Computational Study of the Stability of the Miniprotein Trp-Cage, the GB1 β-Hairpin, and the AK16 Peptide, under Negative Pressure

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Polyelectrolyte Influence on Beta-Hairpin Peptide Stability: A Simulation Study

Assemblies of proteins and charged macromolecules (polyelectrolytes) find important applications as pharmaceutical formulations, biocatalysts, and cell-contacting substrates. A key question is how the polymer component influences the structure and function of the protein. The present paper addresses the influence of charged polymers on the thermal stability of two model beta-hairpin-forming peptides through an all-atom, replica exchange molecular dynamics simulation. The (negatively charged) peptides consist of the terminal 16 amino acids of the B1 domain of Protein G (GB1) and a variant with three of the GB1 residues substituted with tryptophan (Tryptophan Zipper 4, or TZ4). A (cationic) lysine polymer is seen to thermally stabilize TZ4 and destabilize GB1, while a (also cationic) chitosan polymer slightly stabilizes GB1 but has essentially no effect on TZ4. Free energy profiles reveal folded and unfolded conformations to be separated by kinetic barriers generally acting in the direction of the thermodynamically favored state. Through application of an Ising-like statistical mechanical model, a mechanism is proposed based on competition between (indirect) entropic stabilization of folded versus unfolded states and (direct) competition for hydrogen-bonding and hydrophobic interactions. These findings have important implications to the design of polyelectrolyte-based materials for biomedical and biotechnological applications.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Quantum chemistry for molecules at extreme pressure on graphical processing units: Implementation of extreme-pressure polarizable continuum model

Pressure plays essential roles in chemistry by altering structures and controlling chemical reactions. The extreme-pressure polarizable continuum model (XP-PCM) is an emerging method with an efficient quantum mechanical description of small- and medium-sized molecules at high pressure (on the order of GPa). However, its application to large molecular systems was previously hampered by a CPU computation bottleneck: the Pauli repulsion potential unique to XP-PCM requires the evaluation of a large number of electric field integrals, resulting in significant computational overhead compared to the gas-phase or standard-pressure polarizable continuum model calculations. Here, we exploit advances in graphical processing units (GPUs) to accelerate the XP-PCM-integral evaluations. This enables high-pressure quantum chemistry simulation of proteins that used to be computationally intractable. We benchmarked the performance using 18 small proteins in aqueous solutions. Using a single GPU, our method evaluates the XP-PCM free energy of a protein with over 500 atoms and 4000 basis functions within half an hour. The time taken by the XP-PCM-integral evaluation is typically 1% of the time taken for a gas-phase density functional theory (DFT) on the same system. The overall XP-PCM calculations require less computational effort than that for their gas-phase counterpart due to the improved convergence of self-consistent field iterations. Therefore, the description of the high-pressure effects with our GPU-accelerated XP-PCM is feasible for any molecule tractable for gas-phase DFT calculation. We have also validated the accuracy of our method on small molecules whose properties under high pressure are known from experiments or previous theoretical studies.

Molecular dynamics simulation of proteins under high pressure: Structure, function and thermodynamics

BACKGROUND

Molecular dynamics (MD) simulation is well-recognized as a powerful tool to investigate protein structure, function, and thermodynamics. MD simulation is also used to investigate high pressure effects on proteins. For conducting better MD simulation under high pressure, the main issues to be addressed are: (i) protein force fields and water models were originally developed to reproduce experimental properties obtained at ambient pressure; and (ii) the timescale to observe the pressure effect is often much longer than that of conventional MD simulations.

SCOPE OF REVIEW

First, we describe recent developments in MD simulation methodologies for studying the high-pressure structure and dynamics of protein molecules. These developments include force fields for proteins and water molecules, and enhanced simulation techniques. Then, we summarize recent studies of MD simulations of proteins in water under high pressure.

MAJOR CONCLUSIONS

Recent MD simulations of proteins in solution under pressure have reproduced various phenomena identified by experiments using high pressure, such as hydration, water penetration, conformational change, helix stabilization, and molecular stiffening.

GENERAL SIGNIFICANCE

MD simulations demonstrate differences in the properties of proteins and water molecules between ambient and high-pressure conditions. Comparing the results obtained by MD calculations with those obtained experimentally could reveal the mechanism by which biological molecular machines work well in collaboration with water molecules.

Computational Investigation of the Effect of Pressure on Protein Stability

Previous studies show parabolic or elliptical regions of protein stability in the pressure-temperature ( P, T) plane. The construction of stability diagrams requires accessing a sufficiently broad ( P, T) range, which is often frustrated by ice formation in experiments and sampling challenges in simulations. We perform a fully atomistic computational study of the miniprotein Trp-cage over the range of temperatures 210 ≤ T ≤ 420 K and pressures P ≤ 5 kbar and construct the corresponding stability diagram. At ambient temperature, pressure shifts the conformational states toward unfolding. Below 250 K, the native fold's stability depends nonmonotonically on pressure. While cold unfolding and thermal denaturation differ significantly at ambient pressure, they exhibit progressive similarity at elevated pressures. At ambient pressure, cold denaturation is an enthalpically driven process that preserves significant elements of Trp-cage's secondary structure. In contrast, cold unfolding at elevated pressures involves a more substantial loss of secondary and tertiary structure, similar to thermal denaturation.

