Fluctuating hydrogen-bond networks govern anomalous electron transfer kinetics in a blue copper protein

Secondary structure determines electron transport in peptides

Proteins play a key role in biological electron transport, but the structure-function relationships governing the electronic properties of peptides are not fully understood. Despite recent progress, understanding the link between peptide conformational flexibility, hierarchical structures, and electron transport pathways has been challenging. Here, we use single-molecule experiments, molecular dynamics (MD) simulations, nonequilibrium Green's function-density functional theory (NEGF-DFT), and unsupervised machine learning to understand the role of secondary structure on electron transport in peptides. Our results reveal a two-state molecular conductance behavior for peptides across several different amino acid sequences. MD simulations and Gaussian mixture modeling are used to show that this two-state molecular conductance behavior arises due to the conformational flexibility of peptide backbones, with a high-conductance state arising due to a more defined secondary structure (beta turn or 310 helices) and a low-conductance state occurring for extended peptide structures. These results highlight the importance of helical conformations on electron transport in peptides. Conformer selection for the peptide structures is rationalized using principal component analysis of intramolecular hydrogen bonding distances along peptide backbones. Molecular conformations from MD simulations are used to model charge transport in NEGF-DFT calculations, and the results are in reasonable qualitative agreement with experiments. Projected density of states calculations and molecular orbital visualizations are further used to understand the role of amino acid side chains on transport. Overall, our results show that secondary structure plays a key role in electron transport in peptides, which provides broad avenues for understanding the electronic properties of proteins.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

Integrative Physiological, Transcriptome, and Proteome Analyses Provide Insights into the Photosynthetic Changes in Maize in a Maize-Peanut Intercropping System

Intercropping is a traditional and sustainable planting method that can make rational use of natural resources such as light, temperature, fertilizer, water, and CO2. Due to its efficient resource utilization, intercropping, in particular, maize and legume intercropping, is widespread around the world. However, the molecular details of these pathways remain largely unknown. In this study, physiological, transcriptome, and proteome analyses were compared between maize monocropping and maize-peanut intercropping. The results show that an intercropping system enhanced the ability of carbon fixation and carboxylation of maize leaves. Apparent quantum yield (AQY), the light-saturated net photosynthetic rate (LSPn), the light saturation point (LSP), and the light compensation point (LCP) were increased by 11.6%, 9.4%, 8.9%, and 32.1% in the intercropping system, respectively; carboxylation efficiency (CE), the CO2 saturation point (Cisat), the Rubisco maximum carboxylation rate (Vcmax), the maximum electron transfer rate (Jmax), and the triose phosphate utilization rate (TPU) were increased by 28.5%, 7.3%, 18.7%, 29.2%, and 17.0%, respectively; meanwhile, the CO2 compensation point (Γ) decreased by 22.6%. Moreover, the transcriptome analysis confirmed the presence of 588 differentially expressed genes (DEGs), and the numbers of up-regulated and down-regulated genes were 383 and 205, respectively. The DEGs were primarily concerned with ribosomes, plant hormone signal transduction, and photosynthesis. Furthermore, 549 differentially expressed proteins (DEPs) were identified in the maize leaves in both the maize monocropping and maize-peanut intercropping systems. Bioinformatics analysis revealed that 186 DEPs were related to 37 specific KEGG pathways in each of the two treatment groups. Based on the physiological, transcriptome, and proteome analyses, it was demonstrated that the photosynthetic characteristics in maize leaves can be improved by maize-peanut intercropping. This may be related to PS I, PS II, cytochrome b6f complex, ATP synthase, and photosynthetic CO2 fixation, which is caused by the improved CO2 carboxylation efficiency. Our results provide a more in-depth understanding of the high yield and high-efficiency mechanism in maize and peanut intercropping.

