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Effect of population size in a predator-prey model

ECOLOGICAL MODELLING 2012年第C期246卷 1-10页

作者： Campillo, F. Lobry, C. SupAgro Modemic Team Project INRA INRIA F-34060 Montpellier 2 France

We consider a hybrid version of the basic predator-prey differential equation model: a pure jump stochastic model for the prey variable x coupled with a differential equation model for the predator variable y. This hybrid model is derived from the classical birth and death process. The model contains a parameter omega which represents the number of individuals for one unit of prey: x = 1 corresponds to omega individual prey. It is shown by the mean of simulations and explained by a mathematical analysis based on a result from the singular perturbation theory - the so-called theory of Canards - that qualitative properties of the model like persistence or extinction are dramatically sensitive to omega. For instance, in our example, if omega = 10(7) we have extinction and if omega = 10(8) we have persistence. This means that we must be very cautious when we use continuous variables in place of discrete ones in dynamic population modeling even when we use stochastic differential equations in place of deterministic ones. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Predator-prey model Ordinary differential equations Diffusion equations gillespie algorithm Birth and death processes

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Experiments and stochastic simulations of lignite coal during pyrolysis and gasification

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APPLIED ENERGY 2013年第Feb.期102卷 355-363页

作者： Ahmed, I. I. Gupta, A. K. Univ Maryland Dept Mech Engn Combust Lab College Pk MD 20742 USA

Lignite pyrolysis and gasification has been conducted in a semi batch reactor at reactor temperatures of 800-950 degrees C in 50 degrees C intervals. CO2 has been used as the gasifying agent for gasification experiments. The objective of this investigation is to understand the mechanism of syngas evolution during pyrolysis and to unravel the effect of CO2 on pyrolysis mechanism. Stochastic simulations of lignite pyrolysis have been conducted using gillespie algorithm. Two reaction mechanisms have been used in the simulations;first order, single step mechanism and the FLASHCHAIN mechanism. The first order single step mechanism was successful in fitting cumulative yield of CO2, CO, CH4 and other hydrocarbons (CnHm). The first order, single step failed to fit the cumulative yield of hydrogen, which suggests a more complex mechanism for hydrogen evolution. Evolution of CO2, CO, CH4, CnHm, and H-2 flow rates has been monitored. The only effect of CO2 on pyrolysis mechanism is promotion of reverse water gas shift reaction for the experiments described here. Methane evolution extended for slightly longer time than other hydrocarbons and hydrogen evolution extended for a slightly longer time than methane. This indicated the evolution of hydrogen via further pyrolysis of aliphatic hydrocarbon. It is also suggested that this step occurs in series after aliphatic hydrocarbons evolution by bridges scission. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Lignite pyrolysis Lignite gasification CO2 gasification Stochastic simulations gillespie algorithm

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Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations

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PARALLEL COMPUTING 2014年第5-6期40卷 86-99页

作者： Hallock, Michael J. Stone, John E. Roberts, Elijah Fry, Corey Luthey-Schulten, Zaida Univ Illinois Sch Chem Sci Urbana IL 61801 USA Univ Illinois Beckman Inst Urbana IL 61801 USA Johns Hopkins Univ Dept Biophys Baltimore MD 21218 USA Univ Illinois Dept Chem Urbana IL 61801 USA

Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel efficiency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/3.0/).

关键词： GPU Computing Reaction-diffusion master equation gillespie algorithm Stochastic simulation Distributed memory parallel computing Biological cells

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Collective decision with 100 Kilobots: speed versus accuracy in binary discrimination problems

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AUTONOMOUS AGENTS AND MULTI-AGENT SYSTEMS 2016年第3期30卷 553-580页

作者： Valentini, Gabriele Ferrante, Eliseo Hamann, Heiko Dorigo, Marco Univ Libre Bruxelles IRIDIA Brussels Belgium Katholieke Univ Leuven Lab Socioecol & Social Evolut Leuven Belgium Univ Paderborn Dept Comp Sci Heinz Nixdorf Inst Warburger Str 100 D-33098 Paderborn Germany

Achieving fast and accurate collective decisions with a large number of simple agents without relying on a central planning unit or on global communication is essential for developing complex collective behaviors. In this paper, we investigate the speed versus accuracy trade-off in collective decision-making in the context of a binary discrimination problem-i.e., how a swarm can collectively determine the best of two options. We describe a novel, fully distributed collective decision-making strategy that only requires agents with minimal capabilities and is faster than previous approaches. We evaluate our strategy experimentally, using a swarm of 100 Kilobots, and we study it theoretically, using both continuum and finite-size models. We find that the main factor affecting the speed versus accuracy trade-off of our strategy is the agents' neighborhood size-i.e., the number of agents with whom the current opinion of each agent is shared. The proposed strategy and the associated theoretical framework can be used to design swarms that take collective decisions at a given level of speed and/or accuracy.

