Sampling potential energy surface of glycyl glycine peptide: Comparison of Metropolis Monte Carlo and stochastic dynamics

A comparative study was carried out to test the efficiency with which Metropolis Monte Carlo (MC) and stochastic dynamics (SD) sample the potential energy surface of the N-acetyl glycyl glycine methylamide peptide as defined by the united atom AMBER* force field. Boltzmann-weighted ensembles were generated with variations of all internal degrees of freedom (i.e., stretch, bend, and torsion) for a single N-acetyl glycyl glycine methylamide molecule at 300 K by 10⁸-step MC and 100-ns SD simulations. As expected, both methods gave the same final energetic results. However, convergence was found to be ∼10 times faster with MC than with SD as measured by comparisons of the populations of all symmetrically equivalent conformers. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1294–1299, 1998     

Systematic stepsize variation: Efficient method for searching conformational space of polypeptides

A new and efficient method for overcoming the multiple minima problem of polypeptides, the systematic stepsize variation (SSV) method, is presented. The SSV is based on the assumption that energy barriers can be passed over by sufficiently large rotations about rotatable bonds: randomly chosen dihedral angles are updated starting with a small stepsize (i.e., magnitude of rotation). A new structure is accepted only if it possesses a lower energy than the precedent one. Local minima are passed over by increasing the stepsize systematically. When no new structures are found any longer, the simulation is continued with the starting structure, but other trajectories will be followed due to the random order in updating the torsional angles. First, the method is tested with Met-enkephalin, a peptide with a known global minimum structure; in all runs the latter is found at least once. The global minimum conformations obtained in the simulations show deviations of ±0.0004 kcal/mol from the reference structure and, consequently, are perfectly superposable. For comparison, Metropolis Monte Carlo simulated annealing (MMC-SA) is performed. To estimate the efficiency of the algorithm depending on the complexity of the optimization problem, homopolymers of Ala and Gly of different lengths are simulated, with both the SSV and the MMC-SA method. The comparative simulations clearly reveal the higher efficiency of SSV compared with MMC-SA. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1470–1481, 1998     

Predicting the Molecular Arrangements in Polymer‐Based Nanocomposites

Monte Carlo computer simulations have been performed for model polymers containing randomly distributed spherical filler particles (20% in volume) with diameter between 4 times and 28 times the transverse diameter of the chains. By analyzing the results in conjunction with those of previous simulations, a few simple rules are deduced allowing to predict approximately the molecular arrangements in these complex systems.

Schematic two‐dimensional picture of the mutual arrangements of filler particles and chains predicted for system M₁₂.     

MLIMC: Machine Learning-Based Implicit-Solvent Monte Carlo

Monte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule. The two most popular implicit-solvent models are the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way such that the GB model is an approximation to the PB model but is much faster in simulation time. In this work, we develop a machine learning-based implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both implicit solvent models in accuracy and efficiency. Specifically, the MLIMC method uses a fast and accurate PB-based machine learning (PBML) scheme to compute the electrostatic solvation free energy at each step. We validate our MLIMC method by using a benzene-water system and a protein-water system. We show that the proposed MLIMC method has great advantages in speed and accuracy for molecular structure optimization and prediction.     

Coding‐theoretic constructions for (t,m,s)‐nets and ordered orthogonal arrays

(t,m,s)‐nets are point sets in Euclidean s‐space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi‐Monte Carlo methods and coding theory. The ambient space is a metric space generalizing the Hamming space of coding theory. We denote it by NRT space (named after Niederreiter, Rosenbloom and Tsfasman). Our main results are generalizations of coding‐theoretic constructions from Hamming space to NRT space. These comprise a version of the Gilbert‐Varshamov bound, the (u,u+υ)‐construction and concatenation. We present a table of the best known parameters of q‐ary (t,m,s)‐nets for qε{2,3,4,5} and dimension m≤50. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 403–418, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10015     

Fast computation,rotation, and comparison of low resolution spherical harmonic molecular surfaces

A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999     

Application of combined Monte Carlo and molecular dynamics method to simulation of dipalmitoyl phosphatidylcholine lipid bilayer

We describe a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer. The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer, in a constant volume and temperature ensemble. The procedure is described in detail and is applied to a bilayer of 100 molecules of dipalmitoyl phosphatidylcholine (DPPC) and 3205 water molecules. We find that the hybrid simulation procedure enhances the equilibration of the bilayer as measured by the convergence of the area per molecule and the segmental order parameters, as compared with a simulation using only molecular dynamics (MD). Progress toward equilibration is almost three times as fast in CPU time, compared with a purely MD simulation. Equilibration is complete, as judged by the lack of energy drift in three separate 200-ps runs of continuous MD started from different initial states. Results of the simulation are presented and compared with experimental data and with other recent simulations of DPPC. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1153–1164, 1999     

GARCH模型中美式亚式期权价值的蒙特卡罗模拟算法

我们运用 Longstaff和 Schwartz最近提出的用蒙特卡罗模拟法计算美式期权的方法在 GARCH模型中求解美式亚式期权 ,我们的结果表明和其它数值方法相比 ,这个方法不仅有相当的精确度 ,而且使用简便并具有更广泛的适用性 ,对于 GARCH模型中运用格点法难以求解的浮动执行价格的美式亚式期权同样可以得到稳定解 .     

Distribution-free posterior analysis of econometric models

Very often, one needs to perform (classical or Bayesian) inference, when essentially nothing is known about the distribution of the dependent variable given certain covariates. The paper proposes to approximate the unknown distribution by its non-parametric counterpart—a step function—and treat the points of the support and the corresponding density values, as parameters, whose posterior distributions should be determined based on the available data. The paper proposes distributions should be determined based on the available data. The paper proposes Markov chain Monte Carlo methods to perform posterior analysis, and applies the new method to an analysis of stock returns. Copyright © 1999 John Wiley & Sons, Ltd.     

Inspection games in arms control

An inspection game is a mathematical model of a situation in which an inspector verifies the adherence of an inspectee to some legal obligation, such as an arms control treaty, where the inspectee may have an interest in violating that obligation. The mathematical analysis seeks to determine an optimal inspection scheme, ideally one which will induce legal behavior, under the assumption that the potential illegal action is carried out strategically; thus a non-cooperative game with two players, inspector and inspectee, is defined. Three phases of development in the application of such models to arms control and disarmament may be identified. In the first of these, roughly from 1961 through 1968, studies that focused on inspecting a nuclear test ban treaty emphasized game theory, with less consideration given to statistical aspects associated with data acquisition and measurement uncertainty. The second phase, from 1968 to about 1985, involves work stimulated by the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). Here, the verification principle of material accountancy came to the fore, along with the need to include the formalism of statistical decision theory within the inspection models. The third phase, 1985 to the present, has been dominated by challenges posed by such far-reaching verification agreements as the Intermediate Range Nuclear Forces Agreement (INF), the Treaty on Conventional Forces in Europe (CFE) and the Chemical Weapons Convention (CWC), as well as perceived failures of the NPT system in Iraq and North Korea. In this connection, the interface between the political and technical aspects of verification is being examined from the game-theoretic viewpoint.