Extending the essential dynamics analysis to investigate molecular properties: application to the redox potential of proteins

Excitation landscape of the CP43 photosynthetic antenna complex from multiscale simulations

Photosystem II (PSII), the principal enzyme of oxygenic photosynthesis, contains two integral light harvesting proteins (CP43 and CP47) that bind chlorophylls and carotenoids. The two intrinsic antennae play crucial roles in excitation energy transfer and photoprotection. CP43 interacts most closely with the reaction center of PSII, specifically with the branch of the reaction center (D1) that is responsible for primary charge separation and electron transfer. Deciphering the function of CP43 requires detailed atomic-level insights into the properties of the embedded pigments. To advance this goal, we employ a range of multiscale computational approaches to determine the site energies and excitonic profile of CP43 chlorophylls, using large all-atom models of a membrane-bound PSII monomer. In addition to time-dependent density functional theory (TD-DFT) used in the context of a quantum-mechanics/molecular-mechanics setup (QM/MM), we present a thorough analysis using the perturbed matrix method (PMM), which enables us to utilize information from long-timescale molecular dynamics simulations of native PSII-complexed CP43. The excited state energetics and excitonic couplings have both similarities and differences compared with previous experimental fits and theoretical calculations. Both static TD-DFT and dynamic PMM results indicate a layered distribution of site energies and reveal specific groups of chlorophylls that have shared contributions to low-energy excitations. Importantly, the contribution to the lowest energy exciton does not arise from the same chlorophylls at each system configuration, but rather changes as a function of conformational dynamics. An unexpected finding is the identification of a low-energy charge-transfer excited state within CP43 that involves a lumenal (C2) and the central (C10) chlorophyll of the complex. The results provide a refined basis for structure-based interpretation of spectroscopic observations and for further deciphering excitation energy transfer in oxygenic photosynthesis.

Thermodynamic Evolution of a Metamorphic Protein: A Theoretical-Computational Study of Human Lymphotactin

Metamorphic, or fold-switching, proteins feature different folds that are physiologically relevant. The human chemokine XCL1 (or Lymphotactin) is a metamorphic protein that features two native states, an [Formula: see text] and an all[Formula: see text] fold, which have similar stability at physiological condition. Here, extended molecular dynamics (MD) simulations, principal component analysis of atomic fluctuations and thermodynamic modeling based on both the configurational volume and free energy landscape, are used to obtain a detailed characterization of the conformational thermodynamics of human Lymphotactin and of one of its ancestors (as was previously obtained by genetic reconstruction). Comparison of our computational results with the available experimental data show that the MD-based thermodynamics can explain the experimentally observed variation of the conformational equilibrium between the two proteins. In particular, our computational data provide an interpretation of the thermodynamic evolution in this protein, revealing the relevance of the configurational entropy and of the shape of the free energy landscape within the essential space (i.e., the space defined by the generalized internal coordinates providing the largest, typically non-Gaussian, structural fluctuations).

Origins of the pH-Responsive Photoluminescence of Peptide-Functionalized Au Nanoclusters

Ultrasmall peptide-protected gold nanoclusters are a promising class of bioresponsive material exhibiting pH-sensitive photoluminescence. We present a theoretical insight into the effect peptide-ligand environment has on pH-responsive fluorescence, with the aim of enhancing the rational design of gold nanoclusters for bioapplications. Employing a hybrid quantum/classical computational methodology, we systematically calculate deprotonation free energies of N-terminal cysteine amine groups in proximity to the inherently fluorescent core of Au₂₅(Peptide)₁₈ nanoclusters. We find that subtle changes in hexapeptide sequence alter the electrostatic environment and significantly shift the conventional N-terminal amine pK_a expected for amino acids free-in-solution. Our findings provide an insight into how the deprotonation equilibrium of N-terminal amine and side chain carboxyl groups cooperatively respond to solution pH changes, explaining the experimentally observed, yet elusive, pH-responsive fluorescence of peptide-functionalized Au₂₅ clusters.