关键词： Collective decision-making Swarm robotics Majority rule Voter model Self-organization Ordinary differential equations Chemical reaction network gillespie algorithm Kilobot

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Kinetic turbidimetry of patchy colloids aggregation: Latex particles immunoagglutination

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COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS 2017年 516卷 72-79页

作者： Polshchitsin, Alexey A. Nekrasov, Vyacheslav M. Zakovryashin, Valentin S. Yakovleva, Galina E. Maltsev, Valeri P. Yurkin, Maxim A. Chernyshev, Andrei V. Inst Chem Kinet & Combust Inst Skaya 3 Novosibirsk 630090 Russia Novosibirsk State Univ Pirogova 2 Novosibirsk 630090 Russia JSC VECTOR BEST POB 492 Novosibirsk 630117 Russia Novosibirsk State Med Univ Krasny Prospect 52 Novosibirsk 630091 Russia

The paper is devoted to the problem of the kinetic study of aggregation of particles with several active sites (so called "patchy particles") using turbidimetry. Patchy particles are known as chemically-anisotropic reactants, and the kinetics theory of their interaction is far from complete. In this work we theoretically derived and experimentally verified analytical expressions, which are convenient for the treatment of the turbidimetric data on the overall optical density change (due to light scattering of the particles) of the aggregating patchy colloid. Light scattering cross sections of the aggregates were calculated using the superposition T-matrix method. Particularly, we used an analytical approximation for the diffusion limited rate constants of Smoluchowski equations of aggregation of chemically-anisotropic particles (or clusters) with several small active sites assuming that the clusters are of fractal structure. In order to account for the case of a small (<10) number of active sites on particles we used Monte Carlo stochastic algorithm of gillespie method. For the verification, we carried out experiments on kinetic turbidimetric study of the immunoagglutination of 65 nm polystyrene particles covered by anti-CRP IgG antibodies in the water solution of C-reactive protein (CRP). Good agreement of experimental data and theoretical simulations allowed us to evaluate the average number of active antibody molecules per particle as 9.0 +/- 2.2 and the affinity of the antigen-antibody complex as 5.5 +/- 1.5 x 10(7) M-1. A significant kinetic effect of the small number of active sites per particle was found. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Patchy particles Colloid aggregation kinetics Latex immunoagglutination Turbidimetric assay Fractal clusters Rate constant Biospecific binding Monte-Carlo simulation gillespie algorithm

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Equivalence of on-lattice stochastic chemical kinetics with the well-mixed chemical master equation in the limit of fast diffusion

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COMPUTERS & CHEMICAL ENGINEERING 2011年第12期35卷 2602-2610页

作者： Stamatakis, Michail Vlachos, Dionisios G. Univ Delaware Dept Chem Engn Newark DE 19716 USA

Well-mixed and lattice-based descriptions of stochastic chemical kinetics have been extensively used in the literature. Realizations of the corresponding stochastic processes are obtained by the gillespie stochastic simulation algorithm and lattice kinetic Monte Carlo algorithms, respectively. However, the two frameworks have remained disconnected. We show the equivalence of these frameworks whereby the stochastic lattice kinetics reduces to effective well-mixed kinetics in the limit of fast diffusion. In the latter, the lattice structure appears implicitly, as the lumped rate of bimolecular reactions depends on the number of neighbors of a site on the lattice. Moreover, we propose a mapping between the stochastic propensities and the deterministic rates of the well-mixed vessel and lattice dynamics that illustrates the hierarchy of models and the key parameters that enable model reduction. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Master equation Time scale separation Stiffness Kinetic Monte Carlo gillespie algorithm Chemical kinetics

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Block Search Stochastic Simulation algorithm (BlSSSA): A Fast Stochastic Simulation algorithm for Modeling Large Biochemical Networks

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022年第4期19卷 2111-2123页

作者： Ghosh, Debraj De, Rajat K. Indian Stat Inst Machine Intelligence Unit Kolkata 700108 W Bengal India

Stochastic simulation algorithms are extensively used for exploring stochastic behavior of biochemical pathways/networks. Computational cost of these algorithms is high in simulating real biochemical systems due to their large size, complex structure and stiffness. In order to reduce the computational cost, several algorithms have been developed. It is observed that these algorithms are basically fast in simulating weakly coupled networks. In case of strongly coupled networks, they become slow as their computational cost become high in maintaining complex data structures. Here, we develop Block Search Stochastic Simulation algorithm (BlSSSA). BlSSSA is not only fast in simulating weakly coupled networks but also fast in simulating strongly coupled and stiff networks. We compare its performance with other existing algorithms using two hypothetical networks, viz., linear chain and colloidal aggregation network, and three real biochemical networks, viz., B cell receptor signaling network, FceRI signaling network and a stiff 1,3-Butadiene Oxidation network. It has been shown that BlSSSA is faster than other algorithms considered in this study.

