Optimization models and computational methods for systems biology

Abstract

Systems biology is a comprehensive quantitative analysis of the manner in

which all the components of a biological system interact functionally along with

time. Mathematical modeling and computational methods are indispensable

in such kind of studies, especially for interpreting and predicting the complex

interactions among all the components so as to obtain some desirable system

properties. System dynamics, system robustness and control method are three

crucial properties in systems biology. In this thesis, the above properties are

studied in four different biological systems.

The outbreak and spread of infectious diseases have been questioned and

studied for years. The spread mechanism and prediction about the disease could

enable scientists to evaluate isolation plans to have significant effects on a particular

epidemic. A differential equation model is proposed to study the dynamics

of HIV spread in a network of prisons. In prisons, screening and quarantining

are both efficient control manners. An optimization model is proposed to study

optimal strategies for the control of HIV spread in a prison system.

A primordium (plural: primordia) is an organ or tissue in its earliest recognizable

stage of development. Primordial development in plants is critical to the

proper positioning and development of plant organs. An optimization model and

two control mechanisms are proposed to study the dynamics and robustness of primordial systems.

Probabilistic Boolean Networks (PBNs) are mathematical models for studying

the switching behavior in genetic regulatory networks. An algorithm is proposed

to identify singleton and small attractors in PBNs which correspond to

cell types and cell states. The captured problem is NP-hard in general. Our

algorithm is theoretically and computationally demonstrated to be much more

efficient than the naive algorithm that examines all the possible states.

The goal of studying the long-term behavior of a genetic regulatory network is

to study the control strategies such that the system can obtain desired properties.

A control method is proposed to study multiple external interventions meanwhile

minimizing the control cost.

Robustness is a paramount property for living organisms. The impact degree

is a measure of robustness of a metabolic system against the deletion of single

or multiple reaction(s). An algorithm is proposed to study the impact degree

in Escherichia coli metabolic system. Moreover, approximation method based

on Branching process is proposed for estimating the impact degree of metabolic

networks. The effectiveness of our method is assured by testing with real-world

Escherichia coli, Bacillus subtilis, Saccharomyces cerevisiae and Homo Sapiens

metabolic systems.