Boltzmann-Expected Molecular Design with Decoupled Annealing Flows

2026-07-21

AI Summary

Traditional 3D molecular generation methods optimize properties based on a single conformation, neglecting the Boltzmann-weighted conformational ensemble and thus struggling to accurately control ensemble-averaged physicochemical properties. This work proposes DECAF, a novel framework that shifts the design objective toward Boltzmann ensemble expectations. DECAF employs decoupled dual conditional annealing flows—alternating between graph-to-coordinate and coordinate-to-graph mappings—to iteratively refine molecular structures. By integrating simulated annealing with ensemble statistics, it enables multi-objective optimization without retraining. The method further supports the design of higher-order statistical moments (e.g., variance, skewness), effectively modulating molecular flexibility and conformational preferences. Experiments on GEOM-Drugs demonstrate successful optimization of ensemble-averaged radius of gyration and solvent-accessible surface area, with molecular dynamics validation confirming its significant superiority over single-conformation approaches, especially for larger molecules.

Abstract

Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ over the Boltzmann distribution over 3D configurations of a molecular graph. However, existing property-guided generative models tie each property to a single structure, ignoring the underlying ensemble. We recast 3D molecular design as $\textbf{Boltzmann-expected design}$ and realise it with $\textbf{DECAF}$ (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow $p(x\mid\mathcal{G})$, acting as a $\textit{Boltzmann emulator}$, and a coordinate-conditioned flow $p(\mathcal{G}\mid x)$, proposing new graphs from 3D information. By alternating the two flows, DECAF optimises molecular graphs with a simulated-annealing acceptance rule whose scoring function is evaluated on ensembles drawn from $p(x\mid\mathcal{G})$, making ensemble statistics, not single-conformer properties, the design target. The resulting loop requires no retraining to change objectives. On GEOM-Drugs, we show that ensemble-aware optimisation produces graphs whose mean radius of gyration and solvent-accessible surface area consistently shift toward targets, while single-conformer optimisation degrades on larger drug-like molecules where Boltzmann distributions are broadest. DECAF extends to multi-objective trade-offs and, uniquely among 3D generative models, to $\textbf{higher-moment design}$: jointly optimising an ensemble property's variance and skewness to produce flexible molecules biased to a prescribed conformational regime: we verify the conformational distributions of these higher-moment designs with all-atom MD simulations.

Problem

• Boltzmann distribution
• molecular design
• ensemble properties
• 3D molecular generation
• conformational ensemble

Innovation

• Boltzmann-expected design
• Decoupled Annealing Flows
• ensemble-aware optimization
• higher-moment design
• 3D molecular generation