Browsing by Author "Zwolak, Jason W."
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- Computational Tools for Molecular Networks in Biological SystemsZwolak, Jason W. (Virginia Tech, 2004-12-15)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.
- Globally Optimized Parameters for a Model of Mitotic Control in Frog Egg ExtractsZwolak, Jason W.; Tyson, John J.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2004)DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak and Tyson. In a recent publication, we showed that a gradient-based optimization algorithm finds a locally optimal parameter set quite close to the Marlovits estimates. In this paper, we combine global and local optimization strategies to show that the refined Marlovits parameter set, with one minor but significant modification to the Novak-Tyson equations, is the unique, best-fitting solution to the parameter estimation problem.
- ODRPACK95: A Weighted Orthogonal Distance Regression Code with Bound ConstraintsZwolak, Jason W.; Boggs, Paul T.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2004)ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and many more features. The foundation for the algorithm is a stable and efficient trust region Levenberg-Marquardt minimizer that exploits the structure of the orthogonal distance regression problem. ODRPACK95 is a modification of the original ODRPACK code that adds support for bound constraints, uses the newer Fortran 95 language, and simplifies the interface to the user called subroutine.
- Parameter Estimation for a Mathematical Model of the Cell Cycle in Frog EggsZwolak, Jason W.; Tyson, John J.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2002-08-01)Parameter values for a kinetic model of teh nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthodonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.
- Parameter Estimation in Biological Cell Cycle Models Using Deterministic OptimizationZwolak, Jason W. (Virginia Tech, 2001-10-31)Cell cycle models used in biology can be very complex. These models have parameters with initially unknown values. The values of the parameters vastly aect the accuracy of the models in representing real biological cells. Typically people search for the best parameters to these models using computers only as tools to run simulations. In this thesis methods and results are described for a computer program that searches for parameters to a series of related models using well tested algorithms. The code for this program uses ODRPACK for parameter estimation and LSODAR to solve the dierential equations that comprise the model.