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Multi-scale behavior in chemical rea...

Turner, Jesse Hosea, III.

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Multi-scale behavior in chemical reaction systems: Modeling, applications, and results.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Multi-scale behavior in chemical reaction systems: Modeling, applications, and results./
Author:	Turner, Jesse Hosea, III.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2008,
Description:	126 p.
Notes:	Source: Dissertations Abstracts International, Volume: 70-10, Section: B.
Contained By:	Dissertations Abstracts International70-10B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3309974
ISBN:	9780549584513

Multi-scale behavior in chemical reaction systems: Modeling, applications, and results.
Turner, Jesse Hosea, III.

Multi-scale behavior in chemical reaction systems: Modeling, applications, and results. - Ann Arbor : ProQuest Dissertations & Theses, 2008 - 126 p.

Source: Dissertations Abstracts International, Volume: 70-10, Section: B.

Thesis (Ph.D.)--Rice University, 2008.

Four major approaches model the time dependent behavior of chemical reaction systems: ordinary differential equations (ODE's), the &tgr;-leap algorithm, stochastic differential equations (SDE's), and Gillespie's stochastic simulation algorithm (SSA). ODE's are simulated the most quickly of these, but are often inaccurate for systems with slow rates and molecular species present in small numbers. Under ideal conditions, the SSA is exact, but computationally inefficient. Unfortunately, many reaction systems exhibit characteristics not well captured individually by any of these methods. Therefore, hybrid models incorporating aspects from all four must be employed. The aim is to construct an approach that is close in accuracy to the SSA, useful for a wide range of reaction system examples, and computationally efficient. The Adaptive Multi-scale Simulation Algorithm (AMSA) uses the SSA for slow reactions, SDE's for medium-speed reactions, ODE's for fast reactions, and the tau-leap algorithm for non-slow reactions involving species small in number. This article introduces AMSA and applies it to examples of reaction systems involving genetic regulation. A thorough review of existing reaction simulation algorithms is included. The computational performance and accuracy of AMSA's molecular distributions are compared to those of the SSA, which is used as the golden standard of accuracy. The use of supercomputers can generate much larger data sets than serial processors in roughly the same amount of computational time. Therefore, multi-processor machines are also employed to assess the accuracy of AMSA simulations.

ISBN: 9780549584513Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Chemical reactions

Multi-scale behavior in chemical reaction systems: Modeling, applications, and results.
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520 $a Four major approaches model the time dependent behavior of chemical reaction systems: ordinary differential equations (ODE's), the &tgr;-leap algorithm, stochastic differential equations (SDE's), and Gillespie's stochastic simulation algorithm (SSA). ODE's are simulated the most quickly of these, but are often inaccurate for systems with slow rates and molecular species present in small numbers. Under ideal conditions, the SSA is exact, but computationally inefficient. Unfortunately, many reaction systems exhibit characteristics not well captured individually by any of these methods. Therefore, hybrid models incorporating aspects from all four must be employed. The aim is to construct an approach that is close in accuracy to the SSA, useful for a wide range of reaction system examples, and computationally efficient. The Adaptive Multi-scale Simulation Algorithm (AMSA) uses the SSA for slow reactions, SDE's for medium-speed reactions, ODE's for fast reactions, and the tau-leap algorithm for non-slow reactions involving species small in number. This article introduces AMSA and applies it to examples of reaction systems involving genetic regulation. A thorough review of existing reaction simulation algorithms is included. The computational performance and accuracy of AMSA's molecular distributions are compared to those of the SSA, which is used as the golden standard of accuracy. The use of supercomputers can generate much larger data sets than serial processors in roughly the same amount of computational time. Therefore, multi-processor machines are also employed to assess the accuracy of AMSA simulations.
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