Calculation of the Redox Potential of the Protein Azurin and Some Mutants

Assessing the Performance of Non-Equilibrium Thermodynamic Integration in Flavodoxin Redox Potential Estimation

Flavodoxins are enzymes that contain the redox-active flavin mononucleotide (FMN) cofactor and play a crucial role in numerous biological processes, including energy conversion and electron transfer. Since the redox characteristics of flavodoxins are significantly impacted by the molecular environment of the FMN cofactor, the evaluation of the interplay between the redox properties of the flavin cofactor and its molecular surroundings in flavoproteins is a critical area of investigation for both fundamental research and technological advancements, as the electrochemical tuning of flavoproteins is necessary for optimal interaction with redox acceptor or donor molecules. In order to facilitate the rational design of biomolecular devices, it is imperative to have access to computational tools that can accurately predict the redox potential of both natural and artificial flavoproteins. In this study, we have investigated the feasibility of using non-equilibrium thermodynamic integration protocols to reliably predict the redox potential of flavodoxins. Using as a test set the wild-type flavodoxin from Clostridium Beijerinckii and eight experimentally characterized single-point mutants, we have computed their redox potential. Our results show that 75% (6 out of 8) of the calculated reaction free energies are within 1 kcal/mol of the experimental values, and none exceed an error of 2 kcal/mol, confirming that non-equilibrium thermodynamic integration is a trustworthy tool for the quantitative estimation of the redox potential of this biologically and technologically significant class of enzymes.

Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin

As the field of nanoelectronics based on biomolecules such as peptides and proteins rapidly grows, there is a need for robust computational methods able to reliably predict charge transfer properties at bio/metallic interfaces. Traditionally, hybrid quantum-mechanical/molecular-mechanical techniques are employed for systems where the electron hopping transfer mechanism is applicable to determine physical parameters controlling the thermodynamics and kinetics of charge transfer processes. However, these approaches are limited by a relatively high computational cost when extensive sampling of a configurational space is required, like in the case of soft biomatter. For these applications, semi-empirical approaches such as the perturbed matrix method (PMM) have been developed and successfully used to study charge-transfer processes in biomolecules. Here, we explore the performance of PMM on prototypical redox-active protein azurin in various environments, from solution to vacuum interfaces with gold surfaces and protein junction. We systematically benchmarked the robustness and convergence of the method with respect to the quantum-centre size, size of the Hamiltonian, number of samples, and level of theory. We show that PMM can adequately capture all the trends associated with the structural and electronic changes related to azurin oxidation at bio/metallic interfaces.

Machine Learning for Efficient Prediction of Protein Redox Potential: The Flavoproteins Case

Determining the redox potentials of protein cofactors and how they are influenced by their molecular neighborhoods is essential for basic research and many biotechnological applications, from biosensors and biocatalysis to bioremediation and bioelectronics. The laborious determination of redox potential with current experimental technologies pushes forward the need for computational approaches that can reliably predict it. Although current computational approaches based on quantum and molecular mechanics are accurate, their large computational costs hinder their usage. In this work, we explored the possibility of using more efficient QSPR models based on machine learning (ML) for the prediction of protein redox potential, as an alternative to classical approaches. As a proof of concept, we focused on flavoproteins, one of the most important families of enzymes directly involved in redox processes. To train and test different ML models, we retrieved a dataset of flavoproteins with a known midpoint redox potential (E_m) and 3D structure. The features of interest, accounting for both short- and long-range effects of the protein matrix on the flavin cofactor, have been automatically extracted from each protein PDB file. Our best ML model (XGB) has a performance error below 1 kcal/mol (∼36 mV), comparing favorably to more sophisticated computational approaches. We also provided indications on the features that mostly affect the E_m value, and when possible, we rationalized them on the basis of previous studies.

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.

Theoretical Modeling of Redox Potentials of Biomolecules

The estimation of the redox potentials of biologically relevant systems by means of theoretical-computational approaches still represents a challenge. In fact, the size of these systems typically does not allow a full quantum-mechanical treatment needed to describe electron loss/gain in such a complex environment, where the redox process takes place. Therefore, a number of different theoretical strategies have been developed so far to make the calculation of the redox free energy feasible with current computational resources. In this review, we provide a survey of such theoretical-computational approaches used in this context, highlighting their physical principles and discussing their advantages and limitations. Several examples of these approaches applied to the estimation of the redox potentials of both proteins and nucleic acids are described and critically discussed. Finally, general considerations on the most promising strategies are reported.

