Exploring Conformational Landscapes Along Anharmonic Low-Frequency Vibrations.

We aim to automatize the identification of collective variables to simplify and speed up enhanced sampling simulations of conformational dynamics in biomolecules. We focus on anharmonic low-frequency vibrations that exhibit fluctuations on time scales faster than conformational transitions but describe a path of least resistance toward structural change. A key challenge is that harmonic approximations are ill-suited to characterize these vibrations, which are observed at far-infrared frequencies and are easily excited by thermal collisions at room temperature. Here, we approached this problem with a frequency-selective anharmonic (FRESEAN) mode analysis that does not rely on harmonic approximations and successfully isolates anharmonic low-frequency vibrations from short molecular dynamics simulation trajectories. We applied FRESEAN mode analysis to simulations of alanine dipeptide, a common test system for enhanced sampling simulation protocols, and compared the performance of isolated low-frequency vibrations to conventional user-defined collective variables (here backbone dihedral angles) in enhanced sampling simulations. The comparison shows that enhanced sampling along anharmonic low-frequency vibrations not only reproduces known conformational dynamics but can even further improve the sampling of slow transitions compared to user-defined collective variables. Notably, free energy surfaces spanned by low-frequency anharmonic vibrational modes exhibit lower barriers associated with conformational transitions relative to representations in backbone dihedral space. We thus conclude that anharmonic low-frequency vibrations provide a promising path for highly effective and fully automated enhanced sampling simulations of conformational dynamics in biomolecules.

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins.

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Model-Dependent Solvation of the K-18 Domain of the Intrinsically Disordered Protein Tau.

A known imbalance between intra-protein and protein-water interactions in many empirical force fields results in collapsed conformational ensembles of intrinsically disordered proteins in explicit solvent simulations that disagree with experiments. Multiple strategies have been introduced in the literature to modify protein-water interactions, which improve agreement between experiments and simulations. In this work, we combine simulations with standard and modified force fields with a spatially resolved analysis of solvation free energy contributions and compare the consequences of each strategy. We find that enhanced Lennard-Jones (LJ) interactions between protein atoms and water oxygens primarily improve the solvation of nonpolar functional groups of the protein. In contrast, modified electrostatics in the water model or strengthened LJ interactions between the protein and water hydrogens mainly affect the hydration of polar functional groups. Modified electrostatics further impact the average orientation of water molecules in the hydration shell. As a result, protein-water interactions with the first hydration layers are strengthened, while interactions with water molecules in higher hydration shells are weakened. Hence, distinct strategies to balance intra-protein and protein-water interactions in simulations have qualitatively different effects on protein solvation. These differences are not necessarily captured by comparisons to experiments that report on global parameters describing protein conformational ensembles, e.g., the radius of gyration, but will influence the tendency of a protein to form aggregates or phase-separated droplets.

Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins.

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.

Electric-field induced entropic effects in liquid water.

Externally applied electric fields in liquid water can induce a plethora of effects with wide implications in electrochemistry and hydrogen-based technologies. Although some effort has been made to elucidate the thermodynamics associated with the application of electric fields in aqueous systems, to the best of our knowledge, field-induced effects on the total and local entropy of bulk water have never been presented so far. Here, we report on classical TIP4P/2005 and ab initio molecular dynamics simulations measuring entropic contributions carried by diverse field intensities in liquid water at room temperature. We find that strong fields are capable of aligning large fractions of molecular dipoles. Nevertheless, the order-maker action of the field leads to quite modest entropy reductions in classical simulations. Albeit more significant variations are recorded during first-principles simulations, the associated entropy modifications are small compared to the entropy change involved in the freezing phenomenon, even at intense fields slightly beneath the molecular dissociation threshold. This finding further corroborates the idea that electrofreezing (i.e., the electric-field-induced crystallization) cannot take place in bulk water at room temperature. In addition, here, we propose a molecular-dynamics-based analysis (3D-2PT) that spatially resolves the local entropy and the number density of bulk water under an electric field, which enables us to map their field-induced changes in the environment of reference H2O molecules. By returning detailed spatial maps of the local order, the proposed approach is capable of establishing a link between entropic and structural modifications with atomistic resolution.

Solvation free energy arithmetic for small organic molecules.

