) |
), where N is the number of atoms of the molecule. For 11-cis retinaldehyde, N = 49 (20 C + 28 H + 1 O) and nmax = 282. For the rhodopsin molecule as a whole, the number is obviously very large. We do not commit ourselves to any particular idea about the molecular origin of the modes, but note that any value of n up to 282 (i.e., 141 vibrational modes) would as such be consistent with an origin in the chromophore alone.
For purely thermal activation, the rate constant k is proportional to the fraction of molecules that have energy larger than the thermal activation energy, which we denote Ea,H:
 | (4) |
AH is a proportionality constant, often referred to as the "pre-exponential factor". The above expression for k derives from the first term of Eq. 2, which is a good approximation for the full series when E >> RT (
0.6 kcal/mol at 20°C) (Hinshelwood, 1933). The rate constant based on the Boltzmann distribution is obtained from Eq. 1:
 | (5) |
In this case, we give the pre-exponential factor as well as the activation energy the subscript B to emphasize that these values based on Boltzmann statistics (associated with "conventional" Arrhenius analysis) are different from those based on Hinshelwood statistics, denoted by subscript H. For n = 2, Eq. 4 converges to Eq. 5.
When Eq. 4 replaces Eq. 5, the generally accepted values Ea,B derived from experimental data on the temperature dependence of dark-event rates (Baylor et al., 1980) appear as basically arbitrary. The true relation between the energies of thermal and photic activation remains unresolved. In the following, we study the predictions of the model under the simplest possible assumption (itself not essential to the model) that the two activation energies have the same value, i.e., Ea = Ea,H.
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RESULTS |
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data on the temperature dependence of discrete dark events in a total of five individual "red" rods (marked by different symbols) of the toad Bufo marinus. The visual pigment is a usual 503 nm rhodopsin. The purpose is twofold. Firstly, we hereby demonstrate that a good fit can be obtained even under the assumption that the thermal activation energy is equal to the photoactivation energy of the pigment, 44.3 kcal/mol (Ala-Laurila et al., 2002). Secondly, the fit provides an estimate for the parameter n, which we will use in the subsequent modeling. In view of the standardized molecular structure of the chromophore part of visual pigments, we think it is reasonable to assume as a first-order approximation that n is constant for all. We do realize that important differences between pigments may become evident at a higher level of resolution, e.g., different coupling of vibrational modes to the activation process could be one of the tuning mechanisms underlying differences in the interplay of light and heat (Koskelainen et al., 2000).
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from each of the five rods separately. Our rationale for fitting this model (Eq. 4) has been to require that the predicted temperature dependence with Ea,H = Ea = 44.3 kcal/mol should coincide with this "mean" line. (Obviously, the line deviates somewhat from the outcome of simply applying linear regression analysis to the set of data points.) The fitting entails optimizing the value of the parameter n, which was done as follows. The rate of change of lnk with temperature, d lnk/dT according to the "conventional Arrhenius" model (based on Eq. 5) is:
 | (6) |
The corresponding rate of change according to the "Hinshelwood" model (based on Eq. 4) is:
 | (7) |
Obviously, when n is large, a given empirical temperature dependence is indicative of a larger activation energy according to Eq. 7 than according to Eq. 6, the difference being Ea,H – Ea,B = (n/2 – 1)RT (cf. St. George, 1952). To determine n, we set this expression equal to the difference between the Baylor et al. (1980) estimate 21.9 kcal/mol and our present postulate 44.3 kcal/mol:
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The straight line in Fig. 1 represents the identical predictions of, on one hand, the "Arrhenius-Boltzmann" model for Ea,B = 21.9 kcal/mol and on the other hand the "Hinshelwood" model for Ea,H = 44.3 kcal/mol and n = 79. As explained above in connection with Eq. 2, this number of quadratic energy terms (kinetic + potential energy) would arise from half that number of vibrational modes, which (taken as the smallest sufficient integer, i.e., the first integer 79/2) would be 39.
We now fix the value n = 79 and study whether the "Hinshelwood" model with this parameter value can account for the observed correlations between 1/max, Ea, and thermal noise in visual pigments.
