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Approximate Exponential algorithms to Solve the Chemical Master Equation

MATHEMATICAL MODELLING AND ANALYSIS 2015年第3期20卷 382-395页

作者： Mooasvi, Azam Sandu, Adrian Virginia Polytech Inst & State Univ Dept Comp Sci Sci Computat Lab Blacksburg VA 24060 USA

This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.

关键词： stochastic simulation algorithm exact solution tau-leap stochastic chemical kinetics chemical master equation

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Impact of negative feedback in metabolic noise propagation

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IET SYSTEMS BIOLOGY 2016年第5期10卷 179-186页

作者： Borri, Alessandro Palumbo, Pasquale Singh, Abhyudai Italian Natl Res Council IASI CNR Ist Anal Sistemi & Informat A Ruberti Via Taurini 19 I-00185 Rome Italy Univ Delaware Dept Elect & Comp Engn Ctr Bioinformat & Computat Biol Biomed EngnMath Sci Newark DE 19716 USA

Synthetic biology combines different branches of biology and engineering aimed at designing synthetic biological circuits able to replicate emergent properties useful for the biotechnology industry, human health and environment. The role of negative feedback in noise propagation for a basic enzymatic reaction scheme is investigated. Two feedback control schemes on enzyme expression are considered: one from the final product of the pathway activity, the other from the enzyme accumulation. Both schemes are designed to provide the same steady-state average values of the involved players, in order to evaluate the feedback performances according to the same working mode. Computations are carried out numerically and analytically, the latter allowing to infer information on which model parameter setting leads to a more efficient noise attenuation, according to the chosen scheme. In addition to highlighting the role of the feedback in providing a substantial noise reduction, our investigation concludes that the effect of feedback is enhanced by increasing the promoter sensitivity for both schemes. A further interesting biological insight is that an increase in the promoter sensitivity provides more benefits to the feedback from the product with respect to the feedback from the enzyme, in terms of enlarging the parameter design space.

关键词： biotechnology enzymes biological techniques negative feedback impact metabolic noise propagation mathematical modelling synthetic biological circuit biotechnology industry human health environment enzymatic reaction scheme feedback control scheme enzyme expression enzyme accumulation negative autoregulation steady-state average value feedback performance stochastic simulation algorithm stochastic hybrid system modelling noise attenuation substantial noise reduction feedback effect parameter design space

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Application of Monte Carlo techniques to LCO gas oil hydrotreating: Molecular reconstruction and kinetic modelling

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CATALYSIS TODAY 2016年 271卷 188-198页

作者： Abelairas, Maria Lopez de Oliveira, Luis P. Verstraete, Jan J. IFP Energies Nouvelles BP 3 F-69360 Solaize France

The increasing environmental constraints on oil products leads to the need for developing accurate models in order to predict the detailed performances of refining processes. In the current study, a stochastic two-step procedure using Monte Carlo techniques is applied to and validated on the hydrotreating of Light Cycle Oil (LCO) gas oils. In the first step, a mixture of molecules representative of the LCO gas oils is generated using a molecular reconstruction method termed SR-REM. Subsequently, the stochastic simulation algorithm (SSA) is applied to simulate the evolution of the mixture composition during hydrotreating. The results show that an accurate representation of eleven different LCO gas oils was obtained by the application of the molecular reconstruction method. The hydrotreating simulations of three LCO gas oils at different operating conditions showed a good agreement with the experimental data obtained at laboratory scale. The current stochastic procedure is demonstrated to be a valid tool for the reconstruction of the composition of LCO gas oils and the simulation of the hydrotreating process. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Composition modelling Molecular reconstruction Kinetic modelling Kinetic Monte Carlo stochastic simulation algorithm LCO gas oil hydrotreating

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MONALISA for stochastic simulations of Petri net models of biochemical systems

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BMC BIOINFORMATICS 2015年第1期16卷 1-11页

作者： Balazki, Pavel Lindauer, Klaus Einloft, Jens Ackermann, Joerg Koch, Ina Goethe Univ Frankfurt Dept Mol Bioinformat Inst Comp Sci Cluster Excellence Macromol Complex D-60325 Frankfurt Germany Sanofi Aventis Deutschland GmbH D-65926 Frankfurt Germany

