Abstract
Senescence (ageing) and apoptosis (programmed cell death) are phenomena that have troubled theoreticians and experimentalists. Previous research showed that the mortality curve of the yeast population followed the Gompertz-Makeham equation. We develop a generalised theoretical model which shows that the mortality of the organism can be expressed as a function of Ageing Factors such as ERCs. We use this idea to explain why senescence leads to apoptosis. Antagonistic pleiotropy and disposable soma theory suggest that senescence (and accordingly apoptosis) is a `side effect'. Although the altruistic benefits of apoptosis have been suggested before, we are attempting to show that in a resource-restricted environment, apoptosis can be a strategic choice. We show that the interactions between apoptotic and non-apoptotic organisms can be modelled using game theory and differential equations. We find that switching to apoptotic mode gives the organism an advantage over the non-apoptotic organisms in a resource-restricted environment. Mathematical analysis indicates that apoptosis is a stable strategy provided the conditions remain the same. We also find that one apoptotic organism can invade a population of non-apoptotic organisms. This begs the question - why do tumours (which are non-apoptotic) occur if apoptosis is the best strategy? We show that apoptosis and angiogensis play a significant role in the development of tumours. We studied the effects of these two parameters on the dynamics of tumour and apoptotic populations. We find that the mixed strategy of avoidance of apoptosis and angiogenesis gives neoplasms an advantage over apoptotic organisms in certain conditions. Accordingly, the tumour organisms can invade apoptotic tissues. We also find that this strategy is not beneficial in the long-term.