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

Structural, Solvent, and Temperature Effects on Protein Junction Conductance

Cytochrome b562 is a small redox-active heme protein that has served as an important model system for understanding biological electron transfer processes. Here, we present a comprehensive theoretical study of electron transport mechanisms in protein-metal junctions incorporating cytochrome b562 using a multi-scale computational approach. Employing molecular dynamics (MD) simulations, we generated junction geometries for both vacuum-dried and solvated conditions, with the protein covalently bound to gold contacts in various configurations. Coherent tunneling, described by the Landauer-Buttiker formalism within the density functional theory (DFT) framework, is compared to the incoherent hopping charge transport mechanism captured by the semi-classical Marcus theory. The tunneling was identified as the dominant mechanism explaining the experimental data measured on the cytochrome b562 junctions, exhibiting exponential yet very shallow distance dependence. While the structural orientations and protein contacts with the electrodes influence the junction conductance significantly, the solvation effects are relatively small, affecting the electronic properties mostly via the adsorption arrangement. On the other hand, the considerable temperature dependence of the conductance was found strong only for hopping, while the tunneling current magnitudes remain practically unaffected and are a good indicator of the coherent mechanism in this case.

Electron transport through two interacting channels in Azurin-based solid-state junctions

The fundamental question of "what is the transport path of electrons through proteins?" initially introduced while studying long-range electron transfer between localized redox centers in proteins in vivo is also highly relevant to the transport properties of solid-state, dry metal-protein-metal junctions. Here, we report conductance measurements of such junctions, Au-(Azurin monolayer ensemble)-Bismuth (Bi) ones, with well-defined nanopore geometry and ~103 proteins/pore. Our results can be understood as follows. (1) Transport is via two interacting conducting channels, characterized by different spatial and time scales. The slow and spatially localized channel is associated with the Cu center of Azurin and the fast delocalized one with the protein's polypeptide matrix. Transport via the slow channel is by a sequential (noncoherent) process and in the second one by direct, off-resonant tunneling. (2) The two channels are capacitively coupled. Thus, with a change in charge occupation of the weakly coupled (metal center) channel, the broad energy level manifold, responsible for off-resonance tunneling, shifts, relative to the electrodes' Fermi levels. In this process, the off-resonance (fast) channel dominates transport, and the slow (redox) channel, while contributing only negligibly directly, significantly affects transport by intramolecular gating.

Pathways to a Shiny Future: Building the Foundation for Computational Physical Chemistry and Biophysics in 2050

In the last quarter-century, the field of molecular dynamics (MD) has undergone a remarkable transformation, propelled by substantial enhancements in software, hardware, and underlying methodologies. In this Perspective, we contemplate the future trajectory of MD simulations and their possible look at the year 2050. We spotlight the pivotal role of artificial intelligence (AI) in shaping the future of MD and the broader field of computational physical chemistry. We outline critical strategies and initiatives that are essential for the seamless integration of such technologies. Our discussion delves into topics like multiscale modeling, adept management of ever-increasing data deluge, the establishment of centralized simulation databases, and the autonomous refinement, cross-validation, and self-expansion of these repositories. The successful implementation of these advancements requires scientific transparency, a cautiously optimistic approach to interpreting AI-driven simulations and their analysis, and a mindset that prioritizes knowledge-motivated research alongside AI-enhanced big data exploration. While history reminds us that the trajectory of technological progress can be unpredictable, this Perspective offers guidance on preparedness and proactive measures, aiming to steer future advancements in the most beneficial and successful direction.

The organo-metal-like nature of long-range conduction in cable bacteria

Cable bacteria are filamentous, multicellular microorganisms that display an exceptional form of biological electron transport across centimeter-scale distances. Currents are guided through a network of nickel-containing protein fibers within the cell envelope. Still, the mechanism of long-range conduction remains unresolved. Here, we characterize the conductance of the fiber network under dry and wet, physiologically relevant, conditions. Our data reveal that the fiber conductivity is high (median value: 27 S cm-1; range: 2 to 564 S cm-1), does not show any redox signature, has a low thermal activation energy (Ea = 69 ± 23 meV), and is not affected by humidity or the presence of ions. These features set the nickel-based conduction mechanism in cable bacteria apart from other known forms of biological electron transport. As such, conduction resembles that of an organic semi-metal with a high charge carrier density. Our observation that biochemistry can synthesize an organo-metal-like structure opens the way for novel bio-based electronic technologies.

