Multiple time scale algorithms for gene network simulations.

Abstract

The objective of this dissertation is the development and implementation of multiple time scale stochastic models necessary for analysis, design and construction of novel synthetic biological systems, such as gene networks.

At the dawn of the 21 st century, scientists and engineers turned into engineering new biological systems. Synthetic biology emerged as a distinct discipline, combining biology and engineering towards the design and construction of new biological parts, devices and systems with useful applications. This ambitious endeavor would not have been possible, were it not for the recent, impressive discoveries in biology and the equally remarkable advances in biotechnology. Indeed, we can now literally "cut" and "paste" DNA at will.

The impact in everyday life may be significant, with wide-ranging applications: from medicine, where gene regulatory networks can be used for gene therapy applications, to the production of biopolymers, to the removal of environmental pollutants, and to clean energy alternatives.

Even though wet lab experiments have provided ample proof of concept, the challenge facing the scientific and engineering communities is how to rationally design novel biological systems. An answer lies with mathematical models and sophisticated algorithms. It is the same philosophy used to design many of the modern marvels of technology, such as airplanes. Analogously, sophisticated computer-aided design (CAD) algorithms, alongside with a minimal number of experiments, could be the standard in constructing novel biological systems, devices, even entire organisms, alleviating the need for expensive trial and error approaches.

There are primarily three types of challenges in developing new CAD tools for synthetic biological systems, such as gene networks. First, the number of molecular components in biological systems is overwhelming. Second, all living microorganisms are impacted by thermal noise and on occasion behave randomly. Third, the time scales at which many of the biological phenomena occur can differ by many orders of magnitude, resulting in stiff mathematical descriptions.

The aim of this thesis is the CAD of synthetic gene networks addressing these challenges. For that to be accomplished an important step is the development of multiple time scale methods for the efficient and accurate integration of stiff chemical Langevin equations. These describe the dynamics of many biological systems. Methods developed also include the description of noise through classical mathematical descriptions instead of the more demanding stochastic formulation. Algorithms developed as part of this dissertation are incorporated into CAD software tools built by our group. In the last part of this dissertation we discuss how such tools are employed for CAD of novel synthetic gene networks.