Solvent-induced Forces Research Articles

Modeling and measuring the absorption-induced expansion of swellable organically modified silica

We present a theoretical framework that describes the force generated by the expansion of swellable organically modified silica (SOMS) upon exposure to organic solvent. The total swelling force, produced from the differential contributions of localized swelling domains, is related logarithmically to the amount of material confined to a rigid space. The model is further parameterized according to the physical dimensions of that space and the intrinsic swellability of SOMS. This mathematical representation is validated experimentally using a piston force sensor apparatus, which shows that the solvent-induced force and pressure exerted by SOMS increase logarithmically with the amount of material that is present. Comparison with theory implies that the commercially available varieties of SOMS CyclaSorbTM and OsorbTM have Young’s expansion moduli YC ∼ 0.8 MPa and YO ∼ 0.7 MPa, respectively, which succinctly quantifies their relative behavior. The theoretical model and experimental technique should be widely applicable to other swellable and stimuli-responsive materials.

Hydrophobic-hydrophilic forces in protein folding.

The process of protein folding is obviously driven by forces exerted on the atoms of the amino-acid chain. These forces arise from interactions with other parts of the protein itself (direct forces), as well as from interactions with the solvent (solvent-induced forces). We present a statistical-mechanical formalism that describes both these direct and indirect, solvent-induced thermodynamic forces on groups of the protein. We focus on 2 kinds of protein groups, commonly referred to as hydrophobic and hydrophilic. Analysis of this result leads to the conclusion that the forces on hydrophilic groups are in general stronger than on hydrophobic groups. This is then tested and verified by a series of molecular dynamics simulations, examining both hydrophobic alkanes of different sizes and hydrophilic moieties represented by polar-neutral hydroxyl groups. The magnitude of the force on assemblies of hydrophilic groups is dependent on their relative orientation: with 2 to 4 times larger forces on groups that are able to form one or more direct hydrogen bonds.

Water’s contribution in providing strong solvent-induced forces in protein folding

It is commonly accepted that water plays an essential role in determining both the stability of the 3D structure of protein, as well as speed of the protein folding process. How exactly water does that, is still very controversial. Until recently it was believed that various hydrophobic effects, which originate from the solvent, are the dominant factors. In the first part of this article we discuss the paradigm shift from hydrophobic (HϕO), to a hydrophilic (HϕI) based theory of protein folding. Next, we analyze the types of solvent-induced forces that are exerted on various groups on the protein. We find that the HϕI–HϕI solvent-induced forces are likely to be the strongest. These forces originate from water molecules forming hydrogen-bonded-bridges between two, or more hydrophilic groups attached to the protein. Therefore, it is argued that these forces are also the forces that force the protein to fold, in a short time, along a narrow range of pathways. This paradigm shift brings us, as close as we can hope for, to a solution to the general problem of protein folding.

Understanding the Control of Mineralization by Polyelectrolyte Additives: Simulation of Preferential Binding to Calcite Surfaces

Understanding the mechanisms that govern the crystallization of natural minerals such as calcium carbonate, calcium oxalate, or hydroxyapatite and its control by biological and synthetic polymers can help to guide the design of new biomimetic materials. In this paper, the adsorption behavior of oligomers of polystyrene sulfonate (PSS) on calcite surfaces was investigated by molecular dynamics simulations. The binding strengths of PSS oligomers to different calcite surfaces were computed via potential of mean force calculations, and the binding modes were analyzed in detail. These results could be set in relation to and serve as a molecular-level explanation of the experimentally observed PSS-stabilized exposure of (001) surfaces during calcite mineralization. The simulations show that oligomers of PSS preferentially bind to the polar calcite (001) surface, much stronger than to the nonpolar (104) surface. While sharing in common a dominant role of solvent-induced forces, the mode of binding to the two sur...

162 Dominant forces in protein folding

In the first part of this talk, I will discuss the need for a paradigm shift from hydrophobic (HφO) to a hydrophilic ((HφI) based theory of protein folding. Next, I will discuss the various types of solvent-induced forces that are exerted on various groups on the protein. It is argued, both theoretically and by simulations, that the HφI–HφI solvent-induced forces are likely to be the strongest. Therefore, it is suggested that these forces are also the forces that force the protein to fold, in a short time, along a narrow range of pathways. This paradigm shift also answers Levinthal’s question about the factors that “speed” and “guide” the folding of proteins.

