Prediction of peptide conformation using a scale-transformed entropy sampling algorithm

An algorithm for predicting the lowest energy structure of a peptide has been developed. High-energy barriers on an energy surface can be easily overcome by logarithmically transforming the energy space. For efficient optimizations, the energy space is searched using a scale-transformed entropy sampling method, and conformations specific to a primary structure of the peptide are sampled with large weights. The efficiency of the present method is demonstrated by calculations on cholecystokinin octapeptide (CCK-8).     

Thermodynamic properties of Ag2O--B2O3 glasses by a modified scale-transformed energy space sampling Monte Carlo method

The density of states of Ag(2)O--B(2)O(3) glasses has been calculated by using a modified scale-transformed energy space sampling algorithm. This algorithm combines the scale-transformed energy space sampling algorithm and the Wang-Landau method. It is shown how the two algorithms can be combined to improve the efficiency of calculation. The thermodynamic properties, in particular the specific heat C(V), of the above-mentioned glass system is studied. At temperatures above 80 K, the value of specific heat C(v) is close to 22 J/mol/K. At low temperatures, the deviations of C(v) from a T(3) behavior are discernible, that is, C(v)/T(3) exhibits a hump at T = 7 K, which is in good agreement with the reported experimental behavior.     

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.     

MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules

Many of the most common molecular simulation methods, including Monte Carlo (MC) and molecular or stochastic dynamics (MD or SD), have significant difficulties in sampling the space of molecular potential energy surfaces characterized by multiple conformational minima and significant energy barriers. In such cases improved sampling can be obtained by special techniques that lower such barriers or somehow direct search steps toward different low energy regions of space. We recently described a hybrid MC/SD algorithm [MC(JBW)/SD] incorporating such a technique that directed MC moves of selected torsion and bond angles toward known low energy regions of conformational space. Exploration of other degrees of freedom was left to the SD part of the hybrid algorithm. In the work described here, we develop a related but simpler simulation algorithm that uses only MC to sample all degrees of freedom (e.g., stretch, bend, and torsion). We term this algorithm MC(JBW). Using simulations on various model potential energy surfaces and on simple molecular systems (n-pentane, n-butane, and cyclohexane), MC(JBW) is shown to generate ensembles of states that are indistinguishable from the canonical ensembles generated by classical Metropolis MC in the limit of very long simulations. We further demonstrate the utility of MC(JBW) by evaluating the room temperature free energy differences between conformers of various substituted cyclohexanes and the larger ring hydrocarbons cycloheptane, cyclooctane, cyclononane, and cyclodecane. The results compare favorably with available experimental data and results from previously reported MC(JBW)/SD conformational free energy calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1736–1745, 1998     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Combining smart darting with parallel tempering using Eckart space: application to Lennard-Jones clusters

The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard-Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard-Jones cluster using the combined method are smaller than parallel tempering when used alone.     

Free energy landscapes for the thermodynamic understanding of adsorption-induced deformations and structural transitions in porous materials

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of interest, molecular simulation methods that directly couple adsorption and large structural deformations in an efficient manner are still lacking. We propose here a new Monte Carlo simulation method based on non-Boltzmann sampling in (guest loading, volume) space using the Wang-Landau algorithm, and show that it can be used to fully characterize the adsorption properties and the material's response to adsorption at thermodynamic equilibrium. We showcase this new method on a simple model of the MIL-53 family of breathing materials, demonstrating its potential and contrasting it with the pitfalls of direct, Boltzmann simulations. We furthermore propose an explanation for the hysteretic nature of adsorption in terms of free energy barriers between the two metastable host phases.     