Two rod pigments differing only in chromophore
As a first example, we consider the rhodopsin502-porphyropsin525 pigment pair in rods of the adult bullfrog, Rana catesbeiana (Reuter et al., 1971; Firsov et al., 1994). This pair offers some clear advantages for our purpose. Firstly, the A1 
A2 chromophore shift in the same opsin is a comparatively simple molecular mechanism for shifting max, and it may be assumed that the pre-exponential factor AH in Eq. 4 does not change (see Discussion). Secondly, for these two pigments we have direct knowledge of the photoactivation energies Ea as well as the thermal activation rates. Donner et al. (1990) report the rate constant kA2 = 1.2 x 10–11 s–1 for the A2 pigment at 18°C and estimate that the rate in the (remarkably stable) A1 pigment is 10 times lower. The respective photoactivation energies are Ea,A2 = 44.2 kcal/mol and Ea,A1 = 46.5 kcal/mol, consistent with the inverse proportionality between Ea and max hypothesized by Barlow (1957) (Ala-Laurila et al., 2003, 2004). Entering these values into Eq. 4 with n = 79, T = 291.15 K, and assuming that AH does not change, we obtain the prediction kA2/kA1 = 7.6 for the ratio of rate constants. Thus, there is a fair agreement between theory and experiment. The corresponding ratio kA2/kA1 based on the Boltzmann distribution (Eq. 5) would be 53.
The correlation between max and dark-event rate in rod pigments
We now turn to the whole sample of rod pigments from which estimates of the dark-event rate as well as the wavelength of maximum absorbance max are available. Table 1 gives the identity and numerical values of the pigments considered and the data have been plotted in Fig. 2. All dark-event rates have been referred to the same temperature, 21°C, assuming the temperature dependence measured in Bufo marinus rhodopsin by Baylor et al. (1980). Further, some of the original articles report only event rates per photoreceptor cell, and in these cases we have recalculated the values to rates per pigment molecule using values for outer-segment volume and pigment density of the respective species, drawn from other sources as indicated by the references in connection with Table 1. We have included not only results from suction-pipette recordings on single rods, but also estimates based on noise analysis in retinal bipolar cells (dogfish rods) and on the statistics of light detection measured in human psychophysics. A significant correlation between dark-event rate and 1/max is evident (r2 = 0.59).
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max to Ea for the whole data set, we use the empirical equation obtained by Ala-Laurila et al. (2004) by linear regression of Ea on 1/max in 12 visual pigments:
 | (8) |
Equation 8 is a useful statistical relation, although it should be noted that no tight physical connection exists between Ea and max. Two pigments with the same max may have quite different Ea and vice versa (Koskelainen et al., 2000). However, the regression Eq. 8 explains 73% of the variation in Ea in the sample of visual pigments that have been studied in this respect (Ala-Laurila et al., 2004). In testing this model, we now assume that the same equation also describes the relation between the thermal activation energy Ea,H and max.
The solid straight line in Fig. 2 traces the model prediction on this assumption (for n = 79 and T = 294.15 K). The line has been vertically positioned for best fit to the whole data set, which implies fixing the value of the pre-exponential factor AH in Eq. 4. Clearly, the model fairly successfully predicts how steeply the thermal activation rate depends on max. For comparison, the dashed line shows the (excessively steep) relation based on the Boltzmann distribution (Eq. 5), as originally suggested by Barlow (1957). The dotted line shows the prediction of this "Hinshelwood" model under the modified assumption that Ea,H is systematically somewhat smaller than Ea (see below).
