Computational modeling to determine strategies to optimize self-limited assembly

自组装是一个过程，通过这个过程，基本的子单元聚集在一起，形成更大更复杂的结构。生物学中的许多自组装过程都是“自我限制的”，这意味着组装会自动停止在特定的尺寸和结构上。这些自我限制的组合在生物细胞中发挥着重要的功能，因此了解它们的工作原理将促进我们对生命和疾病的理解。此外，学习在合成系统中设计自我限制的装配过程可以使重要的技术应用成为可能。然而，目前可实现的组装结构的尺寸和产量远远小于自然系统。这种限制是因为该领域缺乏理论原则来指导设计亚基和反应条件，以确保稳健，高效的组装。本项目旨在发展这样的理论原理，通过使用计算和理论来理解生物学使用的使自我限制组装高效的机制，并学习如何将其应用于合成组装。该项目将进行三个重点，每个重点研究不同的机制。第一个推力将研究如何使用具有不同相互作用的多种亚基来增加可实现的组装尺寸和产量。第二个推力将研究随时间变化的反应条件如何提高组装率和产率。研究人员将把新的计算方法与称为最优控制理论的理论框架相结合，以开发有效的算法来确定反应条件的时间序列，从而最大化产量。第三个推力将研究相分离液滴内的自组装。液-液相分离是指将溶液分离成具有不同化学成分的液滴，例如油和水分离。在某些病毒感染过程中，病毒重塑其宿主细胞，形成相分离的液滴，新病毒颗粒在其中聚集。该项目将研究组装速率和产量如何取决于相分离液滴的性质，例如它们的大小和亚基在液滴内部局部集中的趋势。每个推力的结果将与合作者进行的实验进行测试，在这些实验中，DNA折纸或蛋白质设计被用来创建亚基，这些亚基组装成对称的壳，螺旋管和其他结构。该研究将为本科生和研究生提供跨学科的科学技术工程和数学（STEM）培训，在物理学和生物学之间的界面。该研究计划旨在招收不同的学生，并训练他们进行计算研究以及与专家和非专家受众进行有效的科学交流。该项目还将包括研究人员向公众描述他们的研究结果的项目。这些努力将包括一个整合在当地高中物理课程中的项目，在这个项目中，学生们参与一个动手活动，解释病毒和技术中自组装的物理和几何，同时传达科学研究的奇迹、兴奋和对社会的影响。技术总结：蛋白质亚基的自我限制组装成具有明确结构的有限大小的结构是生命的标志。这样的结构在自然界中比比皆是，它们在细胞和感染它们的病原体中发挥着基本的功能。最近，DNA折纸和蛋白质设计的进步使得工程合成亚基能够进行自我限制的组装，其原子尺度的精度可以与天然蛋白质相媲美。然而，由于缺乏指导设计亚基和反应条件的理论原则，组装结构的可实现尺寸和产量远远低于自然水平，以实现稳健、高效的组装。该项目旨在克服这一限制，通过使用计算来理解生物学用来规避装配时间尺度限制的机制：可调的“亚单位复杂性”，通过具有特定相互作用的多个亚单位物种，以及非平衡时空变化的装配驱动力。该项目将有三个互补的重点。推力1研究如何自限制组装取决于亚单位的复杂性，以确定提高产量的一般策略。Thrust 2将马尔可夫状态模型与最优控制理论相结合，开发了优化时变装配协议的有效算法。推力3号将使用模拟来了解细胞中一种突出的空间控制形式——液-液相分离——是如何影响自组装的。研究将探讨液-液相分离如何加速组装并增强对参数变化的鲁棒性。每个推力的结果将与合作者进行的实验进行测试，这些实验使用DNA折纸或蛋白质设计来创建亚基，这些亚基可以组装成二十面体衣壳、螺旋管和其他结构。组装大型目标结构具有挑战性，因为组装速率受到热力学和动力学效应的限制。由于自组装理论的关键缺陷，科学界缺乏设计同时满足这些权衡的组装反应的策略：(1)以前的模型关注最小亚基复杂性（来自一个亚基物种的组装）或最大复杂性（可寻址组装，其中每个亚基都是唯一的）；(2)三维系统的时变装配协议优化对大多数系统来说是难以计算的；(3)尽管对液-液相分离的研究非常深入，但其对自组装的影响却相对较少受到关注。该项目旨在开发克服这些限制的计算模型和工具。推力1将提供第一个跨亚单元复杂性全范围的系统研究，以确定复杂性的最佳水平以及在低或高复杂性下出现的几何挫折或冗余相互作用的影响。Thrust 2将利用马尔可夫状态模型的特性来开发一个适用于各种自组装系统的高效优化框架。研究人员将使用该框架来确定三维自限制装配的最佳时间相关协议。推力3将提供与液-液相分离相耦合的自限制装配的第一个模型。通过建立工程亚单元的设计原则，可以预先编程组装成任意三维结构，这项研究将为生物医学和技术应用的纳米结构材料的高度可扩展制造铺平道路。通过阐明生物细胞和病原体基本功能的自组装机制，研究结果也向生物物质理论迈出了关键一步。为本研究开发的计算算法将广泛适用于自组装。该研究将为本科生和研究生提供跨学科的STEM培训，在软物质物理学和细胞生物学之间的界面。该研究计划将招收不同的学生，并训练他们进行计算研究，以及与专家和非专家观众进行有效的科学交流。公共推广将包括一个与当地一所高中的物理课程相结合的项目，在这个项目中，学生们参与一个动手活动，解释病毒和技术中自组装的物理和几何，同时传达科学研究的奇迹、兴奋和对社会的影响。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NON-TECHNICAL SUMMARY Self-assembly is a process by which basic subunits come together to form structures with increased size and complexity. Many self-assembly processes in biology are ‘self-limited’, meaning that assembly automatically stops at a particular size and structure. These self-limited assemblies perform important functions in biological cells, and thus understanding how they work would advance our understanding of life and diseases. Moreover, learning to design self-limited assembly processes in synthetic systems could enable important technological applications. However, the achievable sizes and yields of assembled structures are currently much smaller than those of natural systems. This limitation arises because the field lacks theoretical principles to guide designing the subunits and reaction conditions to ensure robust, efficient assembly. This project aims to develop such theoretical principles, by using computation and theory to understand mechanisms that biology uses make self-limited assembly efficient, and to learn how to apply them to synthetic assemblies. The project will undertake three thrusts, each of which investigates a different mechanism. The first thrust will study how using multiple species of subunits with different interactions can increase achievable assembly sizes and yield. The second thrust will investigate how varying reaction conditions in time can increase assembly rates and yields. The investigators will combine new computational methods with a theoretical framework called optimal control theory to develop efficient algorithms to determine time-sequences of reaction conditions that maximize yields. The third thrust will study self-assembly within phase-separated droplets. Liquid-liquid phase separation refers to the de-mixing of a solution into droplets with different chemical compositions, such as when oil and water separate. During some virus infections, the virus remodels its host cell to form phase-separated droplets within which new viral particles assemble. This project will study how assembly rates and yields depend on properties of the phase-separated droplets, such as their size and the tendency of subunits to locally concentrate inside of the droplets. Results from each thrust will be tested against experiments performed by collaborators, in which DNA origami or protein design is used to create subunits that assemble into symmetric shells, helical tubules, and other structures.The research will provide interdisciplinary science technology engineering and mathematical (STEM) training for undergraduate and graduate students, at the interface between physics and biology. The research program is designed to recruit diverse students, and train them in computational research as well as effective scientific communication to expert and