Evidence for a high pKa of an aspartic acid residue in the active site of CALB by a fully atomistic multiscale approach

Candida antarctica Lipase B (CALB) is a paradigm for the family of lipases. At pH 7, the optimal pH for catalysis, the protonation state of an aspartic acid of the active site (Asp134) could not be conclusively assigned. In fact, the pK_a estimate provided by a widely used computational tool, namely PropKa, that predicts pKa values of ionizable groups in proteins based on the crystallographic structure, is only slightly above 7 (pKa = 7.25). This, along with the lack of an experimental evaluation, makes the assignment of its protonation state at neutral pH challenging. Here, we calculate the pK_a of Asp134 by means of a fully atomistic multiscale computational approach based on classical molecular dynamics (MD) simulation and the perturbed matrix method (PMM), namely the MD-PMM approach. MD-PMM is able to take into account the dynamics of the system and, at the same time, to treat the deprotonation step at the quantum level. The calculations provide a pK_a value of 8.9 ± 1.1, hence suggesting that Asp134 in CALB should be protonated at neutral, and even at slightly basic, pH.

Tuning Proton Transfer Thermodynamics in SARS-CoV-2 Main Protease: Implications for Catalysis and Inhibitor Design

The catalytic reaction in SARS-CoV-2 main protease is activated by a proton transfer (PT) from Cys145 to His41. The same PT is likely also required for the covalent binding of some inhibitors. Here we use a multiscale computational approach to investigate the PT thermodynamics in the apo enzyme and in complex with two potent inhibitors, N3 and the α-ketoamide 13b. We show that with the inhibitors the free energy cost to reach the charge-separated state of the active-site dyad is lower, with N3 inducing the most significant reduction. We also show that a few key sites (including specific water molecules) significantly enhance or reduce the thermodynamic feasibility of the PT reaction, with selective desolvation of the active site playing a crucial role. The approach presented is a cost-effective procedure to identify the enzyme regions that control the activation of the catalytic reaction and is thus also useful to guide the design of inhibitors.

Cooperative protein-solvent tuning of proton transfer energetics: carbonic anhydrase as a case study

We investigate the coupling between the proton transfer (PT) energetics and the protein-solvent dynamics using the intra-molecular PT in wild type (wt) human carbonic anhydrase II and its ten-fold faster mutant Y7F/N67Q as a test case. We calculate the energy variation upon PT, and from that we also calculate the PT reaction free energy, making use of a hybrid quantum mechanics/molecular dynamics approach. In agreement with the experimental data, we obtain that the reaction free energy is basically the same in the two systems. Yet, we show that the instantaneous PT energy is on average lower in the mutant possibly contributing to the faster PT rate. Analysis of the contribution to the PT energetics of the solvent and of each protein residue, also not in the vicinity of the active site, provides evidence for electrostatic tuning of the PT energy arising from the combined effect of the solvent and the protein environment. These findings open up a way to the more general task of the rational design of mutants with either enhanced or reduced PT rate.

Tuning Proton Transfer Thermodynamics in SARS-Cov-2 Main Protease: Implications for Catalysis and Inhibitor Design

In this comutational work a hybrid quantum mechanics/molecular mechanics approach, the MD-PMM approach, is used to investigate the proton transfer reaction the activates the catalytic activity of SARS-CoV-2 main protease. The proton transfer thermodynamics is investigated for the apo ensyme (i.e., without any bound substrate or inhibitor) and in the presence of a inhibitor, N3, which was previously shown to covalently bind SARS-CoV-2 main protease.