Molecular Dynamics Simulation of C60 Encapsulation into Single-Walled Carbon Nanotube in Solvent Conditions

In this work, molecular dynamics simulations were performed to study the process and mechanism of fullerene (C60) encapsulation into single-walled carbon nanotube (SWNT) in three kinds of solvents: supercritical CO2 (scCO2), CS2, and water. It was demonstrated that a C60 molecule could spontaneously insert into the SWNT in scCO2, which is in good agreement with the experimental observation. However, no encapsulation of C60 was observed in CS2 and water during the simulation period. We also, for the first time, simulated the PMF (potential of mean force) profile along the C60 inserting path. The occurring free energy barrier near the entrance of the SWNT could hinder the insertion of C60, which is determined by the interaction strength between solvent and C60, as well as the solvation structures around C60. The C60–SWNT interaction provides the driving force in the filling, whereas the solvent-induced force instead offers an obstructing effect. It is revealed that both the solvent-induced free energy barri...

Three-dimensional molecular theory of solvation coupled with molecular dynamics in Amber.

We present the three-dimensional molecular theory of solvation (also known as 3D-RISM) coupled with molecular dynamics (MD) simulation by contracting solvent degrees of freedom, accelerated by extrapolating solvent-induced forces and applying them in large multi-time steps (up to 20 fs) to enable simulation of large biomolecules. The method has been implemented in the Amber molecular modeling package, and is illustrated here on alanine dipeptide and protein G.

Surface Aggregation of Urinary Proteins and Aspartic Acid-Rich Peptides on the Faces of Calcium Oxalate Monohydrate Investigated by In Situ Force Microscopy

The growth of calcium oxalate monohydrate in the presence of Tamm-Horsfall protein (THP), osteopontin, and the 27-residue synthetic peptides (DDDS)6DDD and (DDDG)6DDD (D = aspartic acid, S = serine, and G = glycine) was investigated via in situ atomic force microscopy. The results show that these four growth modulators create extensive deposits on the crystal faces. Depending on the modulator and crystal face, these deposits can occur as discrete aggregates, filamentary structures, or uniform coatings. These proteinaceous films can lead to either the inhibition of or an increase in the step speeds (with respect to the impurity-free system), depending on a range of factors that include peptide or protein concentration, supersaturation, and ionic strength. While THP and the linear peptides act, respectively, to exclusively increase and inhibit growth on the left( {bar{1}01} right) face, both exhibit dual functionality on the (010) face, inhibiting growth at low supersaturation or high modulator concentration and accelerating growth at high supersaturation or low modulator concentration. Based on analyses of growth morphologies and dependencies of step speeds on supersaturation and protein or peptide concentration, we propose a picture of growth modulation that accounts for the observations in terms of the strength of binding to the surfaces and steps and the interplay of electrostatic and solvent-induced forces at the crystal surface.

Combination of molecular dynamics method and 3D‐RISM theory for conformational sampling of large flexible molecules in solution

We have developed an algorithm for sampling the conformational space of large flexible molecules in solution, which combines the molecular dynamics (MD) method and the three-dimensional reference interaction site model (3D-RISM) theory. The solvent-induced force acting on solute atoms was evaluated as the gradient of the solvation free energy with respect to the solute-atom coordinates. To enhance the computation speed, we have applied a multiple timestep algorithm based on the RESPA (Reversible System Propagator Algorithm) to the combined MD/3D-RISM method. By virtue of the algorithm, one can choose a longer timestep for renewing the solvent-induced force compared with that of the conformational update. To illustrate the present MD/3D-RISM simulation, we applied the method to a model of acetylacetone in aqueous solution. The multiple timestep algorithm succeeded in enhancing the computation speed by 3.4 times for this model case. Acetylacetone possesses an intramolecular hydrogen-bonding capability between the hydroxyl group and the carbonyl oxygen atom, and the molecule is significantly stabilized due to this hydrogen bond, especially in gas phase. The intramolecular hydrogen bond was kept intact during almost entire course of the MD simulation in gas phase, while in the aqueous solutions the bond is disrupted in a significant number of conformations. This result qualitatively agrees with the behavior on a free energy barrier lying upon the process for rotating a torsional degree of freedom of the hydroxyl group, where it is significantly reduced in aqueous solution by a cancellation between the electrostatic interaction and the solvation free energy.