Effect of heterochiral inversions on the structure of a β-hairpin peptide

We study computationally a family of β-hairpin peptides with systematically introduced chiral inversions, in explicit water, and we investigate the extent to which the backbone structure is able to fold in the presence of heterochiral perturbations. In contrast to the recently investigated case of a helical peptide, we do not find a monotonic change in secondary structure content as a function of the number of L- to D-inversions. The effects of L- to D-inversions are instead found to be highly position-specific. Additionally, in contrast to the helical peptide, some inversions increase the stability of the folded peptide: in such cases, we compute an increase in β-sheet content in the aqueous solution equilibrium ensemble. However, the tertiary structures of the stable (folded) configurations for peptides for which inversions cause an increase in β-sheet content show differences from one another, as well as from the native fold of the nonchirally perturbed β-hairpin. Our results suggest that although some chiral perturbations can increase folding stability, chirally perturbed proteins may still underperform functionally, given the relationship between structure and function.

Comparative Study of the Effects of Temperature and Pressure on the Water-Mediated Interactions between Apolar Nanoscale Solutes

We perform molecular dynamics simulations to study the effects of temperature and pressure on the water-mediated interaction (WMI) between two nanoscale (apolar) graphene plates at 240 ≤ T ≤ 400 K and -100 ≤ P ≤ 1200 MPa. These are thermodynamic conditions relevant to, for example, cooling-, heating-, compression-, and decompression-induced protein denaturation. We find that at all ( T, P) studied, the potential of mean force between the graphene plates, as a function of plate separation r, exhibits local minima at specific plate separations r = r _n that can accommodate n water layers ( n = 0,1,2,3). In particular, our results show that isobaric cooling and isothermal compression have a similar effect on WMI between the plates; both processes tend to suppress the attraction and ultimate collapse of the graphene plates by kinetically trapping the plates at the metastable states with r = r _n ( n > 0). In addition, isobaric heating and isothermal decompression also have a similar effect; both processes tend to reduce the range and strength of the interactions between the graphene plates. Interestingly, at low temperatures, the WMI between the plates is affected by crystallization. However, crystallization depends deeply on the water model considered, SPC/E and TIP4P/2005 water models, with the crystallization occurring at different ( T, P) conditions, into different forms of ice.

Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration

Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto-associative artificial neural networks ("autoencoders") to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data-driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp-cage, and have developed an open-source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.

Simulated Force Quench Dynamics Shows GB1 Protein Is Not a Two State Folder

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a "two-state" model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

Multiscale implementation of infinite-swap replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular systems. The idea is to run several replicas of the system in parallel at different temperatures that are swapped periodically. These swaps are typically attempted every few MD steps and accepted or rejected according to a Metropolis-Hastings criterion. This guarantees that the joint distribution of the composite system of replicas is the normalized sum of the symmetrized product of the canonical distributions of these replicas at the different temperatures. Here we propose a different implementation of REMD in which (i) the swaps obey a continuous-time Markov jump process implemented via Gillespie's stochastic simulation algorithm (SSA), which also samples exactly the aforementioned joint distribution and has the advantage of being rejection free, and (ii) this REMD-SSA is combined with the heterogeneous multiscale method to accelerate the rate of the swaps and reach the so-called infinite-swap limit that is known to optimize sampling efficiency. The method is easy to implement and can be trivially parallelized. Here we illustrate its accuracy and efficiency on the examples of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent. In this latter example, our results indicate that the landscape of the protein is a triple funnel with two folded structures and one misfolded structure that are stabilized by H-bonds.

Computational investigation of cold denaturation in the Trp-cage miniprotein

The functional native states of globular proteins become unstable at low temperatures, resulting in cold unfolding and impairment of normal biological function. Fundamental understanding of this phenomenon is essential to rationalizing the evolution of freeze-tolerant organisms and developing improved strategies for long-term preservation of biological materials. We present fully atomistic simulations of cold denaturation of an α-helical protein, the widely studied Trp-cage miniprotein. In contrast to the significant destabilization of the folded structure at high temperatures, Trp-cage cold denatures at 210 K into a compact, partially folded state; major elements of the secondary structure, including the α-helix, are conserved, but the salt bridge between aspartic acid and arginine is lost. The stability of Trp-cage's α-helix at low temperatures suggests a possible evolutionary explanation for the prevalence of such structures in antifreeze peptides produced by cold-weather species, such as Arctic char. Although the 310-helix is observed at cold conditions, its position is shifted toward Trp-cage's C-terminus. This shift is accompanied by intrusion of water into Trp-cage's interior and the hydration of buried hydrophobic residues. However, our calculations also show that the dominant contribution to the favorable energetics of low-temperature unfolding of Trp-cage comes from the hydration of hydrophilic residues.

