Change In Solvation Free Energy Research Articles

Solvation free energy in governing equations for DNA hybridization, protein-ligand binding, and protein folding.

This work examines the thermodynamics of model biomolecular interactions using a governing equation that accounts for the participation of bulk water in the equilibria. In the first example, the binding affinities of two DNA duplexes, one of nine and one of 10 base pairs in length, are measured and characterized by isothermal titration calorimetry (ITC) as a function of concentration. The results indicate that the change in solvation free energy that accompanies duplex formation (ΔGS) is large and unfavorable. The duplex with the larger number of G:C pairings yields the largest change in solvation free energy, ΔGS = +460 kcal·mol-1per base pair at 25 °C. A van't Hoff analysis of the data is complicated by the varying degree of intramolecular base stacking within each DNA strand as a function of temperature. A modeling study reveals how the solvation free energy alters the output of a typical ITC experiment and leads to a good, though misleading, fit to the classical equilibrium equation. The same thermodynamic framework is applied to a model protein-ligand interaction, the binding of ribonuclease A with the nucleotide inhibitor 3'-UMP, and to a conformational equilibrium, the change in tertiary structure of α-lactalbumin in molar guanidinium chloride solutions. The ribonuclease study yields a value of ΔGS = +160 kcal·mol-1, whereas the folding equilibrium yields ΔGS ≈ 0, an apparent characteristic of hydrophobic interactions. These examples provide insight on the role of solvation energy in binding equilibria and suggest a pivot in the fundamental application of thermodynamics to solution chemistry.

Real-time measure of solvation free energy changes upon liquid-liquid phase separation of α-elastin

Biological condensates are known to retain a large fraction of water to remain in a liquid and reversible state. Local solvation contributions from water hydrating hydrophilic and hydrophobic protein surfaces were proposed to play a prominent role for the formation of condensates through liquid-liquid phase separation (LLPS). However, although the total free energy is accessible by calorimetry, the partial solvent contributions to the free energy changes upon LLPS remained experimentally inaccessible so far. Here, we show that the recently developed THz calorimetry approach allows to quantify local hydration enthalpy and entropy changes upon LLPS of α-elastin in real time, directly from experimental THz spectroscopy data. We find that hydrophobic solvation dominates the entropic solvation term, whereas hydrophilic solvation mainly contributes to the enthalpy. Both terms are in the order of hundreds of kJ/mol, which is more than one order of magnitude larger than the total free energy changes at play during LLPS. However, since we show that entropy/enthalpy mostly compensates, a small entropy/enthalpy imbalance is sufficient to tune LLPS. Theoretically, a balance was proposed before. Here we present experimental evidence based on our spectroscopic approach. We finally show that LLPS can be steered by inducing small changes of solvation entropy/enthalpy compensation via concentration or temperature in α-elastin.

Atomic-level thermodynamics analysis of the binding free energy of SARS-CoV-2 neutralizing antibodies.

Understanding how protein-protein binding affinity is determined from molecular interactions at the interface is essential in developing protein therapeutics such as antibodies, but this has not yet been fully achieved. Among the major difficulties are the facts that it is generally difficult to decompose thermodynamic quantities into contributions from individual molecular interactions and that the solvent effect-dehydration penalty-must also be taken into consideration for every contact formation at the binding interface. Here, we present an atomic-level thermodynamics analysis that overcomes these difficulties and illustrate its utility through application to SARS-CoV-2 neutralizing antibodies. Our analysis is based on the direct interaction energy computed from simulated antibody-protein complex structures and on the decomposition of solvation free energy change upon complex formation. We find that the formation of a single contact such as a hydrogen bond at the interface barely contributes to binding free energy due to the dehydration penalty. On the other hand, the simultaneous formation of multiple contacts between two interface residues favorably contributes to binding affinity. This is because the dehydration penalty is significantly alleviated: the total penalty for multiple contacts is smaller than a sum of what would be expected for individual dehydrations of those contacts. Our results thus provide a new perspective for designing protein therapeutics of improved binding affinity.

