A Kirkwood-Buff derived force field for amides

Force fields optimized against experimental data for large compound families using CombiFF: Validation considering non-target properties and polyfunctional compounds

The CombiFF scheme is a workflow for the automated calibration of force-field parameters against condensed-phase experimental data considering simultaneously entire classes of organic molecules. The main steps of this scheme are: (i) selection of a molecule family; (ii) enumeration of all isomers; (iii) query for experimental data; (iv) automatic construction of the molecular topologies; (v) iterative refinement of the force-field parameters considering the entire family. In two recent articles, CombiFF was applied to the design of GROMOS-compatible united-atom force fields for the saturated acyclic haloalkanes and for saturated acyclic compounds involving eight common chemical functional groups of oxygen and nitrogen. This calibration and the subsequent initial validation involved two limitations: (i) the experimental data considered was restricted to values for the pure-liquid density ρ_liq and the vaporization enthalpy ΔH_vap of the compounds; (ii) beyond monofunctional compounds, the training set only involved homo-polyhaloalkanes (possibly mixing halogen types) in the first study, and homo-polyfunctional compounds of the considered oxygen or nitrogen functional groups (no mixing of different group types) in the second one. The goal of this article is to further test the accuracy of CombiFF-generated force fields by extending the validation to: (i) nine additional properties that were not used as optimization targets (pure-liquid thermodynamic, dielectric and transport properties, as well as solvation properties); (ii) hetero-polyfunctional molecules that were not included in the calibration and initial validation sets. The results for the nine additional properties show good agreement with experiment, except for the shear viscosity and the dielectric permittivity. There, larger discrepancies are observed, likely due to the united-atom representation adopted for the aliphatic groups and to the implicit treatment of electronic polarization effects. The results for the hetero-polyfunctional molecules also show reasonable agreement with experiment in terms of the monitored properties.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Thermodynamics of N-Isopropylacrylamide in Water: Insight from Experiments, Simulations, and Kirkwood-Buff Analysis Teamwork

The behavior of thermoresponsive polymer poly(N-isopropylacrylamide) (PNiPAM), an essential building block in the design of smart soft materials, in aqueous solutions has attracted much interest, which contrasts with our knowledge of N-isopropylacrylamide (NiPAM) monomer. Strikingly, the physicochemical properties of aqueous NiPAM are similarly rich, and their understanding is far from being complete. This stems from the lack of accurate thermodynamic data and quantitative model for atomistic simulations. In this joint study, we have probed the thermodynamic behavior of aqueous NiPAM by experimental methods, molecular dynamics (MD) simulations, and Kirkwood-Buff (KB) analysis at ambient conditions. From the partial molar volumes and simultaneously correlated osmotic coefficients, with excess partial molar enthalpies of NiPAM in water, the concentration and temperature dependence of KB integrals was determined. For the purpose of this work, we have developed and employed a novel NiPAM force field, which not only reproduces KB integrals (G_ij) and adequately captures macroscopic thermodynamic quantities but also provides more accurate structural insight than the original force fields. We revealed in the vicinity of NiPAM the competing effect of amide hydration with interaction between nonpolar regions. This microscopic picture is reflected in the experimentally observed NiPAM-NiPAM association, which is present from highly dilute conditions up to the solubility limit and is evidenced by G₂₂. From intermediate concentrations, it is accompanied by the existence of apparent dense-water regions, as indicated by positive G₁₁ values. The here-employed KB-based framework provided a mutually consistent thermodynamic and microscopic insight into the NiPAM solution and may be further extended for ion-specific effects. Moreover, our findings contribute to the understanding of thermodynamic grounds behind PNiPAM collapse transition.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Thermodynamic Analysis of n-Hexane-Ethanol Binary Mixtures Using the Kirkwood-Buff Theory

