Title page for ETD etd-06182007-222927

Type of Document Dissertation
Author Vera-Licona, Martha Paola
Author's Email Address mveralic@vbi.vt.edu
URN etd-06182007-222927
Title Algorithms for modeling and simulation of biological systems; applications to gene regulatory networks
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Laubenbacher, Reinhard C. Committee Chair
Burns, John A. Committee Member
Jarrah, Abdul Salam Committee Member
Mendes, Pedro J. P. Committee Member
Stillman, Michael Committee Member
  • Data Discretization
  • Polynomial Dynamical Systems
  • Discrete Finite Dynamical Systems
  • Biochemical Networks
  • Systems Biology
  • Discrete Mathematics
  • Reverse-engineering
  • Computational Algebra
  • Evolutionary Algorithms
Date of Defense 2007-06-06
Availability unrestricted
Systems biology is an emergent field focused on developing a system-level understanding of biological systems. In the last decade advances in genomics, transcriptomics and proteomics have gathered a remarkable amount data enabling the possibility of a system-level analysis to be grounded at a molecular level. The reverse-engineering of biochemical networks from experimental data has become a central focus in systems biology. A variety of methods have been proposed for the study and identification of the system’s structure and/or dynamics.

The objective of this dissertation is to introduce and propose solutions to some of the challenges inherent in reverse-engineering of biological systems.

First, previously developed reverse engineering algorithms are studied and compared using data from a simulated network. This study draws attention to the necessity for a uniform benchmark that enables an ob jective comparison and performance evaluation of reverse engineering methods.

Since several reverse-engineering algorithms require discrete data as input (e.g. dynamic Bayesian network methods, Boolean networks), discretization methods are being used for this purpose. Through a comparison of the performance of two network inference algorithms that use discrete data (from several different discretization methods) in this work, it has been shown that data discretization is an important step in applying network inference methods to experimental data.

Next, a reverse-engineering algorithm is proposed within the framework of polynomial dynamical systems over finite fields. This algorithm is built for the identification of the underlying network structure and dynamics; it uses as input gene expression data and, when available, a priori knowledge of the system. An evolutionary algorithm is used as the heuristic search method for an exploration of the solution space. Computational algebra tools delimit the search space, enabling also a description of model complexity. The performance and robustness of the algorithm are explored via an artificial network of the segment polarity genes in the D. melanogaster.

Once a mathematical model has been built, it can be used to run simulations of the biological system under study. Comparison of simulated dynamics with experimental measurements can help refine the model or provide insight into qualitative properties of the systems dynamical behavior. Within this work, we propose an efficient algorithm to describe the phase space, in particular to compute the number and length of all limit cycles of linear systems over a general finite field.

This research has been partially supported by NIH Grant Nr. RO1GM068947-01.

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