Quantum–classical simulations of rhodopsin reveal excited-state population splitting and its effects on quantum efficiency

Abstract

The activation of rhodopsin, the light-sensitive G-protein-coupled receptor responsible for dim-light vision in vertebrates, is driven by an ultrafast excited-state double-bond isomerization with a quantum efficiency of almost 70%. The origin of such light sensitivity is not understood and a key question is whether in-phase nuclear motion controls the quantum efficiency value. In this study we used hundreds of quantum-classical trajectories to show that, 15 fs after light absorption, a degeneracy between the reactive excited state and a neighbouring state causes the splitting of the rhodopsin population into subpopulations. These subpopulations propagate with different velocities and lead to distinct contributions to the quantum efficiency. We also show here that such splitting is modulated by protein electrostatics, thus linking amino acid sequence variations to quantum efficiency modulation. Finally, we discuss how such a linkage that in principle could be exploited to achieve higher quantum efficiencies would simultaneously increase the receptor thermal noise leading to a trade-off that may have played a role in rhodopsin evolution.

Isorhodopsin: An Undervalued Visual Pigment Analog

“…The S1 surface can contain thermal transitions, as suggested for isorhodopsin (see text). For rhodopsin, very early interstate mixing between the S1 and S2 states has been proposed, which would lead to excited state population splitting [178].…”

“…The global picture arises that, after photoexcitation of the chromophore into the Franck-Condon state, it rapidly relaxes along a barrierless trajectory on the potential surface, to a minimalenergy conical intersection (Figure 2). Here, productive resonance of the electronic wave packet at the excited-state potential surface, with torsional and HOOP vibrational modes in the twisted C10-C13 segment of the 11-cis chromophore, can prime very effective crossover to a ground-state energy surface, generating a hot all-transoid state (photorhodopsin) after tens of fs [171,178,180]. This relaxes thermally within about 200 fs into the photoproduct Batho, which contains a still highly twisted all-trans chromophore, but is stable below 130 K [78,108,167].…”

“…This relaxes thermally within about 200 fs into the photoproduct Batho, which contains a still highly twisted all-trans chromophore, but is stable below 130 K [78,108,167]. Recent advanced QM/MM simulations suggest excited-state population splitting resulting in several waves of productive crossover to the photoproduct's ground state in the first 150 fs, promoted by vibronic coupling, vibrational phase matching, and electrostatic interactions in the binding site [178].…”

“…The exceptionally high quantum yield of rhodopsin-which is hardly affected by wavelength or temperature [169,170,208]-in combination with its ultrafast photoisomerization [179,180,202,[209][210][211][212][213], is interpreted as reflecting a vibronically coherent photochemical process. This would involve productive vibronic coupling of nuclear vibrational modes of the isomerizing 10-11=12-13 segment and the excited electronic wave packet, resulting in a barrierless S1 potential energy surface trajectory to a minimalenergy conical intersection, with very efficient crossover to the S0 surface of the trans photoproduct via a bicycle pedal motion [79,153,166,170,[178][179][180]207,210,[214][215][216][217][218][219][220]. The important contribution of the coupled 11=12 HOOP vibrational phase is perfectly illustrated by analysis of deuterated analogs, where the 11,12-dideutero derivative ( D C=C D ) even slightly increases the quantum yield (Table 2), while the mono-deuterated analogs substantially decrease the quantum yield [179], similar to other 11-or 12-mono-substituted analogs [149,221].…”

“…Hence, 11-cis ⇒ trans isomerization would require a kind of concerted motion in the 10-14 segment, for which volume-conserving "bicycle-pedal", "hula-twist", and "wring-a-wet-towel" trajectories have been proposed, and slight displacement of the C20 methyl group is required [79,111,225]. A bicycle pedal motion now seems to be generally accepted [178,207,217].…”