Joint regulation of growth and division timing drives size homeostasis in proliferating animal cells

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How organisms maintain cell size homeostasis is a long-standing problem that remains unresolved, especially in multicellular organisms. Recent experiments in diverse animal cell types demonstrate that within a cell population the extent of growth and cellular proliferation (i.e., fitness) is low for small and large cells, but high at intermediate sizes. Here we use mathematical models to explore size-control strategies that drive such a non-monotonic fitness profile resulting in an optimal cell size. Our analysis reveals that if cell size grows exponentially or linearly over time, then fitness always varies monotonically with size irrespective of how timing of division is regulated. Furthermore, if the cell divides upon attaining a critical size (as in the Sizer or size-checkpoint model), then fitness always increases with size irrespective of how growth rate is regulated. These results show that while several size control models can maintain cell size homeostasis, they fail to predict the optimal cell size, and hence unable to explain why cells prefer a certain size. Interestingly, fitness maximization at an optimal size requires two key ingredients: 1) The growth rate decreases with increasing size for large enough cells; and 2) The cell size at the time of division is a function of the newborn size. The latter condition is consistent with the Adder paradigm for division control (division is triggered upon adding a fixed size from birth), or a Sizer-Adder combination. Consistent with theory, Jurkat T cell growth rates, as measured via oxygen consumption or mitochondrial activity, increase with size for small cells, but decrease with size for large cells. In summary, regulation of both growth and cell division is critical for size control in animal cells, and this joint-regulation leads to an optimal size where cellular fitness is maximized.