A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks

The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm (SSA) [Gillespie, J. Phys. Chem. 81, 2340 (1977)]. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [Gibson and Bruck, J. Phys. Chem. A 104, 1876 (2000)]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function.     

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。     

An off-lattice, self-learning kinetic Monte Carlo method using local environments

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface.     

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.     

N2O分解反应的蒙特卡罗模拟

N2O作为大气污染物之一早已受到人们的注意，许多人研究了N2O在金属氧化物上的分解反应得到了一些基本的实验事实[1]：（1）反应速率与原料气中N2O的分压近似成比例．(2)在反应初期，N2的生成速率由大变小，O2的生成速率由小变大，达到平衡时，N2生成速率是O2生成速率的二倍．(3)过渡应答法研究表明，把原料气由N2O和He的混合气体切换成纯He后，N2立即停止发生，而O2的生成仍能维持一段时间．基于上述实验事实，人们对Nzo的催化分解反应提出了一些可能的机理，主要有下面两种看法：另一方面，人们还发现几O的催化分解反应是一个振荡…     

Mechanism-based chemical understanding of chiral symmetry breaking in the Soai reaction. A combined probabilistic and deterministic description of chemical reactions

The experimentally observed distribution of enantiomers in the Soai reaction is interpreted in this Article on the basis of a chemical mechanism using a newly developed stochastic kinetic method, accelerated Monte Carlo simulation combined with deterministic continuation and symmetrization. The method is in principle suitable for handling large mechanisms with realistic particle numbers and could be useful for any case where the kinetics of a process shows inherent random fluctuations. The mechanism shows how a slow initial reaction combined with efficient and highly enantioselective autocatalysis can give rise to chiral symmetry breaking under completely nonchiral external conditions.     

Permeation and gating in proteins: kinetic Monte Carlo reaction path following

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.     

Coarse-graining Calcium Dynamics on Stochastic Reaction-diffusion Lattice Model

We develop a coarse grained (CG) approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and deriving CG reaction rates using local mean field approximation, we perform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMC simulations are in excellent agreement with that of the microscopic ones. Strikingly, there is an appropriate range of coarse proportion m, corresponding to the minimal deviation of the phase transition point compared to the microscopic one. For fixed m, the critical point increases monotonously as the system size increases, especially, there exists scaling law between the deviations of the phase transition point and the system size. Moreover, the CG approach provides significantly faster Monte Carlo simulations which are easy to implement and are directly related to the microscopics, so that one can study the system size effects at the cost of reasonable computational time.     

The Site‐Assembly Determines Catalytic Activity of Nanoparticles

Heterogeneous catalysts are often designed as metal nanoparticles supported on oxide surfaces. Here, the relation between particle morphology and reaction kinetics is investigated by scaling relation kinetic Monte Carlo simulations using CO oxidation over Pt nanoparticles as a model reaction. We find that different particle morphologies result in vastly different catalytic activities. The activity is strongly affected by kinetic couplings between sites, and a wide site distribution generally enhances the activity. The present study highlights the role of site‐assemblies as a concept that, in addition to isolated active sites, can be used to understand catalytic reactions over nanoparticles.     

Combining reactive and configurational-bias Monte Carlo: confinement influence on the propene metathesis reaction system in various zeolites

In order to efficiently calculate chemical equilibria of large molecules in a confined environment the reactive Monte Carlo technique is combined with the configurational-bias Monte Carlo approach. To prove that detailed balance is fulfilled the acceptance rule for this combination of particular Monte Carlo techniques is derived in detail. Notably, by using this derivation all other acceptance rules of any Monte Carlo trial moves usually carried out in combination with the configurational-bias Monte Carlo approach can be deduced from it. As an application of the combination of reactive and configurational-bias Monte Carlo the influence of different zeolitic confinements (MFI, TON, LTL, and FER) on the reaction equilibrium and the selectivity of the propene metathesis reaction system was investigated. Compared to the bulk phase the conversion is increased significantly. The authors study this reaction system in the temperature range between 300 and 600 K, and the pressure range from 1 to 7 bars. In contrast to the bulk phase, pressure and temperature have a strong influence on the composition of the reaction mixture in confinement. At low pressures and temperatures both conversion and selectivity are highest. Furthermore, the equilibrium composition is strongly dependent on the type of zeolite. This demonstrates the important role of the host structure in catalytic systems.     

