Structural biology in the age of X-ray free-electron lasers and exascale computing.

Serial femtosecond X-ray crystallography has emerged as a powerful method for investigating biomolecular structure and dynamics. With the new generation of X-ray free-electron lasers, which generate ultrabright X-ray pulses at megahertz repetition rates, we can now rapidly probe ultrafast conformational changes and charge movement in biomolecules. Over the last year, another innovation has been the deployment of Frontier, the world's first exascale supercomputer. Synergizing extremely high repetition rate X-ray light sources and exascale computing has the potential to accelerate discovery in biomolecular sciences. Here we outline our perspective on each of these remarkable innovations individually, and the opportunities and challenges in yoking them within an integrated research infrastructure.

All-Atom Biomolecular Simulation in the Exascale Era.

Exascale supercomputers have opened the door to dynamic simulations, facilitated by AI/ML techniques, that model biomolecular motions over unprecedented length and time scales. This new capability holds the potential to revolutionize our understanding of fundamental biological processes. Here we report on some of the major advances that were discussed at a recent CECAM workshop in Pisa, Italy, on the topic with a primary focus on atomic-level simulations. First, we highlight examples of current large-scale biomolecular simulations and the future possibilities enabled by crossing the exascale threshold. Next, we discuss challenges to be overcome in optimizing the usage of these powerful resources. Finally, we close by listing several grand challenge problems that could be investigated with this new computer architecture.

Theory and modeling of molecular modes in the NMR relaxation of fluids.

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

MD Simulation of Water Using a Rigid Body Description Requires a Small Time Step to Ensure Equipartition.

In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. We find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation-dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation-dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.

Polarizability Plays a Decisive Role in Modulating Association between Molecular Cations and Anions.

Electrostatic interactions involving proteins depend on not only the ionic charges involved but also their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein-protein and protein-ligand interactions. Cationic analogues of the basic amino acid side chains are simulated, along with oxyanionic analogues of cation-exchange ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a nonpolarizable model. An effective continuum correction to account for electronic polarizability can capture both trends better but at the expense of fidelity to the underlying free energy landscape for ion-pair association. A polarizable model proves decisive in capturing experimentally suggested trends with respect to both cations and anions; critically, the free energy landscape for ion-pair association is itself altered, thus altering configurational sampling.

Influence of Charge Block Length on Conformation and Solution Behavior of Polyampholytes.

We investigate the effect of charge block length on polyampholyte chain conformation and phase behavior using small-angle X-ray scattering (SAXS) and implicit-solvent molecular simulations. To this end, we use solid phase peptide synthesis to precision-tailor a series of polyampholytes consisting of l-glutamic acid (E) and l-lysine (K) monomers arranged in alternating blocks from 2 to 16 monomers. We observe that the polyampholytes tend to phase separate as block size increases. With addition of NaCl, phase separated polyampholytes exhibit a salting-in effect dependent on charge block length. Fourier-transform infrared (FTIR) spectroscopy reveals the presence of intramolecular hydrogen bonds that are disrupted upon the addition of NaCl, implicating both electrostatic interactions and hydrogen bonding in the phase behavior. SAXS spectra at no-added salt conditions show minimal dependence of charge block length on the radius of gyration (Rg) for soluble polyampholytes, but local chain stiffening is found to be dependent on charge block length. With increasing NaCl, consistent with electrostatic screening, all polyampholytes expand and behave as neutral or swollen chains in good solvent conditions. Molecular simulations are qualitatively consistent with experiments. Implications for understanding intracellular condensates and material design are noted.

Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements.

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nanoconfinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nanoconfinement on the 1H NMR relaxation times T1 and T2 of heptane in kerogen. In the case of T1, we discover the important role of confinement in reducing T1 by ∼3 orders of magnitude from that of bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of T2, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces T2 by ∼5 orders of magnitude from the value for bulk heptane. We use the simulated T2 to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nanopores in kerogen, without additional experimental data.

Hydration Free Energies of Polypeptides from Popular Implicit Solvent Models versus All-Atom Simulation Results Based on Molecular Quasichemical Theory.

Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT)─an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecular solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions and thus provides a convenient framework to investigate the assumptions in implicit solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit solvent models for polyglycine and polyalanine solutes covering a range of chain lengths and conformations. The hydration free energies or the differences in hydration free energies between conformers obtained from the implicit solvent models do not agree with explicit solvent results, with the deviations being largest for the group additive EEF1 and ABSINTH models. GB/SA does better in capturing the qualitative trends seen in explicit solvent results. Analysis founded on QCT reveals the critical importance of the cooperativity of hydration that is inherent in the hydrophilic and hydrophobic contributions to hydration─physics that is not well captured in additive models but somewhat better accounted for by means of a dielectric in the GB/SA approach.

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory.

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here, we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F- over Cl- in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory-experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions.

The quasichemical organization of the potential distribution theorem, molecular quasichemical theory (QCT), enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) as a way to regularize an ill-conditioned statistical thermodynamic problem; (b) as an introduction of and emphasis on the neighborship characteristics of a solute of interest; or (c) as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that, in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.

Hydrophilic Interactions Dominate the Inverse Temperature Dependence of Polypeptide Hydration Free Energies Attributed to Hydrophobicity.

We address the association of the hydrophobic driving forces in protein folding with the inverse temperature dependence of protein hydration, wherein stabilizing hydration effects strengthen with increasing temperature in a physiological range. All-atom calculations of the free energy of hydration of aqueous deca-alanine conformers, holistically including backbone and side-chain interactions together, show that attractive peptide-solvent interactions and the thermal expansion of the solvent dominate the inverse temperature signatures that have been interpreted traditionally as the hydrophobic stabilization of proteins in aqueous solution. Equivalent calculations on a methane solute are also presented as a benchmark for comparison. The present study calls for a reassessment of the forces that stabilize folded protein conformations in aqueous solutions and of the additivity of hydrophobic/hydrophilic contributions.

Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of n-Heptane in a Polymer Matrix Revealed by MD Simulations.

The mechanism behind the NMR surface-relaxation times (T1S,2S) and the large T1S/T2S ratio of light hydrocarbons confined in the nanopores of kerogen remains poorly understood and consequently has engendered much debate. Toward bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of 1H NMR relaxation and diffusion of n-heptane in a polymer matrix. The high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. Diffusion of n-heptane shows a power-law dependence on the concentration of n-heptane (ϕC7) in the polymer matrix, consistent with Archie's model of tortuosity. We calculate the autocorrelation function G(t) for 1H-1H dipole-dipole interactions of n-heptane in the polymer matrix and use this to generate the NMR frequency (f0) dependence of T1S,2S as a function of ϕC7. We find that increasing molecular confinement increases the correlation time, which decreases the surface-relaxation times for n-heptane in the polymer matrix. For weak confinement (ϕC7 > 50 vol %), we find that T1S/T2S ≃ 1. Under strong confinement (ϕC7 ≲ 50 vol %), we find that T1S/T2S ≳ 4 increases with decreasing ϕC7 and that the dispersion relation T1S ∝ f0 is consistent with previously reported measurements of polydisperse polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism; instead, our studies suggests that 1H-1H dipole-dipole interactions enhanced by organic nanopore confinement dominate the NMR response in saturated organic-rich shales.

System Size Dependence of Hydration-Shell Occupancy and Its Implications for Assessing the Hydrophobic and Hydrophilic Contributions to Hydration.

The occupancy distribution of water molecules in the first hydration shell around a solute is intimately connected with solvent density fluctuations and is of fundamental interest in understanding hydration. The free energies to evacuate the first hydration shell around a solute and a cavity defined by the first hydration shell depend on the system size, emphasizing that the solvent density fluctuations are themselves dependent on the system size. This observation interpreted within the quasichemical theory shows that both the hydrophilic and the hydrophobic contributions to hydration depend on the system size, decreasing with increasing system size. The net hydration free energy benefits somewhat from the compensation of hydrophilic and hydrophobic contributions; nevertheless a large system appears necessary to describe correctly the balance of these contributions in the hydration of the macromolecule.