A complete thermodynamic analysis of mixtures consisting of molecules with complex chemical constitution can be rather demanding. The Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties, which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (Δ_mix G). In this work, we perform molecular dynamics simulations of n-hexane-ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions. On the basis of the recently published methodology of Galata [ Fluid Phase Equilib. 2018 , 470 , 25 - 37 ] , we first calculate the Kirkwood-Buff integrals in the isothermal-isobaric ( NpT) ensemble, identifying how system size affects their estimation. We then extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy for the n-hexane-ethanol binary mixtures we simulate. We employ two approaches for quantifying composition fluctuations: one based on counting molecular centers of mass and a second one based on counting molecular segments. Results from the two approaches are practically indistinguishable. We compare our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, and find very good agreement. In addition, we develop a simple methodology to identify the hydrogen bonds between ethanol molecules and analyze their effects on mixing properties.

Specific ion effects for polyelectrolytes in aqueous and non-aqueous media: the importance of the ion solvation behavior

We present the results of atomistic molecular dynamics simulations with regard to specific ion effects in water, methanol and N,N-dimethylacetamide (DMAc). As a reference system, we introduce rigid and rod-like models of polyanions and polycations in combination with alkali metal cations and halide anions as counterions. Pronounced specific ion effects can be observed in terms of the individual anion and cation condensation behavior. The outcomes of our simulations thus reveal significant deviations from standard electrostatic mean-field theories. A detailed investigation of the individual energy contributions shows that ion-dipole interactions play a pivotal role in rationalizing the findings. The corresponding deviations in terms of the cation and anion distribution can be brought into agreement with the donor and acceptor numbers of the solvents, which thus highlights the importance of solvent-ion interactions in addition to electrostatic attraction.

A Kirkwood-Buff derived force field for alkaline earth halide salts

The activity and function of many macromolecules in cellular environments are coupled with the binding of divalent ions such as calcium or magnesium. In principle, computer simulations can be used to understand the molecular level aspects of how many important macromolecules interact with ions. However, most of the force fields currently available often fail to accurately reproduce the properties of divalent ions in aqueous environments. Here we develop classical non-polarizable force fields for the aqueous alkaline earth metal halides (MX₂), where M = Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺ and X = Cl^-, Br^-, I^-, which can be used in bimolecular simulations and which are compatible with the Simple Point Charge/Extended (SPC/E) water model. The force field parameters are specifically developed to reproduce the experimental Kirkwood-Buff integrals for aqueous solutions and thereby the experimental activity derivatives, partial molar volumes, and excess coordination numbers. This ensures that a reasonable balance between ion-ion, ion-water, and water-water distributions is obtained. However, this requires a scaling of the cation to water oxygen interaction strength in order to accurately reproduce the integrals. The scaling factors developed for chloride salts are successfully transferable to the bromide and iodide salts. Use of these new models leads to reasonable diffusion constants and dielectric decrements. However, the performance of the models decreases with increasing salt concentration (>4m), and simulations of the pure crystals exhibited unstable behavior.

Efficient Osmotic Pressure Calculations Using Coarse-Grained Molecular Simulations

Osmotic pressure data is increasingly used to parametrize all-atom simulation Force Fields (FFs), leading to large computational cost for larger molecules. Here, we show that the osmotic pressure can be calculated precisely using transferable coarse-grained FFs obtained from short atomistic simulations using an inhomogeneously regularized coarse-graining procedure. This is demonstrated for carbohydrates, where compared to the equivalent atomistic system, an increase of the computational efficiency by a factor of ≈500 is achieved.

Reparameterization of Solute-Solute Interactions for Amino Acid-Sugar Systems Using Isopiestic Osmotic Pressure Molecular Dynamics Simulations

AMBER/GLYCAM and CHARMM are popular force fields for simulations of amino acids and sugars. Here we report excessively attractive amino acid-sugar interactions in both force fields, and corrections to nonbonded interactions that match experimental osmotic pressures of mixed aqueous solutions of diglycine and sucrose. The modified parameters also improve the ΔGtrans of diglycine from water to aqueous sucrose and, with AMBERff99SB/GLYCAM06, eliminate a caging effect seen in previous simulations of the protein ubiquitin with glucose.

