The Impact of Transcriptional Delay on Biochemical Circuit Dynamics: A Large-Deviations Approach

该项目将使用数学工具，即模型设计，模型分析和多尺度模拟，以告知新型合成生物电路设计的设计和测试。合成生物学家利用数学、生物物理学和生物工程学的思想，通过重组有机体来构建这样的电路。应用包括精确靶向治疗药物输送、药物生产成本降低、生物燃料进步和环境污染物的新生物修复技术。该项目将提供所需的数学工具，以了解并利用合成生物电路的新兴复杂性。一个特别的重点将是电路，其中罕见的事件发挥了至关重要的作用，作为生物开关。作为项目的一部分，调查人员将培训学生和初级科学家，进行课程开发，并通过名为“数学丰富网络，培训和研究机会”（MENTOR）的学生丰富计划，通过社区外展加强大休斯顿地区的科学界。MENTOR的活动包括一个研究方法类，STEM系列讲座，夏季研究奖学金，以及每年的本科生研究会议之间的休斯敦大学，路易斯安那州立大学，得克萨斯州A M大学轮换。该项目的重点是量化的复杂，空间扩展的随机系统，其中延迟起着重要作用的稀有事件的行为。动机来自于需要了解基因调控网络的动态，以告知新的合成生物电路的设计。在许多情况下，这种网络的基本功能涉及罕见的事件-无论是亚稳态之间的转换还是突然的活动爆发。由于蛋白质作为调控因子，转录延迟（从转录起始到功能蛋白质形成的时间）是遗传调控网络固有的，并已被证明会显着影响网络动态。在数学上，大偏差理论允许罕见事件量化。从一个亚稳态到另一个亚稳态最可能的转变途径是什么？罕见事件发生的频率是多少？大偏差理论可以从理论和计算上回答这些问题。该项目旨在为非线性时滞随机微分方程，特别是模拟遗传调控网络的非线性时滞随机微分方程，建立一个全面的理论和计算大偏差框架。合成生物学家最近专注于在合成微生物财团内构建基因调控网络。这种分布式方法提供了模块化和构建更复杂生物电路的潜力。然而，由此产生的动力学是相当复杂的，因为聚生体具有时空动力学、细胞周期效应、化学信号传导、群体水平效应和机械传感的特征。本计画旨在建立时空延迟系统的大偏差理论，包括微生物菌群。研究人员一直在开发一个多尺度平台，用于模拟微流体环境中的财团动力学，这将为研究提供模拟支持。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This project will use tools from mathematics, namely model design, model analysis, and multi-scale simulation, to inform the design and testing of novel synthetic biocircuit designs. Synthetic biologists construct such circuits by rewiring organisms, using ideas from mathematics, biophysics, and bioengineering. Applications include precisely-targeted therapeutic drug delivery, cost reductions in drug production, biofuel advances, and new bioremediation technologies for environmental pollutants. This project will provide mathematical tools needed to understand and then harness the emerging complexity of synthetic biocircuits. A particular focus will be circuits wherein rare events play a crucial role as biological switches. The investigators will train students and junior scientists as part of the project, perform curriculum development, and enhance the scientific community in the greater Houston area by community outreach via a student enrichment program known as Mathematics Enrichment for Networking, Training, and Opportunities in Research (MENTOR). MENTOR activities include a research methods class, a STEM lecture series, summer research fellowships, and an annual undergraduate research conference rotating between the University of Houston, Louisiana State University, and Texas A&M University.This project focuses on quantifying rare-event behavior for complex, spatially-extended stochastic systems wherein delay plays important roles. Motivation arises from the need to understand the dynamics of genetic regulatory networks to inform the design of novel synthetic biocircuits. In many cases, the essential function of such a network involves rare events -- be they transitions between metastable states or sudden bursts of activity. Since proteins serve as regulators, transcriptional delay (the time from transcription initiation to the formation of functional protein) is intrinsic to genetic regulatory networks and has been shown to dramatically affect network dynamics. Mathematically, large deviations theories allow for rare event quantification. What is the most likely transition pathway between one metastable state and another? How often do rare events occur? Large deviations theories can answer such questions, both theoretically and computationally. This project aims to develop a comprehensive theoretical and computational large deviations framework for nonlinear stochastic differential equations with delay, particularly the nonlinear delay stochastic differential equations that model genetic regulatory networks. Synthetic biologists have recently focused on building genetic regulatory networks within synthetic microbial consortia. This distributed approach offers modularity and the potential to build ever more complex biocircuits. However, the resultant dynamics are quite complex, as consortia feature spatiotemporal dynamics, cell cycle effects, chemical signaling, population-level effects, and mechano-sensing. This project aims to build a large deviations theory for spatiotemporal delay systems, including microbial consortia. The investigators have been developing a multi-scale platform for the simulation of consortia dynamics within microfluidic environments, which will provide simulational support for the study.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.