Solvation dynamics in protein environments: comparison of fluorescence upconversion measurements of coumarin 153 in monomeric hemeproteins with molecular dynamics simulations

The complexes of the fluorescence probe coumarin 153 with apomyoglobin and apoleghemoglobin are used as model systems to study solvation dynamics in proteins. Time-resolved Stokes shift experiments are compared with molecular dynamics simulations, and very good agreement is obtained. The solvation of the coumarin probe is very rapid with approximately 60% occurring within 300 fs and is attributed to interactions with water (or possibly to the protein itself). Differences in the solvation relaxation (or correlation) function C(t) for the two proteins are attributed to differences in their hemepockets.     

Implicit solvation in the self-consistent mean field theory method: sidechain modelling and prediction of folding free energies of protein mutants

The Atomic Solvation Parameter (ASP) model is one of the simplest models of solvation, in which the solvation free energy of a molecule is proportional to the solvent accessible surface area (SAS) of its atoms. However, until now this model had not been incorporated into the Self-Consistent Mean Field Theory (SCMFT) method for modelling sidechain conformations in proteins. The reason for this is that SAS is a many-body quantity and, thus, it is not obvious how to define it within the Mean Field (MF) framework, where multiple copies of each sidechain exist simultaneously. Here, we present a method for incorporating an SAS-based potential, such as the ASP model, into SCMFT. The theory on which the method is based is exact within the MF framework, that is, it does not depend on a pairwise or any other approximation of SAS. Therefore, SAS can be calculated to arbitrary accuracy. The method is computationally very efficient: only 7.6% slower on average than the method without solvation. We applied the method to the prediction of sidechain conformation, using as a test set high-quality solution structures of 11 proteins. Solvation was found to substantially improve the prediction accuracy of well-defined surface sidechains. We also investigated whether the methodology can be applied to prediction of folding free energies of protein mutants, using a set of barnase mutants. For apolar mutants, the modest correlation observed between calculated and observed folding free energies without solvation improved substantially when solvation was included, allowing the prediction of trends in the folding free energies of this type of mutants. For polar mutants, correlation was not significant even with solvation. Several other factors also responsible for the correlation were identified and analysed. From this analysis, future directions for applying and improving the present methodology are discussed.     

基于原子表面的蛋白质水合自由能预测模型

提出了一种计算蛋白质水合自由能的简化模型（SAWSA 2）.模型把蛋白质分子中的原子分为20种不同的原子类型,通过每类原子的溶剂可及化表面以及相应的溶剂化参数,就可以得到分子的水合自由能.不同原子类型的溶剂化参数通过110个蛋白质分子水合自由能拟合得到,水合自由能的标准值采用了基于求解Possion-Boltzmann方程（PB）以及分子表面计算（SA） 相结合的方法.采用得到的模型,预测了20个蛋白质分子的水合自由能,预测值的相对值和绝对值都能和PB/SA的计算值很好地吻合,大大优于两种已报导的水合自由能模型.     

基于分子表面的水化自由能预测方法

报导了一种基于加权原子表面的水合自由能预测（SAWSA）.对于不同原子类型的溶剂化参数，其参数化分为三个步骤：首先用SMARTS 语言确定不同的原子类型；然后计算每个原子的溶剂可及化表面；最后用遗传算法来优化不同原子类型的溶剂化参数.采用该模型，计算了18个蛋白质分子的水合自由能，预测结果和PB/SA的计算结果呈现了很好的线性关系（r=0.99).计算表明，SAWSA模型对有机小分子和生物大分子都具有很好的预测能力.     

ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions

A new implicit solvation model for use in Monte Carlo simulations of polypeptides is introduced. The model is termed ABSINTH for self-Assembly of Biomolecules Studied by an Implicit, Novel, and Tunable Hamiltonian. It is designed primarily for simulating conformational equilibria and oligomerization reactions of intrinsically disordered proteins in aqueous solutions. The paradigm for ABSINTH is conceptually similar to the EEF1 model of Lazaridis and Karplus (Proteins 1999, 35, 133). In ABSINTH, the transfer of a polypeptide solute from the gas phase into a continuum solvent is the sum of a direct mean field interaction (DMFI), and a term to model the screening of polar interactions. Polypeptide solutes are decomposed into a set of distinct solvation groups. The DMFI is a sum of contributions from each of the solvation groups, which are analogs of model compounds. Continuum-mediated screening of electrostatic interactions is achieved using a framework similar to the one used for the DMFI. Promising results are shown for a set of test cases. These include the calculation of NMR coupling constants for short peptides, the assessment of the thermal stability of two small proteins, reversible folding of both an alpha-helix and a beta-hairpin forming peptide, and the polymeric properties of intrinsically disordered polyglutamine peptides of varying lengths. The tests reveal that the computational expense for simulations with the ABSINTH implicit solvation model increase by a factor that is in the range of 2.5-5.0 with respect to gas-phase calculations.     