Solvent-mediated interactions contribute to ligand binding affinities in computational drug design and provide a challenge for theoretical predictions. In this study, we analyze the solvation free energy of benzene derivatives in water to guide the development of predictive models for solvation free energies and solvent-mediated interactions. We use a spatially resolved analysis of local solvation free energy contributions and define solvation free energy arithmetic, which enable us to construct additive models to describe the solvation of complex compounds. The substituents analyzed in this study are carboxyl and nitro-groups due to their similar sterical requirements but distinct interactions with water. We find that nonadditive solvation free energy contributions are primarily attributed to electrostatics, which are qualitatively reproduced with computationally efficient continuum models. This suggests a promising route for the development of efficient and accurate models for the solvation of complex molecules with varying substitution patterns using solvation arithmetic.

Correlated Evolution of Low-Frequency Vibrations and Function in Enzymes.

Previous studies of the flexibility of ancestral proteins suggest that proteins evolve their function by altering their native state ensemble. Here, we propose a more direct method to analyze such changes during protein evolution by comparing thermally activated vibrations at frequencies below 6 THz, which report on the dynamics of collective protein modes. We analyzed the backbone vibrational density of states of ancestral and extant ß-lactamases and thioredoxins and observed marked changes in the vibrational spectrum in response to evolution. Coupled with previously observed changes in protein flexibility, the observed shifts of vibrational mode densities suggest that protein dynamics and dynamical allostery are critical factors for the evolution of enzymes with specialized catalytic and biophysical properties.

A general method for chemogenetic control of peptide function.

Natural or engineered peptides serve important biological functions. A general approach to achieve chemical-dependent activation of short peptides will be valuable for spatial and temporal control of cellular processes. Here we present a pair of chemically activated protein domains (CAPs) for controlling the accessibility of both the N- and C-terminal portion of a peptide. CAPs were developed through directed evolution of an FK506-binding protein. By fusing a peptide to one or both CAPs, the function of the peptide is blocked until a small molecule displaces them from the FK506-binding protein ligand-binding site. We demonstrate that CAPs are generally applicable to a range of short peptides, including a protease cleavage site, a dimerization-inducing heptapeptide, a nuclear localization signal peptide, and an opioid peptide, with a chemical dependence up to 156-fold. We show that the CAPs system can be utilized in cell cultures and multiple organs in living animals.

Solvent-mediated forces in protein dielectrophoresis.

DEP is an established method to manipulate micrometer-sized particles, but standard continuum theories predict only negligible effects for nanometer-sized proteins despite contrary experimental evidence. A theoretical description of protein DEP needs to consider details on the molecular scale. Previous work toward this goal addressed the role of orientational polarization of static protein dipole moments for dielectrophoretic effects, which successfully predicts the general magnitude of dielectrophoretic forces on proteins but does not readily explain negative DEP forces observed for proteins in some experiments. However, contributions to the protein chemical potential due to protein-water interactions have not yet been considered in this context. Here, we utilize atomistic molecular dynamics simulations to evaluate polarization-induced changes in the protein solvation free energy, which result in a solvent-mediated contribution to dielectrophoretic forces. We quantify solvent-mediated dielectrophoretic forces for two proteins and a small peptide in water, which follow expectations for protein-water dipole-dipole interactions. The magnitude of solvent-mediated dielectrophoretic forces exceeds predictions of nonmolecular continuum theories, but plays a minor role for the total dielectrophoretic force for the simulated proteins due to dominant contributions from the orientational polarization of their static protein dipoles. However, we extrapolate that solvent-mediated contributions to negative protein DEP forces will become increasingly relevant for multidomain proteins, complexes and aggregates with large protein-water interfaces, as well as for high electric field frequencies, which provides a potential mechanism for corresponding experimental observations of negative protein DEP.

Dissecting the Conformational Free Energy of a Small Peptide in Solution.

The free energy surface of a small peptide was analyzed based on an unbiased microsecond molecular dynamics simulation. The peptide sampled disordered conformational ensembles of distinct compactness, and its free energy was decomposed into separate contributions from the intramolecular potential energy, conformational entropy, and solvation free energy. The latter was further broken down into enthalpic and entropic contributions due to peptide-water and water-water interactions. This decomposition was enabled by a generalized linear response relation between the peptide-water interaction energy and the solvation free energy, which was empirically parametrized by explicit solvation free energy calculations for representative peptide conformations. This full dissection of the peptide free energy identifies individual contributions that stabilize and destabilize compact and extended peptide conformational ensembles and reveals the origin of a free energy barrier associated with transitions between them.

Protein flexibility reduces solvent-mediated friction barriers of ligand binding to a hydrophobic surface patch.

