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

这个项目将使用数学中的工具，即模型设计、模型分析和多尺度模拟，来为新型合成生物电路设计和测试提供信息。合成生物学家利用数学、生物物理学和生物工程的思想，通过对生物体重新布线来构建这样的电路。应用包括精确靶向的治疗性药物输送、药物生产成本的降低、生物燃料的进步以及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，以了解并随后利用合成生物电路的新兴复杂性。一个特别的焦点将是罕见事件作为生物开关发挥关键作用的电路。作为该项目的一部分，研究人员将对学生和初级科学家进行培训，进行课程开发，并通过名为数学丰富的研究网络、培训和机会(MENTOR)学生充实计划的社区推广，加强大休斯顿地区的科学社区。导师活动包括研究方法课程、STEM系列讲座、暑期研究奖学金，以及休斯顿大学、路易斯安那州立大学和德克萨斯农工大学之间轮流举行的年度本科生研究会议。该项目专注于量化复杂的、空间扩展的随机系统的罕见事件行为，其中延迟起着重要作用。动机源于需要了解遗传调控网络的动态，以便为新型合成生物电路的设计提供信息。在许多情况下，这种网络的基本功能涉及罕见事件--无论是亚稳态之间的转变还是活动的突然爆发。由于蛋白质作为调节器，转录延迟(从转录起始到功能蛋白形成的时间)是遗传调控网络固有的，并已被证明显著影响网络动态。从数学上讲，大偏差理论允许对罕见事件进行量化。介稳状态之间最有可能的过渡途径是什么？罕见事件多久发生一次？大偏差理论可以从理论和计算上回答这样的问题。本项目旨在为具有时滞的非线性随机微分方程，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联盟内建立基因调控网络。这种分布式方法提供了模块化和构建更复杂的生物电路的潜力。然而，所产生的动力学是相当复杂的，因为联合体具有时空动力学、细胞周期效应、化学信号、种群水平效应和机械感知。该项目旨在建立包括微生物群落在内的时空延迟系统的大偏差理论。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联合体动力学，这将为研究提供模拟支持。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.