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。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，研究者系统地研究了人工合成基因网络在分界面上的随机性。本文首次利用新近发展起来的酵母双基因网络在各自的基片上初始化基因网络。 特别是，吉莱斯皮算法和化学朗之万方程（CLE）的算法在模拟随机过程的分歧点附近的差异进行了研究，分析和实验。有了研究势阱系统的经验，下一步是从数学和实验上分析三个势阱系统中的非线性随机动力学。多势阱系统中的非线性随机动力学尚未得到很好的研究。 该网络是使用可用的，充分表征的组件和技术，并通过结合微流体设备，单细胞活成像和随机建模来观察和研究噪声引起的随机状态切换。 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缺乏。 该项目开发了数学方法，将基因网络的分析从二维扩展到更高维。开发了利用并行计算的高吞吐量网络识别方法。研究了高维动力系统的分叉分析及其在基因网络中的应用。对细胞分化和重编程的新的系统理解来自于对合成多稳态基因网络的研究。 合成多稳态系统提供了独特的机会，研究细胞多能性和分化的核心机制，因为高度连接的小转录网络调节细胞分化与本项目中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态基因网络，加深了我们对多稳态性的理解，多稳态性可能产生于干细胞基因调控的相似拓扑结构。 此外，数学理论和工具，研究高维非线性动力学和随机性的背景下，基因网络的发展。目前，理论上的努力，研究细胞多稳态系统是缺乏的。 这项研究填补了技术进步和现有分析工具之间的差距，以促进未来生物技术的发展。此外，本科生和研究生都进行合成生物学实验和分析。 通过参加国际遗传工程机器（iGEM）竞赛，这些学生促进了亚利桑那州立大学现代生物技术的发展。 凤凰城大都会区的K-12学生和教师也将有机会参加尖端研究活动，并得到主要研究人员和大学的科学和基础设施支持。

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.