标题： 结构化细胞群体中振荡的双稳态出现 显示英文标题

标题： Bistable emergence of oscillations in structured cell populations

摘要： 枯草芽孢杆菌生物膜群落最近被证明可以通过电化学信号表现出集体生长速率振荡，以应对营养饥饿。这些振荡在菌落达到足够多的细胞数量后出现。然而，振荡的振幅，从而其有效性，是随着时间逐渐增加的，还是可以立即以非零振幅出现，这一点尚不清楚。在这里，我们通过结合基于微流控的时间延迟显微镜实验与系统的最小理论描述，即延迟微分方程模型，来解决这个问题。分析和数值方法揭示了振荡是通过次临界霍普夫分支产生的，这使得高振幅振荡能够立即出现。因此，该模型预测了一个双稳态区域，在相空间中振荡和非振荡吸引子共存。我们通过实验证实了这一预测，表明如果生物膜大小处于适当的范围内，可以通过扰动培养基条件来触发振荡。该模型还预测，振荡开始的最小尺寸会随着压力的增加而减小，我们也通过实验验证了这一点。综上所述，我们的结果表明，细胞群体中的集体振荡可以通过不连续转变突然以非零振幅出现。 显示英文摘要

摘要： Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually, or if they can emerge instantly with a non-zero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a non-oscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with non-zero amplitude via a discontinuous transition.