What is Stochastic Modeling

Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality risk, which finally leads to the death of the organism. Modern hygiene and medicine has led to an amazing increase in average life expectancy over the last 150 years, but the underlying biochemical mechanisms of the aging process are still poorly understood. However, a better understanding of these mechanisms is increasingly important since the growing fraction of elderly people in the human population confronts our society with completely new and challenging problems. The aim of this chapter is to provide an overview of the aging process, discuss how it relates to system biological concepts, and explain how mathematical modeling can improve our understanding of biochemical processes involved in the aging process. We concentrate on the modeling of stochastic effects that become important when the number of involved entities (i.e., molecules, organelles, cells) is very small and the reaction rates are low. This is the case for the accumulation of defective mitochondria, which we describe mathematically in detail. In recent years several tools became available for stochastic modeling and we also provide a brief description of the most important of those tools. Of course, mitochondria are not the only target of modeling efforts in aging research. Therefore, the chapter concludes with a brief survey of other interesting computational models in this field of research.