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

Consequences of the failure of equipartition for the p-V behavior of liquid water and the hydration free energy components of a small protein

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step δ t ≤ 0.5 fs to ensure equipartition between translational and rotational modes. Here we extend that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examine integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small δ t is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, and the dielectric constant, a measure of dipole moment fluctuations, are also seen to be sensitive to δ t. Using the mean volume estimated from the NpT simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to δ t. In going from δ t = 2 fs to δ t = 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein.

Electrostatically Mediated Attractive Self-Interactions and Reversible Self-Association of Fc-Fusion Proteins

Attractive self-interactions and reversible self-association are implicated in many problematic solution behaviors for therapeutic proteins, such as irreversible aggregation, elevated viscosity, phase separation, and opalescence. Protein self-interactions and reversible oligomerization of two Fc-fusion proteins (monovalent and bivalent) and the corresponding fusion partner protein were characterized experimentally with static and dynamic light scattering as a function of pH (5 and 6.5) and ionic strength (10 mM to at least 300 mM). The fusion partner protein and monovalent Fc-fusion each displayed net attractive electrostatic self-interactions at pH 6.5 and net repulsive electrostatic self-interactions at pH 5. Solutions of the bivalent Fc-fusion contained higher molecular weight species that prevented quantification of typical interaction parameters (B22 and kD). All three of the proteins displayed reversible self-association at pH 6.5, where oligomers dissociated with increased ionic strength. Coarse-grained molecular simulations were used to model the self-interactions measured experimentally, assess net self-interactions for the bivalent Fc-fusion, and probe the specific electrostatic interactions between charged amino acids that were involved in attractive electrostatic self-interactions. Mayer-weighted pairwise electrostatic energies from the simulations suggested that attractive electrostatic self-interactions at pH 6.5 for the two Fc-fusion proteins were due to cross-domain interactions between the fusion partner domain(s) and the Fc domain.

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.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

The functional role of the hemoglobin-water interface

The interface between hemoglobin (Hb) and its environment, in particular water, is of great physiological relevance. Here, results from in vitro, in vivo, and computational experiments (molecular dynamics simulations) are summarized and put into perspective. One of the main findings from the computations is that the stability of the deoxy, ligand-free T-state (T₀) can be stabilized relative to the deoxy R-state (R₀) only in sufficiently large simulation boxes for the hydrophobic effect to manifest itself. This effect directly influences protein stability and is operative also under physiological conditions. Furthermore, molecular simulations provide a dynamical interpretation of the Perutz model for Hb function. Results from experiments using higher protein concentrations and realistic cellular environments are also discussed. One of the next great challenges for computational studies, which as we show is likely to be taken up in the near future, is to provide a molecular-level understanding of the dynamics of proteins in such crowded environments.

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.

Toward a Suite of Coarse-Grained Models for Molecular Simulation of Monoclonal Antibodies and Therapeutic Proteins

A series of coarse-grained models for molecular simulation of proteins are considered, with emphasis on the application of predicting protein-protein self-interactions for monoclonal antibodies (MAbs). As an illustrative example and for quantitative comparison, the models are used to predict osmotic virial coefficients over a broad range of attractive and repulsive self-interactions and solution conditions for a series of MAbs where the second osmotic virial coefficient has been experimentally determined in prior work. The models are compared based on how well they can predict experimental behavior, their computational burdens, and scalability. An intermediate-resolution model is also introduced that can capture specific electrostatic interactions with improved efficiency and similar or improved accuracy when compared to the previously published models. Guidance is included for the selection of coarse-grained models more generally for capturing a balance of electrostatic, steric, and short-ranged nonelectrostatic interactions for proteins from low to high concentrations.

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.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.