Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure


Like many other types of cancer, colorectal cancer (CRC) develops through multiple pathways of carcinogenesis. This is also true for colorectal carcinogenesis in Lynch syndrome (LS), the most common inherited CRC syndrome. However, a comprehensive understanding of the distribution of these pathways of carcinogenesis, which allows for tailored clinical treatment and even prevention, is still lacking. We suggest a linear dynamical system modeling the evolution of different pathways of colorectal carcinogenesis based on the involved driver mutations. The model consists of different components accounting for independent and dependent mutational processes. We define the driver gene mutation graphs and combine them using the Cartesian graph product. This leads to matrix components built by the Kronecker sum and product of the adjacency matrices of the gene mutation graphs enabling a thorough mathematical analysis and medical interpretation. Using the Kronecker structure, we developed a mathematical model which we applied exemplarily to the three pathways of colorectal carcinogenesis in LS. Beside a pathogenic germline variant in one of the DNA mismatch repair (MMR) genes, driver mutations in APC, CTNNB1, KRAS and TP53 are considered. We exemplarily incorporate mutational dependencies, such as increased point mutation rates after MMR deficiency, and based on recent experimental data, biallelic somatic CTNNB1 mutations as common drivers of LS-associated CRCs. With the model and parameter choice, we obtained simulation results that are in concordance with clinical observations. These include the evolution of MMR-deficient crypts as early precursors in LS carcinogenesis and the influence of variants in MMR genes thereon. The proportions of MMR-deficient and MMR-proficient APC-inactivated crypts as first measure for the distribution among the pathways in LS-associated colorectal carcinogenesis are compatible with clinical observations. The approach provides a modular framework for modeling multiple pathways of carcinogenesis yielding promising results in concordance with clinical observations in LS CRCs.


DOI: 10.1371/journal.pcbi.1008970

Research Groups: Data Mining and Uncertainty Quantification

Publication type: Journal

Journal: PLOS Computational Biology

Publisher: Public Library of Science


Date Published: 1st May 2021


Registered Mode: manually

Authors: Saskia Haupt, Alexander Zeilmann, Aysel Ahadova, Hendrik Bläker, Magnus von Knebel Doeberitz, Matthias Kloor, Vincent Heuveline

help Submitter
Haupt, S., Zeilmann, A., Ahadova, A., Bläker, H., von Knebel Doeberitz, M., Kloor, M., & Heuveline, V. (2021). Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure. In J. Chen (Ed.), PLOS Computational Biology (Vol. 17, Issue 5, p. e1008970). Public Library of Science (PLoS).

Views: 3312

Created: 15th Nov 2021 at 10:00

Last updated: 5th Mar 2024 at 21:24

help Tags

This item has not yet been tagged.

help Attributions


Powered by
Copyright © 2008 - 2023 The University of Manchester and HITS gGmbH