Thermal activation and photoactivation of visual pigments

Abstract

A visual pigment molecule in a retinal photoreceptor cell can be activated not only by absorption of a photon but also "spontaneously" by thermal energy. Current estimates of the activation energies for these two processes in vertebrate rod and cone pigments are on the order of 40-50 kcal/mol for activation by light and 20-25 kcal/mol for activation by heat, which has forced the conclusion that the two follow quite different molecular routes. It is shown here that the latter estimates, derived from the temperature dependence of the rate of pigment-initiated "dark events" in rods, depend on the unrealistic assumption that thermal activation of a complex molecule like rhodopsin (or even its 11-cis retinaldehyde chromophore) happens through a simple process, somewhat like the collision of gas molecules. When the internal energy present in the many vibrational modes of the molecule is taken into account, the thermal energy distribution of the molecules cannot be described by Boltzmann statistics, and conventional Arrhenius analysis gives incorrect estimates for the energy barrier. When the Boltzmann distribution is replaced by one derived by Hinshelwood for complex molecules with many vibrational modes, the same experimental data become consistent with thermal activation energies that are close to or even equal to the photoactivation energies. Thus activation by light and by heat may in fact follow the same molecular route, starting with 11-cis to all-trans isomerization of the chromophore in the native (resting) configuration of the opsin. Most importantly, the same model correctly predicts the empirical correlation between the wavelength of maximum absorbance and the rate of thermal activation in the whole set of visual pigments studied.

FIGURE 1

The temperature dependence of the rate of thermal dark events per rod (Rh^*s⁻¹) in “red” rods of the toad Bufo marinus. The data are from Baylor et al. (1980, their Table 2); each symbol type denotes data from one rod. The Arrhenius plot shows the natural logarithm of the rate constant (ln k) as a function of the inverse value of the absolute temperature (1/T). The straight line represents both the conventional Arrhenius slope for the value E_a = 21.9 kcal/mol (the mean of the values obtained from the five rods studied) and the slope given by the “Hinshelwood” model for parameter values E_a,H = 44.3 kcal/mol and n = 79.

FIGURE 2

The relation between the rate of thermal dark events per molecule of visual pigment () and the wavelength of peak absorbance (λ_max) in rods (data from Table 1). The Briggsian logarithm of the rate constant k is plotted as a function of 1/λ_max. The three straight lines show three model predictions (all vertically positioned for best fit to the data points). (Solid line) This model with n = 79 (derived from the slope in Fig. 1 when thermal and photic activation energies are assumed to be equal) and the relation between E_a (= E_a,H) and 1/λ_max given by Eq. 8. (Dotted line) This model with the modification that E_a − E_a,H = 10 kcal/mol and n = 44 (the value that gives the correct slope in Fig. 1 in this case). (Dashed line) The prediction of Barlow's (1957) original formulation, based on the assumption that the distribution of visual-pigment molecules on thermal energy levels follows Boltzmann statistics. See text for details.

FIGURE 3

The relation between the rate of thermal dark events per molecule of visual pigment () and the wavelength of peak absorbance λ_max in cones (data from Table 2). The Briggsian logarithm of the rate constant k is shown as a function of 1/λ_max. The three straight lines show the three model predictions explained in the legend to Fig. 2. The solid line gives the prediction of this model under our “main” assumptions (E_a = E_a,H, n = 79, E_a and 1/λ_max related by Eq. 8).