Free-energy landscape of a hyperstable RNA tetraloop

We report the characterization of the energy landscape and the folding/unfolding thermodynamics of a hyperstable RNA tetraloop obtained through high-performance molecular dynamics simulations at microsecond timescales. Sampling of the configurational landscape is conducted using temperature replica exchange molecular dynamics over three isochores at high, ambient, and negative pressures to determine the thermodynamic stability and the free-energy landscape of the tetraloop. The simulations reveal reversible folding/unfolding transitions of the tetraloop into the canonical A-RNA conformation and the presence of two alternative configurations, including a left-handed Z-RNA conformation and a compact purine Triplet. Increasing hydrostatic pressure shows a stabilizing effect on the A-RNA conformation and a destabilization of the left-handed Z-RNA. Our results provide a comprehensive description of the folded free-energy landscape of a hyperstable RNA tetraloop and highlight the significant advances of all-atom molecular dynamics in describing the unbiased folding of a simple RNA secondary structure motif.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Comparison of hydration behavior and conformational preferences of the Trp-cage mini-protein in different rigid-body water models

Trp-cage unfolds at different temperatures in different water models revealing the sensitivity of conformational order metrics to the choice of water models.

Contribution of Water to Pressure and Cold Denaturation of Proteins

The mechanisms of cold and pressure denaturation of proteins are matter of debate and are commonly understood as due to water-mediated interactions. Here, we study several cases of proteins, with or without a unique native state, with or without hydrophilic residues, by means of a coarse-grain protein model in explicit solvent. We show, using Monte Carlo simulations, that taking into account how water at the protein interface changes its hydrogen bond properties and its density fluctuations is enough to predict protein stability regions with elliptic shapes in the temperature-pressure plane, consistent with previous theories. Our results clearly identify the different mechanisms with which water participates to denaturation and open the perspective to develop advanced computational design tools for protein engineering.

Free Energy Landscapes of Alanine Oligopeptides in Rigid-Body and Hybrid Water Models

Replica exchange molecular dynamics is used to study the effect of different rigid-body (mTIP3P, TIP4P, SPC/E) and hybrid (H1.56, H3.00) water models on the conformational free energy landscape of the alanine oligopeptides (acAnme and acA5nme), in conjunction with the CHARMM22 force field. The free energy landscape is mapped out as a function of the Ramachandran angles. In addition, various secondary structure metrics, solvation shell properties, and the number of peptide-solvent hydrogen bonds are monitored. Alanine dipeptide is found to have similar free energy landscapes in different solvent models, an insensitivity which may be due to the absence of possibilities for forming i-(i + 4) or i-(i + 3) intrapeptide hydrogen bonds. The pentapeptide, acA5nme, where there are three intrapeptide backbone hydrogen bonds, shows a conformational free energy landscape with a much greater degree of sensitivity to the choice of solvent model, though the three rigid-body water models differ only quantitatively. The pentapeptide prefers nonhelical, non-native PPII and β-sheet populations as the solvent is changed from SPC/E to the less tetrahedral liquid (H1.56) to an LJ-like liquid (H3.00). The pentapeptide conformational order metrics indicate a preference for open, solvent-exposed, non-native structures in hybrid solvent models at all temperatures of study. The possible correlations between the properties of solvent models and secondary structure preferences of alanine oligopeptides are discussed, and the competition between intrapeptide, peptide-solvent, and solvent-solvent hydrogen bonding is shown to be crucial in the relative free energies of different conformers.

Role of solvation in pressure-induced helix stabilization

In contrast to the well-known destabilization of globular proteins by high pressure, recent work has shown that pressure stabilizes the formation of isolated α-helices. However, all simulations to date have obtained a qualitatively opposite result within the experimental pressure range. We show that using a protein force field (Amber03w) parametrized in conjunction with an accurate water model (TIP4P/2005) recovers the correct pressure-dependence and an overall stability diagram for helix formation similar to that from experiment; on the other hand, we confirm that using TIP3P water results in a very weak pressure destabilization of helices. By carefully analyzing the contributing factors, we show that this is not merely a consequence of different peptide conformations sampled using TIP3P. Rather, there is a critical role for the solvent itself in determining the dependence of total system volume (peptide and solvent) on helix content. Helical peptide structures exclude a smaller volume to water, relative to non-helical structures with both the water models, but the total system volume for helical conformations is higher than non-helical conformations with TIP3P water at low to intermediate pressures, in contrast to TIP4P/2005 water. Our results further emphasize the importance of using an accurate water model to study protein folding under conditions away from standard temperature and pressure.

Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering

Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.