Theoretical study of the partial molar volume change associated with the pressure-induced structural transition of ubiquitin

Structural Fluctuation, Relaxation, and Folding of Protein: An Approach Based on the Combined Generalized Langevin and RISM/3D-RISM Theories

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water's degrees of freedom onto the protein's degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena.

Modeling the interaction of SARS-CoV-2 binding to the ACE2 receptor via molecular theory of solvation

The angiotensin-converting enzyme 2 (ACE2) protein is a cell gate receptor for the SARS-CoV-2 virus, responsible for the development of symptoms associated with the Covid-19 disease.

Solvent Composition Effects on the Structural Properties of the Aβ42 Monomer from the 3D-RISM-KH Molecular Theory of Solvation

Structural characterization of amyloid (A)β peptides implicated in Alzheimer's disease is a challenging problem due to their intrinsically disordered nature and their high propensity for aggregation. Only limited information is currently available from experiments on conformational properties and aggregation pathways of the peptides in cellular environments. In silico modeling complements experimental information, providing atomistic insight into structure and dynamics of different Aβ species. All-atom explicit solvent molecular dynamics (MD) simulations with a properly selected force field can deliver reliable structural and dynamic information. In the case of intrinsically disordered Aβ peptides, enhanced sampling simulations beyond the nanosecond time scale are required to obtain statistically meaningful results even for simple solvent conditions. To overcome the challenges of conformational sampling in crowded cellular environments, alternative approaches have to be used, including postprocessing of MD data. In this study, we employ the statistical-mechanical, three-dimensional reference interaction site model with the Kovalenko-Hirata closure integral equation molecular theory of solvation to describe solvent composition effects on the conformational equilibrium in a structural ensemble of the Aβ42 (covering residues 1-42) monomer based on a statistical reweighting technique. The methodology enables a computationally efficient prediction on how different factors in the cellular environment, such as solvent composition, nonpolar solvation, and macromolecular crowding, affect the structural properties of the monomer. Similarities have been identified between changes in the structural ensemble caused by nonpolar solvation and crowded environments modeled by ionic solution with large negative ions. In particular, both solvent conditions reduce the random coil content and enhance the helical structure content of the monomer. In contrast to the previous studies, which reported increased α-helical content of peptides in crowded environments, this work attributes these structural features to the difference in solvent exposure of hydrophilic residues of the monomer for different secondary structure elements, rather than to (entropic) excluded volume effects.

Perspective: Structural fluctuation of protein and Anfinsen's thermodynamic hypothesis

The thermodynamics hypothesis, casually referred to as "Anfinsen's dogma," is described theoretically in terms of a concept of the structural fluctuation of protein or the first moment (average structure) and the second moment (variance and covariance) of the structural distribution. The new theoretical concept views the unfolding and refolding processes of protein as a shift of the structural distribution induced by a thermodynamic perturbation, with the variance-covariance matrix varying. Based on the theoretical concept, a method to characterize the mechanism of folding (or unfolding) is proposed. The transition state, if any, between two stable states is interpreted as a gap in the distribution, which is created due to an extensive reorganization of hydrogen bonds among back-bone atoms of protein and with water molecules in the course of conformational change. Further perspective to applying the theory to the computer-aided drug design, and to the material science, is briefly discussed.

Taurine as a water structure breaker and protein stabilizer

The enhancing effect on the water structure has been confirmed for most of the osmolytes exhibiting both stabilizing and destabilizing properties in regard to proteins. The presented work concerns osmolytes, which should be classified as "structure breaking" solutes: taurine and N,N,N-trimethyltaurine (TMT). Here, we combine FTIR spectroscopy, DSC calorimetry and DFT calculations to gain an insight into the interactions between osmolytes and two proteins: lysozyme and ubiquitin. Despite high structural similarity, both osmolytes exert different influence on protein stability: taurine is a stabilizer, TMT is a denaturant. We show also that taurine amino group interacts directly with the side chains of proteins, whereas TMT does not interact with proteins at all. Although two solutes weaken on average the structure of the surrounding water, their hydration spheres are different. Taurine is surrounded by two populations of water molecules: bonded with weak H-bonds around sulfonate group, and strongly bonded around amino group. The strong hydrogen-bonded network of water molecules around the amino group of taurine further improves properties of enhanced protein hydration sphere and stabilizes the native protein form. Direct interactions of this group with surface side chains provide a proper orientation of taurine and prevents the [Formula: see text] group from negative influence. The weakened [Formula: see text] hydration sphere of TMT breaks up the hydrogen-bonded network of water around the protein and destabilizes it. However, TMT at low concentration stabilize both proteins to a small extent. This effect can be attributed to an actual osmophobic effect which is overcome if the concentration increases.