Ab Initio Evaluation of the Redox Potential of Cytochrome c

Various biochemical activities of metabolism and biosynthesis are fulfilled by redox processes with explicit electron exchange, which furnish redox enzymes with high chemical reactivity. However, theoretical investigation of a redox process, which simultaneously involves a complex electronic change at a redox metal center and conformational reorganization of the surrounding protein environment coupled to the electronic change, requires computationally conflicting approaches, highly accurate quantum chemical calculations, and long-time molecular dynamics (MD) simulations, limiting the physicochemical understanding of biological redox processes. Here, we theoretically examined a redox process of cytochrome c by means of a hybrid molecular simulation technique, which enables one to consistently treat the redox center at the ab initio quantum chemistry level of theory and the protein reorganization with long-time MD simulations on the microsecond timescale. The calculations successfully evaluated a large absolute redox potential, 4.34 eV, with errors of only 0.03 to 0.34 eV to the experimental ones without any problem-specific empirical parameters. Through the long-time MD sampling, large and nonlinear reorganization of the protein environment was unveiled and the molecular determinants for the redox potential were identified. The present ab initio approach significantly expands the applicability of theoretical investigation to biological redox systems with more electronically complicated redox centers such as polynuclear transition metal complexes.

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.

A Fragment Quantum Mechanical Method for Metalloproteins

An accurate energy calculation of metalloprotein is of crucial importance and also a theoretical challenge. In this work, a metal molecular fractionation with conjugate caps (metal-MFCC) approach is developed for efficient linear-scaling quantum calculation of potential energy and atomic forces of metalloprotein. In this approach, the potential energy of a given protein is calculated by a linear combination of potential energies of the neighboring residues, two-body interaction energy between non-neighboring residues that are spatially in close contact and the potential energy of the metal binding group. The calculation of each fragment is embedded in a field of point charges representing the remaining protein environment. Numerical studies were carried out to check the performance of this method, and the calculated potential energies and atomic forces all show excellent agreement with the full system calculations at the M06-2X/6-31G(d) level. By combining the energy calculation with molecular dynamic simulation, we performed an ab initio structural optimization for a zinc finger protein with high efficiency. The present metal-MFCC approach is linear-scaling with a low prefactor and trivially parallelizable. The individual fragment typically contains about 50 atoms, and it is thus possible to be calculated at higher levels of the quantum chemistry method. This fragment method can be routinely applied to perform structural optimization and ab initio molecular dynamic simulation for metalloproteins of any size.

Differences in the mechanical unfolding pathways of apo- and copper-bound azurins

Metalloproteins carry out diverse biological functions including metal transport, electron transfer, and catalysis. At present, the influence of metal cofactors on metalloprotein stability is not well understood. Here, we report the mechanical stability and unfolding pathway of azurin, a cupredoxin family protein with β-barrel topology and type I copper-binding centre. Single-molecule force spectroscopy (SMFS) experiments reveal 2-state and 3-state unfolding pathways for apo-azurin. The intermediate in the 3-state pathway occurs at an unfolding contour length of 7.5 nm from the native state. Steered molecular dynamics (SMD) simulations show that apo-azurin unfolds via a first transition state (TS) where β2Β–β8 and β7–β8 strand pairs rupture to form the intermediate, which subsequently unfolds by the collective rupture of remaining strands. SMFS experiments on holo-azurin exhibit an additional 4-state pathway besides the 2-state and 3-state pathways. The unfolding contour length leading to the first intermediate is 6.7 nm suggesting a sequestration of ~1 nm polypeptide chain length by the copper. SMD simulations reveal atomistic details of the copper sequestration and predict a combined β4–β7 pair and copper coordination sphere rupture to create the third TS in the 4-state pathway. Our systematic studies provide detailed mechanistic insights on modulation of protein mechanical properties by metal-cofactors.

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.

