Equilibrium mechanisms of self-limiting assembly

TL;DR

This review explores the physical principles and mechanisms behind self-limiting equilibrium assembly processes, highlighting how finite structures are thermodynamically stabilized across biological and synthetic systems.

Contribution

It provides a comprehensive classification and analysis of self-limiting assembly mechanisms within a unified thermodynamic framework, including new insights into less-studied systems.

Findings

Classification of self-limiting assemblies into self-closing and open-boundary types

Identification of physical mechanisms that determine finite assembly size

Discussion of limitations and alternative size-control mechanisms

Abstract

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of {\it 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 non-covalent interactions between identical subunits ``measure'' and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: {\it self-closing assemblies} and {\it open-boundary assemblies}. These include well-known cases in biology and synthetic soft matter -- micellization of amphiphiles and shell/tubule formation of tapered subunits -- as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.