Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System

Abstract

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development of the illness evolves very slowly, happens in a specific place (stroma), and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All these aspects make it difficult to understand the pathogenesis of pancreatic cancer and develop a proper therapy. The emergence of pancreatic pre-cancer and cancer cells represents a branching stochastic process engaging populations of 64 cells differing in the number of acquired mutations. In this study, we formulate and calibrate the mathematical model of pancreatic cancer using the quasispecies framework. The mathematical model incorporates the mutation matrix, fineness landscape matrix, and the death rates. Each element of the mutation matrix presents the probability of appearing as a specific mutation in the branching sequence of cells representing the accumulation of mutations. The model incorporates the cancer cell elimination by effect CD8 T cells (CTL). The down-regulation of the effector function of CTLs and exhaustion are parameterized. The symbiotic effect of coexistence of normal and cancer cells is considered. The computational predictions obtained with the model are consistent with empirical data. The modeling approach can be used to investigate other types of cancers and examine various treatment procedures.

Keywords

• pancreatic cancer
• cancer evolution
• tumor microenvironment
• mathematical model
• open quasispecies model