A multiplicative behavioral model of DNA replication initiation in cells

DNA replication is a precisely timed cellular decision rather than a continuous biochemical process. Despite extensive mechanistic detail, no unified framework quantitatively explains how structural, metabolic, chromatin, and phase-dependent factors converge to initiate replication. Here, we introduce the ARCH × Φ model, which defines replication onset as a multiplicative threshold event integrating structural, metabolic, chromatin, and phase-control domains. Derived from the recently formalized ARCH behavioral framework, the model expresses replication initiation as R = Φ(A × D × C), where A denotes the origin-licensing architecture, D the metabolic and kinase drives, C the chromatin context, and Φ the phase-control term governing cell-cycle permissiveness. The model predicts (i) all-or-none S-phase entry, (ii) synergistic inhibition when multiple pathways are partially reduced, and (iii) reversible arrest through checkpoint-mediated suppression of Φ. A simple mathematical formulation enables stability analysis and simulation using standard nonlinear control methods. The framework can be falsified by perturbation-matrix experiments measuring whether replication onset scales multiplicatively rather than additively with A, D, and C. By formalizing replication as a threshold-governed system, ARCH × Φ links molecular control of genome duplication with broader principles of biological decision-making, providing a quantitative bridge between cell-cycle dynamics and systems theory.