Background: The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The stochastic simulation algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. Results: Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. Conclusions: We present a software that combines the modeling power of Petri nets with stocha

关键词： stochastic simulation algorithm Gillespie's algorithm Petri net MonaLisa Insulin receptor recycling

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Tensor product approach to modelling epidemics on networks

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APPLIED MATHEMATICS AND COMPUTATION 2024年 460卷

作者： Dolgov, Sergey Savostyanov, Dmitry Univ Bath Bath BA2 7AY England Univ Essex Wivenhoe Pk Colchester CO4 3SQ England

To improve mathematical models of epidemics it is essential to move beyond the traditional assumption of homogeneous well-mixed population and involve more precise information on the network of contacts and transport links by which a stochastic process of the epidemics spreads. In general, the number of states of the network grows exponentially with its size, and a master equation description suffers from the curse of dimensionality. Almost all methods widely used in practice are versions of the stochastic simulation algorithm (SSA), which is notoriously known for its slow convergence. In this paper we numerically solve the chemical master equation for an SIR model on a general network using recently proposed tensor product algorithms. In numerical experiments we show that tensor product algorithms converge much faster than SSA and deliver more accurate results, which becomes particularly important for uncovering the probabilities of rare events, e.g. for number of infected people to exceed a (high) threshold.

关键词： Epidemiological modelling Networks Chemical master equation Tensor train stochastic simulation algorithm Monte Carlo simulation Rare events High precision

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Lineage grammars: describing, simulating and analyzing population dynamics

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BMC BIOINFORMATICS 2014年第1期15卷 1-15页

作者： Spiro, Adam Cardelli, Luca Shapiro, Ehud Weizmann Inst Sci Dept Comp Sci & Appl Math IL-76100 Rehovot Israel Microsoft Res Cambridge England Weizmann Inst Sci Dept Biol Chem IL-76100 Rehovot Israel

Background: Precise description of the dynamics of biological processes would enable the mathematical analysis and computational simulation of complex biological phenomena. Languages such as Chemical Reaction Networks and Process Algebras cater for the detailed description of interactions among individuals and for the simulation and analysis of ensuing behaviors of populations. However, often knowledge of such interactions is lacking or not available. Yet complete oblivion to the environment would make the description of any biological process vacuous. Here we present a language for describing population dynamics that abstracts away detailed interaction among individuals, yet captures in broad terms the effect of the changing environment, based on environment-dependent stochastic Tree Grammars (eSTG). It is comprised of a set of stochastic tree grammar transition rules, which are context-free and as such abstract away specific interactions among individuals. Transition rule probabilities and rates, however, can depend on global parameters such as population size, generation count, and elapsed time. Results: We show that eSTGs conveniently describe population dynamics at multiple levels including cellular dynamics, tissue development and niches of organisms. Notably, we show the utilization of eSTG for cases in which the dynamics is regulated by environmental factors, which affect the fate and rate of decisions of the different species. eSTGs are lineage grammars, in the sense that execution of an eSTG program generates the corresponding lineage trees, which can be used to analyze the evolutionary and developmental history of the biological system under investigation. These lineage trees contain a representation of the entire events history of the system, including the dynamics that led to the existing as well as to the extinct individuals. Conclusions: We conclude that our suggested formalism can be used to easily specify, simulate and analyze complex biological sys

关键词： Internal State Lineage Tree Operational Semantic Transition Rule stochastic simulation algorithm

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Fine-tuning anti-tumor immunotherapies via stochastic simulations

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BMC BIOINFORMATICS 2012年第s4期13卷 S8-S8页

作者： Caravagna, Giulio Barbuti, Roberto d'Onofrio, Alberto European Inst Oncol Dept Expt Oncol I-20141 Milan Italy CNR Inst Informat & Telemat I-56127 Pisa Italy Univ Pisa Dipartimento Informat I-56127 Pisa Italy

