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Nuclei import and export proteins, including cell cycle regulators. Theseimport-export processes are modulated periodically by the cell cycle, forexample due to the periodic assembly and breakdown of the nuclear envelope. Assuch, replicated DNA can be segregated between the two daughter cells and theproteins that were localized in the nucleus are free to diffuse throughout thecytoplasm. Here, we study a mathematical import-diffusion model to show howproteins, i.e. cell cycle regulators, could be redistributed in the cytoplasmby nuclei that periodically toggle between interphase and mitosis. We show thatwhen the cell cycle period depends on the local concentration of regulators,the model exhibits mitotic waves. We discuss how the velocity and spatialorigin of these mitotic waves depend on the different model parameters. Thiswork is motivated by recent in vitro experiments reporting on mitotic waves incycling cell-free extracts made with Xenopus laevis frog eggs, where multiplenuclei share the same cytoplasm. Such experiments have shown that nuclei act aspacemakers for the cell cycle and thus play an important role in collectivelydefining the spatial origin of mitotic waves.

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm