Stochastic Simulation Of Chemical Reactions Research Articles

Стохастическое моделирование химических реакций в субдиффузионной среде

В последние десятилетия активно развивается теория аномальной диффузии, объединяющая различные транспортные процессы, в которых характерное среднеквадратичное рассеяние растет со временем по степенному закону, а не линейно, как для нормальной диффузии. Так, к примеру, диффузия жидкостей в пористых телах, перенос зарядов в аморфных полупроводниках и молекулярный транспорт в вязких средах демонстрируют аномальное «замедление» по сравнению со стандартной моделью.

Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

Cells exhibit stochastic behavior when the number of molecules is small. Hence a stochastic reaction-diffusion simulator capable of working at scale can provide a more accurate view of molecular dynamics within the cell. This paper describes a parallel discrete event simulator, Neuron Time Warp-Multi Thread (NTW-MT), developed for the simulation of reaction diffusion models of neurons. To the best of our knowledge, this is the first parallel discrete event simulator oriented towards stochastic simulation of chemical reactions in a neuron. The simulator was developed as part of the NEURON project. NTW-MT is optimistic and thread-based, which attempts to capitalize on multi-core architectures used in high performance machines. It makes use of a multi-level queue for the pending event set and a single roll-back message in place of individual anti-messages to disperse contention and decrease the overhead of processing rollbacks. Global Virtual Time is computed asynchronously both within and among processes to get rid of the overhead for synchronizing threads. Memory usage is managed in order to avoid locking and unlocking when allocating and de-allocating memory and to maximize cache locality. We verified our simulator on a calcium buffer model. We examined its performance on a calcium wave model, comparing it to the performance of a process based optimistic simulator and a threaded simulator which uses a single priority queue for each thread. Our multi-threaded simulator is shown to achieve superior performance to these simulators. Finally, we demonstrated the scalability of our simulator on a larger CICR model and a more detailed CICR model.

SOLVING STOCHASTIC CHEMICAL KINETICS BY METROPOLIS-HASTINGS SAMPLING

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master Equation) is employed for obtaining target and proposal distributions in Metropolis-Hastings algorithm to accelerate the accuracy of the tau-leap method. Samples generated by this technique have the same distribution as SSA and the histogram of samples show it's convergence to SSA.

HSIM: A Hybrid Stochastic Simulation System for Systems Biology

This paper describes a method to obtain in a certain sense the best of two well known simulation approaches: Stochastic simulation of chemical reactions and Entity-centered (multi-agents) systems. The stochastic simulation algorithm and its enhanced versions are adapted to simulate the behaviour of well stirred mixture of reactants when spatial localisation is not relevant; Conversely, in entity-centered methods, the causes and consequences due to spatial localisation are well handled. In terms of computational efficiency, the SSA methods are limited by the number of reactions and not by the amount of reactants, whereas it is the opposite for the entity-centered method. We will show how we can benefit from each approach, and also propose a new optimised algorithm for approximate stochastic simulation.

Estimating the Microtubule GTP Cap Size In Vivo

Microtubules (MTs) polymerize via net addition of GTP-tubulin subunits to the MT plus end, which subsequently hydrolyze to GDP-tubulin in the MT lattice. Relatively stable GTP-tubulin subunits create a "GTP cap" at the growing MT plus end that suppresses catastrophe. To understand MT assembly regulation, we need to understand GTP hydrolysis reaction kinetics and the GTP cap size. In vitro, the GTP cap has been estimated to be as small as one layer (13 subunits) or as large as 100-200 subunits. GTP cap size estimates in vivo have not yet been reported. Using EB1-EGFP as a marker for GTP-tubulin in epithelial cells, we find on average (1) 270 EB1 dimers bound to growing MT plus ends, and (2) a GTP cap size of ∼750 tubulin subunits. Thus, in vivo, the GTP cap is far larger than previous estimates in vitro, and ∼60-fold larger than a single layer cap. We also find that the tail of a large GTP cap promotes MT rescue and suppresses shortening. We speculate that a large GTP cap provides a locally concentrated scaffold for tip-tracking proteins and confers persistence to assembly in the face of physical barriers such as the cell cortex.

