共查询到20条相似文献，搜索用时 15 毫秒
1.
We investigate the relative efficiency of thermodynamic integration, three variants of the exponential formula, also referred to as thermodynamic perturbation, and Bennett's acceptance ratio method to compute relative and absolute solvation free energy differences. Our primary goal is the development of efficient protocols that are robust in practice. We focus on minimizing the number of unphysical intermediate states (λ-states) required for the computation of accurate and precise free energy differences. Several indicators are presented which help decide when additional λ-states are necessary. In all tests Bennett's acceptance ratio method required the least number of λ-states, closely followed by the \"double-wide\" variant of the exponential formula. Use of the exponential formula in only strict \"forward\" or \"backward\" mode was not found to be competitive. Similarly, the performance of thermodynamic integration in terms of efficiency was rather poor. We show that this is caused by the use of the trapezoidal rule as method of numerical quadrature. A systematic study focusing on the optimization of thermodynamic integration is presented in a companion paper. 相似文献
2.
The exact computation of free energy differences requires adequate sampling of all relevant low energy conformations. Especially in systems with rugged energy surfaces, adequate sampling can only be achieved by biasing the exploration process, thus yielding non-Boltzmann probability distributions. To obtain correct free energy differences from such simulations, it is necessary to account for the effects of the bias in the postproduction analysis. We demonstrate that this can be accomplished quite simply with a slight modification of Bennett's Acceptance Ratio method, referring to this technique as Non-Boltzmann Bennett. We illustrate the method by several examples and show how a creative choice of the biased state(s) used during sampling can also improve the efficiency of free energy simulations. 相似文献
3.
In the past analyses of the so-called van der Waals end point problem focused on thermodynamic integration. Here we investigate which of the recommendations, such as the need for soft-core potentials, are still valid when Bennett's acceptance ratio method is used. We show that in combination with Bennett's acceptance ratio method intermediate states characterized by the coupling parameter λ can be replaced by intermediate states in which Lennard-Jones interactions are turned on or off on an \"atom by atom\" basis. By doing so, there is no necessity to use soft-core potentials. In fact, one can compute free energy differences without dedicated code, making it possible to use any molecular dynamics program to compute alchemical free energy differences. Such an approach, which we illustrate by several examples, makes it possible to exploit the tremendous computational power of the graphics processing unit. 相似文献
4.
Molecular dynamics-based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This \"singularity\" problem can be addressed with \"soft-core\" potential functions which keep pairwise interaction energies finite for all configurations and provide smooth free energy curves. \"One-step\" transformations, in which electrostatic and van der Waals forces are simultaneously modified, can be simpler and less expensive than \"two-step\" transformations in which these properties are changed in separate calculations. Here, we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters α(LJ) and β(C) controlling the behavior of the soft-core Lennard-Jones and Coulomb potentials and compare one- and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates. 相似文献
5.
In a recent article (Bieler et al., J. Chem. Theory Comput. 2014, 10, 3006), we introduced a combination of λ‐dynamics and local‐elevation umbrella‐sampling termed λ‐LEUS to calculate free‐energy changes associated with alchemical processes using molecular dynamics simulations. This method was suggested to be more efficient than thermodynamic integration (TI), because the dynamical variation of the alchemical variable λ opens up pathways to circumvent barriers in the orthogonal space (defined by the N – 1 degrees of freedom that are not subjected to the sampling enhancement), a feature λ‐LEUS shares with Hamiltonian replica‐exchange (HR) approaches. However, the mutation considered, hydroquinone to benzene in water, was no real challenge in terms of orthogonal‐space properties, which were restricted to solvent‐relaxation processes. In the present article, we revisit the comparison between TI and λ‐LEUS considering non‐trivial mutations of the central residue X of a KXK tripeptide in water (with X = G, E, K, S, F, or Y). Side‐chain interactions that may include salt bridges, hydrogen bonds or steric clashes lead to slow relaxation in the orthogonal space, mainly in the two‐dimensional subspace spanned by the central and ψ dihedral angles of the peptide. The efficiency enhancement afforded by λ‐LEUS is confirmed in this more complex test system and can be attributed explicitly to the improved sampling of the orthogonal space. The sensitivity of the results to the nontrivial choices of a mass parameter and of a thermostat coupling time for the alchemical variable is also investigated, resulting in recommended ranges of 50 to 100 u nm2 and 0.2 to 0.5 ps, respectively. © 2015 Wiley Periodicals, Inc. 相似文献
6.
