Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (macromolecules, particles, etc.) into ordered multiunit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits and the other consisting of a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving noncovalent interactions between identical subunits “measure” and select the size of assembled structures? This review begins with an introduction to the basic statistical mechanical framework for assembly thermodynamics that is used to highlight the key physical ingredients ensuring that equilibrium assembly will terminate at finite dimensions. Then examples of self-limiting assembly systems are introduced, and they are classified within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter (micellization of amphiphiles and shell and tubule formation of tapered subunits) as well as less widely known classes of assemblies, such as short-range attractive or long-range repulsive systems and geometrically frustrated assemblies. For each of these self-limiting mechanisms, the physical mechanisms that select equilibrium assembly size, as well as the potential limitations of finite-size selection, are described. Finally, alternative mechanisms for finite-size assemblies are discussed, and contrasts are drawn with the size control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

中文翻译：

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自限性组装的平衡机制

自组装是合成和生物系统中普遍存在的过程，广泛定义为多个亚基（大分子、颗粒等）自发组织成有序的多单元结构。绝大多数平衡组装过程会产生两种状态：一种由分散的解离亚基组成，另一种由无限大小的块状凝聚态组成。本综述重点关注更专业的自限制组装，它描述了产生有限尺寸结构的平衡组装过程。这些系统提出了一个通用且基本的问题，涉及相同亚基之间非共价相互作用的热力学过程如何“测量”并选择组装结构的尺寸？本综述首先介绍装配热力学的基本统计力学框架，该框架用于强调确保平衡装配在有限尺寸处终止的关键物理成分。然后介绍了自限制装配系统的示例，并在该框架内将它们分为两大类：自封闭装配和开放边界装配。这些包括生物学和合成软物质中众所周知的案例（两亲物的胶束化以及锥形亚基的壳和管的形成）以及不太广为人知的组装类型，例如短程吸引或远程排斥系统以及几何挫败系统组件。对于这些自限制机制中的每一个，都描述了选择平衡装配尺寸的物理机制，以及有限尺寸选择的潜在限制。最后，讨论了有限尺寸组件的替代机制，并与这些可以实现的相对于平衡单物种组件的自我限制的尺寸控制进行了对比。