Solvent fluctuations have been explored in detail for idealized and rigid hydrophobic model systems, but so far it has remained unclear how internal protein motions and their coupling to the surrounding solvent affect the dynamics of ligand binding to biomolecular surfaces. Here, molecular dynamics simulations were used to elucidate the solvent-mediated binding of a model ligand to the hydrophobic surface patch of ubiquitin. The ligand's friction profiles reveal pronounced long-time correlations and enhanced friction in the vicinity of the protein, similar to idealized hydrophobic surfaces. Interestingly, these effects are shaped by internal protein motions. Protein flexibility modulates water density fluctuations near the hydrophobic surface patch and smooths out the friction profile of ligand binding.

Dielectrophoresis of Proteins in Solution.

A nonionic particle placed in the gradient of an electric field experiences the dielectrophoretic force which scales linearly with the gradient of the electric field squared. The proportionality constant is the dielectrophoretic susceptibility, that is, a linear transport coefficient. For proteins in solution, it is mostly affected by the following two parameters: the squared dipole moment and the cavity susceptibility accounting for cross-correlations of the protein dipole with the hydration shell (protein-water Kirkwood factor). Both of these parameters enter the dielectric increment of the solution which fully specifies the dielectrophoretic susceptibility. The link between these two measurable properties is proven here to hold using molecular dynamics simulations of solvated proteins. The dielectrophoretic susceptibility for proteins is in the range of 104, significantly exceeding traditional estimates limiting it to values below unity. Part of this large magnitude of the dielectrophoretic response is the cavity susceptibility of the protein-water interface, which significantly exceeds dielectric estimates. The study analyzes local fields inside the protein in terms of the reaction-field and directing-field components. We find that the local field exceeds the external field by a substantial factor described by the local field susceptibility. The electric field produced by water inside the protein is retarded by 3-4 orders of magnitude compared to the bulk.

Cooperativity and ion pairing in magnesium sulfate aqueous solutions from the dilute regime to the solubility limit.

We report a terahertz absorption spectroscopy study of MgSO4 aqueous solutions in the concentration range 0.1 mol dm-3 to 2.4 mol dm-3. Accompanying classical MD simulations were carried out that use a polarizable force field parameterized to reproduce the solution thermodynamics. Contrary to prior reports, we find no evidence of contact ion pairs, even close to the solubility limit. Only solvent separated and different types of solvent shared ion pairs are found, being abundant even at the lowest concentration investigated here. The structure of the solution is concentration-dependent: the number of both types of ion pairs grows with increasing salt concentration. The combined theoretical and experimental analysis of the spectra in the frequency region 50-640 cm-1 suggests that the dynamics of water directly between two ions in solvent shared configuration is very strongly perturbed, via a cooperative, supra-additive, effect arising from the two ions. At high concentrations, the results support a scenario, where the perturbations in the water dynamics extend up to the third hydration layer via a cooperative, but additive, effect involving multiple ions. The SO42- and its hydration shell are much more strongly perturbed by the presence of the counterions than the first hydration shell of Mg2+. It is further shown that our simulations and observations are in agreement with thermodynamic properties of aqueous MgSO4 solutions derived by other methods.

Pressure Effects on Protein Hydration Water Thermodynamics.

In this molecular dynamics simulation study, we analyze the impact of increasing hydrostatic pressure on the solvation of protein surfaces. Apart from the increasing volume work required for the formation of the protein solute cavity at high hydrostatic pressures, no significant additional trend is observed for solvation free energy contributions due to the protein-water interactions analyzed here. The latter is the result of approximately canceling pressure-induced changes of enthalpic and entropic solvation free energy contributions, which can be traced back to changes in the hydration of hydrophilic and hydrophobic groups of the protein. The 3D-2PT analysis used here allows for the visualization of local solvation free energy contributions in three dimensions with high spatial resolution. Local solvation free energy contributions per water molecule at hydrophobic surfaces are small but mainly favorable for transfer processes from the gas phase. This does not change considerably with increasing pressure, while the number of hydrating water molecules increases due to increased packing of the hydration shell. The number of hydrating water molecules also increases for hydrophilic protein surfaces, but solvation contributions per water molecule become less favorable with pressure in this case. As a consequence, contributions to the total solvation free energy from interactions between water molecules and hydrophobic surfaces become increasingly relevant at high hydrostatic pressures. Our results provide novel insights into solvent-mediated contributions to the thermodynamic driving force of pressure denaturation of proteins.

Hydration-mediated stiffening of collective membrane dynamics by cholesterol.