Fully Atomistic Multiscale Approach for pKa Prediction

The ionization state of titratable amino acids strongly affects proteins structure and functioning in a large number of biological processes. It is therefore essential to be able to characterize the pK_a of ionizable groups inside proteins and to understand its microscopic determinants in order to gain insights into many functional properties of proteins. A big effort has been devoted to the development of theoretical approaches for the prediction of deprotonation free energies, yet the accurate theoretical/computational calculation of pK_a values is recognized as a current challenge. A methodology based on a hybrid quantum/classical approach is here proposed for the computation of deprotonation free energies. The method is applied to calculate the pK_a of formic acid, methylammonium, and methanethiol, providing results in good agreement with the corresponding experimental estimates. The pK_a is also calculated for aspartic acid and lysine as single residues in solution and for three aspartic/glutamic acids inside a well-characterized protein: hen egg white lysozyme. While for small molecules the method is able to deal with multiple protonation states of all titratable groups, this becomes computationally very expensive for proteins. The calculated pK_a values for the single amino acids (except for the zwitterionic aspartic acid) and inside the protein display a systematic shift with respect to the experimental values that suggests that the fine balance between hydrophobic and polar interactions might be not accurately reproduced by the usual classical force-fields, thus affecting the computation of deprotonation free energies. The calculated pK_a shifts inside the protein are in good agreement with the corresponding experimental ones (within 1 pK_a unit), well reproducing the pK_a changes due to the protein environment even in the case of large pK_a shifts.

Tuning Structure and Dynamics of Blue Copper Azurin Junctions via Single Amino-Acid Mutations

In the growing field of biomolecular electronics, blue-copper Azurin stands out as one of the most widely studied protein in single-molecule contacts. Interestingly, despite the paramount importance of the structure/dynamics of molecular contacts in their transport properties, these factors remain largely unexplored from the theoretical point of view in the context of single Azurin junctions. Here we address this issue using all-atom Molecular Dynamics (MD) of Pseudomonas Aeruginosa Azurin adsorbed to a Au(111) substrate. In particular, we focus on the structure and dynamics of the free/adsorbed protein and how these properties are altered upon single-point mutations. The results revealed that wild-type Azurin adsorbs on Au(111) along two well defined configurations: one tethered via cysteine groups and the other via the hydrophobic pocket surrounding the Cu 2 + . Surprisingly, our simulations revealed that single amino-acid mutations gave rise to a quenching of protein vibrations ultimately resulting in its overall stiffening. Given the role of amino-acid vibrations and reorientation in the dehydration process at the protein-water-substrate interface, we suggest that this might have an effect on the adsorption process of the mutant, giving rise to new adsorption configurations.

Mechanical Deformation and Electronic Structure of a Blue Copper Azurin in a Solid-State Junction

Protein-based electronics is an emerging field which has attracted considerable attention over the past decade. Here, we present a theoretical study of the formation and electronic structure of a metal-protein-metal junction based on the blue-copper azurin from pseudomonas aeruginosa. We focus on the case in which the protein is adsorbed on a gold surface and is contacted, at the opposite side, to an STM (Scanning Tunneling Microscopy) tip by spontaneous attachment. This has been simulated through a combination of molecular dynamics and density functional theory. We find that the attachment to the tip induces structural changes in the protein which, however, do not affect the overall electronic properties of the protein. Indeed, only changes in certain residues are observed, whereas the electronic structure of the Cu-centered complex remains unaltered, as does the total density of states of the whole protein.

Evidence of a Thermodynamic Ramp for Hole Hopping to Protect a Redox Enzyme from Oxidative Damage

Redox proteins and enzymes are at risk of irreversible oxidative damage from highly oxidizing intermediates generated in the active site in the case of unsuccessful functional reaction. Chains of tyrosine and/or tryptophan residues have been recently proposed to provide protection to the active site and the whole protein by delivering oxidizing equivalents (holes) out of the protein via a multistep hopping mechanism. In the present work we use a hybrid quantum/classical theoretical-computational methodology based on the perturbed matrix method and on molecular dynamics simulations to calculate the oxidation potential difference along a chain of tyrosine and tryptophan residues in a human redox enzyme of major importance, a superoxide dismutase, which acts as antioxidant defense. We show that the hole hopping is thermodynamically favored along such a chain and that the hopping propensity is strongly affected by the protein environment and in particular by the active site and its second coordination sphere.

