Effects of nonequilibrium fluctuations on ultrafast short-range electron transfer dynamics

Directed ultrafast conformational changes accompany electron transfer in a photolyase as resolved by serial crystallography

Charge-transfer reactions in proteins are important for life, such as in photolyases which repair DNA, but the role of structural dynamics remains unclear. Here, using femtosecond X-ray crystallography, we report the structural changes that take place while electrons transfer along a chain of four conserved tryptophans in the Drosophila melanogaster (6-4) photolyase. At femto- and picosecond delays, photoreduction of the flavin by the first tryptophan causes directed structural responses at a key asparagine, at a conserved salt bridge, and by rearrangements of nearby water molecules. We detect charge-induced structural changes close to the second tryptophan from 1 ps to 20 ps, identifying a nearby methionine as an active participant in the redox chain, and from 20 ps around the fourth tryptophan. The photolyase undergoes highly directed and carefully timed adaptations of its structure. This questions the validity of the linear solvent response approximation in Marcus theory and indicates that evolution has optimized fast protein fluctuations for optimal charge transfer.

Elementary Reactions in the Functional Triads of the Blue-Light Photoreceptor BLUF Domain

The blue light using the flavin (BLUF) domain is one of the smallest photoreceptors in nature, which consists of a unique bidirectional electron-coupled proton relay process in its photoactivation reaction cycle. This perspective summarizes our recent efforts in dissecting the photocycle into three elementary processes, including proton-coupled electron transfer (PCET), proton rocking, and proton relay. Using ultrafast spectroscopy, we have determined the temporal sequence, rates, kinetic isotope effects (KIEs), and concertedness of these elementary steps. Our findings provide important implications for illuminating the photoactivation mechanism of the BLUF domain and suggest an engineering platform to characterize intricate reactions involving proton motions that are ubiquitous in nonphotosensitive protein machines.

Origin of the multi-phasic quenching dynamics in the BLUF domains across the species

Blue light using flavin (BLUF) photoreceptors respond to light via one of nature's smallest photo-switching domains. Upon photo-activation, the flavin cofactor in the BLUF domain exhibits multi-phasic dynamics, quenched by a proton-coupled electron transfer reaction involving the conserved Tyr and Gln. The dynamic behavior varies drastically across different species, the origin of which remains controversial. Here, we incorporate site-specific fluorinated Trp into three BLUF proteins, i.e., AppA, OaPAC and SyPixD, and characterize the percentages for the Wout, WinNHin and WinNHout conformations using 19F nuclear magnetic resonance spectroscopy. Using femtosecond spectroscopy, we identify that one key WinNHin conformation can introduce a branching one-step proton transfer in AppA and a two-step proton transfer in OaPAC and SyPixD. Correlating the flavin quenching dynamics with the active-site structural heterogeneity, we conclude that the quenching rate is determined by the percentage of WinNHin, which encodes a Tyr-Gln configuration that is not conducive to proton transfer.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

Ultrafast Nonequilibrium Dynamics of Vibrationally Hot Electron Transfer in Flavodoxin

The understanding of ultrafast short-range electron transfer (ET) in proteins remains challenging, and thorough studies on well-defined biological systems are demanding. Here, we utilized two types of flavodoxins and designed a series of mutants on two positions to systematically characterize the complete photoinduced redox cycles. We identified one position with a favorable orientation and distance for ultrafast ET in a few femtoseconds and the other position is relatively flexible with a longer ET time scale. We found that all forward and back ET dynamics are ultrafast nonequilibrium processes, occurring through highly vibronic states and ending in vibrationally hot ground states with subsequent cooling relaxation to efficiently dissipate photon energy into the protein environment.