Hannes H. Loeffler Christoph A. Sotriffer Rudolf H. Winger Klaus R. Liedl Bernd M. Rode 《Journal of computational chemistry》2001,22(8):846-860
The relative free energies of hydration of the dipeptides glycylalanine and alanyl‐glycine in their naturally occurring form have been calculated both for the zwitterionic and protonated species. Emphasis was laid on comparisons between the conventional cutoff method and the Particle Mesh Ewald method to account for possible differences in electrostatic contributions to the free energy. Furthermore, the convergence behavior of the total free energy and its individual contributions were examined. The results, obtained by means of the thermodynamic integration technique as implemented in the free energy module of the AMBER program suite, suggest that in aqueous solution glycylalanine is more stable than alanylglycine by 2.7 kcal/mol in the zwitterionic form and by 3.5 kcal/mol in the protonated form. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 846–860, 2001 相似文献
7.
Mihaly Mezei 《Journal of mathematical chemistry》2000,27(3):235-250
The contribution of the molecular flexibility to the solvation excess free energy is expressed in terms of probabilities of reaching hard limits on intramolecular coordinates in a series of calculations successively relaxing those limits. Numerical tests on the harmonic oscillator are also presented and used to make suggestion about computational issues. 相似文献
8.
Relative free energies for a series of not too different compounds can be estimated accurately from a single simulation of an unphysical reference state that encompasses the characteristic molecular features of the compounds. Previously, this method has been applied to the calculation of free energies of solvation and of ligand binding for small molecules. In the present study we investigate the limits to the accuracy of the method by applying it to a realistic model of the binding of a set of rather large ligands to the protein factor Xa, a key protein in current efforts to design anticoagulation drugs. The evaluation of the binding free energies and conformations of nine derivatives of a biphenylamidino inhibitor leads to insights regarding the effect of the size, flexibility, and character of the unphysical part of the ligand in the reference state on the accuracy of the predicted binding free energies. 相似文献
9.
Michael M. H. Graf Manuela Maurer Chris Oostenbrink 《Journal of computational chemistry》2016,37(29):2597-2605
Previous free‐energy calculations have shown that the seemingly simple transformation of the tripeptide KXK to KGK in water holds some unobvious challenges concerning the convergence of the forward and backward thermodynamic integration processes (i.e., hysteresis). In the current study, the central residue X was either alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine. Interestingly, the transformation from alanine to glycine yielded the highest hysteresis in relation to the extent of the chemical change of the side chain. The reason for that could be attributed to poor sampling of φ2/ψ2 dihedral angles along the transformation. Altering the nature of alanine's Cβ atom drastically improved the sampling and at the same time led to the identification of high energy barriers as cause for it. Consequently, simple strategies to overcome these barriers are to increase simulation time (computationally expensive) or to use enhanced sampling techniques such as Hamiltonian replica exchange molecular dynamics and one‐step perturbation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. 相似文献
10.
Alchemical free energy calculations involving the removal or insertion of atoms into condensed phase systems generally make use of soft-core scaling of nonbonded interactions, designed to circumvent numerical instabilities that arise from weakly interacting \"hard\" atoms in close proximity. Current methods model soft-core atoms by introducing a nonlinear dependence between the shape of the interaction potential and the strength of the interaction. In this article, we propose a soft-core method that avoids introducing such a nonlinear dependence, through the application of a smooth flattening of the potential energy only in a region that is energetically accessible under normal conditions. We discuss the benefits that this entails and explore a selection of applications, including enhanced methods for the estimation of free energy differences and for the automated optimization of the placement of intermediate states in multistage alchemical calculations. 相似文献
11.