Osmotic Pressure Simulations of Amino Acids and Peptides Highlight Potential Routes to Protein Force Field Parameterization

Recent molecular dynamics (MD) simulations of proteins have suggested that common force fields overestimate the strength of amino acid interactions in aqueous solution. In an attempt to determine the causes of these effects, we have measured the osmotic coefficients of a number of amino acids using the AMBER ff99SB-ILDN force field with two popular water models, and compared the results with available experimental data. With TIP4P-Ew water, interactions between aliphatic residues agree well with experiment, but interactions of the polar residues serine and threonine are found to be excessively attractive. For all tested amino acids, the osmotic coefficients are lower when the TIP3P water model is used. Additional simulations performed on charged amino acids indicate that the osmotic coefficients are strongly dependent on the parameters assigned to the salt ions, with a reparameterization of the sodium/carboxylate interaction reported by the Aksimentiev group significantly improving description of the osmotic coefficient for glutamate. For five neutral amino acids, we also demonstrate a decrease in solute-solute attractions using the recently reported TIP4P-D water model and using the KBFF force field. Finally, we show that for four two-residue peptides improved agreement with experiment can be achieved by rederiving the partial charges for each peptide.

Effective Approximation of Molecular Volume Using Atom-Centered Dielectric Functions in Generalized Born Models

The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.

Toward Improved Force-Field Accuracy through Sensitivity Analysis of Host-Guest Binding Thermodynamics

Improving the capability of atomistic computer models to predict the thermodynamics of noncovalent binding is critical for successful structure-based drug design, and the accuracy of such calculations remains limited by nonoptimal force field parameters. Ideally, one would incorporate protein-ligand affinity data into force field parametrization, but this would be inefficient and costly. We now demonstrate that sensitivity analysis can be used to efficiently tune Lennard-Jones parameters of aqueous host-guest systems for increasingly accurate calculations of binding enthalpy. These results highlight the promise of a comprehensive use of calorimetric host-guest binding data, along with existing validation data sets, to improve force field parameters for the simulation of noncovalent binding, with the ultimate goal of making protein-ligand modeling more accurate and hence speeding drug discovery.

A comparative Kirkwood-Buff study of aqueous methanol solutions modeled by the CHARMM additive and Drude polarizable force fields

A comparative study on aqueous methanol solutions modeled by the CHARMM additive and Drude polarizable force fields was carried out by employing Kirkwood-Buff analysis. It was shown that both models reproduced the experimental Kirkwood-Buff integrals and excess coordination numbers adequately well over the entire concentration range. The Drude model showed significant improvement over the additive model in solution densities, partial molar volumes, excess molar volumes, concentration-dependent diffusion constants, and dielectric constants. However, the additive model performed somewhat better than the Drude model in reproducing the activity derivative, excess molar Gibbs energy, and excess molar enthalpy of mixing. This is due to the additive achieving a better balance among solute-solute, solute-solvent, and solvent-solvent interactions, indicating the potential for improvements in the Drude polarizable alcohol model.

Kirkwood-Buff analysis of aqueous N-methylacetamide and acetamide solutions modeled by the CHARMM additive and Drude polarizable force fields

Kirkwood-Buff analysis was performed on aqueous solutions of N-methylacetamide and acetamide using the Chemistry at HARvard Molecular Mechanics additive and Drude polarizable all-atom force fields. Comparison of a range of properties with experimental results, including Kirkwood-Buff integrals, excess coordination numbers, solution densities, partial molar values, molar enthalpy of mixing, showed both models to be well behaved at higher solute concentrations with the Drude model showing systematic improvement at lower solution concentrations. However, both models showed difficulties reproducing experimental activity derivatives and the excess Gibbs energy, with the Drude model performing slightly better. At the molecular level, the improved agreement of the Drude model at low solute concentrations is due to increased structure in the solute-solute and solute-solvent interactions. The present results indicate that the explicit inclusion of electronic polarization leads to improved modeling of dilute solutions even when those properties are not included as target data during force field optimization.

