A Hypothesized Master Regulator Providing Positive Feedback to Nanog in the Pluripotency Gene Regulatory Network: A Reproducible Mathematical Modeling Study with an Experimental Discovery Roadmap

Induced pluripotent stem cell (iPSC) reprogramming with the Yamanaka factors remains inefficient (0.01 to 1%), a gap that motivates the hypothesis that the core Oct4, Sox2, and Nanog gene regulatory network (GRN) is missing at least one regulatory component. We formalize this hypothesis as an undiscovered factor X that supplies strong positive feedback to Nanog, and we build a fully reproducible ordinary differential equation (ODE) model of the core GRN with and without X, extend it to a stochastic differential equation (SDE) formulation to capture cell to cell heterogeneity, and analyze its bistability, parameter sensitivity, and basins of attraction. All numerical results in this manuscript are regenerated directly from the accompanying Python code (Appendix A) using a fixed random seed, so every figure and table entry is independently reproducible from the text alone. Under an illustrative, fast turnover parameterization, the model without X settles at a steady state Nanog level of 15.0 (arbitrary units); adding X raises this to 25.0, with X itself stabilizing near 8.0, while ±30% Monte Carlo parameter perturbation reduces the coefficient of variation (CV) of steady state Nanog from 27.2% (no X) to 20.9% (with X), a real, reproducible, but modest robustness gain. A second, physically anchored calibration derives the same rate constants from literature measured, species specific protein half lives and physiologically bounded induction fold assumptions rather than from a target output; it reproduces the Nanog elevation and robustness conclusions, and, once combined with an explicit, biologically motivated double negative repressor motif structurally consistent with documented lineage priming antagonists of Nanog, also reproduces robust bistability at physiological turnover rates (24 of 24 tested parameter combinations). We support these findings with a global Sobol sensitivity analysis identifying Nanog protein turnover as the dominant source of output variance, and with a set of sharply falsifiable, numerically stated predictions, including a 1.8 fold Nanog elevation threshold and a repressor knockdown prediction distinct from the X overexpression prediction. A literature based survey nominates SRSF3, Esrrb, and Tspan8 as motivating, not confirmatory, candidates for X's identity, and we propose a concrete nanoparticle based pull down and mass spectrometry strategy for its empirical discovery. We state the model's falsification conditions, its parameter identifiability limitations, and a staged experimental roadmap toward testing the hypothesis, and we situate the framework quantitatively against three widely cited prior pluripotency network models. The contribution of this work is a rigorously specified, fully reproducible, and quantitatively falsifiable theoretical framework for a testable biological hypothesis, not a claim of biological discovery.