Von Mises Mixture Distributions for Molecular Conformation Generation

TL;DR

This paper introduces VonMisesNet, a graph neural network that efficiently generates molecular conformations by modeling torsion angles with von Mises distributions, enabling faster and more accurate sampling from the Boltzmann distribution.

Contribution

VonMisesNet is a novel GNN that captures conformational variability using a mixture of von Mises distributions for torsion angles, improving sampling speed and accuracy.

Findings

Generates molecular conformations faster than existing methods.

Accurately models conformational variability with von Mises mixtures.

Produces physically realistic conformations consistent with the Boltzmann distribution.

Abstract

Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or $\textit{conformations}$. The resulting distribution on geometries $p(x)$ is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying $\textit{modes}$ in this distribution rather than generating true $\textit{samples}$. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.