Amino Acid Side Chain Interactions in the Presence of Salts

The effects of salt on the intermolecular interactions between polar/charged amino acids are investigated through molecular dynamics simulations. The mean forces and associated potentials are calculated for NaCl salt in the 0-2 M concentration range at 298 K. It is found that the addition of salt may stabilize or destabilize the interactions, depending on the nature of the interacting molecules. The degree of (de)stabilization is quantified, and the origin of the salt-dependent modulation is discussed based upon an analysis of solvent density profiles. To gain insight into the molecular origin of the salt modulation, spatial distribution functions (sdf's) are calculated, revealing a high degree of solvent structuredness in all cases. The peaks in the sdf's are consistent with long-range hydrogen-bonding networks connecting the solute hydrophilic groups, and that contribute to their intermolecular solvent-induced forces. The restructuring of water around the solutes as they dissociate from close contact is analyzed. This analysis offers clues on how the solvent structure modulates the effective intermolecular interactions in complex solutes. This modulation results from a critical balance between bulk electrostatic forces and those exerted by (i) the water molecules in the structured region between the monomers, which is disrupted by ions that transiently enter the hydration shells, and (ii) the ions in the hydration shells in direct interactions with the solutes. The implications of these findings in protein/ligand (noncovalent) association/dissociation mechanisms are briefly discussed.

Competition of hydrophobic and Coulombic interactions between nanosized solutes.

The solvation of charged, nanometer-sized spherical solutes in water, and the effective, solvent-induced force between two such solutes are investigated by constant temperature and pressure molecular dynamics simulations of model solutes carrying various charge patterns. The results for neutral solutes agree well with earlier findings, and with predictions of simple macroscopic considerations: substantial hydrophobic attraction may be traced back to strong depletion ("drying") of the solvent between the solutes. This hydrophobic attraction is strongly reduced when the solutes are uniformly charged, and the total force becomes repulsive at sufficiently high charge; there is a significant asymmetry between anionic and cationic solute pairs, the latter experiencing a lesser hydrophobic attraction. The situation becomes more complex when the solutes carry discrete (rather than uniform) charge patterns. Due to antagonistic effects of the resulting hydrophilic and hydrophobic "patches" on the solvent molecules, water is once more significantly depleted around the solutes, and the effective interaction reverts to being mainly attractive, despite the direct electrostatic repulsion between solutes. Examination of a highly coarse-grained configurational probability density shows that the relative orientation of the two solutes is very different in explicit solvent, compared to the prediction of the crude implicit solvent representation. The present study strongly suggests that a realistic modeling of the charge distribution on the surface of globular proteins, as well as the molecular treatment of water, are essential prerequisites for any reliable study of protein aggregation.

A Breathing Sphere Model for Calculating Frequency Shifts of Polyatomic Molecules in Solution

Molecular vibrational frequency shifts are modeled by treating the vibrating solute as a breathing sphere with repulsive (hard-core) and attractive (mean field) solvent−solute interactions. The solvent-induced repulsive force exerted on the normal mode of a vibrating solute molecule is obtained using the derivative of the molecular volume with respect to the normal mode coordinate in conjunction with an analytical expression for the chemical potential of a hard sphere solute immersed in a solvent of hard spheres. The volume derivative of the vibrating solute molecule is calculated by considering the solvent molecule as an assembly of interpenetrating or fused hard spheres whose individual motions are given by normal mode coordinates. The calculation of the repulsive force is simplified by equating the normal mode volume change of the multisphere solute to a volume change of a spherical solute. The anisotropy of the solute−solvent system is used to adjust the spherical solute diameter so its chemical poten...

