Probing the Photochemistry of Rhodopsin Through Population Dynamics Simulation

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8th Feb 2020 Chemistry Reference this

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1. Introduction

Rhodopsins (Rh’s, also known as retinal or retinylidene proteins) form a family of membrane proteins found in all life domains with various biological functions such as light-sensing, light-powered ion-pumping or light-gated ion-channeling activities.1 Rh’s are of great interest for photochemistry due to their ability to transduce light energy. The need for a detailed mechanistic understanding of the photochemistry of vertebrate Rh’s in particular, is becoming increasingly important due to their fundamental role in vision. Such understanding may lead to potential applications in the medical field. The work presented in this dissertation, which mainly focuses on bovine Rh, is devoted to unveil and understand how an only apparently simple photoisomerization drives one of the most efficient and effective biological processes in nature through a set of computational studies.

Bovine Rh has been the subject of the majority of the studies reported on vertebrate Rh structure and function due to the wide availability of cow eyes for the extraction and purification of the protein.2 All vertebrate Rh’s feature an 11-cis retinal protonated Schiff base (rPSB11) chromophore covalently bound to a protein cavity formed by seven interconnected α-helices through a specific lysine residue.3,4 As illustrated in Scheme 1a, absorption of a photon induces the photoisomerization of rPSB11 to its all-trans isomer (rPSBAT) which, in turn, initiate the photoreceptor photocycle.5 In bovine Rh, such photoisomerization takes place on an ultrafast timescale (200 fs)1 with high (0.67) photoproduct (rPSBAT) quantum yield,6 resulting in an extreme light sensitivity. Past experimental evidence has shown that the reaction is also vibrationally coherent all the way from vertical excitation to photoproduct formation.7,8 Vibrational coherence indicates that certain vibrational modes, implicated in the transfer of the molecular population from the vertical excitation region on first excited state (S1) to the ground state (S0) bathorhodopsin (bathoRh) photocycle intermediate, maintain a phase relationship in a significant population fraction.9 Three vibrational modes have been identified to contribute to such coherent motion (see Scheme 1b).10 These are the C11=C12 counterclockwise twist (α), the hydrogen out-of-plane of the HC11=C12H hydrogens (δop) and the skeletal bond length alternation (BLA) stretching of the conjugated backbone.

The photoisomerization of rPSB11 can be described in terms of the geometrical progression of rPSB11 along its S1 potential energy surface (PES) connecting the vertical excitation region to a conical intersection (CI) where decay to S0 occurs.11,12  (see Scheme 1c, left) For each reacting molecule, such S1 to S0 non-adiabatic transition is critical as the CI structure, featuring a ca. 90 degree twisted C11=C12 bond, would relax either back to the original rPSB11 geometry or proceed towards the distorted rPSBAT geometry of bathoRh. Presently, it is not clear if and to what degree the vibrational coherent motion is biologically relevant. Also direct information on the role of the three critical vibrational modes has not been reported. The work presented in this dissertation is devoted to address these unresolved issue focusing on the connection between vibrational coherence and photoisomerization properties such as quantum yield and excited state lifetime of bovine Rh.

Scheme 1, Photoisomerization of bovine Rh. a. Bovine Rh chromophore isomerization. b.Schematic representation of the evolution of the Rh population (a vibrational wavepacket) on a PES diagram.  Notice that BLA dominates the very early part of the reaction coordinate while a combination of α and δop modes drives the progression toward the CI. c. The reaction coordinate is driven by α (in red), δop (in green) and BLA (in blue). d. The phase relationship between the rotation direction (which can be expressed in terms of α and δop velocities) of C10, C13 and the hydrogens of HC11=C12H in the vicinity of the CI (at decay) determines if the trajectory is successful or unsuccessful.

2. Dissertation outline

My dissertation is structured in four tasks/sections: model construction (Section 2.1), simulation based on single trajectory (Section 2.2), simulation of population dynamics with bovine model featuring reduced retinal chromophore (Section 2.3) and full retinal chromophore (Section 2.4).

 

2.1 Model construction

Prior to start the research, obtaining a high-quality three-dimensional protein structure of bovine Rh is essential. In this work the required quantum mechanics/molecular mechanics (QM/MM) model is constructed from the 2.2 Å resolution crystallographic structure available in the Protein Data Bank (PDB ID 1U1924)13 and using the recently reported automatic rhodopsin modeling protocol (ARM). Briefly, ARM is a Linux command-line software tool that calls a series of computational chemistry programs publically available. Instead of producing the most accurate QM/MM models, ARM is designed to construct basic, gas-phase and computationally fast models aimed to the rationalization and prediction of trends between sequence variability and function.14 It has been tested for 27 different rhodopsins including vertebrate, invertebrate, and microbial pigments. The results indicate that, compared to manual model construction, such automatic approach can, not only reduce accidental errors and avoid biased modeling, but also translate results into experimentally assessable hypothesis and treat Rh’s with large differences in sequence (i.e., from different life domains and kingdoms) automatically.

