Mathematics of Synthetic Gene Networks

该项目使用数学、工程和生物技术的组合来构建、监测和分析新的工程基因网络。这项研究的目的是扩展用于合成基因网络建模和分析的数学框架。首先，研究人员系统地研究了双稳态合成基因网络的分离点的随机性。最近发展起来的酵母双稳基因网络首次被用来初始化它们分离出来的基因网络。特别地，从解析和实验两个方面研究了Gillesbie算法和基于化学朗之万方程(CLE)的算法在模拟分叉点附近的随机过程方面的差异。有了研究双稳系统的经验，下一步是对三个势井系统的非线性随机动力学进行数学和实验分析。多势井系统中的非线性随机动力学还没有得到很好的研究。该网络使用现有的、具有良好特性的组件和技术，并结合微流控设备、单细胞实时成像和随机建模来观察和研究噪声诱导的随机状态切换。最后，发展了基因网络的高维分析方法。高维基因网络的动态分析工具一直很缺乏。该项目开发了数学方法，将基因网络的分析从两个维度扩展到更高的维度。开发了利用并行计算的高通量网络识别方法。测试了高维动力系统的分叉分析及其在基因网络中的应用。对细胞分化和重新编程的新的系统理解源于对合成多稳定基因网络的研究。合成多稳态系统为研究细胞多能性和分化的核心机制提供了独特的机会，因为调节细胞分化的高度连接的小转录网络与本项目所考虑的合成基因网络具有拓扑相似性。构建和分析小的多稳定基因网络加深了我们对多稳定的理解，这种多稳定可能源于干细胞基因调控中的相似拓扑结构。此外，还发展了在基因网络背景下研究高维非线性动力学和随机性的数学理论和工具。目前，对细胞多稳态系统的研究缺乏理论上的努力。这项研究填补了技术进步和促进未来生物技术发展的现有分析工具之间的空白。此外，本科生和研究生都进行合成生物学实验和分析。通过参加国际基因工程机器(IGEM)竞赛，这些学生在亚利桑那州立大学推动现代生物技术的发展。在主要研究人员和大学的科学和基础设施支持下，凤凰城大都市区的K-12学生和教师还将有机会参与尖端研究活动。

This project uses the combination of mathematical, engineering, and biological techniques to construct, monitor, and analyze novel engineered gene networks. The objective of the research is to expand the mathematical framework used in the modeling and analysis of synthetic gene networks. First, the investigators systematically study stochasticity at separatrices of bistable synthetic gene networks. Recently developed yeast bistable gene networks are used for the first time to initialize gene networks on their separatrices. In particular, the difference between Gillespie algorithm and Chemical Langevin equation (CLE) based algorithms in simulating stochastic processes near bifurcation points is investigated, both analytically and experimentally. With the experience in studying bistable systems, the next step is to mathematically and experimentally analyze nonlinear stochastic dynamics in three potential well systems. Nonlinear stochastic dynamics in multi potential well systems have not been well studied. This network is constructed using available, well-characterized components and techniques and by combining microfluidics devices, single cell live imaging and stochastic modeling to observe and study noise induced random state switching. Finally, methods of high dimensional analysis of gene networks are developed. Tools for dynamical analysis of high dimensional gene networks have been lacking. This project develops mathematical methods to expand the analysis of gene networks from two dimensions into higher dimensionalities. High throughput network identification methods that utilize parallel computing are developed. Bifurcation analysis of high dimensional dynamical systems with applications in gene networks is tested. Novel systematic understanding of cell differentiation and reprogramming derives from the study of synthetic multistable gene networks. Synthetic multistable systems provide unique opportunities to study the core mechanisms of cell pluripotency and differentiation because highly connected small transcription networks regulating cell differentiation have topological similarities with the synthetic gene networks under consideration in this project. Constructing and analyzing small multistable gene network deepens our understanding of multistability, which can arise from similar topologies in stem cell gene regulations. Additionally, mathematical theories and tools to study high dimensional nonlinear dynamics and stochasticity in the context of gene networks are developed. Currently, theoretical efforts to study cellular multistable systems are lacking. This research fills the gap between technological progress and available analytical tools to facilitate future biotechnological development. In addition, both undergraduate and graduate students carry out synthetic biology experiments and analysis. By participating in the international Genetically Engineered Machine (iGEM) competition, these students promote developments of modern biological technologies at Arizona State University. K-12 students and teachers in the Phoenix metropolitan area will also have opportunities to participate in cutting-edge research activities with scientific and infrastructure support from the principal investigators and the university.