Mathematical Models of Cancer

Abstract

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. Here we present mathematical models that begin to address this challenge. First we present a model of accumulation of driver and passenger mutations during tumor progression and derive a formula for the number of driver mutations as a function of the total number of mutations in a tumor. Fitting this formula to recent experimental data, we were able to calculate the selective advantage provided by a typical driver mutation. Second, we performed a quantitative analysis of pancreatic cancer metastasis genetic data. The results of this analysis define a broad time window for detection of pancreatic cancer before metastatic dissemination. Finally, we model the evolution of resistance to targeted cancer therapy. We apply our model to experimental data on the response to panitumumab, targeted therapy against colorectal cancer. Our modeling suggested that cells resistant to therapy were likely present in patients’ tumors prior to the start of therapy.