Exploring the Limits of Hard Shape Models for Self-Assembly

Abstract

Effectively coarse-graining particle shape is crucial to extending the time and length scales accessible to particle simulations. While models of biomolecular and other systems with many complex interactions tend to model shape by incrementally collecting smaller degrees of freedom to retain maximum model fidelity, models of colloidal systems where dominant interactions may more easily be identified frequently use highly simplified minimal models based on a single simple interaction potential. Among the most successful examples for modeling the equilibrium behavior of simple spherical particles are the hard sphere and WCA potentials. The justification for these models is the van der Waals picture, which asserts that short-ranged repulsive forces are the dominant driver of ordering phenomena in many systems. This work explores the limits of this picture in the context of anisotropic particle self-assembly and discusses various ways in which these simple approaches may be generalized or augmented to accurately model additional important interactions to effectively model complex molecules like proteins.

I first consider two different experimental systems, a system of polymer coated silica polyhedral nanoparticles and a system of supercharged proteins. I show that in the first case a simple hard shape model sufficiently accurate under various different circumstances, such as in the presence of depletants and when the particles are rounded. Meanwhile, in the second case I find that hard shape is not enough; I develop a model combining hard shape and point charges that explains the relative stability of different configurations of these proteins, but this model lacks both the performance and the accuracy to achieve self-assembly.

I pursue two different approaches to improving coarse-grained models of shape. My first approach uses machine learning techniques to attempt to quantitatively assess the role of different interactions in protein crystallization. I use convolutional neural networks to correlate different physicochemical properties of protein surfaces with properties of the resulting crystals, and I discuss various future studies that may be conducted with this model and data pipeline. My second approach employs a mean-field approach to embed shape into interaction potentials, providing a rigorous means to derive anisotropic analogues to isotropic pair potentials. I implement this approach on GPUs and show that it is faster than the state of the art without sacrificing accuracy.

I next apply this mean-field approach to study the dynamics of anisotropic particles. I show that introducing anisotropy leads to fundamental dynamic changes by introducing additional time scales associated not only with rotational motion, but also with nontrivial modes of translation-rotation coupling. This study illuminates the sensitivity of dynamic as well as thermodynamic properties to particle shape and highlights the further importance of efficient coarse-graining methods to study these dynamic behaviors.

Finally, I discuss the various scientific software packages I have developed as part of my research. I first present the lazy refactoring heuristic I advanced for efficiently developing reusable software in an academic environment. With this context, I review software tools that I developed or contributed to over the course of my dissertation research. I focus in particular on freud, a high-quality, high-performance particle simulations analysis toolkit that I have played a key role in developing.