Quantitative models for the inference of intratumor heterogeneity

Intratumor heterogeneity (ITH) is an omnipresent property of cancers and predicts poor survival in most types of cancer. The propensity to metastasize and the regrowth of tumors after therapy are both associated with ITH. Quantification of the level of ITH in a malignancy is hence of great interest, and accurate inference of ITH could guide clinical decision making. However, ITH is an emergent property of billions of cells and requires mathematical modeling for inference from a limited number of measurements. Over the last decade, numerous mathematical and computational models have been introduced to infer ITH from variant-allele frequencies, copy number variations, or from data of experimental model systems. These quantitative modeling efforts have advanced the understanding of tumor evolution, underlined poor prognosis associated with ITH, and elucidated the importance of functional heterogeneity, that is, cancer stem cells. Yet, a comprehensive overview of the different mathematical models, their underlying assumptions, their limitations, and their strengths is missing. In this Perspective, we highlight the achievements of mathematical modeling and present a framework which allows better understanding of the mathematical models themselves.