Secondary structure bias in generalized Born solvent models: comparison of conformational ensembles and free energy of solvent polarization from explicit and implicit solvation

The effects of the use of three generalized Born (GB) implicit solvent models on the thermodynamics of a simple polyalanine peptide are studied via comparing several hundred nanoseconds of well-converged replica exchange molecular dynamics (REMD) simulations using explicit TIP3P solvent to REMD simulations with the GB solvent models. It is found that when compared to REMD simulations using TIP3P the GB REMD simulations contain significant differences in secondary structure populations, most notably an overabundance of alpha-helical secondary structure. This discrepancy is explored via comparison of the differences in the electrostatic component of the free energy of solvation (DeltaDeltaG(pol)) between TIP3P (via thermodynamic Integration calculations), the GB models, and an implicit solvent model based on the Poisson equation (PE). The electrostatic components of the solvation free energies are calculated using each solvent model for four representative conformations of Ala10. Since the PE model is found to have the best performance with respect to reproducing TIP3P DeltaDeltaG(pol) values, effective Born radii from the GB models are compared to effective Born radii calculated with PE (so-called perfect radii), and significant and numerous deviations in GB radii from perfect radii are found in all GB models. The effect of these deviations on the solvation free energy is discussed, and it is shown that even when perfect radii are used the agreement of GB with TIP3P DeltaDeltaG(pol) values does not improve. This suggests a limit to the optimization of the effective Born radius calculation and that future efforts to improve the accuracy of GB models must extend beyond such optimizations.     

Effective Born radii in the generalized Born approximation: the importance of being perfect

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born radii." Next, the atom-pair contributions are estimated by an analytical function f(GB) that depends upon the effective Born radii and interatomic distance of the atom pairs. Here, the relative impacts of these approximations are investigated by calculating "perfect" effective Born radii from PE theory, and enquiring as to how well the atom-pairwise energy terms from a GB model using these perfect radii in the standard f(GB) function duplicate the equivalent terms from PE theory. In tests on several biological macromolecules, the use of these perfect radii greatly increases the accuracy of the atom-pair terms; that is, the standard form of f(GB) performs quite well. The remaining small error has a systematic and a random component. The latter cannot be removed without significantly increasing the complexity of the GB model, but an alternative choice of f(GB) can reduce the systematic part. A molecular dynamics simulation using a perfect-radii GB model compares favorably with simulations using conventional GB, even though the radii remain fixed in the former. These results quantify, for the GB field, the importance of getting the effective Born radii right; indeed, with perfect radii, the GB model gives a very good approximation to the underlying PE theory for a variety of biomacromolecular types and conformations.     

Studies of viscous antagonism,excess molar volume and isentropic compressibility in aqueous mixed solvent systems at different temperatures

Using experimental data for the melting temperature T _m for four Li halides (F to I), it is demonstrated that T _m Z ^1/3 is close to constant, ? (2530 ± 250) K, where Z is the atomic number of the halogen. This formula is not appropriate for what sometimes is considered the simplest halide, LiH, and therefore alternatives are investigated which involve a characteristic electrostatic energy e ²/εs, with s the internuclear separation and ε the static dielectric constant.     

Membrane protein native state discrimination by implicit membrane models

Four implicit membrane models [IMM1, generalized Born (GB)‐surface area‐implicit membrane (GBSAIM), GB with a simple switching (GBSW), and heterogeneous dielectric GB (HDGB)] were tested for their ability to discriminate the native conformation of five membrane proteins from 450 decoys generated by the Rosetta‐Membrane program. The energy ranking of the native state and Z‐scores were used to assess the performance of the models. The effect of membrane thickness was examined and was found to be substantial. Quite satisfactory discrimination was achieved with the all‐atom IMM1 and GBSW models at 25.4 Å thickness and with the HDGB model at 28.5 Å thickness. The energy components by themselves were not discriminative. Both van der Waals and electrostatic interactions contributed to native state discrimination, to a different extent in each model. Computational efficiency of the models decreased in the order: extended‐atom IMM1 > all‐atom IMM1 > GBSAIM > GBSW > HDGB. These results encourage the further development and use of implicit membrane models for membrane protein structure prediction. © 2012 Wiley Periodicals, Inc.     