O—酰基—α—酮肟光分解反应的Monte Carlo处理

本文首次对光化学反应体系用Monte Carlo方法进行模拟处理。通过5个O-酰基-α-酮肟光分解反应的Monte Carlo模拟,可避免解析解中由于对吸收光强须采用一级近似求解动力学微分方程组,而造成拟合反应在后期产生与实验结果的偏差。     

碘离子催化的H2O2-BAT反应的Monte Carlo模拟

催化动力学分析是痕量分析中检测下限低、选择性较好的一种方法,但目前分析工作者对所用的反应机理常不明瞭,仅能作为“黑箱”应用之。模拟技术可为探讨这类分析反应机理提供有用的信息。前文^[1]报道用溴胺T(BAT)离子电极、跟踪碘离子催化的BAT-H₂O₂反应测定痕量碘效果甚佳。     

A Methodology for Estimating Kinetic Parameters and Reactivity Ratios of Multi‐site Type Catalysts Using Polymerization,Fractionation, and Spectroscopic Techniques

This work describes a polymer reaction engineering framework for understanding how catalyst kinetic parameters affect the microstructure of polyolefins made with single‐ or multi‐site catalysts. Moreover, a methodology for deconvolution and kinetic parameters estimation is presented to estimate the reactivity ratios of multi‐site catalysts based on the combination of polymerization, fractionation, and spectroscopic techniques, namely, gel permeation chromatography‐IR and carbon‐13 nuclear magnetic resonance spectroscopy. The methodology capabilities are then demonstrated and validated using a case study simulated via a Monte Carlo model including random noise in order to better represent experimental result uncertainties. The methodology can reverse engineer experimental results and estimate all relevant reaction performance parameters.     

OPKINE,a multipurpose program for kinetics

The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A Monte Carlo procedure to search for the seeds is also available. Simulated experiments have been used to check the performances of the program. Complex kinetic mechanisms and mixtures of a large number of analytes can be managed with good results.     

A Single‐Molecule‐Level Mechanistic Study of Pd‐Catalyzed and Cu‐Catalyzed Homocoupling of Aryl Bromide on an Au(111) Surface

On‐surface Pd‐ and Cu‐catalyzed C?C coupling reactions between phenyl bromide functionalized porphyrin derivatives on an Au(111) surface have been investigated under ultra‐high vacuum conditions by using scanning tunneling microscopy and kinetic Monte Carlo simulations. We monitored the isothermal reaction kinetics by allowing the reaction to proceed at different temperatures. We discovered that the reactions catalyzed by Pd or Cu can be described as a two‐phase process that involves an initial activation followed by C?C bond formation. However, the distinctive reaction kinetics and the C?C bond‐formation yield associated with the two catalysts account for the different reaction mechanisms: the initial activation phase is the rate‐limiting step for the Cu‐catalyzed reaction at all temperatures tested, whereas the later phase of C?C formation is the rate‐limiting step for the Pd‐catalyzed reaction at high temperature. Analysis of rate constants of the Pd‐catalyzed reactions allowed us to determine its activation energy as (0.41±0.03) eV.     

Long-timescale simulations of diffusion in molecular solids

Kinetic processes play a crucial role in the formation and evolution of molecular layers. In this perspective we argue that adaptive kinetic Monte Carlo is a powerful simulation technique for determining key kinetic processes in molecular solids. The applicability of the method is demonstrated by simulating the diffusion of a CO admolecule on a water ice surface, which is an important process for the formation of organic compounds on interstellar dust grains. CO diffusion is found to follow Arrhenius behavior and the corresponding effective activation energy for diffusion is determined to be 50 ± 1 meV. A coarse graining algorithm is applied which greatly enhances the efficiency of the simulations at low temperatures, down to 10 K, without altering the underlying physical processes. Eventually, we argue that a combination of both on- and off-lattice kinetic Monte Carlo techniques is a good way for simulating large-scale processes in molecular solids over long time spans.     

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.     

Monte Carlo sampling algorithm for searching a scale-transformed energy space of polypeptides

A Monte Carlo sampling algorithm for searching a scale-transformed conformational energy space of polypeptides is presented. This algorithm is based on the assumption that energy barriers can be overcome by a uniform sampling of the logarithmically transformed energy space. This algorithm is tested with Met-enkephalin. For comparison, the entropy sampling Monte Carlo (ESMC) simulation is performed. First, the global minimum is easily found by the optimization of a scale-transformed energy space. With a new Monte Carlo sampling, energy barriers of 3000 kcal/mol are frequently overcome, and low-energy conformations are sampled more efficiently than with ESMC simulations. Several thermodynamic quantities are calculated with good accuracy.     

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy.     

A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo

A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size.