Scalable Normalizing Flows Enable Boltzmann Generators for
  Macromolecules
Joseph C. Kim David Bloore Karan Kapoor Jun Feng Ming-Hong Hao Mengdi Wang
The Boltzmann distribution of a protein provides a roadmap to all of its
functional states. Normalizing flows are a promising tool for modeling this
distribution, but current methods are intractable for typical pharmacological
targets; they become computationally intractable due to the size of the system,
heterogeneity of intra-molecular potential energy, and long-range interactions.
To remedy these issues, we present a novel flow architecture that utilizes
split channels and gated attention to efficiently learn the conformational
distribution of proteins defined by internal coordinates. We show that by
utilizing a 2-Wasserstein loss, one can smooth the transition from maximum
likelihood training to energy-based training, enabling the training of
Boltzmann Generators for macromolecules. We evaluate our model and training
strategy on villin headpiece HP35(nle-nle), a 35-residue subdomain, and protein
G, a 56-residue protein. We demonstrate that standard architectures and
training strategies, such as maximum likelihood alone, fail while our novel
architecture and multi-stage training strategy are able to model the
conformational distributions of protein G and HP35.