Electrochemistry in sensing of molecular interactions of proteins and their behavior in an electric field

Electrochemical methods can be used not only for the sensitive analysis of proteins but also for deeper research into their structure, transport functions (transfer of electrons and protons), and sensing their interactions with soft and solid surfaces. Last but not least, electrochemical tools are useful for investigating the effect of an electric field on protein structure, the direct application of electrochemical methods for controlling protein function, or the micromanipulation of supramolecular protein structures. There are many experimental arrangements (modalities), from the classic configuration that works with an electrochemical cell to miniaturized electrochemical sensors and microchip platforms. The support of computational chemistry methods which appropriately complement the interpretation framework of experimental results is also important. This text describes recent directions in electrochemical methods for the determination of proteins and briefly summarizes available methodologies for the selective labeling of proteins using redox-active probes. Attention is also paid to the theoretical aspects of electron transport and the effect of an external electric field on the structure of selected proteins. Instead of providing a comprehensive overview, we aim to highlight areas of interest that have not been summarized recently, but, at the same time, represent current trends in the field.

Long-Range Conductivity in Proteins Mediated by Aromatic Residues

Single-molecule measurements show that many proteins, lacking any redox cofactors, nonetheless exhibit electrical conductance on the order of a nanosiemen over 10 nm distances, implying that electrons can transit an entire protein in less than a nanosecond when subject to a potential difference of less than 1 V. This is puzzling because, for fast transport (i.e., a free energy barrier of zero), the hopping rate is determined by the reorganization energy of approximately 0.8 eV, and this sets the time scale of a single hop to at least 1 μs. Furthermore, the Fermi energies of typical metal electrodes are far removed from the energies required for sequential oxidation and reduction of the aromatic residues of the protein, which should further reduce the hopping current. Here, we combine all-atom molecular dynamics (MD) simulations of non-redox-active proteins (consensus tetratricopeptide repeats) with an electron transfer theory to demonstrate a molecular mechanism that can account for the unexpectedly fast electron transport. According to our MD simulations, the reorganization energy produced by the energy shift on charging (the Stokes shift) is close to the conventional value of 0.8 eV. However, the non-ergodic sampling of molecular configurations by the protein results in reaction-reorganization energies, extracted directly from the distribution of the electrostatic energy fluctuations, that are only ∼0.2 eV, which is small enough to enable long-range conductivity, without invoking quantum coherent transport. Using the MD values of the reorganization energies, we calculate a current decay with distance that is in agreement with experiment.

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.

Reorganization energy of electron transfer

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

Theory of Protein Charge Transfer: Electron Transfer between Tryptophan Residue and Active Site of Azurin

One reaction step in the conductivity relay of azurin, electron transfer between the Cu-based active site and the tryptophan residue, is studied theoretically and by classical molecular dynamics simulations. Oxidation of tryptophan results in electrowetting of this residue. This structural change makes the free energy surfaces of electron transfer nonparabolic as described by the Q-model of electron transfer. We analyze the medium dynamical effect on protein electron transfer produced by coupled Stokes-shift dynamics and the dynamics of the donor-acceptor distance modulating electron tunneling. The equilibrium donor-acceptor distance falls in the plateau region of the rate constant, where it is determined by the protein-water dynamics, and the probability of electron tunneling does not affect the rate. The crossover distance found here puts most intraprotein electron-transfer reactions under the umbrella of dynamical control. The crossover between the medium-controlled and tunneling-controlled kinetics is combined with the effect of the protein-water medium on the activation barrier to formulate principles of tunability of protein-based charge-transfer chains. The main principle in optimizing the activation barrier is the departure from the Gaussian-Gibbsian statistics of fluctuations promoting activated transitions. This is achieved either by incomplete (nonergodic) sampling, breaking the link between the Stokes-shift and variance reorganization energies, or through wetting-induced structural changes of the enzyme's active site.