Figure 5.

Bifurcation analysis reveals spatial patterns and hysteresis as emergent properties of the gene regulatory network

(A) Bifurcation analysis showing the stable (solid blue lines) and unstable steady state (dashed red lines) solutions in c/EBPα, SOX9, and TGFBR2 levels, as a function of increasing TGFβ levels.

(B) Spatial patterning emergent from the dynamics of the gene regulatory network as a function of a gradient of TGFβ signaling under the influence of gene expression noise.

(C) Experimentally observed expression levels of c/EBPα and SOX9 via RNA-seq data (GSE84498) in different regions of liver (toward central vein or portal vein). ∗ represents a statistically significant difference in SOX9 and c/EBPα expression levels (Students’ two-tailed t test; pvalue<= 0.05).

(D) Effects of different initial conditions on the stochastic dynamics of GRN, showing hysteresis in the system – fraction of hepatocytes, progenitor cells and cholangiocytes. To test for hysteresis, two distinct initial conditions used for the system is either a pure hepatocyte or a progenitor-like population, and the fraction of the two cell populations are plotted. Error bars represent SD values (n = 3).