A complex systems approach to important biological problems.

Abstract

Complex systems are those which exhibit one or more of the following inter-related behaviours: 1. Nonlinear behaviour: the component parts do not act in linear ways, that is the superposition of the actions of the parts is not the output of the system. 2. Emergent behaviour: the output of the system may be inexpressible in terms of the rules or equations of the component parts. 3. Self-organisation: order appears from the chaotic interactions of individuals and the rules they obey. 4. Layers of description: in which a rule may apply at some higher levels of description but not at lower layers. 5. Adaptation: in which the environment becomes encoded in the rules governing the structure and/or behaviour of the parts (in this case strictly agents) that undergo selection in which those that are by some measure better become more numerous than those that are not as “fit”. A single cell is a complex system: we cannot explain all of its behaviour as simply the sum of its parts. Similarly, DNA structures, social networks, cancers, the brain, and living beings are intricate complex systems. This thesis tackles all of these topics from a complex systems approach. I have skirted some of the philosophical issues of complex systems and mainly focussed on appropriate tools to analyse these systems, addressing important questions such as: • What is the best way to extract information from DNA? • How can we model and analyse mutations in DNA? • Can we determine the likely spread of both viruses and ideas in social networks? • How can we model the growth of cancer? • How can we model and analyse interactions between genes in such living systems as the fruit fly, cancers, and humans? • Can complex systems techniques give us some insight into the human brain?