Model binding experiments with cucurbit[7]uril and p-sulfonatocalix[4]arene support use of explicit solvation term in governing equation for binding equilibria

ABSTRACT The thermodynamics of model host–guest-binding reactions is examined in depth using isothermal titration calorimetry. In conflict with classical thermodynamics, the results indicate that the equilibrium-binding quotient, K, is not a constant for all pairings. This outcome is predicted by an equation for binding equilibria that includes an explicit term for the change in solvation free energy that accompanies the formation of a binary complex. Application of this framework to the experimentally observed concentration dependence of K allows one to obtain the energetic contribution of the solvent, a linked equilibrium denoted here as ΔG H2O. The estimated values of ΔG H2O are large and unfavourable for the binding of selected guest molecules to two hosts, cucurbit[7]uril and p-sulfonatocalix[4]arene. Intriguingly, the estimated values of ΔG H2O are near zero for the binding of two hydrophobic guest molecules to β-cyclodextrin, leading to a thought-provoking discussion on the driving force behind the hydrophobic effect.

Local environment effects on charged mutations for developing aggregation-resistant monoclonal antibodies

Protein aggregation is a major concern in biotherapeutic applications of monoclonal antibodies. Introducing charged mutations is among the promising strategies to improve aggregation resistance. However, the impact of such mutations on solubilizing activity depends largely on the inserting location, whose mechanism is still not well understood. Here, we address this issue from a solvation viewpoint, and this is done by analyzing how the change in solvation free energy upon charged mutation is composed of individual contributions from constituent residues. To this end, we perform molecular dynamics simulations for a number of antibody mutants and carry out the residue-wise decomposition of the solvation free energy. We find that, in addition to the previously identified “global” principle emphasizing the key role played by the protein total net charge, a local net charge within sim15 Å from the mutation site exerts significant effects. For example, when the net charge of an antibody is positive, the global principle states that introducing a positively charged mutation will lead to more favorable solvation. Our finding further adds that an even more optimal mutation can be done at the site around which more positively charged residues and fewer negatively charged residues are present. Such a “local” design principle accounts for the location dependence of charged mutations, and will be useful in producing aggregation-resistant antibodies.

Stressing crystals with solutes: Effects of added solutes on crystalline caffeine and their relevance to determining transfer free energies

In calculating transfer free energies of solvated substances, the coexisting crystal state is often taken as the reference. Furthermore, the free energy of this reference state is often assumed to remain constant upon changes made in solution. Yet little is known about the way added cosolutes impact the thermodynamic stability of the out-of-solution crystal phase. To provide insight into the changes in the activity of the coexisting solid state, we used caffeine, a well-studied hydrophobic compound that forms a hydrated crystal in saturated aqueous solutions. By using X-ray powder diffraction, we found that cosolutes, such as trehalose, sucrose, sodium sulfate, and polyethylene glycol (PEG) alter the unit cell volume of crystalline caffeine, in a concentration dependent manner. The dehydration of solid caffeine translates into an overall increase in its free energy, which can be directly calculated as the reversible ΠV work required to compress the crystal. We determined that trehalose, sucrose, and sodium sulfate increase the free energy of the solid, while PEG decreases it. For 2 mol/kg trehalose, this change in free energy corresponds to 17 % of the total change in solvation free energy of monomeric caffeine. Although our results indicate that cosolutes modify the free energy of the solid less than that of the solvated state, this effect is non negligible and measurable, suggesting that it should generally be taken into account as a contribution to changes in solubility, particularly whenever the solid phase is hydrated.

Accurate Estimation of pKb Values for Amino Groups from Surface Electrostatic Potential (VS,min) Calculations: The Isoelectric Points of Amino Acids as a Case Study.

