Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Abstract

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Keywords: Fokker–Planck equation; Langevin equation; Markov model; equation of motion; live-cell imaging; nonequilibrium; single cell genomics.

Figure 1

Reconstructing quantitative models from single cell snapshot data. (A) A Markovian model of cell cycle progression based on ergodic rate analyses. (B) Reconstruction of genome-wide vector fields from scRNA-seq data (50). The vector x represents the cell expression state, which refers s in the splicing-based velocity, and (u + s) in the more accurate metabolic labeling-based velocity. The term ζ refers to residue terms treated as random noises. The function F corresponds to A in Eqn. 1.

Figure 2

Cytomorphological state space dynamics of mouse embryonic fibroblasts (MEFs). (A) Transition vectors in the leading PC space. The vectors are defined as the vector between the measured states of individual cells with four-hour separation. (B) Flux analyses of the transition vectors reveal a transition matrix with unexpected detailed balance between forward and backward states. (C) Quasi-potential defined from the transition matrix. Reproduced from (43) with permission.

Figure 3

Determination of reaction coordinates from single cell trajectories using a revised finite temperature string method. (A) Division of cell state space with Voronoi cells. A, I, and B refer to the initial, intermediate, and final regions of the transition, respectively. (B) Reconstructed parallel EMT transition paths of A549 cells (treated with 4 ng/ml TGF-β) shown in the leading 3-D state space. (C) Individual reaction coordinates overlapped with typical recorded single cell trajectories. (D) Reconstructed quasi-potentials along reaction coordinates from single cell trajectory data of A549 cells (treated with 1 and 4 ng/ml TGF-β). Reproduced from (40).