分子亲脂-亲水性的量子化学描述(Ⅰ)——分子的亲脂和亲水表面

给出基于分子结构的“启发式”亲脂-亲水势HMLP(Heuristic molecular lipophilicity-hydrophilicity potential)的理论分析和有说服力的算例.用量子化学计算其分子表面的静电势V(r)的分布,通过与周围原子表面静电势的比较,构造表达分子静电势的极性和大小的函数L(r).亲脂势L(r)保留了静电势V(r)描述分子静电作用的能力,并把应用范围扩展到疏水性的描述.HMLP不使用原子的经验参数,但在L(r)的构造中使用了经验的函数形式.经参数化和指标化后,HMLP有望用于蛋白质结构与功能的研究和药物分子配体与生物大分子受体结合自由能的估算.     

Heuristic molecular lipophilicity potential (HMLP): lipophilicity and hydrophilicity of amino acid side chains

Heuristic molecular lipophilicity potential (HMLP) is applied in the study of lipophilicity and hydrophilicity of 20 natural amino acids side chains. The HMLP parameters, surface area S(i), lipophilic indices L(i), and hydrophilic indices H(i) of amino acid side chains are derived from lipophilicity potential L(r). The parameters are correlated with the experimental data of phase-transferring free energies of vapor-to-water, vapor-to-cyclohexane, vapor-to-octanol, cyclohexane-to-water, octanol-to-water, and cyclohexane-to-octanol through a linear free energy equation DeltaG(0)(tr,i) = b(0) + b(1)S(i) (+) + b(2)S(i) (-) + b(3)L(i) + b(4)H(i). For all above six phase-transfer free energies, the HMLP parameters of 20 amino acid side chains give good calculation results using linear free energy equation. HMLP is an ab initio quantum chemical approach and a structure-based technique. Except for atomic van der Waals radii, there are no other empirical parameters used. The HMLP has clear physical and chemical meaning and provides useful lipophilic and hydrophilic parameters for the studies of proteins and peptides.     

Heuristic lipophilicity potential for computer-aided rational drug design

In this contribution we suggest a heuristic molecular lipophilicitypotential (HMLP), which is a structure-based technique requiring noempirical indices of atomic lipophilicity. The input data used in thisapproach are molecular geometries and molecular surfaces. The HMLP is amodified electrostatic potential, combined with the averaged influences fromthe molecular environment. Quantum mechanics is used to calculate theelectron density function (r) and the electrostatic potential V(r), andfrom this information a lipophilicity potential L(r) is generated. The HMLPis a unified lipophilicity and hydrophilicity potential. The interactions ofdipole and multipole moments, hydrogen bonds, and charged atoms in amolecule are included in the hydrophilic interactions in this model. TheHMLP is used to study hydrogen bonds and water–octanol partitioncoefficients in several examples. The calculated results show that the HMLPgives qualitatively and quantitatively correct, as well as chemicallyreasonable, results in cases where comparisons are available. Thesecomparisons indicate that the HMLP has advantages over the empiricallipophilicity potential in many aspects. The HMLP is a three-dimensional andeasily visualizable representation of molecular lipophilicity, suggested asa potential tool in computer-aided three-dimensional drug design.     

Heuristic molecular lipophilicity potential (HMLP): a 2D-QSAR study to LADH of molecular family pyrazole and derivatives

The quantum chemical and structure-based technique heuristic molecular lipophilicity potential (HMLP) is used in the liver alcohol dehydrogenase (LADH) study of molecular family pyrazole and derivatives. The molecular lipophilic index LM, molecular hydrophilic index HM, lipophilic indices lss, and hydrophilic indices hss of the substitutes (fragments), and atomic lipophilicity indices las are constructed and used in QSAR study. The HMLP indices are correlated with bioactivities of 18 pyrazole derivatives according to the 2D QSAR procedure. The multiple linear regression equation between the bioactivities of pyrazole derivatives and HMLP indices are built using partial least square (PLS) with the optimal statistical quantity (r=0.987, s=0.479, F=47.19). The inhibition mechanism of LADH of the pyrazole derivatives is explained according to the physical meaning of HMLP indices. During the HMLP calculations for the 2D QSAR, the only input parameters are the atomic van der Waals radius without the need to resort to any empirical parameters. Accordingly, HMLP can provide a rigorous theoretical approach with a crystal clear physical meaning for the 2D QSAR.     

分子亲脂-亲水性的量子化学描述II. 氨基酸侧链的亲水指标和亲脂指标

在启发式亲脂势HMLP(heuristicmolecularlipophilicitypotential)的基础上提出了分子、分子片段和原子的亲水指标和亲脂指标.计算出了20个天然氨基酸侧链的亲水、亲脂指标和亲水、亲脂表面积,并用线性自由能函数表达氨基酸侧链的溶剂化自由能,?Gsol,=b0 b1Li b2Hi b3Si b4Si.应用线性自由能函数和氨基酸侧链的亲水和亲脂! -i指标,计算了20个氨基酸残基的3种相转移自由能(蒸气-水、蒸气-正辛醇、正辛醇-水)和正辛醇-水分配系数logPow,取得了与实验值高度一致的良好效果.HMLP的亲水和亲脂指标是HMLP的指标化,扩展了这一方法的使用范围.氨基酸侧链的亲水、亲脂指标和线性自由能函数有望用于生物大分子受体与配体的结合自由能的估算、蛋白质的结构与功能、蛋白-蛋白相互作用和识别的研究.     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.     

