Title page for ETD etd-12282004-101753


Type of Document Dissertation
Author Zwolak, Jason Walter
Author's Email Address jzwolak@vt.edu
URN etd-12282004-101753
Title Computational Tools for Molecular Networks in Biological Systems
Degree PhD
Department Computer Science
Advisory Committee
Advisor Name Title
Tyson, John J. Committee Co-Chair
Watson, Layne T. Committee Co-Chair
Heath, Lenwood S. Committee Member
Shaffer, Clifford A. Committee Member
Sible, Jill C. Committee Member
Keywords
  • molecular networks
  • cell cycle
  • Computational biology
  • global optimization
Date of Defense 2004-12-15
Availability unrestricted
Abstract
Theoretical molecular biologists try to understand the workings of

cells through mathematics. Some theoreticians use systems of ordinary

differential equations (ODEs) as the basis for mathematical modelling

of molecular networks. This thesis develops algorithms for

estimating molecular reaction rate constants within those mathematical

models by fitting the models to experimental data. An additional step is

taken to fit non-timecourse experimental data (e.g., transformations

must be performed on the ODE solutions before the experimental and

simulation data are similar, and therefore, comparable). VTDIRECT is

used to perform (a deterministic direct search) global estimation and

ODRPACK is used to perform (a trust region Levenberg-Marquardt based)

local estimation of rate constants. One such transformation performed

on the ODE solutions determines the value of the steady state of the ODE

solutions. A new algorithm was developed that finds all steady state solutions

of the ODE system given that the system has a special structure (e.g., the

right hand sides of the ODEs are rational functions). Also, since

the rate constants in the models cannot be negative and may have other

restrictions on the values, ODRPACK was modified to address this problem

of bound constraints. The new Fortran 95 version of ODRPACK is

named ODRPACK95.

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