Determining Relative Dynamic Stability of Cell States Using Boolean Network Model

Jae Il Joo,Joseph X Zhou,Sui Huang,Kwang-Hyun Cho

doi:10.1038/s41598-018-30544-0

Abstract

Cell state transition is at the core of biological processes in metazoan, which includes cell differentiation, epithelial-to-mesenchymal transition (EMT) and cell reprogramming. In these cases, it is important to understand the molecular mechanism of cellular stability and how the transitions happen between different cell states, which is controlled by a gene regulatory network (GRN) hard-wired in the genome. Here we use Boolean modeling of GRN to study the cell state transition of EMT and systematically compare four available methods to calculate the cellular stability of three cell states in EMT in both normal and genetically mutated cases. The results produced from four methods generally agree but do not totally agree with each other. We show that distribution of one-degree neighborhood of cell states, which are the nearest states by Hamming distance, causes the difference among the methods. From that, we propose a new method based on one-degree neighborhood, which is the simplest one and agrees with other methods to estimate the cellular stability in all scenarios of our EMT model. This new method will help the researchers in the field of cell differentiation and cell reprogramming to calculate cellular stability using Boolean model, and then rationally design their experimental protocols to manipulate the cell state transition.

Highlights

The rationale for reprogramming protocols being derived from pathway diagrams involving “fate-determining” master regulators embodies linear causation and only allows for qualitative deterministic predictions of the fate outcome of manipulations
The latter refers to how gene regulatory network (GRN) imposes constraints on the collective change of gene expression and determines trajectories of cell states, thereby affording robustness to cell states by constraining some of the random fluctuations, while still allowing cells to escape the constraints by the GRN
In studies of epithelial-to-mesenchymal transition (EMT) in breast cancer, a third distinct cell state has been observed in addition to the epithelial (E) cell state, and the mesenchymal cell (M) state: an intermediate “hybrid” (H) cell state which displays both epithelial and mesenchymal features with regard to gene expression patterns[41,42]

Summary

Introduction

The rationale for reprogramming protocols being derived from pathway diagrams involving “fate-determining” master regulators embodies linear causation and only allows for qualitative deterministic predictions of the fate outcome of manipulations. When we take the limit of noise to zero, it has been shown that U(x) of a deterministic system x = F(x) is related to transition probability of Freidlin-Wentzell stochastic system and represents the least action needed to work against the regulatory constraints imposed by the GRN (which produce the attractor states in the first place)[21] This theoretical approach assumes Markov property and ergodicity, but the real biological system may not exactly satisfy Markov and ergodic assumptions, for instances, DNA methylation leads to memory effects (non-Markovian) and cells may not visit all possible gene expression states (nonergodic). Basin size is an inadequate measure for relative attractor stability since attractors with the equal size basin, depending on many other properties, may exhibit distinct resilience to random perturbations[34,38,39]

Methods

Results

Conclusion