Simulation study of ion pairing in concentrated aqueous salt solutions with a polarizable force field

The accuracy of empirical force fields is critical for meaningful molecular dynamics simulations of concentrated ionic solutions. Current models are typically developed on the basis of single ion properties such as the monohydrate energy in the gas phase, or the absolute hydration free energy at infinite dilution. However, the failure of these models to represent accurately the properties of concentrated solutions cannot be excluded. Here, these issues are illustrated for a polarizable potential based on classical Drude oscillators. To model accurately concentrated ionic solutions, the parameters of the potential functions are optimized to reproduce osmotic pressure data. The sodium-chloride potential of mean force in solution calculated from the empirically-adjusted model is consistent with the results from that calculated from ab initio CPMD simulations.

Theory and Simulation of Multicomponent Osmotic Systems

Most cellular processes occur in systems containing a variety of components many of which are open to material exchange. However, computer simulations of biological systems are almost exclusively performed in systems closed to material exchange. In principle, the behavior of biomolecules in open and closed systems will be different. Here, we provide a rigorous framework for the analysis of experimental and simulation data concerning open and closed multicomponent systems using the Kirkwood-Buff (KB) theory of solutions. The results are illustrated using computer simulations for various concentrations of the solutes Gly, Gly(2) and Gly(3) in both open and closed systems, and in the absence or presence of NaCl as a cosolvent. In addition, KB theory is used to help rationalize the aggregation properties of the solutes. Here one observes that the picture of solute association described by the KB integrals, which are directly related to the solution thermodynamics, and that provided by more physical clustering approaches are different. It is argued that the combination of KB theory and simulation data provides a simple and powerful tool for the analysis of complex multicomponent open and closed systems.

Towards the physical basis of how intrinsic disorder mediates protein function

Intrinsically disordered proteins (IDPs) are an important class of functional proteins that is highly prevalent in biology and has broad association with human diseases. In contrast to structured proteins, free IDPs exist as heterogeneous and dynamical conformational ensembles under physiological conditions. Many concepts have been discussed on how such intrinsic disorder may provide crucial functional advantages, particularly in cellular signaling and regulation. Establishing the physical basis of these proposed phenomena requires not only detailed characterization of the disordered conformational ensembles, but also mechanistic understanding of the roles of various ensemble properties in IDP interaction and regulation. Here, we review the experimental and computational approaches that may be integrated to address many important challenges of establishing a "structural" basis of IDP function, and discuss some of the key emerging ideas on how the conformational ensembles of IDPs may mediate function, especially in coupled binding and folding interactions.

Residual structures, conformational fluctuations, and electrostatic interactions in the synergistic folding of two intrinsically disordered proteins

To understand the interplay of residual structures and conformational fluctuations in the interaction of intrinsically disordered proteins (IDPs), we first combined implicit solvent and replica exchange sampling to calculate atomistic disordered ensembles of the nuclear co-activator binding domain (NCBD) of transcription coactivator CBP and the activation domain of the p160 steroid receptor coactivator ACTR. The calculated ensembles are in quantitative agreement with NMR-derived residue helicity and recapitulate the experimental observation that, while free ACTR largely lacks residual secondary structures, free NCBD is a molten globule with a helical content similar to that in the folded complex. Detailed conformational analysis reveals that free NCBD has an inherent ability to substantially sample all the helix configurations that have been previously observed either unbound or in complexes. Intriguingly, further high-temperature unbinding and unfolding simulations in implicit and explicit solvents emphasize the importance of conformational fluctuations in synergistic folding of NCBD with ACTR. A balance between preformed elements and conformational fluctuations appears necessary to allow NCBD to interact with different targets and fold into alternative conformations. Together with previous topology-based modeling and existing experimental data, the current simulations strongly support an “extended conformational selection” synergistic folding mechanism that involves a key intermediate state stabilized by interaction between the C-terminal helices of NCBD and ACTR. In addition, the atomistic simulations reveal the role of long-range as well as short-range electrostatic interactions in cooperating with readily fluctuating residual structures, which might enhance the encounter rate and promote efficient folding upon encounter for facile binding and folding interactions of IDPs. Thus, the current study not only provides a consistent mechanistic understanding of the NCBD/ACTR interaction, but also helps establish a multi-scale molecular modeling framework for understanding the structure, interaction, and regulation of IDPs in general.

