Free energy perturbation study of water dimer dissociation kinetics

An efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABC-FEP (ab initio/classical free energy perturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energy perturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmann-weighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energy perturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energy perturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and TIP4PFQ) are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT-5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.     

Molecular vibrational constants of some simple polyatomic molecules. Methyl,silyl, and germyl halides

The force constants and compliance constants of methyl, silyl, and germyl fluoride, chloride, bromide, and iodide have been calculated by the iterative consistency method. Using the force fields so obtained, centrifugal distortion constants, Coriolis coupling constants, and mean amplitudes of vibration have been computed and compared with experimental data, where available.     

Molecular dynamics simulations of LiCl association and NaCl association in water by means of ABEEM/MM

Constrained molecular dynamics simulations have been used to investigate the LiCl and NaCl ionic association in water in terms of atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM). The simulations make use of the seven-site fluctuating charge and flexible ABEEM-7P water model, based on which an ion-water interaction potential has been constructed. The mean force and the potential of mean force for LiCl and NaCl in water, the charge distributions, as well as the structural and dynamical properties of contact ion pair dissociation have been investigated. The results are reasonable and informative. For LiCl ion pair in water, the solvent-separated ion pair configurations are more stable than contact ion pair configurations. The calculated PMF for NaCl in water indicates that contact ion pair and solvent-separated ion pair configurations are of comparable stability.     

Pair interaction potentials of colloids by extrapolation of confocal microscopy measurements of collective suspension structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.     

Prediction of vtbrational spectra by the CNDO/2 force method: I. Out-of-plane vibrations of benzene and fluorobenzenes

The out-of-plane force constants of benzene and 12 fluorobenzenes have been calculated by the CNDO/2 force method. Two empirical scaling factors had to be applied to obtain good agreement. The mean deviation between the 88 calculated and experimental frequencies is 16 cm^?1.     

Calculation of free-energy differences and potentials of mean force by a multi-energy gap method

A method is proposed to significantly accelerate the convergence of free-energy calculations. It introduces a bias factor in Monte Carlo simulations or, equivalently, a bias force in molecular dynamics simulations. The bias factor targets the energy gap, i.e., the difference in energy function between two states, and is therefore specifically designed for calculating free-energy differences. The goal is to make the probability density of the energy gap as uniform as possible, thus allowing for its accurate determination. An iterative procedure, based on simulations at higher temperatures, is devised to obtain the bias factor. The same method naturally extends to the calculation of potentials of mean force. The generalized coordinate, for which the potential of mean force is to be calculated, now plays the role of the energy gap. Applications to model systems confirm the expected increase in accuracy of calculated free-energy differences and potentials of mean force.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

Structure prediction of an S-layer protein by the mean force method

S-layer proteins have a wide range of application potential due to their characteristic features concerning self-assembling, assembling on various surfaces, and forming of isoporous structures with functional groups located on the surface in an identical position and orientation. Although considerable knowledge has been experimentally accumulated on the structure, biochemistry, assemble characteristics, and genetics of S-layer proteins, no structural model at atomic resolution has been available so far. Therefore, neither the overall folding of the S-layer proteins-their tertiary structure-nor the exact amino acid or domain allocations in the lattices are known. In this paper, we describe the tertiary structure prediction for the S-layer protein SbsB from Geobacillus stearothermophilus PV72/p2. This calculation was based on its amino acid sequence using the mean force method (MF method) achieved by performing molecular dynamic simulations. This method includes mainly the thermodynamic aspects of protein folding as well as steric constraints of the amino acids and is therefore independent of experimental structure analysis problems resulting from biochemical properties of the S-layer proteins. Molecular dynamic simulations were performed in vacuum using the simulation software NAMD. The obtained tertiary structure of SbsB was systematically analyzed by using the mean force method, whereas the verification of the structure is based on calculating the global free energy minimum of the whole system. This corresponds to the potential of mean force, which is the thermodynamically most favorable conformation of the protein. Finally, an S-layer lattice was modeled graphically using CINEMA4D and compared with scanning force microscopy data down to a resolution of 1 nm. The results show that this approach leads to a thermodynamically favorable atomic model of the tertiary structure of the protein, which could be verified by both the MF Method and the lattice model.     

The Use of the Finite-Element Method for Calculating the Photophoresis Force Applied to a Large Spheroidal Aerosol Particle

Colloid Journal - The finite-element method has been employed to calculate the photophoresis force applied to a solid spheroidal aerosol particle, the size of which is much larger than the mean...     

Automated Search of Minimum Free‐Energy Path by Umbrella Integration

The free‐energy landscape is an important factor for understanding the conformational equilibria of chemical reactions, and many techniques have been developed to calculate the potential of the mean force. Unfortunately, these methods require a previous knowledge of the system for calculations because the results depend on the reaction coordinates. In this study, we combine the scaled hypersphere search method with the umbrella integration method to obtain the transition states on free‐energy landscapes and minimum‐free‐energy paths (MFEPs). With this approach, the MFEP connections between known and unknown equilibrium points are constructed without the prior knowledge of the free‐energy landscape. The problem of reaction coordinates can be solved by using a multidimensional, fully automated interrogation of MFEPs for acquiring the potential of mean force. The efficiency of the proposed method is demonstrated by applying it to alanine dipeptide and alanine tripeptide. © 2018 Wiley Periodicals, Inc.     

