An Accurate and Stable Filtered Explicit Scheme for Biopolymerization Processes in the Presence of Perturbations
An Accurate and Stable Filtered Explicit Scheme for Biopolymerization Processes in the Presence of Perturbations
复制标题
DOI：
10.11648/j.acm.20211006.11
复制
发表时间：
2021-11
影响因子：
10
通讯作者：
L. Davis;F. Pahlevani;T. S. Rajan
中科院分区：
文献类型：
--
作者：
L. Davis;F. Pahlevani;T. S. Rajan
本文的重点是核糖体RNA在高转录基因中的转录模型的建立、数值模拟和参数分析。受经典的Lighthill-Whitham-理查兹（LWR）交通流模型的启发，采用线性平流连续模型来描述DNA转录过程.在该模型中，假设延伸速度基本上是恒定的，因为RNA聚合酶在基因转录的不同阶段沿链沿着移动。使用线性模型的一个优点是，它允许人们量化伸长速度和流入参数的小扰动如何影响重要的生物学测量，如基因的平均转录时间（ATT）。每个聚合酶的ATT是单个RNAP穿过DNA链所花费的时间量。模型模拟的数值处理包括引入一个低复杂度和时间精度的方法，通过添加一个简单的线性时间滤波器到经典的迎风格式。这种改进的方法是模块化的，并且只需要添加一行代码的最小修改，从而在不增加计算开销的情况下提高了准确性。此外，它消除了逆风的过度阻尼。文中给出了新算法的稳定性条件，数值计算表明了滤波格式的稳定性和收敛性以及改进的ATT估计。
The focus of this paper is the development, numerical simulation and parameter analysis of a model of the transcription of ribosomal RNA in highly transcribed genes. Inspired by the well-known classic Lighthill-Whitham-Richards (LWR) traffic flow model, a linear advection continuum model is used to describe the DNA transcription process. In this model, elongation velocity is assumed to be essentially constant as RNA polymerases move along the strand through different phases of gene transcription. One advantage of using the linear model is that it allows one to quantify how small perturbations in elongation velocity and inflow parameters affect important biology measures such as Average Transcription Time (ATT) for the gene. The ATT per polymerase is the amount of time an individual RNAP spends traveling through the DNA strand. The numerical treatment for model simulations includes introducing a low complexity and time accurate method by adding a simple linear time filter to the classic upwind scheme. This improved method is modular and requires a minimal modification of adding only one line of code resulting in increased accuracy without increased computational expense. In addition, it removes the overdamping of upwind. A stability condition for the new algorithm is derived, and numerical computations illustrate stability and convergence of the filtered scheme as well as improved ATT estimation.