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 ofcells 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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