The correlation between max and light-like dark noise in cones
There is much less reliable data on thermal activation rates in cone pigments. One reason is that discrete dark events can be recorded only in some special cases, notably in the so-called "green rods" of amphibians (Matthews, 1984), which contain an S-cone pigment, (Hisatomi et al., 1999; Ma et al., 2001). In three of the other four available estimates for cone pigments, thermal activation rates have been computed by the original authors (Lamb and Simon, 1977; Schnapf et al., 1990; Sampath and Baylor, 2002) from the "dark" noise power in the frequency band of photoresponses, a procedure fraught with more uncertainty than the analysis of unipolar, photon-like deflections from baseline. The fifth data point represents a human psychophysical estimate, based on the variability of light detection by dark-adapted foveal cones (Donner, 1992). The data are collected in Table 2 and dark-event rates have been plotted as function of 1/max in Fig. 3. Again, a significant correlation is evident (r2 = 0.93). The solid straight line shows the prediction of this model on the same assumptions as for the rod data (Fig. 2), and the dashed line the corresponding prediction based on the Boltzmann distribution. Both have been vertically positioned for best fit to the whole data set. For the cone data, this requires a value of the pre-exponential factor AH that is some four orders of magnitude larger than for the rod data. Yet, just as for rods, the Hinshelwood model predicts the slope of the dependence of thermal activation rate on max rather well, as opposed to the Boltzmann model, which produces a much too steep dependence. Like in Fig. 2, the dotted line shows the prediction of this model under the modified assumption that there is an energy offset between Ea,H and Ea (see below).
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; Mathies, 1999)? To investigate this, we have repeated the calculations assuming that the photic and thermal activation energies are offset by a constant amount 
E = Ea – Ea,H = 10 kcal/mol. For Bufo marinus rhodopsin we then get Ea,H = Ea – E = (44.3 – 10) kcal/mol = 34.3 kcal/mol. Optimizing the fit to the dark-event rate versus temperature data of Baylor et al. (1980) as in Fig. 1 now requires a different n-value, calculated in the same way as before:
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44.
The correlation between max and dark-event rates
The Ea values for Rana catesbeiana porphyropsin and rhodopsin together with n = 44 in Eq. 4 yields the dark-event rate ratio kA2/kA1 = 13.6. Compared with the experimental estimate kA2/kA1 10, this prediction is about equally good as the value 7.6 obtained under the previous assumption Ea,H = Ea and n = 79.
In Figs. 2 and 3, presenting the full sets of data on rod and cone pigments, the predictions of the "energy offset" modification (Ea – Ea,H = 10 kcal/mol and n = 44) are shown as dotted lines. The fits are slightly less good than those for Ea,H = Ea and n = 79 (solid lines), but still much better than the Boltzmann fits (dashed lines).
Thus, the model works well with a moderate offset between Ea and Ea,H, as long as the two are coupled (see Discussion). On the other hand, the modification does not improve the fits obtained under the simplest assumption Ea,H = Ea. In the model parameters, energy offsets are traded against changes in the apparent number of thermal modes (n/2) involved in the activation process. Due to this trade-off, the model is not very helpful for determining the precise relation between Ea,H and Ea, nor the value of n, from the experimental data. Its value lies in showing that the data are consistent with the idea that photoactivation and thermal activation energies are similar or equal, and in explaining the correlation between Ea,H and max on this basis.
We may finally note that in the "Boltzmann" model (Eq. 5), the introduction of a constant offset E, such that Ea,B = Ea – E, will not at all affect the predicted ratio of dark-event rates in two pigments with different activation energies. In the ratio kA2/kA1, the offset E disappears by reduction: if kA1 
exp[–(Ea1 – E)/RT] and kA2 exp[–(Ea2 – E)/RT], then kA2/kA1 = exp[(Ea1 – E – Ea2 + E)/RT] = exp[(Ea1 – Ea2)/RT]. Thus the predicted ratio kA2/kA1 is the same as if Ea,B = Ea, implying that the much too steep dependence of dark-event rates on max remains unaffected.
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DISCUSSION |
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estimated the energy for thermal activation of Bufo marinus rhodopsin to 22 kcal/mol, the incompatibility with photoactivation energies, 40–50 kcal/mol (Lythgoe and Quilliam, 1938; St. George, 1952; Cooper, 1979), has posed a major difficulty for any effort to understand the nature of thermal activation and its relation to the spectral light absorbance of visual pigments. This problem has been approached in different ways.
