Battogtokh Dorjsuren, Tyson John J
Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 1):011910. doi: 10.1103/PhysRevE.73.011910. Epub 2006 Jan 18.
In a differential equation model of the molecular network governing cell growth and division, cell cycle phases and transitions through checkpoints are associated with certain bifurcations of the underlying vector field. If the cell cycle is driven by another rhythmic process, interactions between forcing and bifurcations lead to emergent orbits and oscillations. In this paper, by varying the amplitude and frequency of forcing of the synthesis rates of regulatory proteins and the mass growth rate in a minimal model of the eukaryotic cell cycle, we study changes of the probability distributions of interdivision time and mass at division. By computing numerically the Lyapunov exponent of the model, we show that the splitting of probability distributions is associated with mode-locked solutions. We also introduce a simple, integrate-and-fire model to analyze mode locking in the cell cycle.
在控制细胞生长和分裂的分子网络的微分方程模型中，细胞周期阶段以及通过检查点的转变与基础向量场的某些分岔相关联。如果细胞周期由另一个节律性过程驱动，那么强迫与分岔之间的相互作用会导致出现轨道和振荡。在本文中，通过在真核细胞周期的一个最小模型中改变调节蛋白合成速率和质量生长速率的强迫振幅与频率，我们研究了分裂间隔时间和分裂时质量的概率分布变化。通过数值计算模型的李雅普诺夫指数，我们表明概率分布的分裂与锁模解相关。我们还引入了一个简单的积分发放模型来分析细胞周期中的锁模现象。
