Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics

Systems biology aims at system-level understanding of biological systems, in particular cellular networks. The milestones of this understanding are knowledge of the structure of the system, understanding of its dynamics, effective control methods, and powerful prediction capability. The complexity of biological systems makes it inevitable to consider mathematical modeling in order to achieve these goals. The enormous accumulation of experimental data representing the activities of the living cell has triggered an increasing interest in the reverse engineering of biological networks from data. In particular, construction of discrete models for reverse engineering of biological networks is receiving attention, with the goal of providing a coarse-grained description of such networks. In this dissertation we consider the modeling framework of polynomial dynamical systems over finite fields constructed from experimental data. We present and propose solutions to two problems inherent in this modeling method: the necessity of appropriate discretization of the data and the selection of a particular polynomial model from the set of all models that fit the data. Data discretization, also known as binning, is a crucial issue for the construction of discrete models of biological networks. Experimental data are however usually continuous, or, at least, represented by computer floating point numbers. A major challenge in discretizing biological data, such as those collected through microarray experiments, is the typically small samples size. Many methods for discretization are not applicable due to the insufficient amount of data. The method proposed in this work is a first attempt to develop a discretization tool that takes into consideration the issues and limitations that are inherent in short data time courses. Our focus is on the two characteristics that any discretization method should possess