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

Area of Science:

• Oncology
• Mathematical Biology
• Genetics

Background:

• Colorectal cancer (CRC) develops via multiple carcinogenesis pathways.
• Lynch syndrome (LS) is the most common inherited CRC syndrome, yet its specific carcinogenesis pathways require further understanding.
• A comprehensive grasp of these pathways is crucial for personalized clinical treatment and prevention strategies.

Purpose of the Study:

• To develop and apply a mathematical model for analyzing colorectal carcinogenesis pathways in Lynch syndrome.
• To provide a framework for understanding the distribution and evolution of different CRC development routes in LS.
• To enable more tailored clinical interventions and preventative measures for LS-associated CRC.

Main Methods:

• Development of a linear dynamical system model for colorectal carcinogenesis.
• Utilizing driver gene mutation graphs and the Cartesian graph product.
• Incorporation of Kronecker sum and product for matrix component analysis.
• Application of the model to LS, considering MMR gene variants and key driver mutations (APC, CTNNB1, KRAS, TP53).

Main Results:

• The model successfully simulates colorectal carcinogenesis pathways in LS, aligning with clinical observations.
• Identified MMR-deficient crypts as early precursors in LS carcinogenesis.
• Demonstrated concordance between model-predicted proportions of MMR-deficient/proficient crypts and clinical data.
• Highlighted the influence of MMR gene variants on LS carcinogenesis.

Conclusions:

• The developed mathematical model offers a modular framework for studying multiple carcinogenesis pathways.
• Simulation results are consistent with clinical observations in LS-associated CRCs.
• The model provides valuable insights into the distribution of carcinogenesis pathways, aiding in clinical treatment and prevention for Lynch syndrome patients.