Abstract
Cellular development has traditionally been described as a series of transitions between discrete cell states, such as the sequence of double negative, double positive and single positive stages in T-cell development. Recent advances in single cell transcriptomics suggest an alternative description of development, in which cells follow continuous transcriptomic trajectories. A cell's state along such a trajectory can be captured with pseudotemporal ordering, which however is not able to predict development of the system in real time. We present pseudodynamics, a mathematical framework that integrates time-series and genetic knock-out information with such transcriptome-based descriptions in order to describe and analyze the real-time evolution of the system. Pseudodynamics models the distribution of a cell population across a continuous cell state coordinate over time based on a stochastic differential equation along developmental trajectories and random switching between trajectories in branching regions. To illustrate feasibility, we use pseudodynamics to estimate cell-state-dependent growth and differentiation of thymic T-cell development. The model approximates a developmental potential function (Waddington's landscape) and suggests that thymic T-cell development is biphasic and not strictly deterministic before beta-selection. Pseudodynamics generalizes classical discrete population models to continuous states and thus opens possibilities such as probabilistic model selection to single cell genomics.
