The nonlinear nature of biology

Abstract

In this thesis, we explore the stability and the breakdown of stability of biological systems. The main examples are the blood system and invasion of cancer. However, the models presented in the thesis apply to several other examples.

Biological systems are characterised by both competition and cooperation. Cooperation is based on an unsolvable dilemma: Even though mutual cooperation leads to higher payoff than mutual defection, a defector has higher payoff than a co-operator when they meet. It is not possible to represent this dilemma with a linear and deterministic model. Hence, the dilemma of cooperation must have a nonlinear and/or stochastic representation.

More general, by using a linearised model to describe a biological system, one might lose dimensions inherent in the complexity of the system. In this thesis, we illustrate that a nonlinear description of a biological system is potentially more accurate and might provide new information.

We show that even though a new type of individual is in general not advantageous when it appears in stable population, the newcomers can grow in number due to stochasticity. Moreover, the new type can only become advantageous if it manages to change the environment in such a way that it increases its fitness.

We also propose a model that links self-organisation with symmetric and asymmetric cell division, and we illustrate that if symmetric stem cell division is regulated by differentiated cells, then the fitness of the stem cells can be affected by modifying the death rate of the mature cells. This result is interesting because stem cells are less sensitive than mature cells to medical therapy, and our results imply that stem cells can be manipulated indirectly by medical treatments that target the mature cells.