Penalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction Networks

Hdl Handle:
http://hdl.handle.net/10675.2/348545
Title:
Penalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction Networks
Authors:
Linder, Daniel F. II
Abstract:
Systems biology seeks to understand the formation of macro structures such as cellular processes and higher level cellular phenomena by investigating the interactions of systems’ individual components. For cellular biology, this goal is to understand the dynamic behavior of biological materials within the cell, a container consisting of smaller materials such as mRNA, proteins, enzymes and other intermediates necessary for regulating intracellular functions and chemical species levels. Understanding these cellular dynamics is needed to help develop new drug therapies, which can be targeted to specific molecules or specific genes, in order to perturb the system for a desired result. In this work we develop inferential procedures to estimate reaction rate coefficients in cellular systems of ordinary differential equations (ODEs) from noisy data arising from realizations of molecular trajectories. It is assumed that these systems obey the so called chemical mass action law of kinetics, with corresponding deterministic mass action limit as the system size becomes infinite. The estimation and inference is based on the penalized least squares estimates, where the covariance structure of these estimates corresponds to the solution of a system of coupled nonautonomuous ODEs. Another topic discussed here is that of network topology estimation. The algebraic statistical model (ASM) offers a means of performing this topological inference for the special class of conic networks. We prove that the ASM recovers the true network topology as the number of samples grows without bound, a property known in the literature as sparsistency. We propose a method to extend the ASM to a wider class of networks that are decomposable into multiple cones.
Affiliation:
Department of Biostatistics and Epidemiology
Issue Date:
Jul-2013
URI:
http://hdl.handle.net/10675.2/348545
Additional Links:
http://ezproxy.augusta.edu/login?url=http://search.proquest.com/docview/1448701282?accountid=12365
Type:
Dissertation
Appears in Collections:
Theses and Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.authorLinder, Daniel F. IIen
dc.date.accessioned2015-04-06T18:40:00Zen
dc.date.available2015-04-06T18:40:00Zen
dc.date.issued2013-07en
dc.identifier.urihttp://hdl.handle.net/10675.2/348545-
dc.description.abstractSystems biology seeks to understand the formation of macro structures such as cellular processes and higher level cellular phenomena by investigating the interactions of systems’ individual components. For cellular biology, this goal is to understand the dynamic behavior of biological materials within the cell, a container consisting of smaller materials such as mRNA, proteins, enzymes and other intermediates necessary for regulating intracellular functions and chemical species levels. Understanding these cellular dynamics is needed to help develop new drug therapies, which can be targeted to specific molecules or specific genes, in order to perturb the system for a desired result. In this work we develop inferential procedures to estimate reaction rate coefficients in cellular systems of ordinary differential equations (ODEs) from noisy data arising from realizations of molecular trajectories. It is assumed that these systems obey the so called chemical mass action law of kinetics, with corresponding deterministic mass action limit as the system size becomes infinite. The estimation and inference is based on the penalized least squares estimates, where the covariance structure of these estimates corresponds to the solution of a system of coupled nonautonomuous ODEs. Another topic discussed here is that of network topology estimation. The algebraic statistical model (ASM) offers a means of performing this topological inference for the special class of conic networks. We prove that the ASM recovers the true network topology as the number of samples grows without bound, a property known in the literature as sparsistency. We propose a method to extend the ASM to a wider class of networks that are decomposable into multiple cones.en
dc.relation.urlhttp://ezproxy.augusta.edu/login?url=http://search.proquest.com/docview/1448701282?accountid=12365en
dc.rightsCopyright protected. Unauthorized reproduction or use beyond the exceptions granted by the Fair Use clause of U.S. Copyright law may violate federal law.en
dc.subjectAlgebraic statisticsen
dc.subjectAlgebraic statistical modelen
dc.subjectTopology estimationen
dc.subjectDensity dependent Markov jump processen
dc.subjectDiffusion approximationen
dc.subjectReverse engineeringen
dc.subjectLeast squares estimationen
dc.subjectBootstrap methoden
dc.titlePenalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction Networksen
dc.typeDissertationen
dc.contributor.departmentDepartment of Biostatistics and Epidemiologyen
dc.description.advisorRempala, Grzegorzen
dc.description.committeeNot Listeden
dc.description.degreeDoctor of Philosophy (Ph.D.)en
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