Rare-event sampling of epigenetic landscapes and phenotype transitions
Fig 2
Simulation results show good agreement with a theoretical benchmark for the 2-gene ExMISA (mutual inhibition, self-activation) cell-decision circuit.
The Chemical Master Equation for the 2-gene model, ExMISA, was solved numerically (see Methods) (top) and compared to simulation results from the computational pipeline presented in this paper (bottom). Shown for each are the Quasipotential Landscape (A), Eigenvalue Spectrum (B), and Markov State Model (C). (A) Quasipotential landscapes of the ExMISA network projected onto the two protein coordinates. Deep blue regions denote low potential (high probability) and yellow denote high potential (low probability). The four visible basins in both correspond to combinations of lo/hi expression for the two genes A and B. (For both rows, quasipotential surfaces estimated over discrete states/bins are smoothed for visualization). WE sampling captured both the basin structure and low probability edge and barrier regions. (B) Eigenvalue spectra and corresponding computed global transition timescales. Gaps in the eigenvalue spectrum indicate separation of timescales, i.e., the presence of metastability. C) Four-phenotype coarse-grained models automatically generated from the clustering algorithm (see Methods). Each colored circle represents a cell phenotype, sized proportionally to its probability. Edges are inter-phenotype transitions (colored by source-state, with width proportional to probability). The full CME and simulation pipeline identify similar metastable phenotype networks (see S11 Fig for details).