Anisotropic solvent model of the lipid bilayer. 2. Energetics of insertion of small molecules, peptides, and proteins in membranes

A new computational approach to calculating binding energies and spatial positions of small molecules, peptides, and proteins in the lipid bilayer has been developed. The method combines an anisotropic solvent representation of the lipid bilayer and universal solvation model, which predicts transfer energies of molecules from water to an arbitrary medium with defined polarity properties. The universal solvation model accounts for hydrophobic, van der Waals, hydrogen-bonding, and electrostatic solute-solvent interactions. The lipid bilayer is represented as a fluid anisotropic environment described by profiles of dielectric constant (ε), solvatochromic dipolarity parameter (π*), and hydrogen bonding acidity and basicity parameters (α and β). The polarity profiles were calculated using published distributions of quasi-molecular segments of lipids determined by neutron and X-ray scattering for DOPC bilayer and spin-labeling data that define concentration of water in the lipid acyl chain region. The model also accounts for the preferential solvation of charges and polar groups by water and includes the effect of the hydrophobic mismatch for transmembrane proteins. The method was tested on calculations of binding energies and preferential positions in membranes for small-molecules, peptides and peripheral membrane proteins that have been experimentally studied. The new theoretical approach was implemented in a new version (2.0) of our PPM program and applied for the large-scale calculations of spatial positions in membranes of more than 1000 peripheral and integral proteins. The results of calculations are deposited in the updated OPM database ( http://opm.phar.umich.edu ).     

A new quantum method for electrostatic solvation energy of protein

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.     

Entropy and enthalpy convergence of hydrophobic solvation beyond the hard-sphere limit

The experimentally well-known convergence of solvation entropies and enthalpies of different small hydrophobic solutes at universal temperatures seems to indicate that hydrophobic solvation is dominated by universal water features and not so much by solute specifics. The reported convergence of the denaturing entropy of a group of different proteins at roughly the same temperature as hydrophobic solutes was consequently argued to indicate that the denaturing entropy of proteins is dominated by the hydrophobic effect and used to estimate the hydrophobic contribution to protein stability. However, this appealing picture was subsequently questioned since the initially claimed universal convergence of denaturing entropies holds only for a small subset of proteins; for a larger data collection no convergence is seen. We report extensive simulation results for the solvation of small spherical solutes in explicit water with varying solute-water potentials. We show that convergence of solvation properties for solutes of different radii exists but that the convergence temperatures depend sensitively on solute-water potential features such as stiffness of the repulsive part and attraction strength, not so much on the attraction range. Accordingly, convergence of solvation properties is only expected for solutes of a homologous series that differ in the number of one species of subunits (which attests to the additivity of solvation properties) or solutes that are characterized by similar solute-water interaction potentials. In contrast, for peptides that arguably consist of multiple groups with widely disperse interactions with water, it means that thermodynamic convergence at a universal temperature cannot be expected, in general, in agreement with experimental results.     

Solvation thermodynamics of neutral and charged solutes using the solvation-layer interface condition continuum dielectric model

We demonstrate that the solvation-layer interface condition (SLIC) continuum dielectric model for molecular electrostatics, combined with a simple solvent-accessible-surface-area (SASA)-proportional model for nonpolar solvent effects, accurately predicts solvation entropies of neutral and charged small molecules. The SLIC/SASA model has only seven fitting parameters in total and achieves this accuracy using a training set with only 20 compounds. Despite this simplicity, solvation free energies and entropies are nearly as accurate as those predicted by the more sophisticated Langevin dipoles solvation model. Surprisingly, the model automatically reproduces the negligible contribution of electrostatics to the solvation of hydrophobic compounds. Opportunities for improvement include nonpolar solvation, anion solvation entropies, and heat capacities. More molecular realism may be needed for these quantities. To enable a future, explicit-solvent-based assessment of the SLIC/SASA implicit-solvent model, we predict solvation entropies for the Mobley test set, which are available as Supporting Information.     