关键词： Stochastic processes Biological system modeling Mathematical model Computational modeling Computational efficiency Indexes Statistics gillespie algorithm B cell receptor signaling network FceRI signaling network Stiff network Colloidal aggregation network and stochastic modeling

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How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

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JOURNAL OF SIMULATION 2024年第2期18卷 206-219页

作者： Sottile, Sara Kahramanogullari, Ozan Sensi, Mattia Univ Trento Dept Math Via Sommar 14 I-38123 Povo Trento Italy Univ Cote dAzur INRIA MathNeuro Team Biot France Free Univ Bozen Bolzano Fac Comp Sci Dominikanerpl 3Piazza Domenicani 3 I-39100 Bozen Bolzano Italy

With the premise that social interactions are described by power-law distributions, we study the stochastic dynamics of SIR (Susceptible-Infected-Removed) compartmental models on static scale-free random networks generated via the configuration model. We compare simulations of our model to analytical results, providing a closed formula and a lower bound for the probability of having a minor epidemic of the disease. We explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of the starting node's degree in determining these indices, commonly used to describe epidemic spread. Our results and implementation set a baseline for studying epidemic spread on networks, showing how analytical methods can help in the interpretation of stochastic simulations.

关键词： Epidemic models configuration model scale-free networks spreaders in network gillespie algorithm stochastic simulation

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The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2006年第1期30卷 39-49页

作者： McCollum, JM Peterson, GD Cox, CD Simpson, ML Samatova, NF Oak Ridge Natl Lab Computat Biol Inst Oak Ridge TN 37831 USA Univ Tennessee Dept Elect & Comp Engn Knoxville TN 37996 USA Univ Tennessee Ctr Environm Biotechnol Knoxville TN 37996 USA Univ Tennessee Dept Civil & Environm Engn Knoxville TN 37996 USA Oak Ridge Natl Lab Mol Scale Engn & Nanoscale Technol Res Grp Oak Ridge TN 37831 USA Univ Tennessee Dept Mat Sci & Engn Knoxville TN 37996 USA

A key to advancing the understanding of molecular biology in the post-genomic age is the development of accurate predictive models for genetic regulation, protein interaction, metabolism, and other biochemical processes. To facilitate model development, simulation algorithms must provide an accurate representation of the system, while performing the simulation in a reasonable amount of time. gillespie's stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous models with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, we examine the performance of different versions of the SSA when applied to several biochemical models. Through our analysis, we discover that transient changes in reaction execution frequencies, which are typical of biochemical models with gene induction and repression, can dramatically affect simulator performance. To account for these shifts, we propose a new algorithm called the sorting direct method that maintains a loosely sorted order of the reactions as the simulation executes. Our measurements show that the sorting direct method performs favorably when compared to other well-known exact stochastic simulation algorithms. (C) 2005 Elsevier Ltd. All rights reserved.

关键词： stochastic simulation modeling biochemical systems gillespie algorithm gene networks systems biology

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A kinetic Monte Carlo simulation study of inositol 1,4,5-trisphosphate receptor (IP3R) calcium release channel

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2007年第2期31卷 99-109页

作者： Haeri, H. H. Hashemianzadeh, S. M. Monajjemi, M. Islamic Azad Univ Dept Phys Chem Tehran Shargh Branch Tehran Iran IUST Dept Phys Chem Tehran Iran Islamic Azad Univ Dept Phys Chem Tehran Iran

Most of the previously theoretical studies about the stochastic nature of the IP3R calcium release channel gating use the chemical master equation (CME) approach. Because of the limitations of this approach we have used a stochastic simulation algorithm (SSA) presented by gillespie. A single subunit of De Young-Keizer (DYK) model was simulated using gillespie algorithm. The model has been considered in its complete form with eight states. We investigate the conditions which affect the open state of the model. Calcium concentrations were the subject of fluctuation in the previous works while in this study the population of the states is the subject of stochastic fluctuations. We found out that decreasing open probability is a function of Ca2+ concentration in fast time domain, while in slow time domain it is a function of IP3 concentration. Studying the population of each state shows a time dependent reaction pattern in fast and medium time domains (10(-4) and 10(-3) s). In this pattern the state of X-010 has a determinative role in selecting the open state path. Also, intensity and frequency of fluctuations and Ca2+ inhibitions have been studied. The results indicate that gillespie algorithm can be a better choice for studying such systems, without using any approximation or elimination while having acceptable accuracy. In comparison with the chemical master equation, gillespie algorithm is also provides a wide area for studying biological systems from other points of view. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： ion channel De Young-Keizer model stochastisity gillespie algorithm Monte Carlo complex reactions

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