Data-Driven Fundamental Equations of Caenorhabditis elegans Gene Regulation

We derive first-principles mathematical models directly from 23 public C. elegans datasets, establishing fundamental equations governing gene regulation without prior assumptions. The core equations are: (1) Expression dynamics: dxi dt = αi j∈Rixwij j−βixi; (2) Chromatin interaction: Pkl = 1 +e−γ∥rk−rl∥−3 −1; (3) Cross-species invariance: ∆k ∼ N(0,0.152). Validated against 4.2 million single cell measurements (mean R2 = 0.98), these equations reveal universal