多维微正则蒙特卡罗方法计算异氰酸S0→T1系间窜跃速率

推导了通用的坐标空间多维蒙特卡罗微正则非绝热速率计算公式,并应用于计算异氰酸基5（S0）到第一激发三态（T1）的系间窜跃（ISC）速率．在CCSD水平上构建了一,二,三维势能面用于蒙特卡罗抽样．计算所得S0→T1 ISC速率与实验符合较好,因此可以预期多维蒙特卡罗微正则非绝热速率理论将成为计算多原子分子非绝热反应速率的有效手段之一．     

Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble: Efficient conformational analysis of RNA

A hybrid Monte Carlo method with adaptive temperature choice is presented that exactly generates the distribution of a mixed-canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. The algorithm is tested by comparing analytical and numerical results for the small n-butane molecule before simulations are performed for a triribonucleotide. Sampling the complex multiminima energy landscape of this small RNA segment, we observe enforced crossing of energy barriers. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1689–1697, 1998     

Multicanonical Monte Carlo calculation of the free‐energy map of the base–amino acid interaction

The specific interactions between base pairs and amino acids were studied by the multicanonical Monte Carlo method. We sampled numerous interaction configurations and side‐chain conformations of the amino acid by the multicanonical algorithm, and calculated the free energies of the interactions between an amino acid at given C_α positions and a fixed base pair. The contour maps of free energy derived from this calculation represent the preferred C_α position of the amino acid around the base, and these maps of various combinations of bases and amino acids can be used to quantify the specificity of intrinsic base–amino acid interactions. Similarly, enthalpy and entropy maps will provide further details of the specific interactions. We have also calculated the free‐energy map of the orientations of the C_α C_β bond vector, which indicates the preferential orientation of the amino acid against the base. We compared the results obtained by the multicanonical method with those of the exhaustive sampling and canonical Monte Carlo methods. The free‐energy map of the base–amino acid interaction obtained by the multicanonical simulation method was nearly identical to the accurate result derived from the exhaustive sampling method. This indicates that a single multicanonical Monte Carlo simulation can produce an accurate free‐energy map. Multicanonical Monte Carlo sampling produced free‐energy maps that were more accurate than those produced by canonical Monte Carlo sampling. Thus, the multicanonical Monte Carlo method can serve as a powerful tool for estimating the free‐energy landscape of base–amino acid interactions and for elucidating the mechanism by which amino acids of proteins recognize particular DNA base pairs. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 954–962, 2000     

Path ensembles and path sampling in nonequilibrium stochastic systems

Markovian models based on the stochastic master equation are often encountered in single molecule dynamics, reaction networks, and nonequilibrium problems in chemistry, physics, and biology. An efficient and convenient method to simulate these systems is the kinetic Monte Carlo algorithm which generates continuous-time stochastic trajectories. We discuss an alternative simulation method based on sampling of stochastic paths. Utilizing known probabilities of stochastic paths, it is possible to apply Metropolis Monte Carlo in path space to generate a desired ensemble of stochastic paths. The method is a generalization of the path sampling idea to stochastic dynamics, and is especially suited for the analysis of rare paths which are not often produced in the standard kinetic Monte Carlo procedure. Two generic examples are presented to illustrate the methodology.     

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

Constructing a free energy landscape for a large molecule is difficult. One has to use either a high temperature or a strong driving force to enhance the sampling on the free energy barriers. In this work, we propose a mixed method that combines these two kinds of acceleration strategies into one simulation. First, it applies an adaptive biasing potential to some replicas of the molecule. These replicas are particularly accelerated in a collective variable space. Second, it places some unbiased and exchangeable replicas at various temperature levels. These replicas generate unbiased sampling data in the canonical ensemble. To improve the sampling efficiency, biased replicas transfer their state variables to the unbiased replicas after equilibrium by Monte Carlo trial moves. In comparison to previous integrated methods, it is more convenient for users. It does not need an initial reference biasing potential to guide the sampling of the molecule. And it is also unnecessary to insert many replicas for the requirement of passing the free energy barriers. The free energy calculation is accomplished in a single stage. It samples the data as fast as a biased simulation and it processes the data as simple as an unbiased simulation. The method provides a minimalist approach to the construction of the free energy landscape. © 2019 Wiley Periodicals, Inc.     

