Mathematical models of RNA and protein synthesis dynamics and their integration with gene expression data

基因表达是一个动态复杂系统的终极例子，该系统包括数千个在不同时间尺度上相互作用的调控部分。目前，我们对这些部分的了解远远超过了我们对它们的动力学的了解。例如，我们不知道DNA和RNA序列如何指定RNA和蛋白质的合成速率，这些速率在几个数量级的基因之间存在差异[1]。如果不了解这些变异，我们就不能理解自然序列是如何工作的，我们也无法设计出可靠工作的合成序列。近年来，越来越多的实验方法被开发出来，可以在单分子和全基因组水平上测量基因表达。现在已经有了了解基因表达动力学的数据，需要数学模型来将单分子动力学连接到全基因组数据，并设计具有定义的延伸动力学和合成速率的新序列。在这个项目中，学生将扩展最近开发的随机模型简化技术[2]来求解基于完全不对称简单排除过程(TASEP)[3]的转录和翻译动力学模型，TASEP是一种驱动的扩散格子气体模型，构成了非平衡物理的基石。一个主要的目标是根据最近的实验观察，分析基于TASEP的转录和翻译动力学模型，这些模型解释了不均匀的、序列相关的延伸率。第二个目标是使用这些模型从全基因组测序数据中推断转录和翻译延伸率[3]。最终目标是将这些速率与已知的转录和翻译动力学决定因素进行交叉检查，以更好地了解RNA和蛋白质合成速率的基因特定变异。该项目将使学生在转录和翻译的基本分子生物学以及使用随机模拟进行建模方面奠定坚实的基础。假设没有这些主题的以前的背景知识。必须具备概率论的基本知识和一定的编码经验。该项目非常适合拥有数学或物理学位的学生，他们对使用借用非平衡统计物理的随机模型对生命系统进行定量建模感兴趣。这名学生将在爱丁堡大学合成与系统生物学中心所在的C.H.沃丁顿大楼工作。

Gene expression is the ultimate example of a dynamic complex system that includes thousands of regulatory parts interacting at various time scales. Currently, we know much more about these parts than we know about their dynamics. For example, we don't know how DNA and RNA sequences specify RNA and proteins synthesis rates, which vary between genes over several orders of magnitude [1]. Without understanding these variations, we do not understand how natural sequences work, and we cannot engineer synthetic sequences that work reliably.In recent years, a growing number of experimental methods has been developed that can measure gene expression at the single-molecule and genome-wide level. Now that the data to understanding gene expression dynamics is available, mathematical models are needed to connect single-molecule dynamics to genome-wide data and to design new sequences with defined elongation dynamics and synthesis rate.In this project, the student will extend recently developed stochastic model reduction techniques [2] to solve models of transcription and translation dynamics that are based on the totally asymmetric simple exclusion process (TASEP) [3], a driven diffusive lattice gas model that forms a cornerstone of nonequilibrium physics. A primary goal is to analyse TASEP-based models of transcription and translation dynamics that account for non-uniform, sequence-dependent elongation rates, in accordance with recent experimental observations. A secondary goal is to use these models to infer transcription and translation elongation rates from genome-wide sequencing data [3]. A final goal is to cross-check these rates with known determinants of transcription and translation dynamics to better understand gene-specific variations of RNA and protein synthesis rates.The project will give the student a solid foundation in the basic molecular biology of transcription and translation, and its modelling using stochastic simulations. No previous background on these topics is assumed. A basic knowledge of probability theory and some experience in coding are necessary. The project is ideal for a student with a mathematics or physics degree who is interested in the quantitative modelling of living systems using stochastic models borrowed from nonequilibrium statistical physics. The student will be based in the C. H. Waddington building which houses the Centre for Synthetic and Systems Biology at the University of Edinburgh.