Multidimensional free-energy calculations using the weighted histogram analysis method

The recently formulated weighted histogram analysis method (WHAM)¹ is an extension of Ferrenberg and Swendsen's multiple histogram technique for free-energy and potential of mean force calculations. As an illustration of the method, we have calculated the two-dimensional potential of mean force surface of the dihedrals gamma and chi in deoxyadenosine with Monte Carlo simulations using the all-atom and united-atom representation of the AMBER force fields. This also demonstrates one of the major advantages of WHAM over umbrella sampling techniques. The method also provides an analysis of the statistical accuracy of the potential of mean force as well as a guide to the most efficient use of additional simulations to minimize errors. © 1995 John Wiley & Sons, Inc.     

Calibration of force-field dependency in free energy landscapes of peptide conformations by quantum chemical calculations

The free energy landscapes of peptide conformations were calibrated by ab initio quantum chemical calculations, after the enhanced conformational diversity search using the multicanonical molecular dynamics simulations. Three different potentials of mean force for an isolated dipeptide were individually obtained by the multicanonical molecular dynamics simulations using the conventional force fields, AMBER parm94, AMBER parm96, and CHARMm22. Each potential of mean force was then calibrated based upon the umbrella sampling algorithm from the adiabatic energy map that was calculated separately by the ab initio molecular orbital method, and all of the calibrated potentials of mean force coincided well. The calibration method was also applied to the simulations of a peptide dimer in explicit water models, and it was shown that the calibrated free energy landscapes did not depend on the force field used in the classical simulations, as far as the conformational space was sampled well. The current calibration method fuses the classical free energy calculation with the quantum chemical calculation, and it should generally make simulations for biomolecular systems much more reliable when combining with enhanced conformational sampling.     

An application of the DFT-based scaled quantum mechanical force field method to a weakly bonded system: N2O4

The adequacy of the density functional derived scaled quantum mechanical force field method of Rauhut and Pulay has been tested for a weakly bound dimer, N₂O₄. The Becke3–Lee–Yang–Parr/6-31G^* harmonic force field has been scaled with the transferable scale factors of Rauhut and Pulay (developed originally for `common' organic compounds without any reference to the N–O bond) resulting in 20.7 and 38 cm⁻¹ for the mean and the maximal individual deviations, respectively, as compared with experimental spectra. Consequently, the force field method of Rauhut and Pulay may give reliable results for non-common compounds as well.     

Exploring reaction pathways with transition path and umbrella sampling: application to methyl maltoside

The transition path sampling (TPS) method is a powerful approach to study chemical reactions or transitional properties on complex potential energy landscapes. One of the main advantages of the method over potential of mean force methods is that reaction rates can be directly accessed without knowledge of the exact reaction coordinate. We have investigated the complementary nature of these two differing approaches, comparing transition path sampling with the weighted histogram analysis method to study a conformational change in a small model system. In this case study, the transition paths for a transition between two rotational conformers of a model disaccharide molecule, methyl beta-D-maltoside, were compared with a free energy surface constrained by the two commonly used glycosidic (phi,psi) torsional angles. The TPS method revealed a reaction channel that was not apparent from the potential of mean force method, and the suitability of phi and psi as reaction coordinates to describe the isomerization in vacuo was confirmed by examination of the transition path ensemble. Using both transition state theory and transition path sampling methods, the transition rate was estimated. We have estimated a characteristic time between transitions of approximately 160 ns for this rare isomerization event between the two conformations of the carbohydrate. We conclude that transition path sampling can extract subtle information about the dynamics not apparent from the potential of mean force method. However, in calculating the reaction rate, the transition path sampling method required 27.5 times the computational effort than was needed by the potential of mean force method.     

Extension of the density functional derived scaled quantum mechanical force field procedure

The density functional derived scaled quantum mechanical (SQM) force field method of Rauhut and Pulay [J. Phys. Chem. 99 (1995) 3093] has been extended. The original procedure (employing B3-LYP/6-31G* computations and 11 transferable scale factors for the different kinds of internal coordinates) was capable to reproduce the vibrational fundamentals of 31 simple organic (H, C, N, O) molecules with a total mean deviation of about 13 cm(-1). The present Density Functional Theory based SQM force field method is an extension of the original one: with the help of 20 transferable scale factors can reproduce the fundamentals of 20 inorganic, organic and organosilicon molecules containing nonmetallic first and second-row atoms with a total mean deviation of 10.8 cm(-1). The transferability and reliability of the new set of scale factors are demonstrated on the examples of the a priori SQM vibrational spectra of cis and gauche-cyclopropylchlorosilane.     

Temperature weighted histogram analysis method, replica exchange, and transition paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.     

生物样品中生物素的酶联免疫吸附分析两种包被方法的比较研究

通过对用猪肺炎霉浆菌包被或用其兔抗体包被两种方法的比较研究，得到一种高灵敏度和高准确度对生物样品中生物素含量直接定量的酶联免疫吸附分析（ELISA）法。猪肺炎霉浆菌包被法的检测限仅约为同类文献值的1／150，加标平均回收率为101.13%，均优于猪肺炎霉浆菌抗血清（抗体）包被法结果。表明猪肺炎霉浆菌比其抗体对酶标板有更强的物理吸附力。方法亦可用于其它待测定物的ELISA法。     

三元体系NaCl-KCl-H2O35℃活度系数的研究

研究了35℃ NaCl-KCl-H2O三元体系的活度系数.用Na+、 K+和Cl-的离子选择性电极分别测得了(0.1～ 1.5 mmol/L)不同离子强度下该体系中NaCl和KCl的平均活度系数.回归了该体系Pitzer方程的相互作用参数.实验值与计算值最大相对误差为5.6%,而平均相对误差为2.3%.     

用诱导自洽方法计算振动力常数的研究

本文提出一种迭代方法计算振动力常数,可以比较清楚地显示基频与振动力常数之间的关系,从而能方便地选择合适的力常数限制条件,得到合理的结果.用本方法对一系列不同分子作了计算,结果比较满意,对计算中一些具体问题作了讨论.