The most general way to improve the accuracy of binding‐affinity calculations for protein–ligand systems is to use quantum‐mechanical (QM) methods together with rigorous alchemical‐perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin‐3 at a reasonably high QM level (dispersion‐corrected density functional theory with a triple‐zeta basis set) and with a sufficiently large QM system to include all short‐range interactions with the ligand (744–748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non‐Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ～3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc. 相似文献
12.
Zhou Y Oostenbrink C Jongejan A Van Gunsteren WF Hagen WR De Leeuw SW Jongejan JA 《Journal of computational chemistry》2006,27(7):857-867
The relative stabilities of homochiral and heterochiral forms of selected dipeptides, AA, AS, AC, AV, AF, AD, AK, tripeptides, AAA, AVA, and an acetylpentapeptide, AcGLSFA, have been calculated using thermodynamic integration protocols and the GROMOS 53A6 force field. Integration pathways have been designed that produce minimal disturbance to the system, including the use of soft atoms, low-energy intermediates, and chiral inversion of the smaller amino acid in the peptide. Comparison of the results obtained by thermodynamic integration between the diastereomeric forms (in explicit water, at 300 K) and from exhaustive global minimum-energy searches for the individual dipeptides (implicit water, epsilon = 78, 0 K) suggests that entropic contributions to the relative stability of the chiral forms are important. This conclusion is supported by the results of explicit calculation of the effect of temperature on the relative stability of alanylvalylalanine diastereomers. The Gibbs free energy calculations predict that at ambient temperature and pressure homochiral dipeptides with small side chains or polar groups in the vicinity of the peptide backbone, AA, AS, and AD, are more stable than their heterochiral counterparts by fractions of a kJ/mol. For bigger side chains, AC, AV, AF, and AK, the heterochiral diastereomers appear to be more stable. Predicted relative stabilities are in line with observations reported in the literature for AE and YY. Excellent agreement is found for the calculated and experimentally determined relative stabilities of the diastereomers of the dipeptide AA and of all-L AcGLSFA and its diastereomer containing D-serine in the central position. Addition of counterions to the solvent box has no significant effects on charged and neutral forms. From the present findings it would appear unlikely that the intrinsic stability difference between homo- and heterochiral dipeptides has been a driving force in a primordial selection process leading to the incorporation of amino acids with a single enantiomeric configuration in natural proteins. 相似文献
13.
Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate. 相似文献
14.
《液相色谱法及相关技术杂志》2012,35(10):1385-1391
Abstract UV and circular dichroism spectroscopic measurements showed that the molecular interactions in hexane/ethyl‐acetate solutions between dihydroquinidine tert‐butylcarbamate, used as a model for the quinidine carbamate chiral selector (QD), and 3‐chloro‐1‐phenyl‐propanol are too weak to affect the corresponding spectra of these compounds. The weak interactions between QD and 3‐chloro‐1‐phenyl‐propanol are probably masked by the formation of self‐associated dimeric structures in solution. 相似文献
15.
PdN、PdN2分子的结构与势能函数* 总被引：2，自引：0，他引：2
在Pd 的RECP 近似下, 运用B3LYP 方法, 对Pd 采用基集合SDD, 对N 采用基集合AUG鄄cc鄄pVTZ, 对PdN 和PdN2分子的微观结构进行了理论计算. PdN 分子的基电子状态为4撞-, PdN2分子的最稳定构型为单重态的线性Pd—N—N(C肄V),其电子状态为1撞+. 采用最小二乘法拟合出PdN 分子的Murrell鄄Sorbie 势能函数, 使用多体展式理论导出了势函数中的参数, 进而给出PdN2分子基态势函数的解析表达式, 其势能面准确地复现了平衡稳态结构和能量关系, 表现了Pd 内迁移的详细过程, 存在一个C2V构型的鞍点(RNN=0.11700 nm, RPdN=0.22088nm). 由图得到内迁移的能垒为0.5197 eV, 与计算值0.4560 eV 接近. 相似文献
16.
