Dresch Jacqueline M, Thompson Marc A, Arnosti David N, Chiu Chichia
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711. This author's work was partly supported by a Teaching and Research Postdoctoral Fellowship at Harvey Mudd College.
Department of Bioengineering, North Carolina Agricultural and Technical State University, Greensboro, NC27411.
SIAM J Appl Math. 2013 Mar 1;73(2):804-826. doi: 10.1137/120887588.
High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the model's simulated data. Where protein and -regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.
高通量基因组测序和转录组分析为研究人员提供了定量基础，以便使用各种数学模型对基因表达进行详细建模。用于真核基因调控建模的两种最常用方法是：描述基因网络时间依赖性相互作用的微分方程系统，以及能够探索DNA水平转录调控的热力学平衡方法。为了结合这些方法的优势，我们构建了一个新的两层数学模型，该模型利用基于DNA的详细信息以及空间和时间转录因子浓度数据，对基因调控系统进行动态描述。我们还开发了一种用于求解模型方程的半隐式数值算法，并通过稳定性和收敛性分析证明了该算法的效率。为了测试该模型，我们将其与半隐式算法一起用于模拟一个驱动胚盘阶段胚胎背腹轴发育的基因调控回路，该回路涉及三个基因。为了进行模型验证，我们对实验数据和模型模拟数据进行了数学和统计比较。在有蛋白质和调控信息可用的情况下，我们的两层模型提供了一种概括和预测真核转录系统动态方面的方法，这将极大地增进我们对全球水平基因调控的理解。