The collective behaviour of individual lipid molecules determines the properties of phospholipid membranes. However, the collective molecular motions often remain challenging to characterise at the desired spatial and temporal resolution. Here we study collective vibrational motion on picosecond time scales in dioleoylphosphatidylcholine lipid bilayers with varying cholesterol content using all-atom molecular dynamics simulations. Cholesterol is found to not only laterally compact the lipid bilayer, but also to change the velocity of longitudinal density fluctuations propagating in the plane of the membrane. Cholesterol-induced reduction of the area per lipid alters the collective dynamics of the lipid headgroups, but not of the lipid tails. The introduction of cholesterol reduces the number of water molecules interacting with the lipid headgroups, leading to a decrease in the velocity of the laterally-propagating sound mode. Thus, the stiffening effect of cholesterol is found to be indirect: decreasing the area per lipid weakens the interactions between the lipid headgroups and water. The collective modes characterised in this work can enable the membrane to dissipate excess energy and thus maintain its structural integrity, e.g., under mechanical stress.

Atomistic characterization of collective protein-water-membrane dynamics.

Correlated vibrational motion on the sub-picosecond timescale and associated collective dynamics in a protein-membrane environment are characterized using molecular dynamics simulations. We specifically analyze correlated motion of a membrane-associated protein and a lipid bilayer for distinct separation distances. Correlated vibrations persist up to distances of 25 Å between both biomolecular surfaces. These correlations are mediated by separating layers of water molecules, whose collective properties are altered by the simultaneous presence of protein and lipid bilayer interfaces.

Heterogeneity of water structure and dynamics at the protein-water interface.

In this molecular dynamics simulation study, we analyze the local structural and dynamic properties of water hydrating the protein ubiquitin on a spatial grid with 1 Å resolution. This allows for insights into the spatial distribution of water number densities, molecular orientations, translations, and rotations as a function of distance from the protein surface. Water molecule orientations follow a heterogeneous distribution with preferred local orientations of water dipoles and O-H bond vectors up to 10-15 Å distances from the protein, while local variations of the water number density converge to homogeneous bulk-like values within less than 8 Å. Interestingly, we find that the long-ranged orientational structure of water does not impact either the translational or rotational dynamics of water. Instead, heterogeneous distributions of local dynamical parameters and averaged dynamical retardation factors are only found close to the protein surface and follow a distance dependence comparable to heterogeneities in the local water number density. This study shows that the formation of nanodomains of preferred water orientations far from the protein does not significantly impact dynamical processes probed as a non-local average in most experiments.

Stability Effect of Quinary Interactions Reversed by Single Point Mutations.

In cells, proteins are embedded in a crowded environment that controls their properties via manifold avenues including weak protein-macromolecule interactions. A molecular level understanding of these quinary interactions and their contribution to protein stability, function, and localization in the cell is central to modern structural biology. Using a mutational analysis to quantify the energetic contributions of single amino acids to the stability of the ALS related protein superoxide dismutase I (SOD1) in mammalian cells, we show that quinary interactions destabilize SOD1 by a similar energetic offset for most of the mutants, but there are notable exceptions: Mutants that alter its surface properties can even lead to a stabilization of the protein in the cell as compared to the test tube. In conclusion, quinary interactions can amplify and even reverse the mutational response of proteins, being a key aspect in pathogenic protein misfolding and aggregation.

Role of Conformational Flexibility in Monte Carlo Simulations of Many-Protein Systems.

Efficient computational modeling of biological systems characterized by high concentrations of macromolecules often relies on rigid-body Brownian Dynamics or Monte Carlo (MC) simulations. However, the accuracy of rigid-body models is limited by the fixed conformation of the simulated biomolecules. Multi-conformation Monte Carlo (mcMC) simulations of protein solutions incorporate conformational flexibility via a conformational swap trial move within a predetermined library of discrete protein structures, thereby alleviating artifacts arising from the use of a single protein conformation. Here, we investigate the impact of the number of distinct protein structures in the conformational library and the extent of conformational sampling used in its generation on structural observables computed from simulations of hen egg white lysozyme (HEWL), human γD-Crystallin, and bovine γB-Crystallin solutions. We find that the importance of specific protocols for the construction of the protein structure library is strongly dependent on the nature of the simulated system.

Structural Relaxation Processes and Collective Dynamics of Water in Biomolecular Environments.

In this simulation study, we investigate the influence of biomolecular confinement on dynamical processes in water. We compare water confined in a membrane protein nanopore at room temperature to pure liquid water at low temperatures with respect to structural relaxations, intermolecular vibrations, and the propagation of collective modes. We observe distinct potential energy landscapes experienced by water molecules in the two environments, which nevertheless result in comparable hydrogen bond lifetimes and sound propagation velocities. Hence, we show that a viscoelastic argument that links slow rearrangements of the water-hydrogen bond network to ice-like collective properties applies to both, the pure liquid and biologically confined water, irrespective of differences in the microscopic structure.