It has been suggested that the discrete photon-like events in the rod dark current might not, in fact, reflect spontaneous activation of single-pigment molecules, but arise at some later point in the transduction machinery (for a discussion, see Barlow et al., 1987). At least in the case of vertebrate rods, however, it is hard to believe that the discrete events could originate elsewhere than in the visual pigment. The shape of the electrical response to photoactivation of a single rhodopsin molecule depends on serial activation of some 100 transducins by the rhodopsin and subsequent suppression of rhodopsin catalytic activity by multiple phosphorylation and arrestin binding, as well as a number of other shut-off reactions (Leskov et al., 2000; Pugh and Lamb, 2000; Fain et al., 2001). It is highly improbable that standardized bumps indistinguishable from this repeatedly arise, e.g., from concerted spontaneous activation of hundreds of transducins followed by quenching that just happens to mimic the shut-off kinetics of the light response.
While it is now widely accepted that the dark events originate in the visual pigment, this has led to another state of nescience: the two processes of thermal and photic activation evidently follow different molecular pathways, but nothing is known about the low-energy thermal pathway. The problem is exacerbated by the fact that 22 kcal/mol is not only radically smaller than the photoactivation energy, but too small to allow the reaction to visit the early postisomerization photoproducts of rhodopsin, notably bathorhodopsin, whose ground-state enthalpy lies 35 kcal/mol above that of the native pigment (Cooper, 1979; Mathies, 1999; Okada et al., 2001). The very rapid formation of bathorhodopsin (within 200 fs; Schoenlein et al., 1991; Wang et al., 1994) leaves no time for significant conformational changes in the opsin (cf. Filipek et al., 2003). Thus, entropy stays essentially constant up to the bathorhodopsin stage, and the change in free energy is approximately equal to the enthalpy change.
A cogent and testable hypothesis about the identity of the low-energy activation pathway was proposed by Barlow et al. (1993), stating that the thermal events originate in a small subpopulation of rhodopsin molecules where the Schiff base linking the chromophore to the opsin is unprotonated. The calculations of the authors indicate that Schiff-base deprotonation would lower the activation energy for chromophore isomerization from 45 kcal/mol to about the right level, 23 kcal/mol. This hypothesis, however, now seems implausible, as recent studies have failed to detect any pH dependence either of dark-event rates in rods (Firsov et al., 2002) or the dark-noise-equivalent rate of quantal activations in cones (Sampath and Baylor, 2002).
It is worth remembering that all experimental evidence for low thermal activation energies comes from measurement of dark-event rates at a few temperatures (cf. Fig. 1). The values extracted from such data depend wholly on the theory applied. We here suggest that the low estimates may be analytical artifacts, due to improper application of conventional Arrhenius analysis to a complex molecule. When the thermal energy present in the vibrational modes of the chromophore is taken into account, the data are consistent with the idea that thermal and photic activation energies are close or even equal, 40–50 kcal/mol. We propose that a particular "low-energy" thermal activation pathway simply may not exist.
The pre-exponential factor
It seems remarkable that the rate of thermal activations should show essentially parallel relations to max within the groups of rod and cone pigments (Figs. 2 and 3), although the absolute levels for rods and cones are separated by some four log units. However, this may be perceived to support the notion that the systematic, max-dependent, variation within both classes is due to a similar mechanism, coupling the energy of the first excited state and the ground-state energy barrier for thermal activation. By contrast, the difference in absolute levels would indicate some global difference in the design of rod and cone opsins.
In the formalism of the model, the difference resides in the "pre-exponential factor" AH (see Eq. 4). We can only speculate on its molecular correlate. Rod opsins evidently have a very "closed" chromophore pocket, which probably imparts high thermal stability to the chromophore. (The price is slow chromophore exchange, thus slow recovery from bleaching.) Regardless of the energy barrier, the possible molecular routes for thermal isomerization of the chromophore may be tightly restricted by the opsin. By contrast, the chromophore pocket of cone pigments is much "looser", arguably to ensure fast chromophore exchange, thus fast recovery from bleaching. In at least some cone pigments, there is a continuous exchange of chromophore even in darkness (Matsumoto et al., 1975). This seems consistent with the idea that the opsin control is much less restrictive than in rods.