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

Here, a methodology is proposed to investigate the collective fluctuation modes of an arbitrary set of observables, maximally contributing to the fluctuation of another functionally relevant observable. The methodology, based on the analysis of fully classical molecular dynamics (MD) simulations, exploits the essential dynamics (ED) method, originally developed to analyse the collective motions in proteins. We apply this methodology to identify the residues that are more relevant for determining the reduction potential (E(0)) of a redox-active protein. To this aim, the fluctuation modes of the single-residue electrostatic potentials mostly contributing to the fluctuations of the total electrostatic potential (the main determinant of E(0)) are investigated for wild-type azurin and two of its mutants with a higher E(0). By comparing the results here obtained with a previous study on the same systems [Zanetti-Polzi et al., Org. Biomol. Chem., 2015, 13, 11003] we show that the proposed methodology is able to identify the key sites that determine E(0). This information can be used for a general deeper understanding of the molecular mechanisms on the basis of the redox properties of the proteins under investigation, as well as for the rational design of mutants with a higher or lower E(0). From the results of the present analysis we propose a new azurin mutant that, according to our calculations, shows a further increase of E(0).

Copper Oxidation/Reduction in Water and Protein: Studies with DFTB3/MM and VALBOND Molecular Dynamics Simulations

We apply two recently developed computational methods, DFTB3 and VALBOND, to study copper oxidation/reduction processes in solution and protein. The properties of interest include the coordination structure of copper in different oxidation states in water or in a protein (plastocyanin) active site, the reduction potential of the copper ion in different environments, and the environmental response to copper oxidation. The DFTB3/MM and VALBOND simulation results are compared to DFT/MM simulations and experimental results whenever possible. For a copper ion in aqueous solution, DFTB3/MM results are generally close to B3LYP/MM with a medium basis, including both solvation structure and reduction potential for Cu(II); for Cu(I), however, DFTB3/MM finds a two-water coordination, similar to previous Born-Oppenheimer molecular dynamics simulations using BLYP and HSE, whereas B3LYP/MM leads to a tetrahedron coordination. For a tetraammonia copper complex in aqueous solution, VALBOND and DFTB3/MM are consistent in terms of both structural and dynamical properties of solvent near copper for both oxidation states. For copper reduction in plastocyanin, DFTB3/MM simulations capture the key properties of the active site, and the computed reduction potential and reorganization energy are in fair agreement with experiment, especially when the periodic boundary condition is used. Overall, the study supports the value of VALBOND and DFTB3(/MM) for the analysis of fundamental copper redox chemistry in water and protein, and the results also help highlight areas where further improvements in these methods are desirable.

The "Hot-Solvent/Cold-Solute" Problem Revisited

The temperature steers the equilibrium and nonequilibrium conformational dynamics of macromolecules in solution. Therefore, corresponding molecular dynamics simulations require a strategy for temperature control which should guarantee that the experimental statistical ensemble is also sampled in silico. Several algorithms for temperature control have been proposed. All these thermostats interfere with the macromolecule's "natural" dynamics as given by the Newtonian mechanics. Furthermore, using a single thermostat for an inhomogeneous solute-solvent system can lead to stationary temperature gradients. To avoid this "hot solvent/cold solute" problem, two separate thermostats are frequently applied, one to the solute and one to the solvent. However, such a separate temperature control will perturb the dynamics of the macromolecule much more strongly than a global one and, therefore, can introduce large artifacts into its conformational dynamics. Based on the concept that an explicit solvent environment represents an ideal thermostat concerning the magnitude and time correlation of temperature fluctuations of the solute, we propose a temperature control strategy that, on the one hand, provides a homogeneous temperature distribution throughout the system together with the correct statistical ensemble for the solute molecule while, on the other hand, minimally perturbing its dynamics.

