Investigating cancer development with the help of mathematics

Scientists from Heidelberg have found a way to trace cancer formation using mathematical models. The results have now been published in PLOS Computational Biology.

Cancer is a disease caused by alterations of the genome. The alterations can affect each component of the genome, but only some lead to a change in the functioning of the cell and ultimately cancer. As there are several of those so-called driver mutations, there are different orders in which they can occur. It is currently assumed that the order of driver mutations is linked to the course of the disease and thus to cancer treatment and even prevention. However, cells with a driver mutation, which carry a risk to grow out to become a tumor, remain clinically undetected for a long time. This means the preclinical formation of cancer (also called carcinogenesis) is a hidden process. But new approaches could improve the situation: Tumor data analysis tools and mathematical models offer a way to unravel the black-box and thus, to obtain a better understanding of the biology underlying preclinical carcinogenic processes.

A team of scientists, including researchers from HITS, Heidelberg University, and the University Hospital Heidelberg, has now used a mathematical model for different molecular pathways of carcinogenesis based on ordinary differential equations. This type of models is widely used in current applications associated with evolution, e.g., epidemiology and cancer research. The model makes use of the so-called Kronecker product, a specific structure which allows for a thorough mathematical analysis and medical interpretation. The model consists of multiple components to account for dependent and independent mutational processes, meaning mutations that are or are not influenced by other mutations. The team of mathematicians could therefore include many medical aspects into their analysis. For the published paper, the scientists focused on cancer development in the colon using the example of the most common inherited colorectal cancer syndrome (Lynch syndrome). They obtained simulation results that are in concordance with current clinical tumor data, giving hints to the very first steps of cancer formation. The approach provides a modular framework for modeling multiple pathways of carcinogenesis that could be applied to other organs by slight modifications.

As a next step, the scientists will refine their modeling approach to include newly generated medical data and to analyze the effect of different prevention, diagnosis, and treatment strategies. With this, they aim to support tailored treatment approaches for cancer patients and prevention strategies for individuals with increased cancer risk.

The research was conducted by scientists from various research fields and institutions in the framework of the “Mathematics in Oncology”, a collaborative initiative including Saskia Haupt and Vincent Heuveline (DMQ Group at HITS and EMCL Group at Heidelberg University), Alexander Zeilmann (Heidelberg University), Hendrik Bläker (Institute of Pathology, University of Leipzig Medical Center), and Aysel Ahadova, Magnus von Knebel Doeberitz and Matthias Kloor (Department of Applied Tumor Biology (ATB), Institute of Pathology at the University Hospital Heidelberg). 

Article Source: Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure
Haupt S, Zeilmann A, Ahadova A, Bläker H, von Knebel Doeberitz M, et al. (2021) Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure. PLOS Computational Biology 17(5): e1008970. https://doi.org/10.1371/journal.pcbi.1008970