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.Author summary: Some biomolecules separate into condensed and soluble phases within cells; it is important to study the behavior of these compartments with mathematical models. From chemical physics, there is a macroscale theory for phase-separated systems, but the governing equation is difficult to solve numerically with standard approaches. Here, we encoded and verified a pair of specialized solvers in three programming languages widely used by systems biologists. The math behind each solver is different, enabling them to crosscheck one another for self-consistency. We used the solvers to define a previously unknown relationship within the governing equation that holds for any phase-separated system. When applied to a protein complex whose condensation is debated, the numerical solutions yielded absolute predictions that were remarkably consistent with experiments. This work provides a combined computational–experimental path to parameterizing the governing equation for generalized models of biomolecular condensates.