DHFR Mutants Modulate Their Synchronized Dynamics with the Substrate by Shifting Hydrogen Bond Occupancies

Antibiotic resistance is a global health problem in which mutations occurring in functional proteins render drugs ineffective. The working mechanisms of the arising mutants are seldom apparent; a methodology to decipher these mechanisms systematically would render devising therapies to control the arising mutational pathways possible. Here we utilize C_α-C_β bond vector relaxations obtained from moderate length MD trajectories to determine conduits for functionality of the resistance conferring mutants of Escherichia coli dihydrofolate reductase. We find that the whole enzyme is synchronized to the motions of the substrate, irrespective of the mutation introducing gain-of-function or loss-of function. The total coordination of the motions suggests changes in the hydrogen bond dynamics with respect to the wild type as a possible route to determine and classify the mode-of-action of individual mutants. As a result, nine trimethoprim-resistant point mutations arising frequently in evolution experiments are categorized. One group of mutants that display the largest occurrence (L28R, W30G) work directly by modifying the dihydrofolate binding region. Conversely, W30R works indirectly by the formation of the E139-R30 salt bridge which releases energy resulting from tight binding by distorting the binding cavity. A third group (D27E, F153S, I94L) arising as single, resistance invoking mutants in evolution experiment trajectories allosterically and dynamically affects a hydrogen bonding motif formed at residues 59-69-71 which in turn modifies the binding site dynamics. The final group (I5F, A26T, R98P) consists of those mutants that have properties most similar to the wild type; these only appear after one of the other mutants is fixed on the protein structure and therefore display clear epistasis. Thus, we show that the binding event is governed by the entire enzyme dynamics while the binding site residues play gating roles. The adjustments made in the total enzyme in response to point mutations are what make quantifying and pinpointing their effect a hard problem. Here, we show that hydrogen bond dynamics recorded on sub-μs time scales provide the necessary fingerprints to decipher the various mechanisms at play.

Water does not dance as ions sing: A new approach in elucidation of ion-invariant water fluctuations

Aqueous solutions of salts composed from monovalent ions are explored using temperature-dependent FT-IR spectroscopy in transmission. Water combination band, being extremely sensitive to the network of hydrogen bonds due to the contribution of water librations (ρ_LH₂O), is analyzed in uni- and multivariate fashion. Univariate analysis of the combination band maximum (ν_max) reveals that perturbation of water hydrogen bond network by ions is primary driven by electrostatic interactions between water and ions. Using multivariate curve resolution with alternating least squares and evolving factor analysis this band is separated into two components that represent low- and high-density water. The observed asymmetry in their behavior is interpreted in terms of fluctuations of a hydrogen bond network of two water components. The significance of the found phenomenon is unambiguously confirmed by performing analogous analysis in the spectral range that contains partial signature of water linear bending (δHOH) and is free from ρ_LH₂O, in which the asymmetry is absent. Additionally, we show that this phenomenon, namely ion-invariant behavior of water fluctuations, persists even in the regime of high ionic strengths. Although ions indeed participate in shaping of water hydrogen bond network, this straightforward approach shows that its temperature-dependent fluctuations are ion-independent.

Nonadiabatic instanton rate theory beyond the golden-rule limit

Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ →0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.

Reorganization Free Energy of Copper Proteins in Solution, in Vacuum, and on Metal Surfaces

Metalloproteins, known to efficiently transfer electronic charge in biological systems, recently found their utilization in nanobiotechnological devices where the protein is placed into direct contact with metal surfaces. The feasibility of oxidation/reduction of the protein redox sites is affected by the reorganization free energies, one of the key parameters determining the transfer rates. While their values have been measured and computed for proteins in their native environments, i.e., in aqueous solution, the reorganization free energies of dry proteins or proteins adsorbed to metal surfaces remain unknown. Here, we investigate the redox properties of blue copper protein azurin, a prototypical redox-active metalloprotein previously probed by various experimental techniques both in solution and on metal/vacuum interfaces. We used a hybrid QM/MM computational technique based on DFT to explore protein dynamics, flexibility, and corresponding reorganization free energies in aqueous solution, vacuum, and on vacuum gold interfaces. Somewhat surprisingly, the reorganization free energy only slightly decreases when azurin is dried because the loss of the hydration shell leads to larger flexibility of the protein near its redox site. At the vacuum gold surfaces, the energetics of the structure relaxation depends on the adsorption geometry, however, significant reduction of the reorganization free energy was not observed. These findings have important consequences for the charge transport mechanism in vacuum devices, showing that the free energy barriers for protein oxidation remain significant even under ultra-high vacuum conditions.

