Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1129, Japan.
Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1129, Japan.
J Theor Biol. 2022 Nov 21;553:111260. doi: 10.1016/j.jtbi.2022.111260. Epub 2022 Aug 31.
Bacterial cells maintain their characteristic cell size over many generations. Several rod-shaped bacteria, such as Escherichia coli and the cyanobacteria Synechococcus elongatus, divide after adding a constant length to their length at birth. Through this division control known as the adder mechanism, perturbation in cell length due to physiological fluctuation decays over generations at a rate of 2 per cell division. However, previous experiments have shown that the circadian clock in cyanobacteria reduces cell division frequency at a specific time of day under constant light. This circadian gating should modulate the division control by the adder mechanism, but its significance remains unknown. Here we address how the circadian gating affects cell length, doubling time, and cell length stability in cyanobacteria by using mathematical models. We show that a cell subject to circadian gating grows for a long time, and gives birth to elongated daughter cells. These elongated daughter cells grow faster than the previous generation, as elongation speed is proportional to cell length and divide in a short time before the next gating. Hence, the distributions of doubling time and cell length become bimodal, as observed in experimental data. Interestingly, the average doubling time over the population of cells is independent of gating because the extension of doubling time by gating is compensated by its reduction in the subsequent generation. On the other hand, average cell length is increased by gating, suggesting that the circadian clock controls cell length. We then show that the decay rate of perturbation in cell length depends on the ratio of delay in division by the gating τ to the average doubling time τ as [Formula: see text] . We estimated τ≈2.5, τ≈13.6 hours, and τ/τ≈0.18 from experimental data, indicating that a long doubling time in cyanobacteria maintains the decay rate similar to that of the adder mechanism. Thus, our analysis suggests that the acquisition of the circadian clock during evolution did not impose a constraint on cell size homeostasis in cyanobacteria.
细菌细胞在多代中保持其特征性细胞大小。一些杆状细菌，如大肠杆菌和蓝藻集胞藻，在出生后会在其长度上增加一个恒定的长度来进行分裂。通过这种称为加法器机制的分裂控制，由于生理波动导致的细胞长度的扰动在每细胞分裂两代的速率下衰减。然而，以前的实验表明，在持续光照下，蓝藻中的生物钟会降低特定时间的细胞分裂频率。这种生物钟门控应该调节加法器机制的分裂控制，但它的意义仍然未知。在这里，我们通过数学模型研究了生物钟门控如何影响蓝藻的细胞长度、倍增时间和细胞长度稳定性。我们表明，受生物钟门控的细胞会生长很长时间，并生出拉长的子细胞。这些拉长的子细胞比前一代生长得更快，因为伸长速度与细胞长度成正比，并且在下一个门控之前在短时间内分裂。因此，如实验数据所示，倍增时间和细胞长度的分布呈双峰分布。有趣的是，由于门控导致的倍增时间延长被随后一代的缩短所补偿，因此细胞群体的平均倍增时间独立于门控。另一方面，由于门控导致的平均细胞长度增加，表明生物钟控制细胞长度。然后，我们表明，细胞长度扰动的衰减率取决于门控导致的分裂延迟τ与平均倍增时间τ的比值，即[公式：见文本]。我们从实验数据中估计τ≈2.5，τ≈13.6 小时，以及τ/τ≈0.18，表明蓝藻中较长的倍增时间维持与加法器机制相似的衰减率。因此，我们的分析表明，在进化过程中获得生物钟并没有对蓝藻的细胞大小稳态施加限制。
