Cell-specific Cahn-Hilliard models predict condensed fates of the chromosomal passenger complex

Biomolecular condensates create dynamic subcellular compartments that alter systems-level properties of the networks surrounding them. Standard reaction-diffusion models of systems biology cannot define where these compartments emerge nor track how they evolve. One alternative physicochemical model of soluble and condensed states in space and time is the Cahn-Hilliard equation, which specifies a diffuse interface between the two phases. Customized numerical approaches required to solve this equation are absent from computing environments often used for systems biology, however, and the equation's interfacial energy coefficient lacks empirical constraints. Here, using two complementary numerical strategies, we built stable, self-consistent Cahn-Hilliard solvers in three common systems-biology programming languages. The algorithms simulated the complete time evolution of condensed droplets as they dissolved or persisted, relating critical equilibrium droplet size to the Cahn-Hilliard interfacial energy coefficient. We applied this universal relationship to the chromosomal passenger complex, a multi-protein assembly that reportedly condenses on mitotic chromosomes. The fully constrained Cahn-Hilliard simulations predicted spatiotemporal dewetting and coarsening behaviors that matched experiments in cell types with different interfacial energy coefficients. Together, these results suggest how initially variegated recruitment yields robust localization of the chromosomal passenger complex to the inner centromere by the end of prometaphase. More generally, the Cahn-Hilliard equation tests whether condensate dynamics behave as a simple phase-separated liquid, and its numerical solutions advance generalized modeling of biomolecular systems.