A few key residues determine the high redox potential shift in azurin mutants

The wide range of variability of the reduction potential (E(0)) of blue-copper proteins has been the subject of a large number of studies in the past several years. In particular, a series of azurin mutants have been recently rationally designed tuning E(0) over a very broad range (700 mV) without significantly altering the redox-active site [Marshall et al., Nature, 2009, 462, 113]. This clearly suggests that interactions outside the primary coordination sphere are relevant to determine E(0) in cupredoxins. However, the molecular determinants of the redox potential variability are still undisclosed. Here, by means of atomistic molecular dynamics simulations and hybrid quantum/classical calculations, the mechanisms that determine the E(0) shift of two azurin mutants with high potential shifts are unravelled. The reduction potentials of native azurin and of the mutants are calculated obtaining results in good agreement with the experiments. The analysis of the simulations reveals that only a small number of residues (including non-mutated ones) are relevant in determining the experimentally observed E(0) variation via site-specific, but diverse, mechanisms. These findings open the path to the rational design of new azurin mutants with different E(0).

The mechanochemistry of copper reports on the directionality of unfolding in model cupredoxin proteins

Understanding the directionality and sequence of protein unfolding is crucial to elucidate the underlying folding free energy landscape. An extra layer of complexity is added in metalloproteins, where a metal cofactor participates in the correct, functional fold of the protein. However, the precise mechanisms by which organometallic interactions are dynamically broken and reformed on (un)folding are largely unknown. Here we use single molecule force spectroscopy AFM combined with protein engineering and MD simulations to study the individual unfolding pathways of the blue-copper proteins azurin and plastocyanin. Using the nanomechanical properties of the native copper centre as a structurally embedded molecular reporter, we demonstrate that both proteins unfold via two independent, competing pathways. Our results provide experimental evidence of a novel kinetic partitioning scenario whereby the protein can stochastically unfold through two distinct main transition states placed at the N and C termini that dictate the direction in which unfolding occurs.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

An Overview of Electrostatic Free Energy Computations for Solutions and Proteins

Free energy simulations for electrostatic and charging processes in complex molecular systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calculate the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liquid-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no physical boundary to the system. An important consequence is that the reference value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the volume fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.

Importance of polarization effect in the study of metalloproteins: application of polarized protein specific charge scheme in predicting the reduction potential of azurin

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein-specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild-type azurin (ΔEcal) were calculated and compared with experimental values. The ΔEcal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein-specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations.

Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulation

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio-)chemical thermodynamics. Many important endogenous receptor-binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice-summation scheme or a cutoff-truncation scheme with Barker-Watts reaction-field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest-host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free-energy calculation studies if changes in the net charge are involved.

How the dynamics of the metal-binding loop region controls the acid transition in cupredoxins

Many reduced cupredoxins undergo a pH-dependent structural rearrangement, triggered by protonation of the His ligand belonging to the C-terminal hydrophobic loop, usually termed the acid transition. At variance with several members of the cupredoxin family, the acid transition is not observed for azurin (AZ). We have addressed this issue by performing molecular dynamics simulations of AZ and four mutants, in which the C-terminal loop has been replaced with those of other cupredoxins or with polyalanine loops. All of the loop mutants undergo the acid transition in the pH range of 4.4-5.5. The main differences between AZ and its loop mutants are the average value of the active site solvent accessible surface area and the extent of its fluctuations with time, together with an altered structure of the water layer around the copper center. Using functional mode analysis, we found that these variations arise from changes in nonbonding interactions in the second coordination sphere of the copper center, resulting from the loop mutation. Our results strengthen the view that the dynamics at the site relevant for function and its surroundings are crucial for protein activity and for metal-containing electron transferases.

Lead optimization mapper: automating free energy calculations for lead optimization

Alchemical free energy calculations hold increasing promise as an aid to drug discovery efforts. However, applications of these techniques in discovery projects have been relatively few, partly because of the difficulty of planning and setting up calculations. Here, we introduce lead optimization mapper, LOMAP, an automated algorithm to plan efficient relative free energy calculations between potential ligands within a substantial library of perhaps hundreds of compounds. In this approach, ligands are first grouped by structural similarity primarily based on the size of a (loosely defined) maximal common substructure, and then calculations are planned within and between sets of structurally related compounds. An emphasis is placed on ensuring that relative free energies can be obtained between any pair of compounds without combining the results of too many different relative free energy calculations (to avoid accumulation of error) and by providing some redundancy to allow for the possibility of error and consistency checking and provide some insight into when results can be expected to be unreliable. The algorithm is discussed in detail and a Python implementation, based on both Schrödinger's and OpenEye's APIs, has been made available freely under the BSD license.

