Computational algebra methods in systems biology

Prof. Reinhard Laubenbaucher
Virginia Bioinformatics Institute

Recent advances in measurement technologies have made it possible to obtain experimental data about organisms at system levels and on a large scale. For instance, DNA microarray technology makes possible simultaneous snapshots of the activity levels of all 25,000 genes in a human; new functional MRI technology provides global images of brain activity; and new in vivo imaging technology gives unprecedented insight into the functioning of our immune system. The availability of such data makes it possible for the first time to aim at an understanding of whole subsystems of an organism, from intracellular molecular signaling networks all the way to the structure of organismal networks such as the immune system. This is the goal of systems biology, which plays an increasingly important role in diverse research areas such as drug design and cancer biology. Mathematics provides the natural language and the tool set for systems biology. After an introduction to systems biology and various types of experimental data available, this lecture series will focus on modeling and simulation of biological systems, using methods from discrete mathematics, in particular computational algebra and algebraic geometry. The modeling framework used will be polynomial dynamical systems over finite fields. We will discuss methods to construct such models from state transition data, as well as applications to the study of intracellular biochemical networks, neural response networks, and the approximation of stochastic simulations of biological networks by polynomial systems.