Proton dissociation and transfer in hydrated phosphoric acid clusters

The dynamics and mechanisms of proton dissociation and transfer in hydrated phosphoric acid (H₃PO₄) clusters under excess proton conditions were studied based on the concept of presolvation using the H₃PO₄–H₃O⁺–nH₂O complexes (n = 1–3) as the model systems and ab initio calculations and Born–Oppenheimer molecular dynamics (BOMD) simulations at the RIMP2/TZVP level as model calculations. The static results showed that the smallest, most stable intermediate complex for proton dissociation (n = 1) is formed in a low local‐dielectric constant environment (e.g., ε = 1), whereas proton transfer from the first to the second hydration shell is driven by fluctuations in the number of water molecules in a high local‐dielectric constant environment (e.g., ε = 78) through the Zundel complex in a linear H‐bond chain (n = 3). The two‐dimensional potential energy surfaces (2D‐PES) of the intermediate complex (n = 1) suggested three characteristic vibrational and ¹H NMR frequencies associated with a proton moving on the oscillatory shuttling and structural diffusion paths, which can be used to monitor the dynamics of proton dissociation in the H‐bond clusters. The BOMD simulations over the temperature range of 298–430 K validated the proposed proton dissociation and transfer mechanisms by showing that good agreement between the theoretical and experimental data can be achieved with the proposed rate‐determining processes. The theoretical results suggest the roles played by the polar solvent and iterate that insights into the dynamics and mechanisms of proton transfer in the protonated H‐bond clusters can be obtained from intermediate complexes provided that an appropriate presolvation model is selected and that all of the important rate‐determining processes are included in the model calculations. © 2015 Wiley Periodicals, Inc.     

Monte carlo simulations of proteins at constant pH with generalized born solvent,flexible sidechains,and an effective dielectric boundary

Titratable residues determine the acid/base behavior of proteins, strongly influencing their function; in addition, proton binding is a valuable reporter on electrostatic interactions. We describe a method for pK_a calculations, using constant‐pH Monte Carlo (MC) simulations to explore the space of sidechain conformations and protonation states, with an efficient and accurate generalized Born model (GB) for the solvent effects. To overcome the many‐body dependency of the GB model, we use a “Native Environment” approximation, whose accuracy is shown to be good. It allows the precalculation and storage of interactions between all sidechain pairs, a strategy borrowed from computational protein design, which makes the MC simulations themselves very fast. The method is tested for 12 proteins and 167 titratable sidechains. It gives an rms error of 1.1 pH units, similar to the trivial “Null” model. The only adjustable parameter is the protein dielectric constant. The best accuracy is achieved for values between 4 and 8, a range that is physically plausible for a protein interior. For sidechains with large pK_a shifts, ≥2, the rms error is 1.6, compared to 2.5 with the Null model and 1.5 with the empirical PROPKA method. © 2013 Wiley Periodicals, Inc.     

Influence of the solvent representation on vibrational entropy calculations: Generalized born versus distance‐dependent dielectric model

The harmonic model is the most popular approximation for estimating the “configurational” entropy of a solute in molecular mechanics/Poisson‐Boltzmann solvent accessible surface area (MM/PBSA)‐type binding free energy calculations. Here, we investigate the influence of the solvent representation in the harmonic model by comparing estimates of changes in the vibrational entropies for 30 trypsin/ligand complexes on ligand binding. Second derivatives of Amber generalized Born (GB) solvation models are available in the nucleic acid builder code. They allow one to use these models for the calculation of vibrational entropies instead of using a simpler solvation model based on a distance‐dependent dielectric (DDD) constant. Estimates of changes in the vibrational entropies obtained with a DDD model are systematically and significantly larger, by on average, 6 kcal mol^?1 (at T = 300 K), than estimates obtained with a GB model and so are more favorable for complex formation. The difference becomes larger the more the vibrational entropy contribution disfavors complex formation, that is, the larger the ligand is (for the complexes considered here). A structural decomposition of the estimates into per‐residue contributions reveals polar interactions between the ligand and the surrounding protein, in particular involving charged nitrogens, as a main source of the differences. Snapshots minimized with the DDD model showed a structural deviation from snapshots minimized in explicit water that is larger by, on average, 0.5 Å RMSD compared to snapshots that were minimized with GB^HCT. As experimental vibrational entropies of biomacromolecules are elusive, there is no direct way to establish a solvent model's superiority. Thus, we can only recommend using the GB harmonic model for vibrational entropy calculations based on the reasoning that smaller structural deviations should point to the implicit solvent model that closer approximates the energy landscape of the solute in explicit solvent. © 2012 Wiley Periodicals, Inc.     

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.     

Acridin-9-ylmethoxycarbonyl （Amoc）： A New Photochemically Removable Protecting Group for Alcohols

Synthesis and photochemistry of acridin-9-ylmethoxycarbonyl(Amoc)as a new photochemically removableprotecting group for alcohols were described.Three carbonates of alcohols 1—3 were synthesized throughcondensation of 9-hydroxymethylacridine and chloroformates of alcohols,including benzyl alcohol,phenethylalcohol and one galactose derivative.The photolysis of protected alcohols can efficiently release the correspondingalcohol in the efficiencies(Q_(u1)ε)of 100—200(quantum yield Q_(u1)=0.011—0.023,and molar absorptivity ε=9.1×10~3—9.8×10~3 mol~(-1)·L·cm~(-1))under 360 nm light.     

Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach

An accurate and fast evaluation of the electrostatics in ligand-protein interactions is crucial for computer-aided drug design. The pairwise generalized Born (GB) model, a fast analytical method originally developed for studying the solvation of organic molecules, has been widely applied to macromolecular systems, including ligand-protein complexes. However, this model involves several empirical scaling parameters, which have been optimized for the solvation of organic molecules, peptides, and nucleic acids but not for energetics of ligand binding. Studies have shown that a good solvation energy does not guarantee a correct model of solvent-mediated interactions. Thus, in this study, we have used the Poisson-Boltzmann (PB) approach as a reference to optimize the GB model for studies of ligand-protein interactions. Specifically, we have employed the pairwise descreening approximation proposed by Hawkins et al.(1) for GB calculations and DelPhi for PB calculations. The AMBER all-atom force field parameters have been used in this work. Seventeen protein-ligand complexes have been used as a training database, and a set of atomic descreening parameters has been selected with which the pairwise GB model and the PB model yield comparable results on atomic Born radii, the electrostatic component of free energies of ligand binding, and desolvation energies of the ligands and proteins. The energetics of the 15 test complexes calculated with the GB model using this set of parameters also agrees well with the energetics calculated with the PB method. This is the first time that the GB model has been parametrized and thoroughly compared with the PB model for the electrostatics of ligand binding.     

GBr(6): a parameterization-free, accurate, analytical generalized born method

The Poisson-Boltzmann (PB) equation is widely used for modeling electrostatic effects and solvation for macromolecules. The generalized Born (GB) model has been developed to mimic PB results at substantial lower computational cost. Here, we report an analytical GB method that reproduces PB results with high accuracy. The analytical approach builds on previous work of Gallicchio and Levy (J. Comput. Chem. 2004, 25, 479), and incorporates an improvement, proposed by Grycuk (J. Chem. Phys. 2003, 119, 4817), of the Coulomb-field approximation used in most GB methods. Tested against PB results, our GB method has an average unsigned relative error of only 0.6% for a representative set of 55 proteins and of 0.4% and 0.3%, respectively, for folded and unfolded conformations of cytochrome b562 sampled in molecular dynamics simulations. The dependencies of the electrostatic solvation free energy on solute and solvent dielectric constants and on salt concentration are fully accounted for in our method.     

Implicit solvation based on generalized Born theory in different dielectric environments

In this paper we are investigating the effect of the dielectric environment on atomic Born radii used in generalized Born (GB) methods. Motivated by the Kirkwood expression for the reaction field of a single off-center charge in a spherical cavity, we are proposing extended formalisms for the calculation of Born radii as a function of external and internal dielectric constants. We demonstrate that reaction field energies calculated from environmentally dependent Born radii lead to much improved agreement with Poisson-Boltzmann solutions for low dielectric external environments, such as biological membranes or organic solvent, compared to previous methods where the calculation of Born radii does not depend on the environment. We also examine how this new approach can be applied for the calculation of transfer free energies from vacuum to a given external dielectric for a system with an internal dielectric larger than one. This has not been possible with standard GB theory but is relevant when scoring minimized or average structures with implicit solvent.     

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction‐Field Method for the Solvation Free Energies of Amino Acid Side‐Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model’s accuracy in predicting conformational free‐energy differences. The solvation free energies of neutral and polar amino acid side‐chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol^?1. The new parameters were evaluated for charged side‐chain analogs. The HADES results were compared with explicit‐solvent, generalized Born, Poisson–Boltzmann, and QM‐based methods. The potentials of mean force (PMFs) between pairs of side‐chain analogs obtained by using HADES and explicit‐solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.     

二元无机物标准熵 So298的拓扑研究

为了预测二元无机物的标准熵,基于分子图的连接矩阵和离子参数gi、qi,提出了一种新的连接性指数mQ, mG及其逆指数mQ’, mG’。 qi、gi定义为：qi=(1.1+Zi1.1) /(1.7+ni), gi=(1.4+Zi) /(0.9+ri+ri-1),其中Zi 、ni和 ri分别代表离子i的电荷数、最外层主量子数和半径。从0Q, 0Q’, 1G,和1G’,利用多元线性回归分析方法和人工神经网络方法,可以构建优良的QSPR模型。对371个二元无机物,其多元线性模型及神经网络模型的相关系数、标准偏差和平均绝对偏差分别是：0.9905, 8.29 J.K-1.mol-1, 6.48 J. K-1.mol-1, 0.9960, 5.37 J.K-1.mol-1 和 3.90 J.K-1.mol-1。留一法交叉验证表明,其多元线性模型具有良好的稳定性。两个模型对187个未进入模型的二元无机物的标准熵的预测值和实验值之间的相关系数、标准偏差和平均绝对偏差分别是：0.9897, 8.64 J. K-1.mol-1, 6.84 J. K-1.mol-1, 0.9957, 5.63 J.K-1.mol-1, 和 4.18 J.K-1.mol-1。研究表明,本文方法在预测二元无机物标准熵时比文献方法更有效,两种模型均能较精确的预测二元无机物的标准熵,且神经网络模型的预测结果更精确。     

