Mathematical modeling with single-cell sequencing data

Abstract

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two approaches for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; by solving partial differential equations on a graph representing discrete cell state relationships, and by solving the equations on a continuous cell state-space. We demonstrate how to calibrate model parameters from single or multiple time-point single-cell sequencing data, and examine the effects of data processing algorithms on the model calibration and predictions. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell types during the pathogenesis of acute myeloid leukemia. The mathematical modeling framework we present is general and can be applied to study cell state-transitions in any single-cell genome sequencing dataset.\n\nAuthor summaryHere we compare and contrast graph- and continuum-based approaches for constructing mathematical models of cell state-transitions using single-cell RNA-sequencing data. Using two publicly available datasets, we demonstrate how to calibrate mathematical models of hematopoeisis and how to use the models to predict dynamics of acute myeloid leukemia pathogenesis by mathematically perturbing the process of cellular proliferation and differentiation. We apply these modeling approaches to study the effects of perturbing individual or sets of genes in subsets of cells, or by modeling the dynamics of cell state-transitions directly in a reduced dimensional space. We examine the effects of different graph abstraction and trajectory inference algorithms on calibrating the models and the subsequent model predictions. We conclude that both the graph- and continuum-based modeling approaches can be equally well calibrated to data and discuss situations in which one method may be preferable over the other. This work presents a general mathematical modeling framework, applicable to any single-cell sequencing dataset where cell state-transitions are of interest.