Intrinsically disordered proteins (IDPs) are now widely recognized to play fundamental roles in biology and to be frequently associated with human diseases. Although the potential advantages of intrinsic disorder in cellular signaling and regulation have been widely discussed, the physical basis for these proposed phenomena remains sketchy at best. An integration of multi-scale molecular modeling and experimental characterization is necessary to uncover the molecular principles that govern the structure, interaction, and regulation of IDPs. In this work, we characterize the conformational properties of two IDPs involved in transcription regulation at the atomistic level and further examine the roles of these properties in their coupled binding and folding interactions. Our simulations suggest interplay among residual structures, conformational fluctuations, and electrostatic interactions that allows efficient synergistic folding of these two IDPs. In particular, we propose that electrostatic interactions might play an important role in facilitating rapid folding and binding recognition of IDPs, by enhancing the encounter rate and promoting efficient folding upon encounter.

A Kirkwood-Buff force field for the aromatic amino acids

In a continuation of our efforts to develop a united atom non-polarizable protein force field based upon the solution theory of Kirkwood and Buff i.e., the Kirkwood-Buff Force Field (KBFF) approach, we present KBFF models for the side chains of phenylalanine, tyrosine, tryptophan, and histidine, including both tautomers of neutral histidine and doubly-protonated histidine. The force fields were specifically designed to reproduce the thermodynamic properties of mixtures over the full composition range in an attempt to provide an improved description of intermolecular interactions. The models were developed by careful parameterization of the solution phase partial charges to reproduce the experimental Kirkwood-Buff integrals for mixtures of solutes representative of the amino acid sidechains in solution. The KBFF parameters and simulated thermodynamic and structural properties are presented for the following eleven binary mixtures: benzene + methanol, benzene + toluene, toluene + methanol, toluene + phenol, toluene + p-cresol, pyrrole + methanol, indole + methanol, pyridine + methanol, pyridine + water, histidine + water, and histidine hydrochloride + water. It is argued that the present approach and models provide a reasonable description of intermolecular interactions which ensures that the required balance between solute-solute, solute-solvent, and solvent-solvent distributions is obtained.

A Kirkwood-Buff Derived Force Field for Aqueous Alkali Halides

A classical nonpolarizable force field is presented for the simulation of aqueous alkali halide solutions (MX), where M = Li(+), Na(+), K(+), Rb(+), Cs(+) and X = F(-), Cl(-), Br(-), I(-), and their interactions with biomolecules. The models are specifically designed to reproduce the experimental Kirkwood-Buff integrals, and thereby the solution salt activities, as a function of salt concentration. Additionally, we demonstrate that these models reasonably reproduce other experimental properties including ion diffusion constants, dielectric decrements, and the excess heats of mixing. The parameters are developed by considering the properties of aqueous NaX and MCl solutions using a previously established model for NaCl. Transferability of the parameters to other salts is then established by the successful simulation of additional aqueous salt solutions, KI and CsBr, not originally included in the parameterization procedure.

Intrinsically disordered proteins in a physics-based world

Intrinsically disordered proteins (IDPs) are a newly recognized class of functional proteins that rely on a lack of stable structure for function. They are highly prevalent in biology, play fundamental roles, and are extensively involved in human diseases. For signaling and regulation, IDPs often fold into stable structures upon binding to specific targets. The mechanisms of these coupled binding and folding processes are of significant importance because they underlie the organization of regulatory networks that dictate various aspects of cellular decision-making. This review first discusses the challenge in detailed experimental characterization of these heterogeneous and dynamics proteins and the unique and exciting opportunity for physics-based modeling to make crucial contributions, and then summarizes key lessons from recent de novo simulations of the structure and interactions of several regulatory IDPs.

