Theoretical prediction of free-energy landscapes for complex self-assembly

TL;DR

This paper introduces a theoretical method to predict free-energy landscapes for complex multicomponent self-assembly, emphasizing the role of graph topology and interaction strengths in assembly thermodynamics.

Contribution

It presents a novel approach that predicts assembly thermodynamics based on graph connectivity and interaction design, validated by Monte Carlo simulations.

Findings

Graph topology critically influences nucleation barriers.

Polydispersity in interaction strengths stabilizes intermediates.

Weak incidental interactions can prevent equilibrium assembly.

Abstract

We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity of the target assembly. By considering the designed interactions separately from weaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation barriers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that a few fundamental properties of the connectivity graph determine the most prominent features of the assembly thermodynamics. Surprisingly, we find that polydispersity in the strengths of the designed interactions stabilizes intermediate structures and can be used to sculpt the free-energy landscape for self-assembly. Finally, we demonstrate that weak incidental interactions can preclude assembly at equilibrium due to the combinatorial possibilities for incorrect association.