The theoretical study has been performed to refine the procedure for calculations of Gibbs free energy with a relative accuracy of less than 1 kcal/mol. Three benchmark intermolecular complexes are examined via several quantum-chemical methods, including the second-order Moller-Plesset perturbation (MP2), coupled cluster (CCSD(T)), and density functional (BLYP, B3LYP) theories augmented by Dunnings correlation-consistent basis sets. The effects of electron correlation, basis set size, and anharmonicity are systematically analyzed, and the results are compared with available experimental data. The results of the calculations suggest that experimental accuracy can be reached only by extrapolation of MP2 and CCSD(T) total energies to the complete basis set. The contribution of anharmonicity to the zero point energy and TDeltaSint values is fairly small. The new, economic way to reach chemical accuracy in the calculations of the thermodynamic parameters of intermolecular interactions is proposed. In addition, interaction energy (De) and free energy change (DeltaA) for considered species have been evaluated by Carr-Parrinello molecular dynamics (CPMD) simulations and static BLYP-plane wave calculations. The free energy change along the reaction paths were determined by the thermodynamic integration/\"Blue Moon Ensemble\" technique. Comparison between obtained values, and available experimental and conventional ab initio results has been made. We found that the accuracy of CPMD simulations is affected by several factors, including statistical uncertainty and convergence of constrained forces (TD integration), and the nature of DFT (density functional theory) functional. The results show that CPMD technique is capable of reproducing interaction and free energy with an accuracy of 1 kcal/mol and 2-3 kcal/mol respectively. 相似文献
17.
P. Nuno Palma Maria João Bonifácio Ana Isabel Loureiro Patrício Soares‐da‐Silva 《Journal of computational chemistry》2012,33(9):970-986
Alchemical free energy simulations are amongst the most accurate techniques for the computation of the free energy changes associated with noncovalent protein–ligand interactions. A procedure is presented to estimate the relative binding free energies of several ligands to the same protein target where multiple, low‐energy configurational substates might coexist, as opposed to one unique structure. The contributions of all individual substates were estimated, explicitly, with the free energy perturbation method, and combined in a rigorous fashion to compute the overall relative binding free energies and dissociation constants. It is shown that, unless the most stable bound forms are known a priori, inaccurate results may be obtained if the contributions of multiple substates are ignored. The method was applied to study the complex formed between human catechol‐O‐methyltransferase and BIA 9‐1067, a newly developed tight‐binding inhibitor that is currently under clinical evaluation for the therapy of Parkinson's disease. Our results reveal an exceptionally high‐binding affinity (Kd in subpicomolar range) and provide insightful clues on the interactions and mechanism of inhibition. The inhibitor is, itself, a slowly reacting substrate of the target enzyme and is released from the complex in the form of O‐methylated product. By comparing the experimental catalytic rate (kcat) and the estimated dissociation rate (koff) constants of the enzyme‐inhibitor complex, one can conclude that the observed inhibition potency (Ki) is primarily dependent on the catalytic rate constant of the inhibitor's O‐methylation, rather than the rate constant of dissociation of the complex. © 2012 Wiley Periodicals, Inc. 相似文献
18.
A new approach to prepare W/O/W-double emulsions is described. The inner W/O-phase is composed of a thermodynamically stable micellar solution of inverse type, an L2-phase. A protein, caseinate, is then used to stabilize the dispersion of this phase in water. Release from the inner to the outer water phase was followed by dialysis. Phase equilibria of the two ternary systems monolaurin-water-soybean oil and tetraglycerol monolaurin-water-soybean oil are described. 相似文献
19.
Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca2+ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α‐helix form in the presence Ca2+‐loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca2+‐loaded CaM must be simultaneously treated. However, it is time‐consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi‐scale divide‐and‐conquer MD (MSDC‐MD), which combines AAM‐MD and coarse‐grained model MD (CGM‐MD). To speed up the conformation sampling, MSDC‐MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM‐MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC‐MD; the root‐mean‐square distance (RMSD) with respect to the experimental structure was 2.23 Å. 相似文献
20.
Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard‐Jones and Coulomb Softcore potentials parameters in the one‐step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one‐step TI in a protein‐ligand binding system. The best performing model, the one‐step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM‐GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure‐activity relationship insights, and suggest the parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well‐known halogen bond favoring enzyme. © 2015 Wiley Periodicals, Inc. 相似文献