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self-consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field-dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.     

Nitrile and thiocyanate IR probes: molecular dynamics simulation studies

Nitrile- and thiocyanate-derivatized amino acids have been found to be useful IR probes for investigating their local electrostatic environments in proteins. To shed light on the CN stretch frequency shift and spectral lineshape change induced by interactions with hydrogen-bonding solvent molecules, we carried out both classical and quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations for MeCN and MeSCN in water. These QM/MM and conventional force field MD simulation results were found to be inconsistent with the experimental results as well as with the high-level ab initio calculation results of MeCN-water and MeSCN-water potential energies. Thus, a new set of atomic partial charges of MeCN and MeSCN is obtained. By using the MD simulation trajectories and the electrostatic potential model recently developed, the CN and SCN stretching mode frequency trajectories were obtained and used to simulate the IR spectra. The C[Triple Bond]N frequency blueshifts of MeCN and MeSCN in water are estimated to be 9.0 and 1.9 cm(-1), respectively, in comparison with those of gas phase values. These values are found to be in reasonable agreement with the experimentally measured IR spectra of MeCN, MeSCN, beta-cyano-L-alanine, and cyanylated cysteine in water and other polar solvents.     

Differential geometry based solvation model. III. Quantum formulation

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model.     

Density functional theory for efficient ab initio molecular dynamics simulations in solution

We present a density functional for first-principles molecular dynamics simulations that includes the electrostatic effects of a continuous dielectric medium. It allows for numerical simulations of molecules in solution in a model polar solvent. We propose a smooth dielectric model function to model solvation into water and demonstrate its good numerical properties for total energy calculations and constant energy molecular dynamics.     

Nonuniform charge scaling (NUCS): a practical approximation of solvent electrostatic screening in proteins

In molecular mechanics calculations, electrostatic interactions between chemical groups are usually represented by a Coulomb potential between the partial atomic charges of the groups. In aqueous solution these interactions are modified by the polarizable solvent. Although the electrostatic effects of the polarized solvent on the protein are well described by the Poisson--Boltzmann equation, its numerical solution is computationally expensive for large molecules such as proteins. The procedure of nonuniform charge scaling (NUCS) is a pragmatic approach to implicit solvation that approximates the solvent screening effect by individually scaling the partial charges on the explicit atoms of the macromolecule so as to reproduce electrostatic interaction energies obtained from an initial Poisson--Boltzmann analysis. Once the screening factors have been determined for a protein the scaled charges can be easily used in any molecular mechanics program that implements a Coulomb term. The approach is particularly suitable for minimization-based simulations, such as normal mode analysis, certain conformational reaction path or ligand binding techniques for which bulk solvent cannot be included explicitly, and for combined quantum mechanical/molecular mechanical calculations when the interface to more elaborate continuum solvent models is lacking. The method is illustrated using reaction path calculations of the Tyr 35 ring flip in the bovine pancreatic trypsin inhibitor.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

Polar solvation dynamics of lysozyme from molecular dynamics studies

The solvation dynamics of a protein are believed to be sensitive to its secondary structures. We have explored such sensitivity in this article by performing room temperature molecular dynamics simulation of an aqueous solution of lysozyme. Nonuniform long-time relaxation patterns of the solvation time correlation function for different segments of the protein have been observed. It is found that relatively slower long-time solvation components of the α-helices and β-sheets of the protein are correlated with lower exposure of their polar probe residues to bulk solvent and hence stronger interactions with the dynamically restricted surface water molecules. These findings can be verified by appropriate experimental studies.     

分子亲脂-亲水性的量子化学描述II. 氨基酸侧链的亲水指标和亲脂指标

在启发式亲脂势HMLP (heuristic molecular lipophilicity potential)的基础上提出了分子、分子片段和原子的亲水指标和亲脂指标. 计算出了20个天然氨基酸侧链的亲水、亲脂指标和亲水、亲脂表面积, 并用线性自由能函数表达氨基酸侧链的溶剂化自由能, ΔG_sol,i^θ＝b₀＋b₁L_i＋b₂H_i＋b₃S_i^＋＋b₄S_i^－. . 应用线性自由能函数和氨基酸侧链的亲水和亲脂指标, 计算了20个氨基酸残基的3种相转移自由能(蒸气-水、蒸气-正辛醇、正辛醇-水)和正辛醇-水分配系数logP_ow, 取得了与实验值高度一致的良好效果. HMLP的亲水和亲脂指标是HMLP的指标化, 扩展了这一方法的使用范围. 氨基酸侧链的亲水、亲脂指标和线性自由能函数有望用于生物大分子受体与配体的结合自由能的估算、蛋白质的结构与功能、蛋白-蛋白相互作用和识别的研究.     