Nonadditive empirical force fields for short-chain linear alcohols: methanol to butanol. Hydration free energetics and Kirkwood-Buff analysis using charge equilibration models

Building upon the nonadditive electrostatic force field for alcohols based on the CHARMM charge equilibration (CHEQ) formalism, we introduce atom-pair specific solute-solvent Lennard-Jones (LJ) parameters for alcohol-water interaction force fields targeting improved agreement with experimental hydration free energies of a series of small molecule linear alcohols as well as ab initio water-alcohol geometries and energetics. We consider short-chain, linear alcohols from methanol to butanol as they are canonical small-molecule organic model compounds to represent the hydroxyl chemical functionality for parametrizing biomolecular force fields for proteins. We discuss molecular dynamics simulations of dilute aqueous solutions of methanol and ethanol in TIP4P-FQ water, with particular discussion of solution densities, structure defined in radial distribution functions, electrostatic properties (dipole moment distributions), hydrogen bonding patterns of water, as well as a Kirkwood-Buff (KB) integral analysis. Calculation of the latter provides an assessment of how well classical force fields parametrized to at least semiquantitatively match experimental hydration free energies capture the microscopic structures of dilute alcohol solutions; the latter translate into macroscopic thermodynamic properties through the application of KB analysis. We find that the CHEQ alcohol force fields of this work semiquantitatively match experimental KB integrals for methanol and ethanol mole fractions of 0.1 and 0.2. The force field combination qualitatively captures the concentration dependence of the alcohol-alcohol and water-water KB integrals, but due to inadequacies in the representation of the microscopic structures in such systems (which cannot be parametrized in any systematic fashion), a priori quantitative description of alcohol-water KB integrals remains elusive.

Preferential interactions between small solutes and the protein backbone: a computational analysis

To improve our understanding of the effects of small solutes on protein stability, we conducted atomistic simulations to quantitatively characterize the interactions between two broadly used small solutes, urea and glycine betaine (GB), and a triglycine peptide, which is a good model for a protein backbone. Multiple solute concentrations were analyzed, and each solute-peptide-water ternary system was studied with approximately 200-300 ns of molecular dynamics simulations with the CHARMM force field. The comparison between calculated preferential interaction coefficients (Gamma(23)) and experimentally measured values suggests that semiquantitative agreement with experiments can be obtained if care is exercised to balance interactions among the solute, protein, and water. On the other hand, qualitatively incorrect (i.e., wrong sign in Gamma(23)) results can be obtained if a solute model is constructed by directly taking parameters for chemically similar groups from an existing force field. Such sensitivity suggests that small solute thermodynamic data can be valuable in the development of accurate force field models of biomolecules. Further decomposition of Gamma(23) into group contributions leads to additional insights regarding the effects of small solutes on protein stability. For example, use of the CHARMM force field predicts that urea preferentially interacts with not only amide groups in the peptide backbone but also aliphatic groups, suggesting a role for these interactions in urea-induced protein denaturation; quantitatively, however, it is likely that the CHARMM force field overestimates the interaction between urea and aliphatic groups. The results with GB support a simple thermodynamic model that assumes additivity of preferential interaction between GB and various biomolecular surfaces.