Protein folding simulation with solvent-induced force field: folding pathway ensemble of three-helix-bundle proteins.

We propose a coarse-grained model of proteins that take into account solvent effects and apply it for simulating folding of a three-helix-bundle protein. The energy functional form, refined from our previous work (Takada et al., J Chem Phys 1999;110:11616-11629), tries to closely imitate real physico-chemical interactions. In particular, the hydrogen bond that depends on local dielectric constant, the helix capping effect, and side-chain entropic effects are included. With use of the model, we simulate folding of the GA module of an albumin binding domain, 1prb(7-53), finding most trajectories reach at the native topology within 1 micros. In the simulation, helices 1 and 3 are mostly formed earlier accompanied by non-specific collapse, while second helix is intrinsically less stable and is formed with the help of tertiary contacts at later stage. We compute an analog of the transition state ensemble and compare it with those of other three-helix-bundle proteins. The transition state of 1prb(7-53) includes a few specific tertiary contacts of C terminus of helix 3 with the loop region between helices 1 and 2. This resembles, but is not equivalent to, an early formed region of fragment B of staphylococcal protein A, but is quite different from the folding transient structures of a de novo designed three-helix-bundle peptide.

Interaction of explicit solvent with hydrophobic/philic/charged residues of a protein: Residue character vs. conformational context

Molecular dynamics simulations of model solutes in explicit molecular water have recently elicited novel aspects of the strong nonpair additivity of the potential of mean force (PMF) and related solvent-induced forces (SIFs) and hydration. Here we present the results of the same type of work on SIFs acting on bovine pancreatic trypsin inhibitor (BPTI) at single residue/sidechain resolution. In this system, nonpair additivity and the consequent dependence of SIFs on the protein conformational context are sufficiently strong to overturn SIFs on some individual residues, relative to expectations based on their individual characters. This finding calls for a revisitation and offers a richer and diversified understanding of the role of hydrophobic/philic/charged groups in establishing the exquisite specificity of biomolecular folding and functional conformation. Its relevance is appreciated by noting that the work of a typical SIF acting on one residue, when displaced across a distance of 1 A, is the equivalent of up to a few kcal/mol, which is the range of the stability/function free energy of a protein.

Interaction of explicit solvent with hydrophobic/philic/charged residues of a protein: Residue character vs. conformational context

Molecular dynamics simulations of model solutes in explicit molecular water have recently elicited novel aspects of the strong nonpair additivity of the potential of mean force (PMF) and related solvent-induced forces (SIFs) and hydration. Here we present the results of the same type of work on SIFs acting on bovine pancreatic trypsin inhibitor (BPTI) at single residue/sidechain resolution. In this system, nonpair additivity and the consequent dependence of SIFs on the protein conformational context are sufficiently strong to overturn SIFs on some individual residues, relative to expectations based on their individual characters. This finding calls for a revisitation and offers a richer and diversified understanding of the role of hydrophobic/philic/charged groups in establishing the exquisite specificity of biomolecular folding and functional conformation. Its relevance is appreciated by noting that the work of a typical SIF acting on one residue, when displaced across a distance of 1 Å, is the equivalent of up to a few kcal/mol, which is the range of the stability/function free energy of a protein. Proteins 32:129–135, 1998. © 1998 Wiley-Liss, Inc.

Physics and biophysics of solvent induced forces: hydrophobic interactions and context-dependent hydration

Solvent induced forces (SIFs) among solutes derive from solvent structural modification due to solutes, and consequent thermodynamic drive towards minimization of related free energy costs. The role of SIFs in biomolecular conformation and function is appreciated by observing that typical SIF values fall within the 20–200 pN interval, and that proteins are stable by only a few kcal mol–1 (1 kcal mol–1 corresponds to 70 pN A). Here we study SIFs, in systems of increasing complexity, using Molecular Dynamics (MD) simulations which give time- and space-resolved details on the biologically significant scale of single protein residues and sidechains. Of particular biological relevance among our results are a strong modulability of hydrophobic SIFs by electric charges and the dependence of this modulability upon charge sign. More generally, the present results extend our understanding of the recently reported strong context-dependence of SIFs and the related potential of mean force (PMF). This context-dependence can be strong enough to propagate (by relay action) along a composite solute, and to reverse SIFs acting on a given element, relative to expectations based on its specific character (hydrophobic/ philic, charged). High specificity such as that of SIFs highlighted by the present results is of course central to biological function. Biological implications of the present results cover issues such as biomolecular functional interactions and folding (including chaperoning and pathological conformational changes), coagulation, molecular recognition, effects of phosphorylation and more.

