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

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dc.contributor.advisorCox, Dennis D.en_US
dc.creatorTurner, Jesse Hosea, IIIen_US
dc.date.accessioned2009-06-03T19:50:56Zen_US
dc.date.available2009-06-03T19:50:56Zen_US
dc.date.issued2008en_US
dc.description.abstractFour 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.en_US
dc.format.extent126 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS STAT. 2008 TURNERen_US
dc.identifier.citationTurner, Jesse Hosea, III. "Multi-scale behavior in chemical reaction systems: Modeling, applications, and results." (2008) Diss., Rice University. <a href="https://hdl.handle.net/1911/22206">https://hdl.handle.net/1911/22206</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/22206en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.subjectStatisticsen_US
dc.subjectPhysical chemistryen_US
dc.titleMulti-scale behavior in chemical reaction systems: Modeling, applications, and resultsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentStatisticsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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