Differences in the pre-exponential factor (AH) within either group of pigments (rod or cone) will appear as random variation when the dark-event rate is considered as a function of max. The AH difference is expected to be negligible between the A1 and A2 members of a pigment pair, as both are restricted by the same opsin. For rod pigments with different opsins, the "unexplained" component of experimental variation (cf. Fig. 2) may at present be the only clue to the possible range of variation in AH. In contrast to the rod opsins, the cone opsins phylogenetically belong to several subfamilies (see, e.g., Yokoyama and Yokoyama, 2000), and one might expect even more variation, e.g., in the topology of the chromophore pocket. In the small experimental material available, however, it is not possible to assess the true degree of "random" scatter of cone dark-event rates.
The correlation between the excited-state energy minimum and the ground-state barrier for chromophore isomerization
The model by no means requires the assumption that the photic and thermal activation energies be the same. Weaker forms of correlation will work just as well, but of course some form of coupling is assumed. This is the essence of Barlow's (1957) original proposition that a bathochromic spectral shift always carries a cost in terms of increased thermal noise. The hypothesis has been criticized on the grounds that there are no good physical reasons why the two kinds of activation energies would have to correlate (see, e.g., Goldsmith, 1989a,b, referring to Cundall, 1964). However, there seem to be good reasons to expect they should. The all-trans bleaching intermediate bathorhodopsin, some 5–6 kcal/mol downhill from the peak of the ground-state energy surface for chromophore isomerization, is formed within the first 200 fs from photon absorption (Schoenlein et al., 1991; Wang et al., 1994). The rapidity of this reaction, one of the fastest photochemical reactions known, requires that the excited-state and ground-state surfaces be close, hence a fairly strict coupling between the ground-state barrier and the photoactivation energy Ea (Mathies, 1999). Although the modeling has been based on one specific rhodopsin (bovine), it may be assumed that the main features, i.e., the relation between the energy surfaces and the crossover from the excited state to the ground state, remain similar in different pigments with different photoexcitation energies Ea.
It is also instructive to apply a teleological argument. A visual pigment ought to combine a high quantum efficiency for photoisomerization with high thermal stability. Thermal stability would be maximized if the ground-state barrier for chromophore isomerization were "infinitely" high, but such a molecule would have zero quantum efficiency, because it would always drop back to the 11-cis ground state from the excited state. High quantum efficieny for photoisomerization requires that the ground-state barrier be equal or lower than the excited-state surface in the direction of the isomerization coordinate. In view of the stability requirement, it is optimal to have a barrier as high as possible consistent with this. To the extent that the properties can be tuned by natural selection, the result would be a close coupling of the photic excitation energy and the thermal energy barrier.
Relation of this model to molecular theory
Our model shows that the multimodal character of thermal activation will critically affect the temperature dependence of the rate of such activations, thus undermining the assumptions on which generally accepted estimates of the activation energy are based. It is a purely statistical model, making no detailed claims about molecular processes. In this sense it is complementary to a large body of sophisticated work involving molecular orbital theory and molecular dynamic modeling (Martin and Birge, 1998; Kalé et al., 1999; Kusnetzow et al., 2001; Ben-Nun et al., 2002; Saam et al., 2002). On the other hand, our assumptions and parameters, particularly the number of vibrational modes required, must of course not conflict with what is known about the molecular events in chromophore isomerizaton. It is gratifying to note that evidence from resonance Raman spectroscopy suggests that several tens of modes can contribute to isomerization (Loppnow and Mathies, 1988; Lin et al., 1998; Kim et al., 2003).
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CONCLUSION |
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rather than Boltzmann statistics. The large difference between current estimates of thermal activation energies and photoactivation energies then disappears as an analytical artifact. The experimental data are consistent with the two kinds of activation energy being close or even equal. This has at least two important consequences. Firstly, it allows that the molecular pathways for activation by light and by heat may be identical from the initial event of chromophore isomerization in the native (resting) configuration of the opsin. Secondly, it makes understandable the biologically important correlation between high sensitivity to long-wavelength light and high rates of spontaneous activations in visual pigments. |
ACKNOWLEDGEMENTS |
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This work was supported by the Academy of Finland (grants 49947 and 206221), the Emil Aaltonen Foundation, and the Ella and Georg Ehrnrooth Foundation.
Submitted on October 7, 2003; accepted for publication February 25, 2004.
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REFERENCES |
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