Second derivatives in generalized Born theory

Generalized Born solvation models offer a popular method of including electrostatic aspects of solvation free energies within an analytical model that depends only upon atomic coordinates, charges, and dielectric radii. Here, we describe how second derivatives with respect to Cartesian coordinates can be computed in an efficient manner that can be distributed over multiple processors. This approach makes possible a variety of new methods of analysis for these implicit solvation models. We illustrate three of these methods here: the use of Newton-Raphson optimization to obtain precise minima in solution; normal mode analysis to compute solvation effects on the mechanical properties of DNA; and the calculation of configurational entropies in the MM/GBSA model. An implementation of these ideas, using the Amber generalized Born model, is available in the nucleic acid builder (NAB) code, and we present examples for proteins with up to 45,000 atoms. The code has been implemented for parallel computers using both the OpenMP and MPI environments, and good parallel scaling is seen with as many as 144 OpenMP processing threads or MPI processing tasks.     

FAMBE-pH: a fast and accurate method to compute the total solvation free energies of proteins

A fast and accurate method to compute the total solvation free energies of proteins as a function of pH is presented. The method makes use of a combination of approaches, some of which have already appeared in the literature; (i) the Poisson equation is solved with an optimized fast adaptive multigrid boundary element (FAMBE) method; (ii) the electrostatic free energies of the ionizable sites are calculated for their neutral and charged states by using a detailed model of atomic charges; (iii) a set of optimal atomic radii is used to define a precise dielectric surface interface; (iv) a multilevel adaptive tessellation of this dielectric surface interface is achieved by using multisized boundary elements; and (v) 1:1 salt effects are included. The equilibrium proton binding/release is calculated with the Tanford-Schellman integral if the proteins contain more than approximately 20-25 ionizable groups; for a smaller number of ionizable groups, the ionization partition function is calculated directly. The FAMBE method is tested as a function of pH (FAMBE-pH) with three proteins, namely, bovine pancreatic trypsin inhibitor (BPTI), hen egg white lysozyme (HEWL), and bovine pancreatic ribonuclease A (RNaseA). The results are (a) the FAMBE-pH method reproduces the observed pK a's of the ionizable groups of these proteins within an average absolute value of 0.4 p K units and a maximum error of 1.2 p K units and (b) comparison of the calculated total pH-dependent solvation free energy for BPTI, between the exact calculation of the ionization partition function and the Tanford-Schellman integral method, shows agreement within 1.2 kcal/mol. These results indicate that calculation of total solvation free energies with the FAMBE-pH method can provide an accurate prediction of protein conformational stability at a given fixed pH and, if coupled with molecular mechanics or molecular dynamics methods, can also be used for more realistic studies of protein folding, unfolding, and dynamics, as a function of pH.     

Solvation model based on order parameters and a fast sampling method for the calculation of the solvation free energies of peptides

An analytical solvation model is proposed as a function of an order parameter, which represents the local arrangement of water molecules in the first solvation shell of peptide atoms. The model is combined with a fast sampling method, rotational isomeric state Monte Carlo, to sample efficiently the torsional degrees of freedom on a peptide backbone. This order parameter solvation model is shown to reproduce without ad hoc fitting parameters the solvation free energies of single amino acids and tripeptides with slightly better accuracy than the generalized Born model but with several orders of magnitude improvement in efficiency. This method is a potential candidate for efficiently and accurately tackling some important issues in biophysical chemistry that are related to solvation, for example, protein folding, ligand binding, etc. Our results also present fundamental new insights into solvation. Specifically, the local water geometry, represented in this work by a properly defined order parameter, carries the majority, if not all, of the energetic information of solvation, including solute-solvent interactions and solvent reorganization in the presence of the solute.     

Accounting for electronic polarization in non-polarizable force fields

The issues of electronic polarizability in molecular dynamics simulations are discussed. We argue that the charges of ionized groups in proteins, and charges of ions in conventional non-polarizable force fields such as CHARMM, AMBER, GROMOS, etc should be scaled by a factor about 0.7. Our model explains why a neglect of electronic solvation energy, which typically amounts to about a half of total solvation energy, in non-polarizable simulations with un-scaled charges can produce a correct result; however, the correct solvation energy of ions does not guarantee the correctness of ion-ion pair interactions in many non-polarizable simulations. The inclusion of electronic screening for charged moieties is shown to result in significant changes in protein dynamics and can give rise to new qualitative results compared with the traditional non-polarizable force field simulations. The model also explains the striking difference between the value of water dipole μ～ 3D reported in recent ab initio and experimental studies with the value μ(eff)～ 2.3D typically used in the empirical potentials, such as TIP3P or SPC/E. It is shown that the effective dipole of water can be understood as a scaled value μ(eff) = μ/√ε(el), where ε(el) = 1.78 is the electronic (high-frequency) dielectric constant of water. This simple theoretical framework provides important insights into the nature of the effective parameters, which is crucial when the computational models of liquid water are used for simulations in different environments, such as proteins, or for interaction with solutes.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent.     