Background: Anti-tumor therapies aim at reducing to zero the number of tumor cells in a host within their end or, at least, aim at leaving the patient with a sufficiently small number of tumor cells so that the residual tumor can be eradicated by the immune system. Besides severe side-effects, a key problem of such therapies is finding a suitable scheduling of their administration to the patients. In this paper we study the effect of varying therapy-related parameters on the final outcome of the interplay between a tumor and the immune system. Results: This work generalizes our previous study on hybrid models of such an interplay where interleukins are modeled as a continuous variable, and the tumor and the immune system as a discrete-state continuous-time stochastic process. The hybrid model we use is obtained by modifying the corresponding deterministic model, originally proposed by Kirschner and Panetta. We consider Adoptive Cellular Immunotherapies and Interleukin-based therapies, as well as their combination. By asymptotic and transitory analyses of the corresponding deterministic model we find conditions guaranteeing tumor eradication, and we tune the parameters of the hybrid model accordingly. We then perform stochastic simulations of the hybrid model under various therapeutic settings: constant, piece-wise constant or impulsive infusion and daily or weekly delivery schedules. Conclusions: Results suggest that, in some cases, the delivery schedule may deeply impact on the therapy-induced tumor eradication time. Indeed, our model suggests that Interleukin-based therapies may not be effective for every patient, and that the piece-wise constant is the most effective delivery to stimulate the immune-response. For Adoptive Cellular Immunotherapies a metronomic delivery seems more effective, as it happens for other anti-angiogenesis therapies and chemotherapies, and the impulsive delivery seems more effective than the piece-wise constant. The expected synergistic e

关键词： Hybrid Model Therapy Session stochastic simulation algorithm Propensity Function Adoptive Cellular Immunotherapy

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Slow-scale tau-leaping method

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2008年第43-44期197卷 3472-3479页

作者： Cao, Yang Petzold, Linda Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA Virginia Tech Dept Comp Sci Blacksburg VA 24061 USA

For chemical systems involving both fast and slow-scales, stiffness presents challenges for efficient stochastic simulation. Two different avenues have been explored to solve this problem. One is the slow-scale stochastic simulation (ssSSA) based on the stochastic partial equilibrium assumption. The other is the tau-leaping method. In this paper, we propose a new algorithm, the slow-scale tau-leaping method, which combines some of the best features of these two methods. Numerical experiments are presented which illustrate the effectiveness of this approach. (C) 2008 Elsevier B.V. All rights reserved.

关键词： tau-leaping stochastic simulation algorithm chemically reacting systems partial equilibrium discrete stochastic simulation

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Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

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COMPUTER PHYSICS COMMUNICATIONS 2019年 240卷 30-37页

作者： St-Onge, Guillaume Young, Jean-Gabriel Hebert-Dufresne, Laurent Dube, Louis J. Univ Laval Dept Phys Genie Phys & Opt Quebec City PQ G1V 0A6 Canada Univ Laval Ctr Interdisciplinaire Modelisat Math Quebec City PQ G1V 0A6 Canada Univ Vermont Dept Comp Sci Burlington VT 05401 USA Univ Vermont Vermont Complex Syst Ctr Burlington VT 05401 USA

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O(log N) or even O(1) operations per update - where N is the number of nodes - display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O[log(log N)] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Spreading process Complex network stochastic simulation algorithm

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APPROXIMATING PROBABILISTIC INFERENCE IN BAYESIAN BELIEF NETWORKS

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1993年第3期15卷 246-255页

作者： DAGUM, P CHAVEZ, RM ROCKWELL INT CORP PALO ALTO LABPALO ALTOCA

A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. We present such a stochastic simulation algorithm D-BNRAS that is a randomized approximation scheme. To analyze the run time, we parameterize belief networks by the dependence value D(xi), which is a measure of the cumulative strengths of the belief network dependencies given background evidence xi. This parameterization defines the class of f-dependence networks. The run time of D-BNRAS is polynomial when f is a polynomial function. Thus, the results of this paper prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm.

关键词： Intelligent networks Bayesian methods Inference algorithms stochastic processes Approximation algorithms Computational modeling Polynomials Medical simulation Knowledge representation Sampling methods INSPEC: Controlled Indexing uncertainty handling Bayes methods belief maintenance inference mechanisms polynomials probabilistic logic INSPEC: Non-Controlled Indexing polynomial probabilistic inference approximation reasoning Bayesian belief networks conditional probabilities stochastic simulation algorithm D-BNRAS

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