The Active Site Loop Modulates the Reorganization Energy of Blue Copper Proteins by Controlling the Dynamic Interplay with Solvent

Understanding the factors governing the rate of electron transfer processes in proteins is crucial not only to a deeper understanding of redox processes in living organisms but also for the design of efficient devices featuring biological molecules. Here, molecular dynamics simulations performed on native azurin and four chimeric cupredoxins allow for the calculation of the reorganization energy and of structure-related quantities that were used to clarify the molecular determinants to the dynamics/function relationship in blue copper proteins. We find that the dynamics of the small, metal-binding loop region controls the outer-sphere reorganization energy not only by determining the exposure of the active site to solvent but also through the modulation of the redox-dependent rearrangement of the whole protein scaffold and of the surrounding water molecules.

Perspective: Alchemical free energy calculations for drug discovery

Computational techniques see widespread use in pharmaceutical drug discovery, but typically prove unreliable in predicting trends in protein-ligand binding. Alchemical free energy calculations seek to change that by providing rigorous binding free energies from molecular simulations. Given adequate sampling and an accurate enough force field, these techniques yield accurate free energy estimates. Recent innovations in alchemical techniques have sparked a resurgence of interest in these calculations. Still, many obstacles stand in the way of their routine application in a drug discovery context, including the one we focus on here, sampling. Sampling of binding modes poses a particular challenge as binding modes are often separated by large energy barriers, leading to slow transitions. Binding modes are difficult to predict, and in some cases multiple binding modes may contribute to binding. In view of these hurdles, we present a framework for dealing carefully with uncertainty in binding mode or conformation in the context of free energy calculations. With careful sampling, free energy techniques show considerable promise for aiding drug discovery.

The reversible opening of water channels in cytochrome c modulates the heme iron reduction potential

Dynamic protein-solvent interactions are fundamental for life processes, but their investigation is still experimentally very demanding. Molecular dynamics simulations up to hundreds of nanoseconds can bring to light unexpected events even for extensively studied biomolecules. This paper reports a combined computational/experimental approach that reveals the reversible opening of two distinct fluctuating cavities in Saccharomyces cerevisiae iso-1-cytochrome c. Both channels allow water access to the heme center. By means of a mixed quantum mechanics/molecular dynamics (QM/MD) theoretical approach, the perturbed matrix method (PMM), that allows to reach long simulation times, changes in the reduction potential of the heme Fe(3+)/Fe(2+) couple induced by the opening of each cavity are calculated. Shifts of the reduction potential upon changes in the hydration of the heme propionates are observed. These variations are relatively small but significant and could therefore represent a tool developed by cytochrome c for the solvent driven, fine-tuning of its redox functionality.

Calculating chemically accurate redox potentials for engineered flavoproteins from classical molecular dynamics free energy simulations

The tricyclic isoalloxazine nucleus of the redox cofactors flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD) acts as an electron sink in life-sustaining biological electron transfer (eT). The functional diversity of flavin-containing proteins (flavoproteins) transcends that of free flavins. A large body of experimental evidence attributes natural control of flavoprotein-mediated eT to tuning of the thermodynamic driving force by the protein environment. Understanding and engineering such modulation by the protein environment of the flavin redox potential (DeltaE(o)) is valuable in biotechnology and device design. In this study we employed classical molecular dynamics free energy simulations (MDFES), within a thermodynamic integration (TI) formalism, to calculate the change in FMN first reduction potential (DeltaDeltaE(o)(ox/sq)) imparted by 6 flavoprotein active site mutations. The combined performance of the AMBER ff03 (protein) and GAFF (cofactor) force fields was benchmarked against experimental data for mutations close to the isoalloxazine re- and si-faces that perturb the wild-type DeltaE(o)(ox/sq) value in Anabaena flavodoxin. The classical alchemical approach used in this study overestimates the magnitude of DeltaE(o) values, in common with other studies. Nevertheless, chemically accurate DeltaDeltaE(o) values--calculated to within 1 kcal mol(-1) of the experimental value--were obtained for five of the six mutations studied. We have shown that this approach is practical for quantitative in silico screening of the effect of mutations on the first reduction potential where experimental values and structural data are available for the wild-type flavoprotein. This approach promises to be useful as an integral part of future interdisciplinary strategies to engineer desired thermodynamic properties in flavoproteins of biotechnological interest.

