An ordinary differential equation model for the multistep transformation to cancer

Abstract

Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the transformation of normal cells to malignant cells. In doing so, we derive an ordinary differential equation model that explores how the balance of angiogenesis, cell death rates, genetic instability, and replication rates give rise to different kinetics in the development of cancer. The key predictions of the model are that cancer develops fastest through a particular ordering of mutations and that mutations in genes that maintain genomic integrity would be the most deleterious type of mutations to inherit. In addition, we perform a sensitivity analysis on the parameters included in the model to determine the probable contribution of each. This paper presents a novel approach to viewing the genetic basis of cancer from a systems biology perspective and provides the groundwork for other models that can be directly tied to clinical and molecular data.