The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate existence of a phase transition, which can be continuous or first-order, by which a non-zero fraction of the population becomes localized at a minimal division time. Just below the transition, we demonstrate coexistence of localized and delocalized age-structure phases, and power law decay of correlation functions. Above it, we observe self-synchronization of cell cycles, collective divisions, and slow `aging’ of population growth rates.

中文翻译：

---

增长群体的细胞周期遗传力和定位相变

细胞周期持续时间是一个可变的细胞表型，是长期种群增长和年龄结构的基础。通过分析具有可遗传的细胞分裂时间的分支过程的平稳解，我们证明了相变的存在，该相变可以是连续的或一阶的，通过该相变，人口的非零部分位于最小的分裂时间。在过渡之下，我们证明了本地化和非本地化年龄结构阶段的共存，以及相关函数的幂律衰减。在它之上，我们观察到细胞周期的自我同步，集体分裂以及人口增长率的缓慢“老化”。