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比我们对它们的动力学的了解要多得多。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，这些速率在基因之间的变化超过几个数量级[1]。如果不了解这些变异，我们就无法理解天然序列是如何工作的，我们也无法设计出可靠的合成序列。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，了解基因表达动力学的数据是可用的，需要数学模型将单分子动力学与全基因组数据联系起来，并设计具有定义的延伸动力学和合成速率的新序列。学生将扩展最近开发的随机模型简化技术[2]为了解决基于完全不对称简单排除过程（TASEP）的转录和翻译动力学模型[3]，一个驱动扩散晶格气模型，形成了非平衡物理学的基石。一个主要目标是分析基于TASEP的转录和翻译动力学模型，根据最近的实验观察，解释非均匀的，序列依赖性的延伸率。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的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异性变化。该项目将为学生提供转录和翻译的基础分子生物学以及使用随机模拟进行建模的坚实基础。没有关于这些主题的背景假设。有基本的概率论知识和编码经验是必要的。该项目非常适合具有数学或物理学位的学生，他们对使用从非平衡统计物理学借来的随机模型对生命系统进行定量建模感兴趣。学生将在C。H.爱丁堡大学合成与系统生物学中心所在的沃丁顿大楼。

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.