Dynamics accelerate the kinetics of ion diffusion through channels: Continuous-time random walk models beyond the mean field approximation.

Ion channels are proteins that play a significant role in physiological processes, including neuronal excitability and signal transduction. However, the precise mechanisms by which these proteins facilitate ion diffusion through cell membranes are not well understood. This is because experimental techniques to characterize ion channel activity operate on a time scale too large to understand the role of the various protein conformations on diffusion. Meanwhile, computational approaches operate on a time scale too short to rationalize the observed behavior at the microscopic scale. In this paper, we present a continuous-time random walk model that aims to bridge the scales between the atomistic models of ion channels and the experimental measurement of their conductance. We show how diffusion slows down in complex systems by using 3D lattices that map out the pore geometry of two channels: Nav1.7 and gramicidin. We also introduce spatial and dynamic site disorder to account for system heterogeneity beyond the mean field approximation. Computed diffusion coefficients show that an increase in spatial disorder slows down diffusion kinetics, while dynamic disorder has the opposite effect. Our results imply that microscopic or phenomenological models based on the potential of mean force data overlook the functional importance of protein dynamics on ion diffusion through channels.

Understanding Cysteine Reactivity in Protein Environments with Electric Fields.

The role cysteine residues play in proteins is mediated by their protonation state, whereby the thiolate form of the side chain is highly reactive while the thiol form is more inert. However, the pKa of cysteine residues is hard to predict as it can differ widely from its reference value in solution, an effect that is accentuated by local effects in the heterogeneous protein environment. Here, we present a new approach to the prediction of cysteine reactivity based on electric field calculations at the thiol/thiolate group. We validated our approach by predicting the protonation state of cysteine residues in different protein environments (in the active site, at the protein surface, and buried within the protein interior), including Cys-25 in papaya protease omega, which was proven problematic for the more traditional constant pH molecular dynamics (MD) technique. We predict pKa shifts consistent with experimental observations, and the decomposition of the electric fields into contributions from molecular fragments provides a direct handle to rationalize local pH and pKa effects in proteins without introducing parameters other than those of the force field used for MD simulations.

Characterizing Ion-Polymer Interactions in Aqueous Environment with Electric Fields.

Polymers make the basis of highly tunable materials that could be designed and optimized for metal recovery from aqueous environments. While experimental studies show that this approach has potential, it suffers from a limited knowledge of the detailed molecular interaction between polymers and target metal ions. Here, we propose to calculate intrinsic electric fields from polarizable force field molecular dynamics simulations to characterize the driving force behind Eu3+ motion in the presence of poly(ethylenimine methylenephosphonate), a specifically designed metal chelating polymer. Focusing on the metal chelation initiation step (i.e., before binding), we can rationalize the role of each molecule on ion dynamics by projecting these electric fields along the direction of ion motion. We find that the polymer functional groups act indirectly, and the polymer-metal ion interaction is actually mediated by water. This result is consistent with the experimental observation that metal sequestration by these polymers is entropically driven. This study suggests that electric field calculations can help the design of metal chelating polymers, for example, by seeking to optimize polymer-solvent interactions rather than polymer-ion interactions.

Tuning the Catalytic Activity of Synthetic Enzyme KE15 with DNA.

Efficiency improvement of synthetic enzymes through scaffold modifications suffers from limitations in terms of effectiveness, cost, and potential devastating consequences for protein structural stability. Here, we propose an alternative to scaffold modification, within electrostatic preorganization theory, where the enzyme's greater environment is designed to support the evolution of the reaction in the active site. We demonstrate the feasibility of such an approach by placing a (polar) DNA fragment in the surroundings of the Kemp eliminase enzyme KE15 (structure from Houk's group) and computing the resulting change in catalytic activity. We find that the introduction of a DNA fragment magnifies the contribution of protein residues to the stabilization of the transition state, estimated from electric field calculations with polarizable molecular dynamics. Our randomly generated test systems reveal a 2.0 kcal/mol reduction in activation energy, suggesting that even more significant catalytic improvements could be made by optimizing DNA size, sequence, and orientation with respect to the enzyme, validating our approach.

Structural Dynamics Support Electrostatic Interactions in the Active Site of Adenylate Kinase.