Pattern recognition strategies for molecular surfaces. I. Pattern generation using fuzzy set theory

A new method for the characterization of molecules based on the model approach of molecular surfaces is presented. We use the topographical properties of the surface as well as the electrostatic potential, the local lipophilicity/hydrophilicity, and the hydrogen bond density on the surface for characterization. The definition and the calculation method for these properties are reviewed shortly. The surface is segmented into overlapping patches with similar molecular properties. These patches can be used to represent the characteristic local features of the molecule in a way that is beyond the atomistic resolution but can nevertheless be applied for the analysis of partial similarities of different molecules as well as for the identification of molecular complementarity in a very general sense. The patch representation can be used for different applications, which will be demonstrated in subsequent articles.     

O(NlogN) continuous electrostatics method for fast calculation of solvation energies of biomolecules

We report the development of a new, fast, surface-based method for numerical calculations of the solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size, both in time and memory requirements, produces explicit values for the reaction field potential and stable values of the polar energy within only a few percent error margin practically for any molecular configurations. The method works well both for large and small molecules and thus gives stable energy differences for quantities such as the polar energy contributions to molecular complex formation energies.     

Computation of methodology-independent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids

The computation of ionic solvation free energies from atomistic simulations is a surprisingly difficult problem that has found no satisfactory solution for more than 15 years. The reason is that the charging free energies evaluated from such simulations are affected by very large errors. One of these is related to the choice of a specific convention for summing up the contributions of solvent charges to the electrostatic potential in the ionic cavity, namely, on the basis of point charges within entire solvent molecules (M scheme) or on the basis of individual point charges (P scheme). The use of an inappropriate convention may lead to a charge-independent offset in the calculated potential, which depends on the details of the summation scheme, on the quadrupole-moment trace of the solvent molecule, and on the approximate form used to represent electrostatic interactions in the system. However, whether the M or P scheme (if any) represents the appropriate convention is still a matter of on-going debate. The goal of the present article is to settle this long-standing controversy by carefully analyzing (both analytically and numerically) the properties of the electrostatic potential in molecular liquids (and inside cavities within them). Restricting the discussion to real liquids of "spherical" solvent molecules (represented by a classical solvent model with a single van der Waals interaction site), it is concluded that (i) for Coulombic (or straight-cutoff truncated) electrostatic interactions, the M scheme is the appropriate way of calculating the electrostatic potential; (ii) for non-Coulombic interactions deriving from a continuously differentiable function, both M and P schemes generally deliver an incorrect result (for which an analytical correction must be applied); and (iii) finite-temperature effects, including intermolecular orientation correlations and a preferential orientational structure in the neighborhood of a liquid-vacuum interface, must be taken into account. Applications of these results to the computation methodology-independent ionic solvation free energies from molecular simulations will be the scope of a forthcoming article.     

基于分子动力学模拟和连续介质模型的自由能计算方法*

近些年,基于分子动力学模拟和连续介质模型的自由能计算方法受到了越来越多的关注,其中MM/PBSA就是最具代表性的方法.在MM/PBSA中,体系的焓变采用分子力学(MM)的方法计算得到;溶剂效应中极性部分对自由能的贡献通过解Poisson-Boltzmann(PB)方程的方法计算得到;溶液效应中非极性部分对自由能的贡献则通过分子表面积(SA)计算得到.本文结合我们科研组的工作,就近几年MM/PBSA方法的最新进展做了较为详细的阐述,同时对MM/PBSA的发展前景进行了展望.     

Heuristic lipophilicity potential for computer-aided rational drug design: Optimizations of screening functions and parameters

In this research we test and compare three possible atom-basedscreening functions used in the heuristic molecular lipophilicity potential(HMLP). Screening function 1 is a power distance-dependent function, b , screening function 2is an exponential distance-dependent function, b_iexp( , and screening function 3 is aweighted distance-dependent function, For every screening function, the parameters ( ,d₀, and are optimized using 41 common organic molecules of 4 types of compounds:aliphatic alcohols, aliphatic carboxylic acids, aliphatic amines, andaliphatic alkanes. The results of calculations show that screening function3 cannot give chemically reasonable results, however, both the powerscreening function and the exponential screening function give chemicallysatisfactory results. There are two notable differences between screeningfunctions 1 and 2. First, the exponential screening function has largervalues in the short distance than the power screening function, thereforemore influence from the nearest neighbors is involved using screeningfunction 2 than screening function 1. Second, the power screening functionhas larger values in the long distance than the exponential screeningfunction, therefore screening function 1 is effected by atoms at longdistance more than screening function 2. For screening function 1, thesuitable range of parameter d₀ is 1.5 < d₀ < 3.0, and d₀ = 2.0 is recommended. HMLP developed in this researchprovides a potential tool for computer-aided three-dimensional drugdesign.