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

Theoretical insights into the reduction of Azurin metal site with unnatural amino acid substitutions

Copper-containing proteins play crucial roles in biological systems. Azurin is a copper-containing protein which has a Type 1 copper site that facilitates electron transfer in the cytochrome chain. Previous research has highlighted the significant impact of mutations in the axial Met121 of the copper site on the reduction potential. However, the mechanism of this regulation has not been fully established. In this study, we employed theoretical modeling to investigate the reduction of the Type 1 copper site, focusing on how unnatural amino acid substitutions at Met121 influence its behavior. Our findings demonstrated a strong linear correlation between electrostatic interactions and the reduction potential of the copper site, which indicates that the perturbation of the reduction potential is primarily influenced by electrostatic interactions between the metal ion and the ligating atom. Furthermore, we found that CF/π and CF…H interactions could induce subtle changes in geometry and hence impact the electronic properties of the systems under study. In addition, our calculations suggest the coordination mode and ion-ligand distance could significantly impact the reduction potential of a copper site. Overall, this study offers valuable insights into the structural and electronic properties of the Type 1 copper site, which could potentially guide the design of future artificial catalysts.

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.

DFT-based QM/MM with Particle-Mesh Ewald for Direct, Long-Range Electrostatic Embedding

We present a DFT-based, QM/MM implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid, from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections, and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages, as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and BMIM/BF4 ionic liquid were considered as ``simple' and ``complex' solvents respectively, with water and p-phenylenediamine (PPD) solute molecules treated at QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible error for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe error even at 2-3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms, with our presented algorithm providing a general and robust approach.

Molecular Insight into the High Thermal Stability of Metalloprotein Azurin

We investigate the events characterizing the steps of the unfolding pathway of blue copper metalloprotein azurin using replica exchange molecular dynamics (REMD). Our studies show that the unfolding of azurin begins with the melting of α-helix and β-sheets II and V. This is followed by the melting of other β-sheets and the exposure of hydrophobic protein core to the solvent, resulting in disruptions of its tertiary structure. Free energy surfaces constructed at different temperatures portray different basins that signify the stability of different melted structures in the unfolding process. The contact maps at different temperatures reveal that the strong hydrophobic interaction within the core of the protein is the vital force that renders high stability to this protein. Analysis of the individual β-sheets by looking into their amino acid sequence shows that β-sheets with charged side chains on the surface melt fast compared to others. The β-barrel of azurin is able to dynamically rearrange, and it helps the protein to preserve its hydrophobic core, holding back the native topology from melting fast. B-factor analysis shows that residues of β-sheets III, IV, and VII deviate less from their initial structure at the transition temperature.

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.

Revealing the Underestimated Anticancer Effect of Azurin by Mechanical Unfolding

As a potential anticancer agent, azurin has attracted extensive attraction among chemists, physicists, and material scientists. Its structural and unfolding/folding information has been partially understood, but some detailed information, such as the difference in the unfolding processes between apo-azurin and holo-azurin, the mechanical stability, and the role of the copper cluster in its stability, has not been addressed adequately, especially at the single-molecule level. Here, we employed AFM-based single-molecule force spectroscopy to investigate the unfolding process of azurin in the apo and holo forms under an external force. The results indicated that the unfolding processes of apo-azurin and holo-azurin are different, and holo-azurin requires a stronger force to unfold than does apo-azurin. The copper cluster exhibited a more significant impact on the stability and the folding process of holo-azurin: the copper cluster was completely broken, and the copper ion left the unfolded azurin during the unfolding process of azurin. We suspected that the presence of the disulfide bond in azurin made the unfolding of the copper cluster different from that in pseudoazurin, which is also a type I copper protein like azurin. Rarely reported in previous studies, the mechanical strength of the Cu-N(His) bond of the copper cluster was obtained in this study, which is weaker than that of most metal-S(Cys) bonds but higher than that of the Fe-N(His) bond. Altogether, our results offer a possible new scenario for azurin to widely extend its anticancer activity.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.

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.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

Computing Proton-Coupled Redox Potentials of Fluorotyrosines in a Protein Environment

The oxidation of tyrosine to form the neutral tyrosine radical via proton-coupled electron transfer is essential for a wide range of biological processes. The precise measurement of the proton-coupled redox potentials of tyrosine (Y) in complex protein environments is challenging mainly because of the highly oxidizing and reactive nature of the radical state. Herein, a computational strategy is presented for predicting proton-coupled redox potentials in a protein environment. In this strategy, both the reduced Y-OH and oxidized Y-O^• forms of tyrosine are sampled with molecular dynamics using a molecular mechanical force field. For a large number of conformations, a quantum mechanical/molecular mechanical (QM/MM) electrostatic embedding scheme is used to compute the free-energy differences between the reduced and oxidized forms, including the zero-point energy and entropic contributions as well as the impact of the protein electrostatic environment. This strategy is applied to a series of fluorinated tyrosine derivatives embedded in a de novo α-helical protein denoted as α₃Y. The force fields for both the reduced and oxidized forms of these noncanonical fluorinated tyrosine residues are parameterized for general use. The calculated relative proton-coupled redox potentials agree with experimentally measured values with a mean unsigned error of 24 mV. Analysis of the simulations illustrates that hydrogen-bonding interactions between tyrosine and water increase the redox potentials by ∼100-250 mV, with significant variations because of the fluctuating protein environment. This QM/MM approach enables the calculation of proton-coupled redox potentials of tyrosine and other residues such as tryptophan in a variety of protein systems.