Modeling acute myeloid leukemia in a continuum of differentiation states

Abstract

Here we present a mathematical model of movement in an abstract space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single cell RNA sequencing data to characterize cellular states in a high-dimensional space, which is then mapped into R² or R³ with dimension reduction techniques. We represent trajectories in the differentiation space as a graph, and model directed and random movement on the graph with partial differential equations. We hypothesize that flow in this space can be used to model normal differentiation processes as well as predict the evolution of abnormal differentiation processes such as those observed during pathogenesis of acute myeloid leukemia (AML).