Inferring the hydrophobic interaction from the properties of neat water.

The present paper by Hummer et al. (1), building on previous developments in scaled-particle theory (2) and information theory (3-6) and using molecular simulations to test theoretical ideas, shows how one can predict the free energies of the hydration and the interaction of solutes composed of hard spheres from an analysis of spontaneous cavity formation in neat liquid water. Hummer et al. (1) dramatically extend ideas from scaled particle theory and demonstrate a simple, highly efficient approach to computing solution thermodynamic properties from either simulation or theory. This paper is a commentary on the background and the ideas presented in the paper by Hummer et al. (1). The whole field of condensed matter chemistry has been greatly advanced by the power of computer simulation (7). It wasn't until the second half of the 1960s that the first molecular dynamics simulations were performed on simple molecular liquids (8, 9). Molecular simulations provide clear data for theories of liquids, allow direct tests of theoretical approximations, and often point the way to better simplifying approximations to be made in analytical theories. The present paper uses both theory and simulation data to find simple answers to an apparently complicated question. It is difficult to imagine this kind of simplicity without the extensive development of simulation techniques that have gone before. Water has been studied with simple force fields (10) since the 1970s, and the solubility of inert gases in water has been modeled by treating the inert gas atom as a hard sphere that excludes the center of the water molecule from a region around it (11). Studies of such systems give insight into hydrophobic hydration, the reorganization of water structure around the hard sphere, as well as the free energy of hydration of the sphere. More realistic solute-solvent interactions can then be treated by statistical perturbation (12) theory using the hard sphere reference system. Such an approach was pioneered by Pratt and Chandler (11). When two hard spheres of type A are dissolved in water, there is a solvent-induced force driving the spheres into association. This is the so-called hydrophobic interaction. The free energy change, W(R), on bringing the two spheres together from infinity to a separation R, called the potential of mean force (pmf), is related to the radial distribution function of the two spheres, gAA(R), through the relation (12, 13)

Correlated solvent-induced forces on a protein at single residue resolution: relation to conformation, stability, dynamics and function

Solvent-induced forces (SIFs) acting on single residues of BPTI (bovine pancreatic trypsin inhibitor) are obtained by molecular dynamics simulations. Our procedure takes into full account the demonstrated inherently strong non-additivity of SIFs. Cross-correlations of instantaneous SIFs on distant residue pairs endorse the view that SIFs are caused by the concurrent action of all residues on solvent configurations. This agrees with the many-body character of the potential of mean force. The elicited collective origin of SIFs helps towards a sounder understanding of their role.

Solvent-induced forces on a molecular scale: non-additivity, modulation and causal relation to hydration

This work concerns solvent-induced interactions and their most familiar subset, hydrophobic interactions. Molecular dynamics simulations allow the eliciting of: (i) the inherently strong non-additivity of solvent-induced forces (SIFs) in water, caused by the failure of Kirkwood's superposition approximation and (ii) the quantitative microscopically space-resolved relation of SIFs to configurational changes of the solvent caused by solutes. These results provide the ground for understanding quantitatively and microscopically many biologically significant findings related to hydration and SIF modulation. Also, they suggest the existence of highly specific solute-solute interactions and of otherwise forbidden pathways for chemical and biological processes in solution, including protein folding and biomolecular recognition.

Solute-solute solvent-induced interaction: molecular dynamics simulation of a mixed model system in water

Previous simulations of aqueous solutions of immobilized pairs of simple hydrophilic or hydrophobic model solutes have been extended to consider a mixed hydrophobic-hydrophilic pair. Resultsl show that the replacement of a hydrophilic group with a hydrophobic group can induce relevant changes in the solvent-induced forces acting on the solutes.