Incorporating variable dielectric environments into the generalized Born model

A generalized Born (GB) model is proposed that approximates the electrostatic part of macromolecular solvation free energy over the entire range of the solvent and solute dielectric constants. The model contains no fitting parameters, and is derived by matching a general form of the GB Green function with the exact Green's function of the Poisson equation for a random charge distribution inside a perfect sphere. The sphere is assumed to be filled uniformly with dielectric medium epsilon(in), and is surrounded by infinite solvent of constant dielectric epsilon(out). This model is as computationally efficient as the conventional GB model based on the widely used functional form due to Still et al. [J. Am. Chem. Soc. 112, 6127 (1990)], but captures the essential physics of the dielectric response for all values of epsilon(in) and epsilon(out). This model is tested against the exact solution on a perfect sphere, and against the numerical Poisson-Boltzmann (PB) treatment on a set of macromolecules representing various structural classes. It shows reasonable agreement with both the exact and the numerical solutions of the PB equation (where available) considered as reference, and is more accurate than the conventional GB model over the entire range of dielectric values.     

Ester Carbonyl Vibration as a Sensitive Probe of Protein Local Electric Field

The ability to quantify the local electrostatic environment of proteins and protein/peptide assemblies is key to gaining a microscopic understanding of many biological interactions and processes. Herein, we show that the ester carbonyl stretching vibration of two non‐natural amino acids, L ‐aspartic acid 4‐methyl ester and L ‐glutamic acid 5‐methyl ester, is a convenient and sensitive probe in this regard, since its frequency correlates linearly with the local electrostatic field for both hydrogen‐bonding and non‐hydrogen‐bonding environments. We expect that the resultant frequency–electric‐field map will find use in various applications. Furthermore, we show that, when situated in a non‐hydrogen‐bonding environment, this probe can also be used to measure the local dielectric constant (ε). For example, its application to amyloid fibrils formed by Aβ_16–22 revealed that the interior of such β‐sheet assemblies has an ε value of approximately 5.6.     

The Gaussian Generalized Born model: application to small molecules

This work presents a Generalized Born model for the computation of the electrostatic component of solvation energies which is based on volume integration. An analytic masking function is introduced to remove Coulombic singularities. This approach leads to analytic formulae for the computation of Born radii, which are differentiable to arbitrary order, and computationally straightforward to implement.     

Correlated Coordination and Redox Activity of a Hemilabile Noninnocent Ligand in Nickel Complexes

The compound [Ni(Q_M)₂], Q_M=4,6‐di‐tert‐butyl‐N‐(2‐methylthiomethylphenyl)‐o‐iminobenzoquinone, is a singlet diradical species with approximately planar configuration at the tetracoordinate metal atom and without any Ni?S bonding interaction. One‐electron oxidation results in additional twofold Ni?S coordination (d_Ni?S≈2.38 Å) to produce a complex cation of [Ni(Q_M)₂](PF₆) with hexacoordinate Ni^II and two distinctly different mer‐configurated tridentate ligands. The O,O′‐trans arrangement in the neutral precursor is changed to an O,O′‐cis configuration in the cation. The EPR signal of [Ni(Q_M)₂](PF₆) has a very large g anisotropy and the magnetic measurements indicate an S=3/2 state. The dication was structurally characterized as [Ni(Q_M)₂](ClO₄)₂ to exhibit a similar NiN₂O₂S₂ framework as the monocation. However, the two tridentate (O,N,S) ligands are now equivalent according to the formulation [Ni^II(Q_M⁰)₂]²⁺. Cyclic voltammetry reflects the qualitative structure change on the first, but not on the second oxidation of [Ni(Q_M)₂], and spectroelectrochemistry reveals a pronounced dependence of the 800–900 nm absorption on the solvent and counterion. Reduction of the neutral form occurs in an electrochemically reversible step to yield an anion with an intense near‐infrared absorption at 1345 nm (ε=10400 M ^?1 cm^?1) and a conventional g factor splitting for a largely metal‐based spin (S=1/2), suggesting a [(Q_M ^{. ?})Ni^II(Q_M^2?)]^? configuration with a tetracoordinate metal atom with antiferromagnetic Ni^II–(Q_M ^{. ?}) interactions and symmetry‐allowed ligand‐to‐ligand intervalence charge transfer (LLIVCT). Calculations are used to understand the Ni?S binding activity as induced by remote electron transfer at the iminobenzoquinone redox system.