Hydrogen bonding rearrangement by a mitochondrial disease mutation in cytochrome bc 1 perturbs heme b H redox potential and spin state

To perform their specific electron-transfer relay functions, hemes commonly adopt low spin states with fine-tuned redox potentials. Understanding molecular elements controlling these properties is crucial for the description of natural proteins and engineering redox-active systems. We describe unusual effects of mitochondrial disease-related mutation in cytochrome bc₁, based on which we identify a dual role of hydrogen bonding to the propionate group of heme b_H. We observe that stabilization of the hydrogen bond in mutant enhances the redox potential but destabilizes the low spin state of oxidized heme. This demonstrates a critical role of the hydrogen bonding, and heme-protein interactions in general, to secure a suitable redox potential and spin state, a notion that might be universal for other heme proteins.

Hemes are common elements of biological redox cofactor chains involved in rapid electron transfer. While the redox properties of hemes and the stability of the spin state are recognized as key determinants of their function, understanding the molecular basis of control of these properties is challenging. Here, benefiting from the effects of one mitochondrial disease–related point mutation in cytochrome b, we identify a dual role of hydrogen bonding (H-bond) to the propionate group of heme b_H of cytochrome bc₁, a common component of energy-conserving systems. We found that replacing conserved glycine with serine in the vicinity of heme b_H caused stabilization of this bond, which not only increased the redox potential of the heme but also induced structural and energetic changes in interactions between Fe ion and axial histidine ligands. The latter led to a reversible spin conversion of the oxidized Fe from 1/2 to 5/2, an effect that potentially reduces the electron transfer rate between the heme and its redox partners. We thus propose that H-bond to the propionate group and heme-protein packing contribute to the fine-tuning of the redox potential of heme and maintaining its proper spin state. A subtle balance is needed between these two contributions: While increasing the H-bond stability raises the heme potential, the extent of increase must be limited to maintain the low spin and diamagnetic form of heme. This principle might apply to other native heme proteins and can be exploited in engineering of artificial heme-containing protein maquettes.

Temperature Dependence of Charge and Spin Transfer in Azurin

The steady-state charge and spin transfer yields were measured for three different Ru-modified azurin derivatives in protein films on silver electrodes. While the charge-transfer yields exhibit weak temperature dependences, consistent with operation of a near activation-less mechanism, the spin selectivity of the electron transfer improves as temperature increases. This enhancement of spin selectivity with temperature is explained by a vibrationally induced spin exchange interaction between the Cu(II) and its chiral ligands. These results indicate that distinct mechanisms control charge and spin transfer within proteins. As with electron charge transfer, proteins deliver polarized electron spins with a yield that depends on the protein's structure. This finding suggests a new role for protein structure in biochemical redox processes.

Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed TCF using the Wigner representation for both the nuclear degrees of freedom and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrating these modes out from the expression of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium TCF. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics methods in the future.

Ring polymer quantization of the photon field in polariton chemistry

We use the ring polymer (RP) representation to quantize the radiation field inside an optical cavity to investigate polariton quantum dynamics. Using a charge transfer model coupled to an optical cavity, we demonstrate that the RP quantization of the photon field provides accurate rate constants of the polariton mediated electron transfer reaction compared to Fermi's golden rule. Because RP quantization uses extended phase space to describe the photon field, it significantly reduces the computational costs compared to the commonly used Fock state description of the radiation field. Compared to the other quasi-classical descriptions of the photon field, such as the classical Wigner based mean-field Ehrenfest model, the RP representation provides a much more accurate description of the polaritonic quantum dynamics because it alleviates the potential quantum distribution leakage problem associated with the photonic degrees of freedom (DOF). This work demonstrates the possibility of using the ring polymer description to treat the quantized radiation field in polariton chemistry, offering an accurate and efficient approach for future investigations in cavity quantum electrodynamics.

