Theoretical aspects of pressure and solute denaturation of proteins: A Kirkwood-buff-theory approach

Correlation between protein conformations and water structure and thermodynamics at high pressure: A molecular dynamics study of the Bovine Pancreatic Trypsin Inhibitor (BPTI) protein

Pressure-induced perturbation of a protein structure leading to its folding-unfolding mechanism is an important yet not fully understood phenomenon. The key point here is the role of water and its coupling with protein conformations as a function of pressure. In the current work, using extensive molecular dynamics simulation at 298 K, we systematically examine the coupling between protein conformations and water structures of pressures of 0.001, 5, 10, 15, 20 kbar, starting from (partially) unfolded structures of the protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We also calculate localized thermodynamics at those pressures as a function of protein-water distance. Our findings show that both protein-specific and generic effects of pressure are operating. In particular, we found that (1) the amount of increase in water density near the protein depends on the protein structural heterogeneity; (2) the intra-protein hydrogen bond decreases with pressure, while the water-water hydrogen bond per water in the first solvation shell (FSS) increases; protein-water hydrogen bonds also found to increase with pressure, (3) with pressure hydrogen bonds of waters in the FSS getting twisted; and (4) water's tetrahedrality in the FSS decreases with pressure, but it is dependent on the local environment. Thermodynamically, at higher pressure, the structural perturbation of BPTI is due to the pressure-volume work, while the entropy decreases with the increase of pressure due to the higher translational and rotational rigidity of waters in the FSS. The local and subtle effects of pressure, found in this work, are likely to be typical of pressure-induced protein structure perturbation.

Hydrostatic High-Pressure-Induced Denaturation of LH2 Membrane Proteins

The denaturation of globular proteins by high pressure is frequently associated with the release of internal voids and/or the exposure of the hydrophobic protein interior to a polar aqueous solvent. Similar evidence with respect to membrane proteins is not available. Here, we investigate the impact of hydrostatic pressures reaching 12 kbar on light-harvesting 2 integral membrane complexes of purple photosynthetic bacteria using two types of innate chromophores in separate strategic locations: bacteriochlorophyll-a in the hydrophobic interior and tryptophan at both protein-solvent interfacial gateways to internal voids. The complexes from mutant Rhodobacter sphaeroides with low resilience against pressure were considered in parallel with the naturally robust complexes of Thermochromatium tepidum. In the former case, a firm correlation was established between the abrupt blue shift of the bacteriochlorophyll-a exciton absorption, a known indicator of the breakage of tertiary structure pigment-protein hydrogen bonds, and the quenching of tryptophan fluorescence, a supposed result of further protein solvation. No such effects were observed in the reference complex. While these data may be naively taken as supporting evidence of the governing role of hydration, the analysis of atomistic model structures of the complexes confirmed the critical part of the structure in the pressure-induced denaturation of the membrane proteins studied.

The aqueous environment as an active participant in the protein folding process

Existing computational models applied in the protein structure prediction process do not sufficiently account for the presence of the aqueous solvent. The solvent is usually represented by a predetermined number of H₂O molecules in the bounding box which contains the target chain. The fuzzy oil drop (FOD) model, presented in this paper, follows an alternative approach, with the solvent assuming the form of a continuous external hydrophobic force field, with a Gaussian distribution. The effect of this force field is to guide hydrophobic residues towards the center of the protein body, while promoting exposure of hydrophilic residues on its surface. This work focuses on the following sample proteins: Engrailed homeodomain (RCSB: 1enh), Chicken villin subdomain hp-35, n68h (RCSB: 1yrf), Chicken villin subdomain hp-35, k65(nle), n68h, k70(nle) (RCSB: 2f4k), Thermostable subdomain from chicken villin headpiece (RCSB: 1vii), de novo designed single chain three-helix bundle (a3d) (RCSB: 2a3d), albumin-binding domain (RCSB: 1prb) and lambda repressor-operator complex (RCSB: 1lmb).

Excess Volumes from the Pressure Derivative of the Excess Chemical Potential: Testing Simple Models for Cavity Formation in Water

Excess volumes and excess compressibilities for hard spheres in water were computed by pressure derivatives of the excess chemical potential, which is equivalent to the work of cavity formation. This is relevant to the application of continuum solvation methods at various pressures. The excess chemical potential was modeled within phenomenological expressions for curved surfaces plus a pressure-volume term, for which two approaches were adopted, differing for the radius of the spherical volume. This implies a different dependence on pressure of parameters. In all cases, in the surface term, for the pressure derivative of parameters of the curvature function, use was made of the previously proposed expressions for the first two moments obtained from the density and radial distribution of oxygens in liquid water. Only for the parameter which has the dimension of surface tension (γ̃) was explicit dependence on pressure considered and results are affected by the specific polynomial used. In agreement with what inferred from simulation results obtained for cavities in TIP4P water, negative and positive adsorptions at the contact radius were extrapolated for a very large cavity at 1 and 8000 atm, respectively. The expressions here employed for the excess chemical potential predict the zero value of asymptotic adsorption to be at a pressure between 500 and 800 atm, which can be compared to results from the revised scaled particle theory. In the same range, for a nanometer-sized cavity, a change of behavior occurs regarding the ratio between the excess Helmholtz free energy and the product between pressure and excess volume.