The effect of urea on the morphology of NaCl crystals: A combined theoretical and simulation study

It has been known for over a century that the presence of cosolvents such as urea and formamide can alter the morphology of NaCl crystals grown from solution. To help understand this effect we have been developing a theoretical approach based on the Kirkwood-Buff (KB) theory of solutions, and have combined this with computer simulations of the interation of urea with different crystal faces of NaCl. In this way one can predict the effect of urea on the thermodynamic stability of different NaCl faces, with atomic level detail provided by the simulations. We observe that urea is preferentially excluded from 100 and 111 crystal faces, but is less excluded from 111 faces which present chloride ions at the surface. The results indicate that the 111 face is stabilized in urea solutions and promotes the formation of octahedral over cubic NaCl crystals. The approach is totally general and can be applied to understand a variety of interfacial properties. Furthermore, we apply KB theory to study several other issues regarding the simulation of crystal growth.

Developing Force Fields from the Microscopic Structure of Solutions

We have been developing force fields designed for the eventual simulation of peptides and proteins using the Kirkwood-Buff (KB) theory of solutions as a guide. KB theory provides exact information on the relative distributions for each species present in solution. This information can also be obtained from computer simulations. Hence, one can use KB theory to help test and modify the parameters commonly used in biomolecular studies. A series of small molecule force fields representative of the fragments found in peptides and proteins have been developed. Since this approach is guided by the KB theory, our results provide a reasonable balance in the interactions between self-association of solutes and solute solvation. Here, we present our progress to date. In addition, our investigations have provided a wealth of data concerning the properties of solution mixtures, which is also summarized. Specific examples of the properties of aromatic (benzene, phenol, p-cresol) and sulfur compounds (methanethiol, dimethylsulfide, dimethyldisulfide) and their mixtures with methanol or toluene are provided as an illustration of this kind of approach.

A Kirkwood-Buff derived force field for thiols, sulfides, and disulfides

A force field has been developed for molecular simulations of methanethiol, dimethyl sulfide, and dimethyl disulfide mixtures. The force field specifically attempts to balance the solvation and self-association of these solutes in solution mixtures with methanol. The force field is based on the Kirkwood-Buff (KB) theory of solutions and is parametrized using the KB integrals obtained from the experimental activity coefficients for the solution mixtures. The transferability of the force field was tested and confirmed by the accurate prediction of the activity coefficients for methanethiol/dimethyl sulfide solutions, which were not used in the initial parametrization of the force fields. The ideality of this latter solution is excellently reproduced. The applicability of the force field to simulations in water was corroborated with a reasonably accurate prediction for the low solubility of dimethyl sulfide in water. The aggregation of methanol molecules at low methanol mole fractions displayed by all the mixtures is reproduced and further analyzed.

Concentration fluctuations and microheterogeneity in aqueous amide mixtures

The relationship between concentration fluctuations and the microheterogeneous status of aqueous amide mixtures is addressed through the molecular dynamics study of three different amides, namely, formamide, N-methylformamide, and dimethylformamide. The computer simulations provide structural evidence that these mixtures exhibit considerable microheterogeneity, in apparent contrast to the experimentally obtained Kirkwood-Buff integrals which indicate that these mixtures should be near ideal. This contradiction is addressed by distinguishing microheterogeneity from concentration fluctuations. The former is the result of mixing H-bonding species under specific constraints due to various bonding possibilities between the molecules, while the second is related to the average relative distribution of the molecules. The relationship between these two different quantities is analyzed and illustrated in terms of the partial site-site structure factors. Small wave-number prepeaks relate to the microheterogeneity while zero wave-number value relates to the concentration fluctuations. A simple analytical statistical model for the microheterogeneity is formulated, which allows to discuss the small wave-number behavior of these structure factors in terms of the kinetics of the transient cluster formation, as observed in the computer simulations.