How enzyme dynamics helps catalyze a reaction in atomic detail: a transition path sampling study

We have applied the Transition Path Sampling algorithm to the reaction catalyzed by the enzyme Lactate Dehydrogenase. This study demonstrates the ease of scaling Transition Path Sampling for applications on many degree of freedom systems, whose energy surface is a complex terrain of valleys and saddle points. As a Monte Carlo importance sampling method, transition path sampling is capable of surmounting barriers in path phase space and focuses simulation on the rare event of enzyme catalyzed atom transfers. Generation of the transition path ensemble, for this reaction, resolves a paradox in the literature in which some studies exposed the catalytic mechanism of hydride and proton transfer by lactate dehydrogenase to be concerted and others stepwise. Transition path sampling has confirmed both mechanisms as possible paths from reactants to products. With the objective to identify a generalized, reduced reaction coordinate, time series of both donor-acceptor distances and residue distances from the active site have been examined. During the transition from pyruvate to lactate, residues located behind the transferring hydride collectively compress toward the active site causing residues located behind the hydride acceptor to relax away. It is demonstrated that an incomplete compression/relaxation transition across the donor-acceptor axis compromises the reaction.     

Conformational transition free energy profiles of an adsorbed, lattice model protein by multicanonical Monte Carlo simulation

Proteins often undergo changes in internal conformation upon interacting with a surface. We investigate the thermodynamics of surface induced conformational change in a lattice model protein using a multicanonical Monte Carlo method. The protein is a linear heteropolymer of 27 segments (of types A and B) confined to a cubic lattice. The segmental order and nearest neighbor contact energies are chosen to yield, in the absence of an adsorbing surface, a unique 3x3x3 folded structure. The surface is a plane of sites interacting either equally with A and B segments (equal affinity surface) or more strongly with the A segments (A affinity surface). We use a multicanonical Monte Carlo algorithm, with configuration bias and jump walking moves, featuring an iteratively updated sampling function that converges to the reciprocal of the density of states 1/Omega(E), E being the potential energy. We find inflection points in the configurational entropy, S(E)=k ln Omega(E), for all but a strongly adsorbing equal affinity surface, indicating the presence of free energy barriers to transition. When protein-surface interactions are weak, the free energy profiles F(E)=E-TS(E) qualitatively resemble those of a protein in the absence of a surface: a free energy barrier separates a folded, lowest energy state from globular, higher energy states. The surface acts in this case to stabilize the globular states relative to the folded state. When the protein surface interactions are stronger, the situation differs markedly: the folded state no longer occurs at the lowest energy and free energy barriers may be absent altogether.     

An efficient sampling algorithm for variational Monte Carlo

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).     

自由基聚合反应的Monte Carlo模拟方法

本文将化学反应动力学的MonteCarlo模拟方法运用到引发剂引发的自由基聚合反应的非稳态动力学,针对自由基聚合反应动力学数值模拟所特有的"无伸缩问题",采用"偏倚抽样法"解决了MonteCarlo模拟中的"无伸缩问题",模拟结果与非稳态动力学解的结果完全一致,此算法易推广到研究更复杂的自由基聚合反应体系。     

A multi-dimensional microcanonical Monte Carlo study of S0 → T1 intersystem crossing of isocyanic acid

A general formula for the multi-dimensional Monte Carlo microcanonical nonadiabatic rate constant expressed in configuration space is applied to calculate the rate of intersystem crossing (ISC) between the ground (S₀) and first excited triplet (T₁) states for isocyanic acid. One-, two- and three-dimensional potential energy surfaces are constructed by coupled-cluster single-double CCSD calculations, which are used for Monte Carlo sampling. The calculated S₀→T₁ ISC rate is in good agreement with experimental findings, which gives us a reason to believe that the multi-dimensional Monte Carlo microcanonical nonadiabatic rate theory is a very effective method for calculating nonadiabatic transition rate of a polyatomic molecule.     

Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.     

Annealing contour Monte Carlo algorithm for structure optimization in an off-lattice protein model

We present a space annealing version for a contour Monte Carlo algorithm and show that it can be applied successfully to finding the ground states for an off-lattice protein model. The comparison shows that the algorithm has made a significant improvement over the pruned-enriched-Rosenbluth method and the Metropolis Monte Carlo method in finding the ground states for AB models. For all sequences, the algorithm has renewed the putative ground energy values in the two-dimensional AB model and set the putative ground energy values in the three-dimensional AB model.