Department of Physics, University of California, San Diego, La Jolla, CA 92093;
Department of Cell Biology, Duke University Medical Center, Durham, NC 27710.
Proc Natl Acad Sci U S A. 2018 Mar 6;115(10):E2165-E2174. doi: 10.1073/pnas.1714873115. Epub 2018 Feb 15.
Early embryogenesis of most metazoans is characterized by rapid and synchronous cleavage divisions. Chemical waves of Cdk1 activity were previously shown to spread across embryos, and the underlying molecular processes were dissected. Here, we present the theory of the physical mechanisms that control Cdk1 waves in The in vivo dynamics of Cdk1 are captured by a transiently bistable reaction-diffusion model, where time-dependent reaction terms account for the growing level of cyclins and Cdk1 activation across the cell cycle. We identify two distinct regimes. The first one is observed in mutants of the mitotic switch. There, waves are triggered by the classical mechanism of a stable state invading a metastable one. Conversely, waves in wild type reflect a transient phase that preserves the Cdk1 spatial gradients while the overall level of Cdk1 activity is swept upward by the time-dependent reaction terms. This unique mechanism generates a wave-like spreading that differs from bistable waves for its dependence on dynamic parameters and its faster speed. Namely, the speed of "sweep" waves strikingly decreases as the strength of the reaction terms increases and scales as the powers 3/4, -1/2, and 7/12 of Cdk1 molecular diffusivity, noise amplitude, and rate of increase of Cdk1 activity in the cell-cycle S phase, respectively. Theoretical predictions are supported by numerical simulations and experiments that couple quantitative measurements of Cdk1 activity and genetic perturbations of the accumulation rate of cyclins. Finally, our analysis bears upon the inhibition required to suppress Cdk1 waves at the cell-cycle pause for the maternal-to-zygotic transition.
大多数后生动物的早期胚胎发生以快速和同步的卵裂分裂为特征。先前已经表明，Cdk1 活性的化学波在胚胎中传播，并且已经解析了潜在的分子过程。在这里，我们提出了控制 Cdk1 波的物理机制理论。通过瞬态双稳态反应扩散模型捕获体内 Cdk1 的动力学，其中时变反应项解释了细胞周期中 cyclin 和 Cdk1 激活水平的增长。我们确定了两种不同的状态。第一种状态发生在有丝分裂开关的突变体中。在那里，波是由稳定状态侵入亚稳定状态的经典机制触发的。相反，在野生型中，波反映了一个瞬态阶段，该阶段在整体 Cdk1 活性水平被时变反应项向上扫动的同时，保留了 Cdk1 的空间梯度。这种独特的机制产生了一种不同于双稳态波的波状传播，因为它依赖于动态参数，并且速度更快。也就是说，作为反应项强度增加的函数，“扫掠”波的速度惊人地减小，并且与 Cdk1 分子扩散率、噪声幅度和细胞周期 S 期 Cdk1 活性增加率的 3/4、-1/2 和 7/12 的幂次成比例。理论预测得到了数值模拟和实验的支持，这些实验将 Cdk1 活性的定量测量和 cyclin 积累率的遗传扰动相结合。最后，我们的分析涉及在母体到合子过渡的细胞周期暂停期间抑制 Cdk1 波所需的抑制。
