iPSC Reprogramming Landscape: Yamanaka Factor Dosage (2D)

Reprogramming Factor Dosage

OCT4 40%

SOX2 40%

KLF4 40%

MYC 40%

Stochastic noise (D) 0.35

Culture speed 1.0×

Culture Readouts

Reprogrammed

Day

0.0

Barrier ΔV

–

Mean dosage F0.40

How it works

Each of the N cells carries a single reprogramming coordinate x ∈ [0,1]: x=0 is the stable somatic (fibroblast) epigenetic state, x=1 is induced pluripotency. Its motion is overdamped Langevin dynamics on a double-well epigenetic potential, driven by the mean Yamanaka-factor dosage F = (OCT4+SOX2+KLF4+MYC)/4:

V(x)  = 4B·x²(1−x)² − k·F·x
dx/dt = −dV/dx + √(2D)·η(t)      (η = unit Gaussian noise)

F = 0 — the landscape is a symmetric double well; cells parked at x=0 almost never cross the central barrier, so the culture stays fibroblast-like.
F ↑ — the −k·F·x tilt term lowers the barrier and deepens the x=1 well until pluripotency becomes the global energy minimum, exactly how ectopic OCT4/SOX2/KLF4/MYC expression destabilizes the somatic chromatin state and stabilizes the pluripotency network (Takahashi & Yamanaka, 2006).
Noise D — thermal/transcriptional fluctuations; without any noise a cell can only cross the barrier once the tilt removes it entirely (deterministic reprogramming), while realistic noise lets a fraction cross early — mirroring the low (~0.1–1%) efficiency seen in real retroviral reprogramming.
Reprogrammed — the fraction of cells with x > 0.8 (committed to the pluripotent well). Barrier ΔV is the current potential-energy gap between the somatic well and the saddle point the cells must climb over.

Cells are integrated with the Euler–Maruyama method each frame. Top panel: the potential curve V(x) re-shapes live as dosage changes, with each cell drawn as a marble sitting on the curve at its own x — drag the curve to pan, scroll/pinch to zoom, or use "Fit view". Middle panel: a live histogram of the population across x. Bottom panel: reprogramming efficiency traced over culture days.

Somatic cell Reprogrammed (iPSC)

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