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.

An improved path-integral method for golden-rule rates

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.

Conductance and configuration of molecular gold-water-gold junctions under electric fields

Water molecules can mediate charge transfer in biological and chemical reactions by forming electronic coupling pathways. Understanding the mechanism requires a molecular-level electrical characterization of water. Here, we describe the measurement of single water molecular conductance at room temperature, characterize the structure of water molecules using infrared spectroscopy, and perform theoretical studies to assist in the interpretation of the experimental data. The study reveals two distinct states of water, corresponding to a parallel and perpendicular orientation of the molecules. Water molecules switch from parallel to perpendicular orientations on applying an electric field, producing switching from high to low conductance states, thus enabling the determination of single water molecular dipole moments. The work further shows that water-water interactions affect the atomic scale configuration and conductance of water molecules. These findings demonstrate the importance of the discrete nature of water molecules in electron transfer and set limits on water-mediated electron transfer rates.

Charge transfer in DHICA eumelanin-like oligomers: role of hydrogen bonds

The building blocks of eumelanin can be used as versatile material with enhanced charge transfer properties.

Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer

We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.

Single electron transfer events and dynamical heterogeneity in the small protein azurin from Pseudomonas aeruginosa

Monitoring the fluorescence of single-dye-labeled azurin molecules, we observed the reaction of azurin with hexacyanoferrate under controlled redox potential yielding data on the timing of individual (forward and backward) electron transfer (ET) events. Change-point analysis of the time traces demonstrates significant fluctuations of ET rates and of mid-point potential E 0. These fluctuations are a signature of dynamical heterogeneity, here observed on a 14 kDa protein, the smallest to date. By correlating changes in forward and backward reaction rates we found that 6% of the observed change events could be explained by a change in midpoint potential, while for 25% a change of the donor-acceptor coupling could explain the data. The remaining 69% are driven by variations in complex association constants or structural changes that cause forward and back ET rates to vary independently. Thus, the observed spread in individual ET rates could be related in a unique way to variations in molecular parameters. The relevance for the understanding of metabolic processes is briefly discussed.

What Are We Missing by Not Measuring the Net Charge of Proteins?

The net electrostatic charge (Z) of a folded protein in solution represents a bird's eye view of its surface potentials-including contributions from tightly bound metal, solvent, buffer, and cosolvent ions-and remains one of its most enigmatic properties. Few tools are available to the average biochemist to rapidly and accurately measure Z at pH≠pI. Tools that have been developed more recently seem to go unnoticed. Most scientists are content with this void and estimate the net charge of a protein from its amino acid sequence, using textbook values of pK_a . Thus, Z remains unmeasured for nearly all folded proteins at pH≠pI. When marveling at all that has been learned from accurately measuring the other fundamental property of a protein-its mass-one wonders: what are we missing by not measuring the net charge of folded, solvated proteins? A few big questions immediately emerge in bioinorganic chemistry. When a single electron is transferred to a metalloprotein, does the net charge of the protein change by approximately one elementary unit of charge or does charge regulation dominate, that is, do the pK_a values of most ionizable residues (or just a few residues) adjust in response to (or in concert with) electron transfer? Would the free energy of charge regulation (ΔΔG_z ) account for most of the outer sphere reorganization energy associated with electron transfer? Or would ΔΔG_z contribute more to the redox potential? And what about metal binding itself? When an apo-metalloprotein, bearing minimal net negative charge (e.g., Z=-2.0) binds one or more metal cations, is the net charge abolished or inverted to positive? Or do metalloproteins regulate net charge when coordinating metal ions? The author's group has recently dusted off a relatively obscure tool-the "protein charge ladder"-and used it to begin to answer these basic questions.