Theoretical calculation of equilibrium dissociation constants is a very computationally demanding and time-consuming process since it requires an extremely accurate computation of the solvation free energy changes for each of the species involved. By correlating the minimum surface electrostatic potential (VS,min) on the nitrogen atom of several aliphatic amino groups-calculated at the density functional theory (DFT) ωB97X-D/cc-pVDZ level of theory-we obtained regression models for each kind of substitution pattern from which we interpolate their corresponding pKb values with remarkable accuracy: primary R2 = 0.9519; secondary R2 = 0.9112; and tertiary R2 = 0.8172 (N = 20 for each family). These models were validated with tests sets (N = 5) with mean absolute error (MAE) values of 0.1213 (primary), 0.4407 (secondary), and 0.3057 (tertiary). Combining this ansatz with another previously reported by our group to estimate pKa values [Caballero-García, G.; et al. Molecules 2019, 24(1), 79] we are able to reproduce the isoelectric points of 13 amino acids with no titrable side chains with MAE = 0.4636 pI units.

Investigating the effect of mutation on the thermo stability of GB1 protein

The thermo stability of wild-type and mutants of the B1 domain of Protein G (GB1 protein) have been studied using molecular dynamics simulation and free energy perturbation simulation. This research is aimed to examine what residue or what interaction that has a major role in the thermo stability of GB1 protein thermo stability by using the point mutation method. Based on the analysis, the unfolding of wild-type protein occurred in 500 K simulation at 704 ps. The mutations were chosen based on the changes in some analysis parameters and the calculated net solvation free energy change. It was found that a simple replacement of a positively charged residue in the β-sheet (K4S) decreases the stability of GB1 protein (unfolding at 452 ps), while the replacement of a negatively charged residue in the α-helix (E27G) increases the stability (unfolding at 846 ps). It was also found that the K4A mutation will break the α-helix and all β-sheet into the coil and turn. All those results suggest that the non-bonded interaction has the major role in the thermo stability of GB1 protein with the β-sheets were identified as the most important structure in the thermo stability of GB1 protein..

Solvation energies of the proton in ammonia explicitly versus temperature.

We provide in this work, the absolute solvation enthalpies and the absolute solvation free energies of the proton in ammonia explicitly versus temperature. As a result, the absolute solvation free energy of the proton remains quite constant for temperatures below 200 K. Above this temperature, it increases as a linear function of the temperature: ΔGam(H+,T)=-1265.832+0.210 T. This indicates that a temperature change of 100 K would induce a solvation free energy change of 21 kJ mol-1. Thus, ignoring this free energy change would lead to a bad description of hydrogen bonds and an unacceptable error higher than 3.7 pKa units. However, the absolute solvation enthalpy of the proton in ammonia is not significantly affected by a temperature change and, the room temperature value is -1217 kJ mol-1. The change of the solvation enthalpy is only within 3 kJ mol-1 for a temperature change up to 200 K.

Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions.

Implicit solvation calculations based on a Stern-layer corrected size-modified Poisson-Boltzmann (SMPB) model are an effective approach to capture electrolytic effects in first-principles electronic structure calculations. For a given salt solution, they require a range of ion-specific parameters, which describe the size of the dissolved ions as well as thickness and shape of the Stern layer. Out of this defined parameter space, we show that the Stern layer thickness expressed in terms of the solute's electron density and the resulting ionic cavity volume completely determine ion effects on the stability of neutral solutes. Using the efficient SMPB functionality of the full-potential density-functional theory package FHI-aims, we derive optimized such Stern layer parameters for neutral solutes in various aqueous monovalent electrolytes. The parametrization protocol relies on fitting to reference Setschenow coefficients that describe solvation free energy changes with ionic strength at low to medium concentrations. The availability of such data for NaCl solutions yields a highly predictive SMPB model that allows to recover the measured Setschenow coefficients with an accuracy that is comparable to prevalent quantitative regression models. Correspondingly derived SMPB parameters for other salts suffer from a much scarcer experimental data base but lead to Stern layer properties that follow a physically reasonable trend with ionic hydration numbers.