Electrostatic preorganization as well as structural and dynamic heterogeneity are often used to rationalize the remarkable catalytic efficiency of enzymes. However, they are often presented as incompatible because the generation of permanent electrostatic effects implies that the protein structure remains rigid. Here, we use a metric, electric fields, that can treat electrostatic contributions and dynamics effects on equal footing, for a unique perspective on enzymatic catalysis. We find that the residues that contribute the most to electrostatic interactions with the substrate in the active site of Adenylate Kinase (our working example) are also the most flexible residues. Further, entropy-tuning mutations raise flexibility at the picosecond timescale where more conformations can be visited on short time periods, thereby softening the sharp heterogeneity normally visible at the microsecond timescale.

Critical Role of Thermal Fluctuations for CO Binding on Electrocatalytic Metal Surfaces.

This work considers the evaluation of density functional theory (DFT) when comparing against experimental observations of CO binding trends on the strong binding Pt(111) and intermediate binding Cu(111) and for weak binding Ag(111) and Au(111) surfaces important in electrocatalysis. By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we find that the RPBE and B97M-rV DFT functionals yield qualitatively better metal surface strain trends and CO enthalpies of binding for Cu(111) and Pt(111) than found at 0 K, thereby correcting the overbinding by 0.2 to 0.3 eV to yield better agreement with the enthalpies determined from experiment. The importance of dispersion effects are manifest for the weak CO binding Ag(111) and Au(111) surfaces at finite temperatures in which the RPBE functional does not bind CO at all, while the B97M-rV functional shows that the CO-metal interactions are a mixture of chemisorbed and physisorbed species with binding enthalpies that are within ∼0.05 eV of experiment. Across all M(111) surfaces, we show that the B97M-rV functional consistently predicts the correct atop site preference for all metals due to thermally induced surface distortions that preferentially favor the undercoordinated site. This study demonstrates the need to fully account for finite temperature fluctuations to make contact with the binding enthalpies from surface science experiments and electrocatalysis applications.

Environment-controlled water adsorption at hydroxyapatite/collagen interfaces.

Water contributes to the structure of bone by coupling hydroxyapatite to collagen over the hierarchical levels of tissue organization. Bone water exists in two states, bound or mobile, each accomplishing different roles. Although many experimental studies show that the amount of bound water correlates with bone strength, a molecular understanding of the interactions between hydroxyapatite, collagen and water is missing. In this work, we unveil the water adsorption properties of bone tissues at the nanoscale using advanced density functional theory methods. We demonstrate that environmental factors such as collagen conformation or degree of confinement, rather than the surface itself, dictate the adsorption mode, strength and density of water on hydroxyapatite. While the results derived in this paper come from a simplified model of bone tissues, they are consistent with experimental observations and constitute a reasonable starting point for more realistic models of bone tissues. For example, we show that environmental changes expected in aging bone lead to reduced water adsorption capabilities, which is consistent with weaker bones at the macroscale. Our findings provide a new interpretation of molecular interactions in bone tissues with the potential to impact bone repair strategies.

Computational Design of Synthetic Enzymes.

We review the standard model for de novo computational design of enzymes, which primarily focuses on the development of an active-site geometry, composed of protein functional groups in orientations optimized to stabilize the transition state, for a novel chemical reaction not found in nature. Its emphasis is placed on the structure and energetics of the active site embedded in an accommodating protein that serves as a physical support that shields the reaction chemistry from solvent, which is typically improved upon by laboratory-directed evolution. We also provide a review of design strategies that move beyond the standard model, by placing more emphasis on the designed enzyme as a whole catalytic construct. Starting with complete de novo enzyme design examples, we consider additional design factors such as entropy of individual residues, correlated motion between side chains (mutual information), dynamical correlations of the enzyme motions that could aid the reaction, reorganization energy, and electric fields as ways to exploit the entire protein scaffold to improve upon the catalytic rate, thereby providing directed evolution with better starting sequences for increasing biocatalytic performance.

Electrostatics Generated by a Supramolecular Capsule Stabilizes the Transition State for Carbon-Carbon Reductive Elimination from Gold(III) Complex.

Tetrahedral assemblies of stoichiometry M4L6 have been proven to catalyze a range of chemical reactions including the carbon-carbon reductive elimination reaction from transition metals such as gold. Here, we perform quantum chemical calculations of Gold(III) transition metal complexes in vacuum, and encapsulated in Ga4L612- or Si4L68- assemblies within both a reaction field continuum solvent and in an aqueous molecular environment with counterions, to rationalize the rate enhancements observed experimentally for the reductive elimination reaction. We find that the Ga4L612- assembly lowers the energy barrier of the reaction compared to Si4L68-, which is consistent with kinetic trends observed experimentally. We have determined that the primary factor for catalytic rate acceleration stems from the electrostatic environment emanating from the Ga4L612- capsule as opposed to the water or counterions.