Measurements of cell size dynamics have revealed phenomenological principles by which individual cells control their size across diverse organisms. One of the emerging paradigms of cell size homeostasis is the adder, where the cell cycle duration is established such that the cell size increase from birth to division is independent of the newborn cell size. We provide a mechanistic formulation of the adder, considering that cell size follows any arbitrary nonexponential growth law. Our results show that the main requirement to obtain an adder regardless of the growth law (the time derivative of cell size) is that cell cycle regulators are produced at a rate proportional to the growth law, and cell division is triggered when these molecules reach a prescribed threshold level. Among the implications of this generalized adder, we investigate fluctuations in the proliferation of single-cell-derived colonies. Considering exponential cell size growth, random fluctuations in clonal size show a transient increase and then eventually decay to zero over time (i.e., clonal populations become asymptotically more similar). In contrast, several forms of nonexponential cell size dynamics (with adder-based cell size control) yield qualitatively different results: clonal size fluctuations monotonically increase over time, reaching a nonzero value. These results characterize the interplay between cell size homeostasis at the single-cell level and clonal proliferation at the population level, explaining the broad fluctuations in clonal sizes seen in barcoded human cell lines.

中文翻译：

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细胞大小稳态的广义加法器：对随机克隆增殖的影响


细胞大小动力学的测量揭示了现象学原理，单个细胞通过这些原理控制不同生物体的大小。细胞大小稳态的新兴范式之一是加法器，其中建立了细胞周期持续时间，使得细胞大小从出生到分裂的增加与新生细胞大小无关。我们提供了一个加法器的机理公式，考虑到细胞大小遵循任何任意的非指数增长定律。我们的结果表明，无论生长规律（细胞大小的时间导数）如何，获得加法器的主要要求是细胞周期调节剂以与生长规律成正比的速率产生，当这些分子达到规定的阈值水平时，就会触发细胞分裂。在这种广义加法器的意义中，我们研究了单细胞衍生菌落增殖的波动。考虑到指数细胞大小增长，克隆大小的随机波动表现出短暂的增加，然后随着时间的推移最终衰减到零（即，克隆群体越来越近地变得更加相似）。相比之下，几种形式的非指数细胞大小动力学（使用基于加法器的细胞大小控制）产生定性不同的结果：克隆大小波动随着时间的推移单调增加，达到非零值。这些结果表征了单细胞水平的细胞大小稳态与种群水平的克隆增殖之间的相互作用，解释了条形码人类细胞系中克隆大小的广泛波动。