On the effect of a point mutation on the reactivity of CuZn superoxide dismutase: a theoretical study

In this paper, we investigate the effects of a point mutation on the enzymatic activity of copper-zinc superoxide dismutase, which we recently studied in detail by means of a theoretical-computational procedure. Comparison of the reactivity of the initial catalytic steps in this mutant (G93A mutation far from the active site) with our previous data, reveals the beautiful mechanical-dynamical architecture of the enzyme, altered by such an apparently irrelevant mutation. Finally, our results suggest a possible atomic-molecular-based explanation for the mutant-pathology correlation, in line with the most recent experimental data.

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.

The Confine-and-Release Method: Obtaining Correct Binding Free Energies in the Presence of Protein Conformational Change

Free energy calculations are increasingly being used to estimate absolute and relative binding free energies of ligands to proteins. However, computed free energies often appear to depend on the initial protein conformation, indicating incomplete sampling. This is especially true when proteins can change conformation on ligand binding, as free energies associated with these conformational changes are either ignored or assumed to be included by virtue of the sampling performed in the calculation. Here, we show that, in a model protein system (a designed binding site in T4 Lysozyme), conformational changes can make a difference of several kcal/mol in computed binding free energies, and that they are neglected in computed binding free energies if the system remains kinetically trapped in a particular metastable state on simulation timescales. We introduce a general "confine-and-release" framework for free energy calculations that accounts for these free energies of conformational change. We illustrate its use in this model system by demonstrating that an umbrella sampling protocol can obtain converged binding free energies that are independent of the starting protein structure and include these conformational change free energies.

Active site structures and the redox properties of blue copper proteins: atomic resolution structure of azurin II and electronic structure calculations of azurin, plastocyanin and stellacyanin

Understanding how the active site structures of blue copper proteins determine their redox properties is the central structure-function relationship question of this important class of protein, also referred to as cupredoxins. We here describe both experimental and computational studies of azurin, plastocyanin and stellacyanin designed to define more accurately the geometric structures of the active site of the reduced and oxidized species, and thus to understand how these structures determine the redox potentials of these proteins. To this end the crystal structure of reduced azurin II has been determined at an atomic resolution of 1.13 Angstrom and is presented here. Co-ordinates and structure factors have been deposited in the RCSB Protein Data Bank with accession codes 2ccw and r2ccwsf respectively. The improved accuracy provided by the atomic resolution for the metal stereochemistry are utilised in conjunction with the EXAFS data for theoretical calculations. Multilevel calculations involving density functional theory and molecular mechanical potentials are used to predict both the geometric and electronic structure of the active sites of azurin, plastocyanin and stellacyanin and to estimate the relative redox potentials of these three proteins. We have also compared the relative energies of the structures obtained from experiment at varying resolutions, and from the isolated and embedded cluster calculations. We find significant energy differences between low and high (atomic) resolution structures arising primarily due to inaccuracies in the Cu-ligand distances in the lower resolution structures, emphasising the importance of accurate, very high resolution structural information. QM/MM structures are only approximately 1 kcal mol(-1) lower in energy than the 1.13 Angstrom structure while the optimized gas phase structure is 13.0 kcal mol(-1) lower in energy.

The GROMOS software for biomolecular simulation: GROMOS05

We present the latest version of the Groningen Molecular Simulation program package, GROMOS05. It has been developed for the dynamical modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization. An overview of GROMOS05 is given, highlighting features not present in the last major release, GROMOS96. The organization of the program package is outlined and the included analysis package GROMOS++ is described. Finally, some applications illustrating the various available functionalities are presented.

A computational protocol to probe the role of solvation effects on the reduction potential of azurin mutants

Semiquantitative relationships between thermodynamic parameters of Cu2+ reduction experimentally measured for a series of azurin mutants and the solvation free energy of the oxidized state of the proteins were derived. Solvation free energy calculations were carried out within an ONIOM/PCM scheme specifically adapted to this protein series. The method proved to be able to capture the main determinants of the measured reduction parameters, providing satisfactory predictions of the E degrees '.