Contribution Factors of the First Kind Calculated for the Marcus Electron-Transfer Rate and Their Applications

In this study, we applied the concept of the "contribution factor of the first kind (CFFK)" to the original electron-transfer (ET) rate theory proposed by Marcus. Mathematical derivations provided simple and convenient formulas for estimating the relative contributions of ten physical and chemical parameters involved in the Marcus ET rate formula: (1) the maximum strength of the electronic coupling energy between two molecules, (2) the exponential decay rate of the electronic coupling energy versus the distance between both molecules, (3) the distance between both molecules, (4) the equilibrium distance between both molecules, (5) the Gibbs free energy, (6) reorganization free energy in the prefactor of the Marcus ET rate equation, (7) reorganization free energy in the denominator of the exponential term, (8) reorganization free energy in the argument of the exponential term, (9) Boltzmann constant times absolute temperature in the prefactor of the rate equation, and (10) Boltzmann constant times absolute temperature in the denominator of the exponential term. We applied our theories to (i) ET reactions at bacterial photosynthesis reaction centers, PSI and PSII, and soluble ferredoxins (Fd); (ii) intraprotein ET reactions for designed azurin mutants; and (iii) ET reactions in flavodoxin (Fld). The formulas and calculations suggest that the theory behind the CFFK is useful for quantitatively identifying major and minor physical and chemical factors and corresponding trade-offs, all of which affect the magnitude of the Marcus ET rate.

Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Solvent Dynamics of Aqueous Halides before and after Photoionization

Electron transfer reactions can be strongly influenced by solvent dynamics. We study the photoionization of halides in water as a model system for such reactions. There are no internal nuclear degrees of freedom in the solute, allowing the dynamics of the solvent to be uniquely identified. We simulate the equilibrium solvent dynamics for Cl^-, Br^-, I^-, and their respective neutral atoms in water, comparing quantum mechanical/molecular mechanical (QM/MM) and classical molecular dynamics (MD) methods. On the basis of the obtained configurations, we calculate the extended X-ray absorption fine structure (EXAFS) spectra rigorously based on the MD snapshots and compare them in detail with other theoretical and experimental results available in the literature. We find our EXAFS spectra based on QM/MM MD simulations in good agreement with their experimental counterparts for the ions. Classical MD simulations for the ions lead to EXAFS spectra that agree equally well with the experiment when it comes to the oscillatory period of the signal, even though they differ from the QM/MM radial distribution functions extracted from the MD. The amplitude is, however, considerably overestimated. This suggests that to judge the reliability of theoretical simulation methods or to elucidate fine details of the atomistic dynamics of the solvent based on EXAFS spectra, the amplitude as well as the oscillatory period need to be considered. If simulations fail qualitatively, as does the classical MD for the aqueous neutral halogen atoms, the resulting EXAFS will also be strongly affected in both oscillatory period and amplitude. The good reliability of QM/MM-based EXAFS simulations, together with clear qualitative differences in the EXAFS spectra found between halides and their atomic counterparts, suggests that a combined theory and experimental EXAFS approach is suitable for elucidating the nonequilibrium solvent dynamics in the photoionization of halides and possibly also for electron transfer reactions in more complex systems.

Dissecting the Ultrafast Stepwise Bidirectional Proton Relay in a Blue-Light Photoreceptor

Proton relays through H-bond networks are essential in realizing the functionality of protein machines such as in photosynthesis and photoreceptors. It has been challenging to dissect the rates and energetics of individual proton-transfer steps during the proton relay. Here, we have designed a proton rocking blue light using a flavin (BLUF) domain with the flavin mononucleotide (FMN)-glutamic acid (E)-tryptophan (W) triad and have resolved the four individual proton-transfer steps kinetically using ultrafast spectroscopy. We have found that after the photo-induced charge separation forming FMN^·-/E-COOH/WH^·+, the proton first rapidly jumps from the bridging E-COOH to FMN^- (τ_fPT2 = 3.8 ps; KIE = 1.0), followed by a second proton transfer from WH^·+ to E-COO^- (τ_fPT1 = 336 ps; KIE = 2.6) which immediately rocks back to W^· (τ_rPT1 = 85 ps; KIE = 6.7), followed by a proton return from FMNH^· to E-COO^- (τ_rPT2 = 34 ps; KIE = 3.3) with the final charge recombination between FMN^·- and WH^·+ to close the reaction cycle. Our results revisited the Grotthuss mechanism on the ultrafast timescale using the BLUF domain as a paradigm protein.