Accurate Quantum Mechanical/Molecular Mechanical Calculations of Reduction Potentials in Azurin Variants

Understanding the regulation mechanism and molecular determinants of the reduction potential of metalloprotein is a major challenge. An ab initio quantum mechanical/molecular mechanical (QM/MM) method combining the minimum free energy path (MFEP) and fractional number of electron (FNE) approaches has been developed in our group to simulate the redox processes of large systems. The FNE scheme provides an efficient unique description for the redox process, while the MFEP method provides improved conformational sampling on complex environments such as protein in the QM/MM calculations. The reduction potentials of wild-type and seven mutants of azurin, a type 1 copper metalloprotein, were simulated with the QM/MM-MFEP+FNE approach in this paper. A range of 350 mV for the variations of the reduction potentials of these azurin proteins was reproduced faithfully with relative errors around 20 mV. The correlation between structural interactions and reduction potentials observed in simulations provides in-depth insight into the regulation of reduction potentials, which potentially can also be very useful to the engineering of metalloprotein-based electrocatalysts in artificial photosynthesis. The excellent accuracy and efficiency of the QM/MM-MFEP+FNE approach demonstrate the potential for simulations of many electron transfer processes in condensed phases and biochemical systems.

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

We combine experimental and computational methods to address the anomalous kinetics of long-range electron transfer (ET) in mutants of Pseudomonas aeruginosa azurin. ET rates and driving forces for wild type (WT) and three N47X mutants (X = L, S, and D) of Ru(2,2'-bipyridine)₂ (imidazole)(His83) azurin are reported. An enhanced ET rate for the N47L mutant suggests either an increase of the donor-acceptor (DA) electronic coupling or a decrease in the reorganization energy for the reaction. The underlying atomistic features are investigated using a recently developed nonadiabatic molecular dynamics method to simulate ET in each of the azurin mutants, revealing unexpected aspects of DA electronic coupling. In particular, WT azurin and all studied mutants exhibit more DA compression during ET (>2 Å) than previously recognized. Moreover, it is found that DA compression involves an extended network of hydrogen bonds, the fluctuations of which gate the ET reaction, such that DA compression is facilitated by transiently rupturing hydrogen bonds. It is found that the N47L mutant intrinsically disrupts this hydrogen-bond network, enabling particularly facile DA compression. This work, which reveals the surprisingly fluctional nature of ET in azurin, suggests that hydrogen-bond networks can modulate the efficiency of long-range biological ET.

On the nature of solvatochromic effect: The riboflavin absorption spectrum as a case study

We present here the calculation of the absorption spectrum of riboflavin in acetonitrile and dimethyl sulfoxide using a hybrid quantum/classical approach, namely the perturbed matrix method, based on quantum mechanical calculations and molecular dynamics simulations. The calculated spectra are compared to the absorption spectrum of riboflavin previously calculated in water and to the experimental spectra obtained in all three solvents. The experimentally observed variations in the absorption spectra upon change of the solvent environment are well reproduced by the calculated spectra. In addition, the nature of the excited states of riboflavin interacting with different solvents is investigated, showing that environment effects determine a recombination of the gas-phase electronic states and that such a recombination is strongly affected by the polarity of the solvent inducing significant changes in the absorption spectra.

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.

Prediction of Reduction Potentials of Copper Proteins with Continuum Electrostatics and Density Functional Theory

Blue copper proteins, such as azurin, show dramatic changes in Cu²⁺/Cu⁺ reduction potential upon mutation over the full physiological range. Hence, they have important functions in electron transfer and oxidation chemistry and have applications in industrial biotechnology. The details of what determines these reduction potential changes upon mutation are still unclear. Moreover, it has been difficult to model and predict the reduction potential of azurin mutants and currently no unique procedure or workflow pattern exists. Furthermore, high‐level computational methods can be accurate but are too time consuming for practical use. In this work, a novel approach for calculating reduction potentials of azurin mutants is shown, based on a combination of continuum electrostatics, density functional theory and empirical hydrophobicity factors. Our method accurately reproduces experimental reduction potential changes of 30 mutants with respect to wildtype within experimental error and highlights the factors contributing to the reduction potential change. Finally, reduction potentials are predicted for a series of 124 new mutants that have not yet been investigated experimentally. Several mutants are identified that are located well over 10 Å from the copper center that change the reduction potential by more than 85 mV. The work shows that secondary coordination sphere mutations mostly lead to long‐range electrostatic changes and hence can be modeled accurately with continuum electrostatics.