Sassi Alberto Stefano, Garcia-Alcala Mayra, Aldana Maximino, Tu Yuhai
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
Department of Molecular and Cellular Biology, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
Phys Rev X. 2022 Jan-Mar;12(1). doi: 10.1103/physrevx.12.011051. Epub 2022 Mar 17.
Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single . cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.
由于生长和分裂过程中的噪声，活细胞中的蛋白质浓度会随时间波动。在高表达状态下，发现细胞中蛋白质浓度的方差与均值的平方成比例，这属于一种称为泰勒定律（TL）的普遍现象。为了理解这些波动的起源，我们测量了一组具有可变荧光蛋白表达的菌株中单个细胞的蛋白质浓度动态。蛋白质表达由一组具有不同强度的组成型启动子控制，这使得能够在不引入转录调节因子波动噪声的情况下将表达水平改变2个数量级。我们的数据证实了平方泰勒定律，但前置因子存在细胞间差异，且与启动子强度无关。发现不同启动子的归一化蛋白质浓度分布会汇聚到同一条曲线上。为了解释这些观察结果，我们使用了一个最小机制模型来描述单个细胞中的随机生长和分裂过程以及调节细胞分裂的反馈机制。在外部噪声占主导的高表达状态下，该模型定量地再现了我们的实验结果。通过在最小模型中使用平均场近似，我们表明蛋白质浓度的随机动力学由具有乘性噪声的朗之万方程描述。朗之万方程具有尺度不变性，这是平方泰勒定律的原因。通过求解朗之万方程，我们得到了与实验相符的蛋白质浓度分布函数的解析解。该解明确显示了前置因子如何依赖于不同噪声源的强度，这解释了其细胞间的变异性。通过使用这种方法分析我们的单细胞数据，我们发现生产率噪声主导了细胞分裂噪声。通过在生产率中纳入内在噪声，我们的模型也可以捕捉到低表达状态下与平方泰勒定律的偏差。