Theory of Protein Charge Transfer: Electron Transfer between Tryptophan Residue and Active Site of Azurin

One reaction step in the conductivity relay of azurin, electron transfer between the Cu-based active site and the tryptophan residue, is studied theoretically and by classical molecular dynamics simulations. Oxidation of tryptophan results in electrowetting of this residue. This structural change makes the free energy surfaces of electron transfer nonparabolic as described by the Q-model of electron transfer. We analyze the medium dynamical effect on protein electron transfer produced by coupled Stokes-shift dynamics and the dynamics of the donor-acceptor distance modulating electron tunneling. The equilibrium donor-acceptor distance falls in the plateau region of the rate constant, where it is determined by the protein-water dynamics, and the probability of electron tunneling does not affect the rate. The crossover distance found here puts most intraprotein electron-transfer reactions under the umbrella of dynamical control. The crossover between the medium-controlled and tunneling-controlled kinetics is combined with the effect of the protein-water medium on the activation barrier to formulate principles of tunability of protein-based charge-transfer chains. The main principle in optimizing the activation barrier is the departure from the Gaussian-Gibbsian statistics of fluctuations promoting activated transitions. This is achieved either by incomplete (nonergodic) sampling, breaking the link between the Stokes-shift and variance reorganization energies, or through wetting-induced structural changes of the enzyme's active site.

Semiclassical Theory of Multistage Nonequilibrium Electron Transfer in Macromolecular Compounds in Polar Media with Several Relaxation Timescales

Many specific features of ultrafast electron transfer (ET) reactions in macromolecular compounds can be attributed to nonequilibrium configurations of intramolecular vibrational degrees of freedom and the environment. In photoinduced ET, nonequilibrium nuclear configurations are often produced at the stage of optical excitation, but they can also be the result of electron tunneling itself, i.e., fast redistribution of charges within the macromolecule. A consistent theoretical description of ultrafast ET requires an explicit consideration of the nuclear subsystem, including its evolution between electron jumps. In this paper, the effect of the multi-timescale nuclear reorganization on ET transitions in macromolecular compounds is studied, and a general theory of ultrafast ET in non-Debye polar environments with a multi-component relaxation function is developed. Particular attention is paid to designing the multidimensional space of nonequilibrium nuclear configurations, as well as constructing the diabatic free energy surfaces for the ET states. The reorganization energies of individual ET transitions, the equilibrium energies of ET states, and the relaxation properties of the environment are used as input data for the theory. The effect of the system-environment interaction on the ET kinetics is discussed, and mechanisms for enhancing the efficiency of charge separation in macromolecular compounds are analyzed.

The nature of proton-coupled electron transfer in a blue light using flavin domain

Proton-coupled electron transfer (PCET) is key to the activation of the blue light using flavin (BLUF) domain photoreceptors. Here, to elucidate the photocycle of the central FMN-Gln-Tyr motif in the BLUF domain of OaPAC, we eliminated the intrinsic interfering W90 in the mutant design. We integrated the stretched exponential function into the target analysis to account for the dynamic heterogeneity arising from the active-site solvation relaxation and the flexible H-bonding network as shown in the molecular dynamics simulation results, facilitating a simplified expression of the kinetics model. We find that, in both the functional wild-type (WT) and the nonfunctional Q48E and Q48A, forward PCET happens in the range of 105 ps to 344 ps, with a kinetic isotope effect (KIE) measured to be ∼1.8 to 2.4, suggesting that the nature of the forward PCET is concerted. Remarkably, only WT proceeds with an ultrafast reverse PCET process (31 ps, KIE = 4.0), characterized by an inverted kinetics of the intermediate FMNH˙. Our results reveal that the reverse PCET is driven by proton transfer via an intervening imidic Gln.

