(605b) Systematic Inference of Self-Assembly Pathways By Nonlinear Machine Learning

Controllable self-assembly has opened a new frontier for the fabrication of sophisticated functional aggregates, such as self-healing membranes for biomedical devices, nanoscale optoelectronics for photonic computing, and “smart” drug delivery vessels. Computer simulations provide a means to probe the structural mechanisms and interactions driving micro and nanoscale self-assembly, but it remains a challenge to identify the dynamic structural rearrangements driving these phenomena. The absence of good order parameters describing assembly has frustrated the establishment of a quantitative theoretical framework explicitly accounting for its thermodynamic and kinetic features, and hindered the rational design of programmable building blocks.

We have confronted this challenge by coupling nonlinear data mining algorithms to molecular simulation trajectories of self-assembly. Our approach enables us to systematically extract kinetically meaningful order parameters for assembly, infer assembly pathways and mechanisms, and quantify fluxes through competing assembly routes. In brief, we map the assembly trajectory to a dynamically updating interaction graph, in which nodes are monomers and edges bonds, enabling us to compute the structural similarity of the partially assembled clusters through graph matching. Using the quality of the match as a proxy measure for the dynamic proximity of pairs of clusters, we use the diffusion map nonlinear machine learning algorithm to extract the underlying self-assembly pathways describing the sequence of structural steps by which the system evolves into its terminal assembled state. The order parameters computed by the diffusion map correspond to the collective modes governing the long time evolution of the system, furnishing a kinetically meaningful low-dimensional subspace in which to infer assembly pathways and construct dynamically meaningful projections of the underlying free energy landscape for assembly.

We have applied our approach to the self-assembly of patchy colloids into icosahedral aggregates as a coarse-grained biomimetic model for viral capsid formation. In good agreement with previous work employing cluster size as a heuristic order parameter, our approach systematically identifies two qualitatively different assembly pathways corresponding to 1) monomeric addition, and 2) budding of aggregates from a liquid-like phase, and we recover kinetically meaningful collective order parameters describing the dynamic structural rearrangements along each path. Further, we quantify the flux through each pathway to compute a quantitative measure of the assembly propensity through each route as a function of temperature and chemistry of the colloidal monomers. Finally, we discuss how “assembly landscapes” may be used to guide the design of building blocks programmed to assemble desired aggregates that are both thermodynamically stable and kinetically accessible, by rational manipulation of the underlying free energy landscape.