Parsing partial molar volumes of small molecules: a molecular dynamics study

Molecular Dynamics Calculations of Partial Molar Volumes of Amino Acids in Aqueous Solutions

Partial molar volumes of amino acids in their zwitterionic and molecular forms have been calculated using molecular dynamics simulations of these systems in aqueous solutions. Calculations performed with the TIP4P, SPC (rigid and flexible), SPC/E, and polarizable water models show that the choice of water model can have a significant impact on the calculated volumes. The effect of treatment of long-range electrostatic interactions on the calculated results was also investigated. Volumes obtained in simulations with a properly chosen water model fit well the experimental data for both molecular and zwitterionic forms of amino acids.

Volumetric Properties of Four-Stranded DNA Structures

Four-stranded non-canonical DNA structures including G-quadruplexes and i-motifs have been found in the genome and are thought to be involved in regulation of biological function. These structures have been implicated in telomere biology, genomic instability, and regulation of transcription and translation events. To gain an understanding of the molecular determinants underlying the biological role of four-stranded DNA structures, their biophysical properties have been extensively studied. The limited libraries on volume, expansibility, and compressibility accumulated to date have begun to provide insights into the molecular origins of helix-to-coil and helix-to-helix conformational transitions involving four-stranded DNA structures. In this article, we review the recent progress in volumetric investigations of G-quadruplexes and i-motifs, emphasizing how such data can be used to characterize intra-and intermolecular interactions, including solvation. We describe how volumetric data can be interpreted at the molecular level to yield a better understanding of the role that solute-solvent interactions play in modulating the stability and recognition events of nucleic acids. Taken together, volumetric studies facilitate unveiling the molecular determinants of biological events involving biopolymers, including G-quadruplexes and i-motifs, by providing one more piece to the thermodynamic puzzle describing the energetics of cellular processes in vitro and, by extension, in vivo.

Assessment of the DNA partial specific volume and hydration layer properties from CHARMM Drude polarizable and additive MD simulations

In this study we report on the accurate computation of the biomolecular partial specific volume (PSV) from explicit-solvent molecular dynamics (MD) simulations. The case of DNA is considered, and the predictions from two state-of-the-art biomolecular force fields, the CHARMM36 additive (C36) and Drude polarizable models, are presented. Unlike most of the existing approaches to assess the biomolecular PSV, our proposed method bypasses the need for the arbitrarily defined volume partitioning scheme into the intrinsic solute and solvent contributions. At the same time, to assess the density of the hydration layer water, we combine our simulation analysis approach with some of the existing fixed-size methods to determine the solute's intrinsic volume, and also propose our own approach to compute all required quantities exclusively from MD simulations. Our findings provide useful insights into the properties of the hydration layer, specifically its size and density, parameters of great importance to the variety of techniques used to model hydrodynamic and structural properties of biological molecules. The computed PSV values are found to be in close agreement with the values obtained from analytical ultracentrifugation (AUC) experiments performed on canonical B-form duplex DNAs and single-stranded DNAs forming G-quadruplex structures. Since the biomolecular PSV represents an important quantitative measure of solute-solvent interactions, near quantitative agreement with AUC measurements is indicative of the quality of the all-atom models used in the MD simulations, particularly the reliability of the CHARMM force-field parameters for nucleic acids, water, mobile ions, and interactions among these entities.

On empirical decomposition of volumetric data

Volumetric characterization of proteins and their recognition events has been instrumental in providing information on the role of intra- and intermolecular interactions, including hydration, in stabilizing biomolecules. The credibility of molecular models and interpretation schemes used to rationalize experimental data are essential for the validity of microscopic insights derived from volumetric results. Current empirical schemes used to interpret volumetric data suffer from a lack of theoretical and computational substantiation. In this contribution, we take advantage age of recent MD simulations of proteins in solution coupled with Voronoi-Delaunay tessellation of simulated structures that have provided an exceptional level of structural detail on the nature of protein-water interfaces. We use these structural insights to re-evaluate empirical frameworks used for interpretation of volumetric data. An important issue in this respect is the actual dividing surface between water and protein atoms that is used in volumetric studies when the solute and solvent are treated as hard spheres enclosed within their respective van der Waals surfaces. In one development, using Voronoi tessellation of MD simulated protein-water systems the dividing surface has been defined as the points equidistant from the water and protein atoms. The interstitial void volume between the solute and the dividing surface corresponds to thermal volume envisaged by Scaled Particle Theory. In this communication, we explicitly account for the contributions of thermal volume to the partial molar volume, compressibility, and expansibility of proteins and re-examine and redefine the intrinsic and hydration volumetric contributions. We discuss the implications of our results for protein transitions and association events.

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.

Simulated pressure denaturation thermodynamics of ubiquitin

Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues.

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.

The unfolding effects on the protein hydration shell and partial molar volume: a computational study

In this paper we apply the computational analysis recently proposed by our group to characterize the solvation properties of a native protein in aqueous solution, and to four model aqueous solutions of globular proteins in their unfolded states thus characterizing the protein unfolded state hydration shell and quantitatively evaluating the protein unfolded state partial molar volumes.