Ultrafast Dynamics of Nonequilibrium Short-Range Electron Transfer in Semiquinone Flavodoxin

Short-range protein electron transfer (ET) is crucially important in light-induced biological processes such as in photoenzymes and photoreceptors and often occurs on time scales similar to those of environment fluctuations, leading to a coupled dynamic process. Herein, we use semiquinone Anabaena flavodoxin to characterize the ultrafast photoinduced redox cycle of the wild type and seven mutants by ultrafast spectroscopy. We have found that the forward and backward ET dynamics show stretched behaviors in a few picoseconds (1-5 ps), indicating a coupling with the local protein fluctuations. By comparison with the results from semiquinone D. vulgaris flavodoxin, we find that the electronic coupling is crucial to the ET rates. With our new nonergodic model, we obtain smaller values of the outer reorganization energy (λ_o^γ) of environment fluctuations and the reaction free energy force (ΔG^γ), a signature of nonequilibrium ET dynamics.

Ultrafast nonequilibrium dynamics of short-range protein electron transfer in flavodoxin

Short-range protein electron transfer (ET) is ubiquitous in biology and is often observed in photosynthesis, photoreceptors and photoenzymes. These ET processes occur on an ultrafast timescale from femtoseconds to picoseconds at a short donor-acceptor distance within 10 Å, and thus couple with local environmental fluctuations. Here, we use oxidized Anabaena flavodoxin as a model system and have systematically studied the photoinduced redox cycle of the wild type and seven mutant proteins by femtosecond spectroscopy. We observed a series of ultrafast dynamics from the initial charge separation in 100-200 fs, subsequent charge recombination in 1-2 ps and final vibrational cooling process of the products in 3-6 ps. We further characterized the active-site solvation and observed the relaxations in 1-200 ps, indicating a nonergodic ET dynamics. With our new ET model, we uncovered a minor outer (solvent) reorganization energy and a large inner (donor and acceptor) reorganization energy, suggesting a frozen active site in the initial ultrafast ET while the back ET couples with the environment relaxations. The vibronically coupled back ET dynamics was first reported in D. vulgaris flavodoxin and here is observed in Anabaena flavodoxin again, completely due to the faster ET dynamics than the cooling relaxations. We also compared the two flavodoxin structures, revealing a stronger coupling with the donor tyrosine in Anabaena. All ultrafast ET dynamics are from the large donor-acceptor couplings and the minor activation barriers due to the reaction free energies being close to the inner reorganization energies. These observations should be general to many redox reactions in flavoproteins.

Exact eigenenergies of a model of vibronically coupled electron transfer reactions

We present the first exact solution to the time-independent Schrödinger equation of a model Hamiltonian consisting of a vibrational mode coupled to three electronic states. This Hamiltonian serves as a generic model for photo-induced electronic transfer reactions. The solution is non-perturbative and can be applied to ET reactions with weak and strong electronic and vibrational coupling strengths. This work suggests a new direction towards understanding the vibronic effects in ET dynamics beyond the non-adiabatic limit and Condon approximation.

Biomolecular Basis of Cellular Consciousness via Subcellular Nanobrains

Cells emerged at the very beginning of life on Earth and, in fact, are coterminous with life. They are enclosed within an excitable plasma membrane, which defines the outside and inside domains via their specific biophysical properties. Unicellular organisms, such as diverse protists and algae, still live a cellular life. However, fungi, plants, and animals evolved a multicellular existence. Recently, we have developed the cellular basis of consciousness (CBC) model, which proposes that all biological awareness, sentience and consciousness are grounded in general cell biology. Here we discuss the biomolecular structures and processes that allow for and maintain this cellular consciousness from an evolutionary perspective.