Monitoring protein folding through high pressure NMR spectroscopy

High-pressure is a well-known perturbation method used to destabilize globular proteins. It is perfectly reversible, which is essential for a proper thermodynamic characterization of a protein equilibrium. In contrast to other perturbation methods such as heat or chemical denaturant that destabilize protein structures uniformly, pressure exerts local effects on regions or domains of a protein containing internal cavities. When combined with NMR spectroscopy, hydrostatic pressure offers the possibility to monitor at a residue level the structural transitions occurring upon unfolding and to determine the kinetic properties of the process. High-pressure NMR experiments can now be routinely performed, owing to the recent development of commercially available high-pressure sample cells. This review summarizes recent advances and some future directions of high-pressure NMR techniques for the characterization at atomic resolution of the energy landscape of protein folding.

High-pressure NMR techniques for the study of protein dynamics, folding and aggregation

High-pressure is a well-known perturbation method used to destabilize globular proteins and dissociate protein complexes or aggregates. The heterogeneity of the response to pressure offers a unique opportunity to dissect the thermodynamic contributions to protein stability. In addition, pressure perturbation is generally reversible, which is essential for a proper thermodynamic characterization of a protein equilibrium. When combined with NMR spectroscopy, hydrostatic pressure offers the possibility of monitoring at an atomic resolution the structural transitions occurring upon unfolding and determining the kinetic properties of the process. The recent development of commercially available high-pressure sample cells greatly increased the potential applications for high-pressure NMR experiments that can now be routinely performed. This review summarizes the recent applications and future directions of high-pressure NMR techniques for the characterization of protein conformational fluctuations, protein folding and the stability of protein complexes and aggregates.

In silico characterization of protein partial molecular volumes and hydration shells

In this paper we present a computational approach, based on NVT molecular dynamics trajectories, that allows the direct evaluation of the protein partial molecular volume. The results obtained for five different globular proteins demonstrate the accuracy of this computational procedure in reproducing protein partial molecular volumes, providing quantitative characterization of the hydration shell in terms of the protein excluded volume, hydration shell ellipsoidal volume and related solvent density. Remarkably, our data indicate for the hydration shell a ≈10% solvent density increase with respect to the liquid water bulk density, in excellent agreement with the available experimental data.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Pressure adaptation of 3-isopropylmalate dehydrogenase from an extremely piezophilic bacterium is attributed to a single amino acid substitution

3-Isopropylmalate dehydrogenase (IPMDH) from the extreme piezophile Shewanella benthica (SbIPMDH) is more pressure-tolerant than that from the atmospheric pressure-adapted Shewanella oneidensis (SoIPMDH). To understand the molecular mechanisms of this pressure tolerance, we analyzed mutated enzymes. The results indicate that only a single mutation at position 266, corresponding to Ala (SbIPMDH) and Ser (SoIPMDH), essentially affects activity under higher-pressure conditions. Structural analyses of SoIPMDH suggests that penetration of three water molecules into the cleft around Ser266 under high-pressure conditions could reduce the activity of the wild-type enzyme; however, no water molecule is observed in the Ala266 mutant.

Octanol-Water Partition Coefficient from 3D-RISM-KH Molecular Theory of Solvation with Partial Molar Volume Correction

The octanol-water partition coefficient is an important physical-chemical characteristic widely used to describe hydrophobic/hydrophilic properties of chemical compounds. The partition coefficient is related to the transfer free energy of a compound from water to octanol. Here, we introduce a new protocol for prediction of the partition coefficient based on the statistical-mechanical, 3D-RISM-KH molecular theory of solvation. It was shown recently that with the compound-solvent correlation functions obtained from the 3D-RISM-KH molecular theory of solvation, the free energy functional supplemented with the correction linearly related to the partial molar volume obtained from the Kirkwood-Buff/3D-RISM theory, also called the "universal correction" (UC), provides accurate prediction of the hydration free energy of small compounds, compared to explicit solvent molecular dynamics [ Palmer , D. S. ; J. Phys.: Condens. Matter 2010 , 22 , 492101 ]. Here we report that with the UC reparametrized accordingly this theory also provides an excellent agreement with the experimental data for the solvation free energy in nonpolar solvent (1-octanol) and so accurately predicts the octanol-water partition coefficient. The performance of the Kovalenko-Hirata (KH) and Gaussian fluctuation (GF) functionals of the solvation free energy, with and without UC, is tested on a large library of small compounds with diverse functional groups. The best agreement with the experimental data for octanol-water partition coefficients is obtained with the KH-UC solvation free energy functional.

