Fig 6. Mathematical model predicts filtering of Brn2 inputs based upon their duration.

A) Energy landscape depiction of duration thresholding through the dynamics of two-state Nanog switch. Brn2 induction destabilizes Nanog-on (pluripotent) state, and cell begins to transition to Nanog-off (differentiated) state through intrinsic Nanog degradation. For an input that is “short” relative to the Nanog half-life, Brn2 begins to fall before the cell can transition past a critical point, and the cell returns to the Nanog-on state following the light pulse. For a long pulse, B) the cell transitions beyond the critical Nanog concentration during the pulse and so transitions to and remains in the Nanog-off state following the pulse. C) Nanog and Brn2 dynamics from mathematical model for “short” and “long” Brn2 pulses. D) 2D depiction of Nanog steady states and dynamic flows vs Brn2 input level. Stable Nanog concentrations (black curves) and dynamic Nanog flows (gray arrows) indicated as a function of [Brn2]. The Nanog-on stable state is lost at a sharp Brn2 threshold due to a saddle node bifurcation. Schematic Nanog/Brn2 trajectories for “short” (blue arrow) and “long” (green arrow) square Brn2 pulses. For short pulse, Brn2 exceeds switching threshold but returns below the threshold before Nanog passes a “critical concentration” defined by presence of an unstable fixed point (dotted gray curve).