complex dynamics of biological systems
Open Access
- Author:
- Campbell, Colin Edward
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 23, 2012
- Committee Members:
- Reka Z Albert, Dissertation Advisor/Co-Advisor
Dezhe Jin, Committee Member
Alexay Kozhevnikov, Committee Member
Istvan Albert, Committee Member - Keywords:
- complex systems
network theory
systems biology
cancer
ecosystem stability
immune system - Abstract:
- The analysis of complex systems has become intertwined with, and driven by, network theory: the study of a system within the context of discrete, interacting components. A network-based investigation of a complex system enables analysis of its structure, function, and dynamics, even in the face of noisy or otherwise incomplete data. This is particularly relevant to the biological sciences, as recent advances in data-collection techniques have made a systems-level study of biological systems feasible. Here, I present applications and advancements of network theory within the context of three biological systems that range in scale from cellular to ecological. First, the dynamic “tug of war” between the human immune system and cancer of the brain, bones, and pancreas is studied with a model of coupled ordinary differential equations, with the ultimate goal of directing researchers towards curative therapies. Known qualitative and quantitative time-course data are replicated, and several predictions of the model are experimentally validated. Second, a set of topological network measures are proposed and applied to a network representation of the immune response to attack by respiratory bacteria and allergen. The measures elucidate the functioning of the network, and along with analysis of the small-scale structure of the network, identify key regulators in the immune system response to the joint attack. Finally, a novel, dynamic model of the formation of ecological communities consisting of plants and their pollinators is proposed and shown to replicate expected ecological behavior. The model is used as the basis for a study of the stability of the communities in the face of species extinctions, and successfully identifies key properties in critical species and communities susceptible to significant damage from the loss of a single species. In this dissertation, mathematical models are developed, networks are formed, network topologies are analyzed, and both discrete- and continuous-time dynamics are studied. Novel measures and models are proposed and discussed. Thus, in addition to offering significant insight into each of the studied biological systems, this dissertation constitutes an advancement of the techniques by which complex systems are studied.