Wetting of the Protein Active Site Leads to Non-Marcusian Reaction Kinetics

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

Reorganization energy of electron transfer

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

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.

Assessing Thermal Response of Redox Conduction for Anti-Arrhenius Kinetics in a Microbial Cytochrome Nanowire

A micrometers-long helical homopolymer of the outer-membrane cytochrome type S (OmcS) from Geobacter sulfurreducens is proposed to transport electrons to extracellular acceptors in an ancient respiratory strategy of biogeochemical and technological significance. OmcS surprisingly exhibits higher conductivity upon cooling (anti-Arrhenius kinetics), an effect previously attributed to H-bond restructuring and heme redox potential shifts. Herein, the temperature sensitivity of redox conductivity is more thoroughly examined with conventional and constant-redox and -pH molecular dynamics and quantum mechanics/molecular mechanics. A 30 K drop in temperature constituted a weak perturbation to electron transfer energetics, changing electronic couplings (⟨H_mn⟩), reaction free energies (ΔG_mn), reorganization energies (λ_mn), and activation energies (E_a) by at most |0.002|, |0.050|, |0.120|, and |0.045| eV, respectively. Changes in ΔG_mn reflected -0.07 ± 0.03 V shifts in redox potentials that were caused in roughly equal measure by altered electrostatic interactions with the solvent and protein. Changes in intraprotein H-bonding reproduced the earlier observations. Single-particle diffusion and multiparticle steady-state flux models, parametrized with Marcus theory rates, showed that biologically relevant incoherent hopping cannot qualitatively or quantitatively describe electrical conductivity measured by atomic force microscopy in filamentous OmcS. The discrepancy is attributed to differences between solution-phase simulations and solid-state measurements and the need to model intra- and intermolecular vibrations explicitly.

Active-Site Environmental Factors Customize the Photophysics of Photoenzymatic Old Yellow Enzymes

The development of non-natural photoenzymatic systems has reinvigorated the study of photoinduced electron transfer (ET) within protein active sites, providing new and unique platforms for understanding how biological environments affect photochemical processes. In this work, we use ultrafast spectroscopy to compare the photoinduced electron transfer in known photoenzymes. 12-Oxophytodienoate reductase 1 (OPR1) is compared to Old Yellow Enzyme 1 (OYE1) and morphinone reductase (MR). The latter enzymes are structurally homologous to OPR1. We find that slight differences in the amino acid composition of the active sites of these proteins determine their distinct electron-transfer dynamics. Our work suggests that the inside of a protein active site is a complex/heterogeneous dielectric network where genetically programmed heterogeneity near the site of biological ET can significantly affect the presence and lifetime of various intermediate states. Our work motivates additional tunability of Old Yellow Enzyme active-site reorganization energy and electron-transfer energetics that could be leveraged for photoenzymatic redox approaches.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.