Resolution:
standard / ## Figure 4.
Valleys on the computed epigenetic landscape represent high-occupancy stable steady
states, while ridges represent barriers to stochastic transitions between those stable
states. For the tristable two-gene system, increasing the Hill coefficient n_{H}, which represents the degree of ultrasensitivity in autoregulation and mutual inhibition
of the two genes (see Methods), makes the ridges (barriers) higher and steeper relative to the valleys (attractors).
Higher ridges reduce the probability of stochastic switching among adjacent attractors.
(A) n_{H }= 2; (B) n_{H }= 3; (C) n_{H }= 4; (D) n_{H }= 10. Left Panels: Colored circles represent a population of 1000 stochastically simulated "cells"
residing in the three stable steady states A (blue), B (green) and C (red). States A and B represent two alternative differentiated cell fates, and state C their common progenitor state [8,13,42]. All simulations were started from state B as the initial condition, and run to time t = 10,000 (dimensionless units). As the ridges separating the steady states grow higher,
fewer cells are able to escape state B for states A and C through stochastic fluctuations.
Middle Panels: Projections of the epigenetic landscape onto the x-y phase plane. Numbers refer to the percentage of simulated cells residing in the respective
steady states. Dashed yellow lines show boundaries between the basins of attraction
of the steady states. Right Panels: An alternative view of the epigenetic landscape. The vertical dashed red lines are
guides to the eye to show that the relative distance between the steady states on
the x-y phase plane does not change appreciably even as the Hill coefficient n_{H }is increased from 2 to 6. The change in relative occupancy of the attractors can therefore
be attributed to the increased height and steepness of the barriers separating them.
Bhattacharya |