Espinasse, T. | bioRxiv Science

bioRxiv2021

Hematopoietic differentiation is characterized by a transient peak of cell-to-cell gene expression variability in normal and pathological conditions.

Hematopoietic differentiation has been metaphorically represented as linear trajectories with discrete steps from hematopoietic stem cells to mature cells. While the transcriptional state of cells at the beginning or at the end of these trajectories are well described from bulk analysis, what happens in the intermediate states has remained elusive until the use of single cell approaches. Applying Shannon entropy to measure cell-to-cell variability among cells at the same stage of differentiation, we observed a transient peak of gene expression variability in all the hematopoietic differentiation pathways. Strikingly, genes with the highest entropy variation in a given differentiation pathway matched genes known as pathway-specific, whereas genes with the highest expression variation were common to all pathways. Finally, we showed that the level of cell-to-cell variation is increased in the most immature compartment of hematopoiesis in myelodysplastic syndromes. These data suggest that differentiation could be better conceptualized as a dynamical stochastic process with a transient stage of cellular indetermination.

cell biology↗

bioRxiv2020

Reduction of a stochastic model of gene expression: Lagrangian dynamics gives acces to basins of attraction as cell types and metastability

Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In this work we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit of which the basins of attraction can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an approximation of the stationary distribution of the PDMP system, which appears as a Beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types.

systems biology↗