2.2 Single trajectory simulation

The ARM output structure provides us with the model of the S0 equilibrium structures, which are capable of reproducing the observed absorption maximum λmax of the corresponding Rh and can be used for the subsequent molecular dynamics (MD) simulations based on ensembles of semi-classical (i.e. non-adiabatic) trajectories. In this work we initially perform MD simulation with a single Franck−Condon trajectory (i.e. the S1 trajectories starting from the corresponding S0 equilibrium structures with zero initial velocities) as for short timescales Franck−Condon trajectories provide a representation of the average motion of the excited state population.15 The calculation unveils a correlation between the S1 lifetime and electronic state mixing between S1 and its higher neighbor S2.16,17  The results show that unlike bovine Rh, which shows S1 and S2 states splitting in energy and, therefore, decrease their mixing along the S1 potential energy surface, certain microbial rhodopsins and rPSB11 in methanol solution exhibit stronger S1/S2 mixing and longer S1 lifetime.

2.3 Population dynamics simulation with a reduced retinal chromphore

We then investigate the potential impact of electronic state mixing on the vibrational coherence and photoisomerization at the population level. In this work, we propose a protocol to generate a room temperature Boltzmann-like population (i.e. distribution) defined by a number of initial conditions (geometries and velocities). Briefly we extract snapshots  (geometries and velocities) from a classical MD performed at room temperature at constant time intervals and then relax the obtained geometries on S0 at a quantum chemical level of theory. The final geometries and velocities are taken as the initial conditions for the subsequent non-adiabatic trajectory calculations. Such protocol is benchmarked with a low-cost reduced 3 double-bond chromophore model of Anabaena sensory rhodopsin18 and then applied on bovine Rh.

Combined with recent experimental studies employing chromophores with a deuterated HC11=C12H moiety, the population dynamics simulation on bovine Rh model featuring reduced retinal chromophore has shown that modifying the δop mode (see Scheme 1b) significantly changes the photoisomerization QY while introducing smaller changes in the photoisomerization timescale.19 More specifically, our calculation displays that the outcome of the photoisomerization depends on the relationship between the vibrational phases of specific vibrational modes. In fact, as illustrated in Scheme 1d, when the C10 and C13 carbon (described by α) and the HC11=C12H hydrogens (described by δop) rotate in phase the decay to S0 leads to a successful isomerization while when their changes are out-of-phase the decay leads to an unsuccessful event. Since in bovine Rh α changes exclusively in the negative direction from around 0 to -90 degrees (i.e. a quarter of an oscillation), the in-phase condition is equivalent to having a positive δop velocity at the point of decay. When such mechanism is considered at the population level, one concludes that the QY reflects the fraction of rPSB11 chromophores with a positive δop velocity at decay. This hypothesis is supported by a complementary experimental study which shows that the photoisomerization QY of Rh is sensitive to deuterium substitution in HC11=C12H. Indeed, the QY is found to decrease in DC11=C12H and HC11=C12D and to increase in DC11=C12D which is easily interpreted in terms of a change in δop frequency due to the deuterium substitution and, in turn, a change in the δop phase with respect to α.

 

2.4 Population dynamics simulation of full retinal chromphore

Encouraged by the agreement between simulation and experiment, we expand the bovine Rh population dynamics simulation using a model featuring a full retinal chromophore. The 200 initial conditions that we generated are capable of reproducing the protein absorption spectrum and the subsequent excited state trajectories predict a quantum yield (0.68) and S1 lifetime (92 fs) in qualitative agreement with the experimentally observed data. Based on such computational results, we look at how vibrational coherence of atomic motion impact the efficiency of light-induced photoisomerization. We find that the correlation between relative phasing of α and δop modes at the CI and the reaction outcome is still valid even with when performing the population dynamics simulation with the full chromophore. We also find that the all-trans photoproduct formation requires an in-phase modes motion while the out-of-phase modes motion drives the isomerization back to the 11-cis reactant.

A trajectory analysis can be performed to investigate the mechanistic impact of different type of trajectories. analysis. In fact, we also observe a bifurcating dynamics (in fast and slower trajectories) when folling the time-evolution of the α coordinate. resulted from the state mixing between the ionic S1 and diradical S2 introduced by the protein environment contribute to different decay timescale. The subpopulation of early decay is most likely responsible for the observed sub-50 fs photoproduct absorption.9 Also the various α modes together with coherent harmonic δop motion drives different subpopulations cross CI region at different timescale, result in an oscillatory photoproduct formation.

References

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(18)                      Manathunga, M.; Yang, X.; Luk, H. L.; Gozem, S.; Frutos, L. M.; Valentini, A.; Ferrè, N.; and Olivucci, M. J Chem Theory Comput. 2016.

(19)                      Schnedermann, C.; Yang, X.; Liebel, M.; Spillane, K. M.; Lugtenburg, J.; Fernández, I.; Valentini, A.; Schapiro, I.; Olivucci, M.; Kukura, P.; and Mathies, R. A. Nat Chem. 2018, 10, 449-455.

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