Virtual substitution scan via single-step free energy perturbation.

With the rapid expansion of our computing power, molecular dynamics (MD) simulations ranging from hundreds of nanoseconds to microseconds or even milliseconds have become increasingly common. The majority of these long trajectories are obtained from plain (vanilla) MD simulations, where no enhanced sampling or free energy calculation method is employed. To promote the "recycling" of these trajectories, we developed the Virtual Substitution Scan (VSS) toolkit as a plugin of the open-source visualization and analysis software VMD. Based on the single-step free energy perturbation (sFEP) method, VSS enables the user to post-process a vanilla MD trajectory for a fast free energy scan of substituting aryl hydrogens by small functional groups. Dihedrals of the functional groups are sampled explicitly in VSS, which improves the performance of the calculation and is found particularly important for certain groups. As a proof-of-concept demonstration, we employ VSS to compute the solvation free energy change upon substituting the hydrogen of a benzene molecule by 12 small functional groups frequently considered in lead optimization. Additionally, VSS is used to compute the relative binding free energy of four selected ligands of the T4 lysozyme. Overall, the computational cost of VSS is only a fraction of the corresponding multi-step FEP (mFEP) calculation, while its results agree reasonably well with those of mFEP, indicating that VSS offers a promising tool for rapid free energy scan of small functional group substitutions. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 324-336, 2016.

Prediction of Solvation Free Energies with Thermodynamic Integration Using the General Amber Force Field.

Computer-aided drug design (CADD) techniques can be very effective in reducing costs and speeding up drug discovery. The determination of binding and solvation free energies is pivotal for this process and is, therefore, the subject of many studies. In this work, the solvation free energy change (ΔΔGsolv) for a total of 92 transformations in small molecules was predicted using Thermodynamic Integration (TI). It was our aim to compare experimental and calculated solvation free energies for typical and prime additions considered in drug optimizations, analyzing trends, and optimizing a TI protocol. The results showed a good agreement between experimental and predicted values, with an overestimation of the predicted values for CH3, halogens, and NH2, as well as an underestimation for CONH2, but all fall within ±1 kcal/mol. NO2 addition showed a larger and systematic underestimation of the predicted ΔΔGsolv, indicating the need for special attention in these cases. For small molecules, if no experimental data is available, using TI as a theoretical strategy thus appears to be a suitable choice in CADD. It provides a good compromise between time and accuracy.

Helmholtz Energy Change between Neutral and Zwitterionic Forms of Glycine in Aqueous Solution Using Ab Initio Expanded QM/MM-MC with QM Solvent

Abstract We present an extended methodology of the quantum mechanical/molecular mechanical framework with Metropolis Monte Carlo method (QM/MM-MC), in which close surrounding solvent molecules are included in QM subsystem to evaluate quantitatively the solvation free energy change. The neutral (N) and zwitterionic (Z) structures of glycine in aqueous solution were optimized in the combination procedure of simulated annealing with MC at MM level and QM/MM-vib geometry optimization. Helmholtz energy change between N and Z forms of glycine in aqueous solution was calculated stepwise with expanded QM/MM-MC method, and the computational result was in good agreement with the experimental value.

Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson-Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane-alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM-based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane-alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane-alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug-binding in computer-aided drug design.

The Influence of Water on the Solubility of Carbon Dioxide in Imidazolium Based Ionic Liquids

Abstract We explore the influence of small amounts of water dissolved in 1-alkyl-3-methyl-imidazolium based ionic liquids (ILs) on the solubility of CO2 as a function of water content and temperature. We observe a decreasing solubility of CO2 as function of increasing water content in almost quantitative agreement with recent experimental data by Husson et al. [Fluid Phase Eq. 294, 98 (2010)]. In addition, a purely repulsive variant of CO2 is employed as a test-case to elucidate the solvation behavior of small sized molecules in absence of favorable interactions. We find that the decreasing solubility is about one third due to the increasing solvent number density, and about two thirds due to the change in solvation free energy. In addition, we observe that the computed solvation free energy of a purely repulsive test-molecule increases even more strongly with increasing water content, indicating that small favorable “interaction sites” within the liquid, well suited for accommodating a CO2 molecule, become increasingly rare due to the competition with the water molecules.

Combined QM/MM (ONIOM) and QSAR Approach to the Study of Complex Formation of Matrix Metalloproteinase-9 with a Series of Biphenylsulfonamides–LERE-QSAR Analysis (V)

We previously proposed a novel QSAR (quantitative structure-activity relationship) procedure called LERE (linear expression by representative energy terms)-QSAR involving molecular calculations such as an ab initio fragment molecular orbital ones. In the present work, we applied LERE-QSAR to complex formation of matrix metalloproteinase-9 (MMP-9) with a series of substituted biphenylsulfonamides. The results shows that the overall free-energy change accompanying complex formation is due to predominantly the contribution from the electrostatic interaction with the zinc atom in the active site of MMP-9. Carbonic anhydrase (CA) belongs to the zinc-containing protease family. In contrast to the current case of MMP-9, the overall free-energy change during complex formation of CA with a series of benzenesulfonamides is due to the contributions from the solvation and dissociation free-energy changes, as previously reported. Comparison of the two sets of results indicates quantitative differences in the relative contributions of free-energy components to the overall free-energy change between the two data sets, corresponding with those in the respective classical QSAR equations. The LERE-QSAR procedure was demonstrated to quantitatively reveal differences in the binding mechanisms between the two cases involving similar but different zinc-containing proteins at the electronic and atomic levels.

Stabilization by Urea during Thermal Unfolding-Mediated Aggregation of Recombinant Human Interleukin-1 Receptor (Type II): Does Solvation Entropy Play a Role?

The protein denaturing properties of urea are well-known and still the subject of debate. It has been noted that in some cases where urea concentrations are relatively low stabilization is afforded against aggregation. An explanation for this unusual effect has seemingly remained elusive. Evidence is offered to propose urea stabilization is related to its influence on the solvation property of the protein molecules when in contact with an unfolded hydrophobic surface that tends to increase the entropy of the local aqueous solvent. This property of urea is expected to lower the entropic driving force of unfolded-mediated aggregation despite the increase in enthalpy. The data presented from toluene transfer experiments into 2 M urea + 0.1 M sodium phosphate solutions showed that the solvation free energy change was negative up to ∼75 °C. The associated ΔΔH was positive, leading to the conclusion that entropy drives the solvation process within the temperature domain from ∼20° to 75 °C. Using thermodynamic parameters from the toluene solvation experiments, it was possible to accurately determine the T(m) shift of recombinant human interleukin-1 receptor type II (rhuIL-1R(II)). Heating experiments above the apparent T(m) in the same urea/phosphate solution support the thesis that urea inhibits the entropy-driven aggregation process of rhuIL-1R(II), adding yet another molecule to the list of low urea concentration stabilized molecules.

Hydration patterns and salting effects in sodium chloride solution

The salting effects of 2M sodium chloride electrolyte are studied based on a series of model solutes with properties ranging from hydrophobic to hydrophilic. Generally, hydrophobic solutes will be salted out and hydrophilic solutes will be salted in by NaCl solution. The solvation free energy changes are highly correlated with Kirkwood-Buff integrals. The underlying mechanism resorts to the preferential binding of ions and water to solutes. Our results demonstrate that the salting effect not only depends on the salt's position in Hofmeister series, but also on the solutes' specifics. Taking the hydration free energies of solutes and ions as independent variables, a schematic diagram of salting effects is suggested. The resolved multifaceted salting effects rely on the sensitive balance of the tripartite interaction among solutes, ions, and water.

Accurate Predictions of Nonpolar Solvation Free Energies Require Explicit Consideration of Binding-Site Hydration

Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aβ42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aβ42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.