Algorithms for modeling and simulation of biological systems; applications to gene regulatory networks

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Vera-Licona, Martha Paola

Chair dc:contributor.committeechair

• Laubenbacher, Reinhard C.

Committee members dc:contributor.committeemember

• Mendes, Pedro J. P.
• Stillman, Michael
• Burns, John A.
• Jarrah, Abdul Salam

• Discrete Mathematics
• Systems Biology
• Biochemical Networks
• Discrete Finite Dynamical Systems
• Polynomial Dynamical Systems
• Data Discretization
• Reverse-engineering
• Computational Algebra
• Evolutionary Algorithms

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-06182007-222927

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28073