Mathematical modeling of a minimal protocell with coordinated growth and division

Self-replication is an essential attribute of life but the molecular-level mechanisms involved are not well understood. Cellular self-replication requires not only duplicating all cellular components and doubling volume and membrane area, but also replicating cellular geometry. A whole-cell modeling framework is presented in which an assumed reaction network determines both concentration changes of cellular components and cell geometry. Cell shape is calculated by minimizing membrane-bending energy. Using this framework, simultaneous doubling of volume, surface area, and all components was found to be insufficient to provide mid-cell "pinching" of the parental cell to form two daughter cells. This prompted the design of a minimal protocell that includes a growing shell, a cell-cycle engine, and a contractile ring to enforce cytokinesis. Kinetic parameters were found such that the system exhibited periodic behavior with fundamental aspects of self-replication. This involved simultaneous doubling of all cellular components during a cell cycle, doubling cell volume and membrane area, achieving periodic changes in surface/volume ratio, and forming daughter cells that were geometrically equivalent to each other and to the "newborn" parental cell. The results presented here impact the design of laboratory protocells and the development of a modular strategy for constructing a comprehensive in silico whole-cell model.