一组和AMBER力场配合的普适波恩模型参数

提出了一套和AMBER力场相匹配的普适波恩模型参数.新的参数集包含21种原子类型的初始半径和屏蔽因子.参数通过遗传算法拟合359个小分子水合自由能的实验值得到.采用新的参数，预测了44个小分子的水合自由能，预测值和实验值能很好地吻合，而且大大优于采用Jayaram参数得到的结果.此外，采用新的参数，还预测了15个蛋白质的水合自由能，预测值和PB/SA预测得到的结果能很好地吻合.     

Anchor points for the unified Brønsted acidity scale: the rCCC model for the calculation of standard Gibbs energies of proton solvation in eleven representative liquid media

The COSMO cluster-continuum (CCC) solvation model is introduced for the calculation of standard Gibbs solvation energies of protons. The solvation sphere of the proton is divided into an inner proton-solvent cluster with covalent interactions and an outer solvation sphere that interacts electrostatically with the cluster. Thus, the solvation of the proton is divided into two steps that are calculated separately: 1) The interaction of the proton with one or more solvent molecules is calculated in the gas phase with high-level quantum-chemical methods (modified G3 method). 2) The Gibbs solvation energy of the proton-solvent cluster is calculated by using the conductor-like screening model (COSMO). For every solvent, the solvation of the proton in at least two (and up to 11) proton-solvent clusters was calculated. The resulting Gibbs solvation energies of the proton were weighted by using Boltzmann statistics. The model was evaluated for the calculation of Gibbs solvation energies by using experimental data of water, MeCN, and DMSO as a reference. Allowing structural relaxation of the proton-solvent clusters and the use of structurally relaxed Gibbs solvation energies improved the accordance with experimental data especially for larger clusters. This variation is denoted as the relaxed COSMO cluster-continuum (rCCC) model, for which we estimate a 1σ error bar of 10 kJ mol(-1) . Gibbs solvation energies of protons in the following representative solvents were calculated: Water, acetonitrile, sulfur dioxide, dimethyl sulfoxide, benzene, diethyl ether, methylene chloride, 1,2-dichloroethane, sulfuric acid, fluorosulfonic acid, and hydrogen fluoride. The obtained values are absolute chemical standard potentials of the proton (pH=0 in this solvent). They are used to anchor the individual solvent specific acidity (pH) scales to our recently introduced absolute acidity scale.     

One-dimensional model for water and aqueous solutions. II. Solvation of inert solutes in water

The two one-dimensional models introduced in Part I are used to study the thermodynamics of solvation of inert solutes in water. It is shown that the anomalously large Gibbs energy of solvation of inert solutes in water, on one hand, and the large negative entropy of solvation, on the other hand, arise from different molecular sources. While the primitive model can give rise to a large positive solvation Gibbs energy, it fails to show large negative entropy and enthalpy of solvation. It is remarkable that the primitive cluster model can show both the large positive Gibbs energy and enthalpy of solvation.     

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.     

Generalized born model with a simple smoothing function

Based on recent developments in generalized Born (GB) theory that employ rapid volume integration schemes (M. S. Lee, F. R. Salabury, Jr., and C. L. Brooks III, J Chem Phys 2002, 116, 10606) we have recast the calculation of the self-electrostatic solvation energy to utilize a simple smoothing function at the dielectric boundary. The present GB model is formulated in this manner to provide consistency with the Poisson-Boltzmann (PB) theory previously developed to yield numerically stable electrostatic solvation forces based on finite-difference methods (W. Im, D. Beglov, and B. Roux, Comp Phys Commun 1998, 111, 59). Our comparisons show that the present GB model is indeed an efficient and accurate approach to reproduce corresponding PB solvation energies and forces. With only two adjustable parameters--a(0) to modulate the Coulomb field term, and a(1) to include a correction term beyond Coulomb field--the PB solvation energies are reproduced within 1% error on average for a variety of proteins. Detailed analysis shows that the PB energy can be reproduced within 2% absolute error with a confidence of about 95%. In addition, the solvent-exposed surface area of a biomolecule, as commonly used in calculations of the nonpolar solvation energy, can be calculated accurately and efficiently using the simple smoothing function and the volume integration method. Our implicit solvent GB calculations are about 4.5 times slower than the corresponding vacuum calculations. Using the simple smoothing function makes the present GB model roughly three times faster than GB models, which attempt to mimic the Lee-Richards molecular volume.