Solvation free energies of alanine peptides: the effect of flexibility.

The electrostatic (ΔGel), van der Waals cavity-formation (ΔGvdw), and total (ΔG) solvation free energies for 10 alanine peptides ranging in length (n) from 1 to 10 monomers were calculated. The free energies were computed both with fixed, extended conformations of the peptides and again for some of the peptides without constraints. The solvation free energies, ΔGel, and components ΔGvdw, and ΔG, were found to be linear in n, with the slopes of the best-fit lines being γel, γvdw, and γ, respectively. Both γel and γ were negative for fixed and flexible peptides, and γvdw was negative for fixed peptides. That γvdw was negative was surprising, as experimental data on alkanes, theoretical models, and MD computations on small molecules and model systems generally suggest that γvdw should be positive. A negative γvdw seemingly contradicts the notion that ΔGvdw drives the initial collapse of the protein when it folds by favoring conformations with small surface areas. When we computed ΔGvdw for the flexible peptides, thereby allowing the peptides to assume natural ensembles of more compact conformations, γvdw was positive. Because most proteins do not assume extended conformations, a ΔGvdw that increases with increasing surface area may be typical for globular proteins. An alternative hypothesis is that the collapse is driven by intramolecular interactions. We find few intramolecular H-bonds but show that the intramolecular van der Waals interaction energy is more favorable for the flexible than for the extended peptides, seemingly favoring this hypothesis. The large fluctuations in the vdw energy may make attributing the collapse of the peptide to this intramolecular energy difficult.

Pressure denaturation of staphylococcal nuclease studied by neutron small-angle scattering and molecular simulation.

We studied the pressure-induced folding/unfolding transition of staphylococcal nuclease (SN) over a pressure range of approximately 1-3 kilobars at 25 degrees C by small-angle neutron scattering and molecular dynamics simulations. We find that applying pressure leads to a twofold increase in the radius of gyration derived from the small-angle neutron scattering spectra, and P(r), the pair distance distribution function, broadens and shows a transition from a unimodal to a bimodal distribution as the protein unfolds. The results indicate that the globular structure of SN is retained across the folding/unfolding transition although this structure is less compact and elongated relative to the native structure. Pressure-induced unfolding is initiated in the molecular dynamics simulations by inserting water molecules into the protein interior and applying pressure. The P(r) calculated from these simulations likewise broadens and shows a similar unimodal-to-bimodal transition with increasing pressure. The simulations also reveal that the bimodal P(r) for the pressure-unfolded state arises as the protein expands and forms two subdomains that effectively diffuse apart during initial stages of unfolding. Hydrophobic contact maps derived from the simulations show that water insertions into the protein interior and the application of pressure together destabilize hydrophobic contacts between these two subdomains. The findings support a mechanism for the pressure-induced unfolding of SN in which water penetration into the hydrophobic core plays a central role.

Density functional study of the mechanism of a tyrosine phosphatase: I. Intermediate formation.

The first step in the catalytic mechanism of a protein tyrosine phosphatase, the transfer of a phosphate group from the phosphotyrosine substrate to a cysteine side chain of the protein to form a phosphoenzyme intermediate, has been studied by combining density functional calculations of an active-site cluster with continuum electrostatic descriptions of the solvent and the remainder of the protein. This approach provides the high level of quantum chemical methodology needed to adequately model phosphotransfer reactions with a reasonable description of the environment around the active site. Energy barriers and geometries along a reaction pathway are calculated. In the literature, mechanisms assuming both a monoanionic and a dianionic substrate have been proposed; this disagreement is addressed by performing calculations for both possibilities. For the dianionic substrate, a dissociative reaction pathway with early proton transfer to the leaving group and a 9 kcal/mol energy barrier is predicted (the experimental estimate is ca. 14 kcal/mol), while for the monoanionic substrate, an associative pathway with late proton transfer and a 22 kcal/mol energy barrier is predicted. These results, together with a review of experimental evidence, support the dianionic-substrate/dissociative-pathway alternative. The relationship between a dianionic or monoanionic substrate and a dissociative or associative pathway, respectively, can be understood in terms of classical organic chemical reaction pathways.