Determination of partial molar volumes from free energy perturbation theory

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.

Exploring volume, compressibility and hydration changes of folded proteins upon compression

Understanding the physical basis of the structure, stability and function of proteins in solution, including extreme environmental conditions, requires knowledge of their temperature and pressure dependent volumetric properties. One physical-chemical property of proteins that is still little understood is their partial molar volume and its dependence on temperature and pressure. We used molecular dynamics simulations of aqueous solutions of a typical monomeric folded protein, staphylococcal nuclease (SNase), to study and analyze the pressure dependence of the apparent volume, Vapp, and its components by the Voronoi-Delaunay method. We show that the strong decrease of Vapp with pressure (βT = 0.95 × 10(-5) bar(-1), in very good agreement with the experimental value) is essentially due to the compression of the molecular volume, VM, ultimately, of its internal voids, V. Changes of the intrinsic volume (defined as the Voronoi volume of the molecule), the contribution of the solvent to the apparent volume, and of the contribution of the boundary voids between the protein and the solvent have also been studied and quantified in detail. The pressure dependences of the volumetric characteristics obtained are compared with the temperature dependent behavior of these quantities and with corresponding results for a natively unfolded polypeptide.

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.

Note: Nonpolar solute partial molar volume response to attractive interactions with water

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Variation and decomposition of the partial molar volume of small gas molecules in different organic solvents derived from molecular dynamics simulations

The partial molar volumes, V(i), of the gas solutes H2, CO, and CO2, solvated in acetone, methanol, heptane, and diethylether are determined computationally in the limit of infinite dilution and standard conditions. Solutions are described with molecular dynamics simulations in combination with the OPLS-aa force field for solvents and customized force field for solutes. V(i) is determined with the direct method, while the composition of V(i) is studied with Kirkwood-Buff integrals (KBIs). Subsequently, the amount of unoccupied space and size of pre-formed cavities in pure solvents is determined. Additionally, the shape of individual solvent cages is analyzed. Calculated V(i) deviate only 3.4 cm(3) mol(-1) (7.1%) from experimental literature values. Experimental V(i) variations across solutions are reproduced qualitatively and also quantitatively in most cases. The KBI analysis identifies differences in solute induced solvent reorganization in the immediate vicinity of H2 (<0.7 nm) and solvent reorganization up to the third solvation shell of CO and CO2 (<1.6 nm) as the origin of V(i) variations. In all solutions, larger V(i) are found in solvents that exhibit weak internal interactions, low cohesive energy density and large compressibility. Weak internal interactions facilitate solvent displacement by thermal solute movement, which enhances the size of solvent cages and thus V(i). Additionally, attractive electrostatic interactions of CO2 and the solvents, which do not depend on internal solvent interactions only, partially reversed the V(i) trends observed in H2 and CO solutions where electrostatic interactions with the solvents are absent. More empty space and larger pre-formed cavities are found in solvents with weak internal interactions, however, no evidence is found that solutes in any considered solvent are accommodated in pre-formed cavities. Individual solvent cages are found to be elongated in the negative direction of solute movement. This wake behind the moving solute is more pronounced in case of mobile H2 and in solvents with weaker internal interactions. However, deviations from a spherical solvent cage shape do not influence solute-solvent radial distribution functions after averaging over all solvent cage orientations and hence do not change V(i). Overall, the applied methodology reproduces V(i) and its variations reliably and the used V(i) decompositions identify the underlying reasons behind observed V(i) variations.

Role of dynamics in the autoinhibition and activation of the exchange protein directly activated by cyclic AMP (EPAC)

The exchange protein directly activated by cAMP (EPAC) is a key receptor of cAMP in eukaryotes and controls critical signaling pathways. Currently, no residue resolution information is available on the full-length EPAC dynamics, which are known to be pivotal determinants of allostery. In addition, no information is presently available on the intermediates for the classical induced fit and conformational selection activation pathways. Here these questions are addressed through molecular dynamics simulations on five key states along the thermodynamic cycle for the cAMP-dependent activation of a fully functional construct of EPAC2, which includes the cAMP-binding domain and the integral catalytic region. The simulations are not only validated by the agreement with the experimental trends in cAMP-binding domain dynamics determined by NMR, but they also reveal unanticipated dynamic attributes, rationalizing previously unexplained aspects of EPAC activation and autoinhibition. Specifically, the simulations show that cAMP binding causes an extensive perturbation of dynamics in the distal catalytic region, assisting the recognition of the Rap1b substrate. In addition, analysis of the activation intermediates points to a possible hybrid mechanism of EPAC allostery incorporating elements of both the induced fit and conformational selection models. In this mechanism an entropy compensation strategy results in a low free-energy pathway of activation. Furthermore, the simulations indicate that the autoinhibitory interactions of EPAC are more dynamic than previously anticipated, leading to a revised model of autoinhibition in which dynamics fine tune the stability of the autoinhibited state, optimally sensitizing it to cAMP while avoiding constitutive activation.