Hole Hopping Across a Protein-Protein Interface

We have investigated photoinduced hole hopping in a Pseudomonas aeruginosa azurin mutant Re126WWCuI, where two adjacent tryptophan residues (W124 and W122) are inserted between the CuI center and a Re photosensitizer coordinated to a H126 imidazole (Re = ReI(H126)(CO)3(dmp)+, dmp = 4,7-dimethyl-1,10-phenanthroline). Optical excitation of this mutant in aqueous media (≤40 μM) triggers 70 ns electron transport over 23 Å, yielding a long-lived (120 μs) ReI(H126)(CO)3(dmp•-)WWCuII product. The Re126FWCuI mutant (F124, W122) is not redox-active under these conditions. Upon increasing the concentration to 0.2-2 mM, {Re126WWCuI}2 and {Re126FWCuI}2 are formed with the dmp ligand of the Re photooxidant of one molecule in close contact (3.8 Å) with the W122' indole on the neighboring chain. In addition, {Re126WWCuI}2 contains an interfacial tryptophan quadruplex of four indoles (3.3-3.7 Å apart). In both mutants, dimerization opens an intermolecular W122' → //*Re ET channel (// denotes the protein interface, *Re is the optically excited sensitizer). Excited-state relaxation and ET occur together in two steps (time constants of ∼600 ps and ∼8 ns) that lead to a charge-separated state containing a Re(H126)(CO)3(dmp•-)//(W122•+)' unit; then (CuI)' is oxidized intramolecularly (60-90 ns) by (W122•+)', forming ReI(H126)(CO)3(dmp•-)WWCuI//(CuII)'. The photocycle is closed by ∼1.6 μs ReI(H126)(CO)3(dmp•-) → //(CuII)' back ET that occurs over 12 Å, in contrast to the 23 Å, 120 μs step in Re126WWCuI. Importantly, dimerization makes Re126FWCuI photoreactive and, as in the case of {Re126WWCuI}2, channels the photoproduced "hole" to the molecule that was not initially photoexcited, thereby shortening the lifetime of ReI(H126)(CO)3(dmp•-)//CuII. Although two adjacent W124 and W122 indoles dramatically enhance CuI → *Re intramolecular multistep ET, the tryptophan quadruplex in {Re126WWCuI}2 does not accelerate intermolecular electron transport; instead, it acts as a hole storage and crossover unit between inter- and intramolecular ET pathways. Irradiation of {Re126WWCuII}2 or {Re126FWCuII}2 also triggers intermolecular W122' → //*Re ET, and the Re(H126)(CO)3(dmp•-)//(W122•+)' charge-separated state decays to the ground state by ∼50 ns ReI(H126)(CO)3(dmp•-)+ → //(W122•+)' intermolecular charge recombination. Our findings shed light on the factors that control interfacial hole/electron hopping in protein complexes and on the role of aromatic amino acids in accelerating long-range electron transport.

Charge-Transfer versus Charge-Separated Triplet Excited States of [ReI (dmp)(CO)3 (His124)(Trp122)]+ in Water and in Modified Pseudomonas aeruginosa Azurin Protein

A computational investigation of the triplet excited states of a rhenium complex electronically coupled with a tryptophan side chain and bound to an azurin protein is presented. In particular, by using high-level molecular modeling, evidence is provided for how the electronic properties of the excited-state manifolds strongly depend on coupling with the environment. Indeed, only upon explicitly taking into account the protein environment can two stable triplet states of metal-to-ligand charge transfer or charge-separated nature be recovered. In addition, it is also demonstrated how the rhenium complex plus tryptophan system in an aqueous environment experiences too much flexibility, which prevents the two chromophores from being electronically coupled. This occurrence disables the formation of a charge-separated state. The successful strategy requires a multiscale approach of combining molecular dynamics and quantum chemistry. In this context, the strategy used to parameterize the force fields for the electronic triplet states of the metal complex is also presented.

Ab initio electronic structure calculations of entire blue copper azurins

We present a theoretical study of the blue-copper azurin extracted from Pseudomonas aeruginosa and several of its single amino acid mutants.