Atomistic details of the disordered states of KID and pKID. Implications in coupled binding and folding

Intrinsically disordered proteins (IDPs) are a newly recognized class of functional proteins for which a lack of stable tertiary fold is required for function. Because of the heterogeneous and dynamical nature, molecular modeling is necessary to provide the missing details of disordered states of IDP that are crucial for understanding their functions. In particular, generalized Born (GB) implicit solvent, combined with replica exchange (REX), might offer an optimal balance between accuracy and efficiency for modeling IDPs. We carried out extensive REX simulations in an optimized GB force field to characterize the disordered states of a regulatory IDP, KID domain of transcription factor CREB, and its phosphorylated form, pKID. The results revealed that both KID and pKID, though highly disordered on the tertiary level, are compact and mainly occupy a small number of helical substates. Interestingly, although phosphorylation of KID Ser133 leads only to marginal changes in average helicities on the ensemble level, underlying conformational substates differ significantly. In particular, pSer133 appears to restrict the accessible conformational space of the loop region and thus reduces the entropic cost of KID folding upon binding to the KIX domain of CREB-binding protein. Such an expanded role of phosphorylation in the KID:KIX recognition was not previously recognized because of a lack of substantial conformational changes on the ensemble level and inaccessibility of the structural details from experiments. The results also suggest that an implicit solvent-based modeling framework, despite various existing limitations, might be feasible for accurate atomistic simulation of small IDPs in general.

Intrinsically disordered p53 extreme C-terminus binds to S100B(betabeta) through "fly-casting"

Intrinsically disordered proteins (IDPs) are functional proteins where a lack of stable tertiary structures is required for function. Many of the IDPs involved in cellular regulation and signaling have substantial residual structures in the unbound state and fold into stable structures upon binding to their biological partners. Specific roles of these residual structures in and the underlying mechanisms of coupled binding and folding are poorly understood. Here we use physics-based atomistic simulations to compute the multidimensional free energy surfaces of coupled folding and binding of the intrinsically disordered p53 extreme C-terminus to protein S100B(betabeta). The results show that, even though the unbound p53 peptide appears to sample several alternative folded states previously observed when in complex with various targets, it binds to S100B(betabeta) through formation of nonspecific complexes, i.e., a "fly-casting"-like process. The current work, together with previous NMR and coarse-grained modeling studies of another prototypical system, suggests that the main role of the residual structures in the unbound states of regulatory IDPs might be to provide thermodynamic control of binding through modulating the entropic cost of folding and not to enhance the binding rate by acting as initial contact sites.

Molecular crowding and solvation: direct and indirect impact on protein reactions

The typical environment for biomolecules in vivo is highly crowded. Under such conditions chemical activities, rather than simply concentrations, govern the behavior of the molecules. In this chapter we discuss the underlying solvation principles that give rise to the chemical activities. We focus on simple experimentally accessible examples, macromolecular crowding, protein folding, and ligand binding under crowded conditions. We discuss effects of high concentrations of both macromolecules and small molecules in terms of the Kirkwood-Buff theory, which couples solution structure to thermodynamics.

Theory and computer simulation of solute effects on the surface tension of liquids

A complete description of the thermodynamics of planar mixed solute-solvent interfaces suitable for the analysis of computer simulation data is provided. The approach uses surface probability distributions to characterize the interface regions, coupled with radial distribution functions and the Kirkwood-Buff theory of solutions to characterize the bulk solution properties. The approach is then used to understand the relationship between changes in the surface tension, the degree of surface adsorption or depletion, and the bulk solution properties of two aqueous solute systems. The first, aqueous NaCl solutions, provides an example of a surface excluded solute. The second, aqueous methanol solutions, provides an example of a surface adsorbed solute. The numerical results support the theoretical relationships described here and provide a consistent picture of the thermodynamics of solution interfaces involving any number of components which can be applied to a wide variety of systems.

Recent applications of Kirkwood-Buff theory to biological systems

The effect of cosolvents on biomolecular equilibria has traditionally been rationalized using simple binding models. More recently, a renewed interest in the use of Kirkwood-Buff (KB) theory to analyze solution mixtures has provided new information on the effects of osmolytes and denaturants and their interactions with biomolecules. Here we review the status of KB theory as applied to biological systems. In particular, the existing models of denaturation are analyzed in terms of KB theory, and the use of KB theory to interpret computer simulation data for these systems is discussed.

Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute-solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one's ability to study protein folding and large conformational transitions at atomistic detail.