High-pressure protein crystallography of hen egg-white lysozyme

Crystal structures of hen egg-white lysozyme (HEWL) determined under pressures ranging from ambient pressure to 950 MPa are presented. From 0.1 to 710 MPa, the molecular and internal cavity volumes are monotonically compressed. However, from 710 to 890 MPa the internal cavity volume remains almost constant. Moreover, as the pressure increases to 950 MPa, the tetragonal crystal of HEWL undergoes a phase transition from P43212 to P43. Under high pressure, the crystal structure of the enzyme undergoes several local and global changes accompanied by changes in hydration structure. For example, water molecules penetrate into an internal cavity neighbouring the active site and induce an alternate conformation of one of the catalytic residues, Glu35. These phenomena have not been detected by conventional X-ray crystal structure analysis and might play an important role in the catalytic activity of HEWL.

Water Turns the "Non-biological" Fluctuation of Protein into "Biological" One

Structural fluctuation of protein is not just an mechanical "oscillation," but an event induced by an interplay of mechanical and thermodynamic processes in which water plays crucial role. The chapter is devoted to provide a theoretical description concerning the concept of structural fluctuation of protein, based on methods of the statistical mechanics.

Volume and Compressibility of Proteins

The partial specific (or molar) volume, expansibility, and compressibility of a protein are fundamental thermodynamic quantities for characterizing its structure in solution. We review the definitions, measurements, and implications of these volumetric quantities in relation to protein structural biology. The partial specific volumes under constant molality (isomolal) and chemical potential (isopotential) conditions of the cosolvent (multicomponent systems) are explained in terms of preferential solvent interactions relevant to the solubility and stability of proteins. The partial expansibility is briefly discussed in terms of the effects of temperature on protein-solvent interactions (hydration) and internal packing defects (cavities). We discuss the compressibility-structure-function relationships of proteins based on analyses of the correlations between the partial adiabatic compressibilities and the structures or functions of various globular proteins (including mutants), focusing on the roles of the internal cavities in structural fluctuations. The volume and compressibility changes associated with various conformational transitions are also discussed in terms of the changes in hydration and cavities in order to elucidate the nonnative structures and the transition mechanisms, especially those associated with pressure denaturation.

Single-molecule analysis of the rotation of F₁-ATPase under high hydrostatic pressure

F1-ATPase is the water-soluble part of ATP synthase and is an ATP-driven rotary molecular motor that rotates the rotary shaft against the surrounding stator ring, hydrolyzing ATP. Although the mechanochemical coupling mechanism of F1-ATPase has been well studied, the molecular details of individual reaction steps remain unclear. In this study, we conducted a single-molecule rotation assay of F1 from thermophilic bacteria under various pressures from 0.1 to 140 MPa. Even at 140 MPa, F1 actively rotated with regular 120° steps in a counterclockwise direction, showing high conformational stability and retention of native properties. Rotational torque was also not affected. However, high hydrostatic pressure induced a distinct intervening pause at the ATP-binding angles during continuous rotation. The pause was observed under both ATP-limiting and ATP-saturating conditions, suggesting that F1 has two pressure-sensitive reactions, one of which is evidently ATP binding. The rotation assay using a mutant F1(βE190D) suggested that the other pressure-sensitive reaction occurs at the same angle at which ATP binding occurs. The activation volumes were determined from the pressure dependence of the rate constants to be +100 Å(3) and +88 Å(3) for ATP binding and the other pressure-sensitive reaction, respectively. These results are discussed in relation to recent single-molecule studies of F1 and pressure-induced protein unfolding.

High-pressure-induced water penetration into 3-isopropylmalate dehydrogenase

Hydrostatic pressure induces structural changes in proteins, including denaturation, the mechanism of which has been attributed to water penetration into the protein interior. In this study, structures of 3-isopropylmalate dehydrogenase (IPMDH) from Shewanella oneidensis MR-1 were determined at about 2 Å resolution under pressures ranging from 0.1 to 650 MPa using a diamond anvil cell (DAC). Although most of the protein cavities are monotonically compressed as the pressure increases, the volume of one particular cavity at the dimer interface increases at pressures over 340 MPa. In parallel with this volume increase, water penetration into the cavity could be observed at pressures over 410 MPa. In addition, the generation of a new cleft on the molecular surface accompanied by water penetration could also be observed at pressures over 580 MPa. These water-penetration phenomena are considered to be initial steps in the pressure-denaturation process of IPMDH.