non-expert audiences. The project will also include programs in which the researchers describe their results to the public. These efforts will include a program integrated in the physics curriculum of a local high school, in which students engage in a hands-on activity that explains the physics and geometry of self-assembly in viruses and technology, while conveying the wonder, excitement, and impact on society of scientific research.TECHNICAL SUMMARYThe self-limited assembly of protein subunits into finite-sized structures with well-defined architectures is a hallmark of life. Such structures abound in nature, where they perform essential functions of cells and the pathogens that infect them. Recently, advances in DNA origami and protein design have enabled engineering synthetic subunits that are programmed for self-limited assembly, with atomic-scale precision rivaling that of natural proteins. Yet, achievable sizes and yields of assembled structures fall far short of nature, due to a lack of theoretical principles to guide designing subunits and reaction conditions for robust, efficient assembly. This project aims to overcome this limitation, by using computation to understand mechanisms that biology uses to circumvent constraints on assembly timescales: tunable ‘subunit complexity’, by having multiple subunit species with specific interactions, and nonequilibrium spatiotemporally varying assembly driving forces. The project will undertake three complementary thrusts. Thrust 1 investigates how self-limited assembly depends on subunit complexity, to identify general strategies to increase yields. Thrust 2 combines Markov state models with optimal control theory to develop efficient algorithms for optimizing time-dependent assembly protocols. Thrust 3 will use simulations to understand how self-assembly is affected by a prominent form of spatial control in cells – liquid-liquid phase separation. The research will investigate how liquid-liquid phase separation can accelerate assembly and enhance robustness against parameter variations. Results from each thrust will be tested against experiments performed by collaborators, in which DNA origami or protein design is used to create subunits that assemble into icosahedral capsids, helical tubules, and other structures. Assembling large target structures is challenging because assembly rates are constrained by competing thermodynamic and kinetic effects. The scientific community lacks strategies to engineer assembly reactions that simultaneously satisfy these trade-offs, due to crucial gaps in self-assembly theory: (1) Previous models have focused on minimal subunit complexity (assembly from one subunit species) or maximal complexity (addressable assembly, in which each subunit is unique); (2) Optimizing time-dependent assembly protocols for three-dimensional systems has been computationally intractable for most systems; (3) Despite intensive research on liquid-liquid phase separation, its effect on self-assembly has received relatively little attention. This project aims to develop computational models and tools that overcome these limitations. Thrust 1 will provide the first systematic study across the full range of subunit complexity, to identify optimal levels of complexity and the effects of geometric frustration or redundant interactions that arise at low or high complexity. Thrust 2 will leverage the properties of Markov state models to develop a highly efficient optimization framework that is applicable to diverse self-assembly systems. The investigators will use this framework to determine optimal time-dependent protocols for three-dimensional self-limited assembly. Thrust 3 will provide the first models for self-limited assembly coupled to liquid-liquid phase separation. By establishing design principles for engineering subunits that can be preprogrammed to assemble into arbitrary three-dimensional structures, this research will pave the way to highly scalable manufacturing of nanostructured materials for biomedical and technological applications. The results also make a key step toward a theory of living matter, by elucidating self-assembly mechanisms that underlie essential functions in biological cells and pathogens. The computational algorithms developed for this research will be broadly applicable to self-assembly. The research will provide interdisciplinary STEM training for undergraduate and graduate students, at the interface between soft matter physics and cell biology. The research program will recruit diverse students, and train them in computational research as well as effective scientific communication to expert and non-expert audiences. Public outreach will include a program integrated in the physics curriculum of a local high school, in which students engage in a hands-on activity that explains the physics and geometry of self-assembly in viruses and technology, while conveying the wonder, excitement, and impact on society of scientific research.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.