In vitro cell cycle oscillations exhibit a robust and hysteretic response to changes in cytoplasmic density

Cells control the properties of the cytoplasm to ensure proper functioning
of biochemical processes. Recent studies showed that cytoplasmic density
varies in both physiological and pathological states of cells undergoing
growth, division, differentiation, apoptosis, senescence, and metabolic
starvation. Little is known about how cellular processes cope with these
cytoplasmic variations. Here, we study how a cell cycle oscillator
comprising cyclin-dependent kinase (Cdk1) responds to changes in
cytoplasmic density by systematically diluting or concentrating cycling
Xenopus egg extracts in cell-like microfluidic droplets. We found that the
cell cycle maintains robust oscillations over a wide range of deviations
from the endogenous density: as low as 0.2× to more than 1.22× relative
cytoplasmic density (RCD). A further dilution or concentration from these
values arrested the system in a low or high steady state of Cdk1 activity,
respectively. Interestingly, diluting an arrested cytoplasm of 1.22× RCD
recovers oscillations at lower than 1× RCD. Thus, the cell cycle switches
reversibly between oscillatory and stable steady states at distinct
thresholds depending on the direction of tuning, forming a hysteresis
loop. We propose a mathematical model which recapitulates these
observations and predicts that the Cdk1/Wee1/Cdc25 positive feedback loops
do not contribute to the observed robustness, supported by experiments.
Our system can be applied to study how cytoplasmic density affects other
cellular processes.

细胞可通过调控细胞质的特性，保障生化过程的正常运行。近年来的研究表明，在细胞生长、分裂、分化、凋亡、衰老以及代谢饥饿等生理与病理状态下，细胞质密度会发生动态变化。目前学界对细胞如何适应这类细胞质密度变化的机制仍知之甚少。本研究通过在类细胞微流体液滴中系统性稀释或浓缩周期性非洲爪蟾卵提取物，探究了由细胞周期蛋白依赖性激酶（Cdk1）构成的细胞周期振荡器对细胞质密度变化的响应机制。研究发现，在与内源密度偏差范围广泛的条件下（低至0.2倍，最高可超过1.22倍相对细胞质密度（RCD）），细胞周期仍可维持稳定的振荡。若进一步偏离该范围进行稀释或浓缩，系统则会分别停滞于Cdk1活性的低稳态或高稳态。值得注意的是，将处于1.22倍RCD停滞状态的细胞质进行稀释后，可在低于1倍RCD的条件下恢复振荡。由此可见，细胞周期可根据调控方向的不同，在不同阈值下于振荡态与稳定稳态之间可逆切换，形成滞后环。我们提出了可复现上述实验现象的数学模型，且实验验证表明，该模型预测Cdk1/Wee1/Cdc25正反馈回路并未对观测到的鲁棒性产生贡献。本研究体系可用于探究细胞质密度对其他细胞过程的影响。