Structural analysis of 3-isopropylmalate dehydrogenase from the obligate piezophile Shewanella benthica DB21MT-2 and the nonpiezophile Shewanella oneidensis MR-1

Organisms living in deep seas such as the Mariana Trench must be adapted to the extremely high pressure environment. For example, the 3-isopropylmalate dehydrogenase from the obligate piezophile Shewanella benthica DB21MT-2 (SbIPMDH) remains active in extreme conditions under which that from the land bacterium S. oneidensis MR-1 (SoIPMDH) becomes inactivated. In order to unravel the differences between these two IPMDHs, their structures were determined at ~1.5 Å resolution. Comparison of the structures of the two enzymes shows that SbIPMDH is in a more open form and has a larger internal cavity volume than SoIPMDH at atmospheric pressure. This loosely packed structure of SbIPMDH could help it to avoid pressure-induced distortion of the native structure and to remain active at higher pressures than SoIPMDH.

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This "unfolding-up-on-squeezing" is counter-intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results-that pressure denatured states are water-swollen, and theoretical results-that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states-their water-swollen nature, retention of secondary structure, and overall compactness-mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure-dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately -60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500-2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water-swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies.

Association thermodynamics and conformational stability of beta-sheet amyloid beta(17-42) oligomers: effects of E22Q (Dutch) mutation and charge neutralization

Amyloid fibrils are associated with many neurodegenerative diseases. It was found that amyloidogenic oligomers, not mature fibrils, are neurotoxic agents related to these diseases. Molecular mechanisms of infectivity, pathways of aggregation, and molecular structure of these oligomers remain elusive. Here, we use all-atom molecular dynamics, molecular mechanics combined with solvation analysis by statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D-RISM-KH) in a new MM-3D-RISM-KH method to study conformational stability, and association thermodynamics of small wild-type Abeta(17-42) oligomers with different protonation states of Glu(22), as well the E22Q (Dutch) mutants. The association free energy of small beta-sheet oligomers shows near-linear trend with the dimers being thermodynamically more stable relative to the larger constructs. The linear (within statistical uncertainty) dependence of the association free energy on complex size is a consequence of the unilateral stacking of monomers in the beta-sheet oligomers. The charge reduction of the wild-type Abeta(17-42) oligomers upon protonation of the solvent-exposed Glu(22) at acidic conditions results in lowering the association free energy compared to the wild-type oligomers at neutral pH and the E22Q mutants. The neutralization of the peptides because of the E22Q mutation only marginally affects the association free energy, with the reduction of the direct electrostatic interactions mostly compensated by the unfavorable electrostatic solvation effects. For the wild-type oligomers at acidic conditions such compensation is not complete, and the electrostatic interactions, along with the gas-phase nonpolar energetic and the overall entropic effects, contribute to the lowering of the association free energy. The differences in the association thermodynamics between the wild-type Abeta(17-42) oligomers at neutral pH and the Dutch mutants, on the one hand, and the Abeta(17-42) oligomers with protonated Glu(22), on the other, may be explained by destabilization of the inter- and intrapeptide salt bridges between Asp(23) and Lys(28). Peculiarities in the conformational stability and the association thermodynamics for the different models of the Abeta(17-42) oligomers are rationalized based on the analysis of the local physical interactions and the microscopic solvation structure.

Pressure effects on structures formed by entropically driven self-assembly: illustration for denaturation of proteins

We propose a general framework of pressure effects on the structures formed by the self-assembly of solute molecules immersed in solvent. The integral equation theory combined with the morphometric approach is employed for a hard-body model system. Our picture is that protein folding and ordered association of proteins are driven by the solvent entropy: At low pressures, the structures almost minimizing the excluded volume (EV) generated for solvent particles are stabilized. Such structures appear to be even more stabilized at high pressures. However, it is experimentally known that the native structure of a protein is unfolded, and ordered aggregates such as amyloid fibrils and actin filaments are dissociated by applying high pressures. This initially puzzling result can also be elucidated in terms of the solvent entropy. A clue to the basic mechanism is in the phenomenon that, when a large hard-sphere solute is immersed in small hard spheres forming the solvent, the small hard spheres are enriched near the solute and this enrichment becomes greater as the pressure increases. We argue that "attraction" is entropically provided between the solute surface and solvent particles, and the attraction becomes higher with rising pressure. Due to this effect, at high pressures, the structures possessing the largest possible solvent-accessible surface area together with sufficiently small EV become more stable in terms of the solvent entropy. To illustrate this concept, we perform an analysis of pressure denaturation of three different proteins. It is shown that only the structures that have the characteristics described above exhibit interesting behavior. They first become more destabilized relative to the native structure as the pressure increases, but beyond a threshold pressure the relative instability begins to decrease and they eventually become more stable than the native structure.