Mathematical models for order of mutation problem in myeloproliferative neoplasm: non-additivity and non-commutativity

TL;DR

This paper develops nonlinear differential equation and Markov chain models to understand how the order of mutations affects gene regulation in myeloproliferative neoplasm, highlighting non-additive and non-commutative effects.

Contribution

It introduces novel mathematical models capturing the impact of mutation order on gene expression regulation in myeloproliferative neoplasm.

Findings

Models explain mutation order effects on gene regulation.

Highlight non-additivity and non-commutativity in mutation interactions.

Provide a framework for analyzing mutation sequence impacts.

Abstract

In some patients of myeloproliferative neoplasm, two genetic mutations can be found: JAK2 V617F and TET2. When one mutation is present or not, the other mutation has different effects on regulating gene expressions. Besides, when both mutations are present, the order of occurrence might make a difference. In this paper, we build nonlinear ordinary differential equation models and Markov chain models to explain such phenomena.