Effect of cosolvent on protein stability: a theoretical investigation

We developed a statistical thermodynamic algorithm for analyzing solvent-induced folding/unfolding transitions of proteins. The energetics of protein transitions is governed by the interplay between the cavity formation contribution and the term reflecting direct solute-cosolvent interactions. The latter is viewed as an exchange reaction in which the binding of a cosolvent to a solute is accompanied by release of waters of hydration to the bulk. Our model clearly differentiates between the stoichiometric and non-stoichiometric interactions of solvent or co-solvent molecules with a solute. We analyzed the urea- and glycine betaine (GB)-induced conformational transitions of model proteins of varying size which are geometrically approximated by a sphere in their native state and a spherocylinder in their unfolded state. The free energy of cavity formation and its changes accompanying protein transitions were computed based on the concepts of scaled particle theory. The free energy of direct solute-cosolvent interactions were analyzed using empirical parameters previously determined for urea and GB interactions with low molecular weight model compounds. Our computations correctly capture the mode of action of urea and GB and yield realistic numbers for (∂ΔG°/∂a3)T,P which are related to the m-values of protein denaturation. Urea is characterized by negative values of (∂ΔG°/∂a3)T,P within the entire range of urea concentrations analyzed. At concentrations below ∼1 M, GB exhibits positive values of (∂ΔG°/∂a3)T,P which turn positive at higher GB concentrations. The balance between the thermodynamic contributions of cavity formation and direct solute-cosolvent interactions that, ultimately, defines the mode of cosolvent action is extremely subtle. A 20% increase or decrease in the equilibrium constant for solute-cosolvent binding may change the sign of (∂ΔG°/∂a3)T,P thereby altering the mode of cosolvent action (stabilizing to destabilizing or vice versa).

Protein denaturants at aqueous-hydrophobic interfaces: self-consistent correlation between induced interfacial fluctuations and denaturant stability at the interface

The notion of direct interaction between denaturing cosolvent and protein residues has been proposed in dialogue relevant to molecular mechanisms of protein denaturation. Here we consider the correlation between free energetic stability and induced fluctuations of an aqueous-hydrophobic interface between a model hydrophobically associating protein, HFBII, and two common protein denaturants, guanidinium cation (Gdm(+)) and urea. We compute potentials of mean force along an order parameter that brings the solute molecule close to the known hydrophobic region of the protein. We assess potentials of mean force for different relative orientations between the protein and denaturant molecule. We find that in both cases of guanidinium cation and urea relative orientations of the denaturant molecule that are parallel to the local protein-water interface exhibit greater stability compared to edge-on or perpendicular orientations. This behavior has been observed for guanidinium/methylguanidinium cations at the liquid-vapor interface of water, and thus the present results further corroborate earlier findings. Further analysis of the induced fluctuations of the aqueous-hydrophobic interface upon approach of the denaturant molecule indicates that the parallel orientation, displaying a greater stability at the interface, also induces larger fluctuations of the interface compared to the perpendicular orientations. The correlation of interfacial stability and induced interface fluctuation is a recurring theme for interface-stable solutes at hydrophobic interfaces. Moreover, observed correlations between interface stability and induced fluctuations recapitulate connections to local hydration structure and patterns around solutes as evidenced by experiment (Cooper et al., J. Phys. Chem. A 2014, 118, 5657.) and high-level ab initio/DFT calculations (Baer et al., Faraday Discuss 2013, 160, 89).

Driving Forces in Pressure-Induced Protein Transitions

The molecular mechanisms underlying pressure-induced protein denaturation can be analyzed based on the pressure-dependent differences in the apparent volume occupied by amino acids inside the protein and when exposed to water in an unfolded conformation. This chapter presents a volumetric analysis of the peptide group and the 20 naturally occurring amino acid side chains in the interior of the native state, the micelle-like interior of the pressure-induced denatured state, and in the unfolded conformation modeled by low-molecular analogs of proteins. The transfer of a peptide group from the protein interior to water becomes increasingly favorable as pressure increases. This observation classifies solvation of peptide groups as a major driving force in pressure-induced protein denaturation. Polar side chains do not appear to exhibit significant pressure-dependent changes in their preference for the protein interior or solvent. The transfer of nonpolar side chains from the protein interior to water becomes more unfavorable as pressure increases. An inference can be drawn that a sizeable population of nonpolar side chains remains buried inside a solvent-inaccessible core of the pressure-induced denatured state. At elevated pressures this core, owing to the absence of structural constraints, may become packed almost as tightly as the interior of the native state. The presence and partial disappearance of large intraglobular voids is another driving force facilitating pressure-induced protein denaturation. Volumetric data presented here have implications for the kinetics of protein folding and shed light on the nature of the folding transition state ensembles.

Infinitely dilute partial molar properties of proteins from computer simulation

A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.