Smoldyn on Graphics Processing Units: Massively Parallel Brownian Dynamics Simulations

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

Abstract Next Subvolume Method: A logical process-based approach for spatial stochastic simulation of chemical reactions

AbstractThe spatial stochastic simulation of biochemical systems requires significant calculation efforts. Parallel discrete-event simulation is a promising approach to accelerate the execution of simulation runs. However, achievable speedup depends on the parallelism inherent in the model. One of our goals is to explore this degree of parallelism in the Next Subvolume Method type simulations. Therefore we introduce the Abstract Next Subvolume Method, in which we decouple the model representation from the sequential simulation algorithms, and prove that state trajectories generated by its executions statistically accord with those generated by the Next Subvolume Method. The experimental performance analysis shows that optimistic synchronization algorithms, together with careful controls over the speculative execution, are necessary to achieve considerable speedup and scalability in parallel spatial stochastic simulation of chemical reactions. Our proposed method facilitates a flexible incorporation of different synchronization algorithms, and can be used to select the proper synchronization algorithm to achieve the efficient parallel simulation of chemical reactions.

A Convenient Tool for the Stochastic Simulation of Reaction Mechanisms

The article introduces the stochastic simulation of chemical reactions with Chemical Kinetics Simulator, CKS, a free, easy-to-use, and powerful program. After familiarizing themselves with the Monte Carlo method of stochastic simulation and CKS, students model reactions with both kinetically and thermodynamically controlled products and study a mechanism where the steady-state approximation gives inaccurate results. Students subsequently model enzyme kinetics, an oscillatory reaction, and the mechanism responsible for the circadian rhythms of cyanobacteria. This computational exercise gives students an opportunity to appreciate the stochastic nature of chemical reactions at the molecular level, stresses the limits of applicability of kinetic approximations, and introduces the modeling of oscillatory reactions.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Stochastic reaction-diffusion simulation with MesoRD

MesoRD is a tool for stochastic simulation of chemical reactions and diffusion. In particular, it is an implementation of the next subvolume method, which is an exact method to simulate the Markov process corresponding to the reaction-diffusion master equation. MesoRD is free software, written in C++ and licensed under the GNU general public license (GPL). MesoRD runs on Linux, Mac OS X, NetBSD, Solaris and Windows XP. It can be downloaded from http://mesord.sourceforge.net. johan.elf@icm.uu.se; johan.hattne@embl-hamburg.de 'MesoRD User's Guide' and other documents are available at http://mesord.sourceforge.net.

Stochastic simulation of chemical reactions with spatial resolution and single molecule detail

Methods are presented for simulating chemical reaction networks with a spatial resolution that is accurate to nearly the size scale of individual molecules. Using an intuitive picture of chemical reaction systems, each molecule is treated as a point-like particle that diffuses freely in three-dimensional space. When a pair of reactive molecules collide, such as an enzyme and its substrate, a reaction occurs and the simulated reactants are replaced by products. Achieving accurate bimolecular reaction kinetics is surprisingly difficult, requiring a careful consideration of reaction processes that are often overlooked. This includes whether the rate of a reaction is at steady-state and the probability that multiple reaction products collide with each other to yield a back reaction. Inputs to the simulation are experimental reaction rates, diffusion coefficients and the simulation time step. From these are calculated the simulation parameters, including the ‘binding radius’ and the ‘unbinding radius’, where the former defines the separation for a molecular collision and the latter is the initial separation between a pair of reaction products. Analytic solutions are presented for some simulation parameters while others are calculated using look-up tables. Capabilities of these methods are demonstrated with simulations of a simple bimolecular reaction and the Lotka–Volterra system.

Stochastic simulation of chemical reactions by digital computer, II. Applications

The computer program aimed at the realization of a stochastic model of complex chemical reactions /1/ is described. Two applications of the program are given: (i) a reaction taking place on an adsorbent surface, and (ii) a reaction occurring under plasma conditions.