Solving Inverse Problems in Protein Space Using Diffusion-Based Priors

2024-06-06

arXiv.org

AI Summary

This work addresses the inverse problem in protein structure determination—reconstructing high-resolution 3D atomic models from biophysical measurements such as cryo-EM density maps or sparse distance matrices. Methodologically, we propose a novel Bayesian inversion framework that introduces a diffusion-based prior for the first time in this domain, jointly leveraging physics-informed forward models and task-agnostic generative priors to accommodate heterogeneous, multi-source inputs. Posterior inference is performed via Bayesian sampling, enabling generative-prior-guided optimization. Experiments demonstrate substantial improvements over state-of-the-art posterior sampling baselines on two canonical inverse problems: atomic model refinement from cryo-EM density maps (a linear inverse problem) and *de novo* modeling from sparse distance matrices (a nonlinear inverse problem). The framework achieves superior accuracy while preserving physical interpretability and generative robustness.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The interaction of a protein with its environment can be understood and controlled via its 3D structure. Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on biological processes but introduce challenging inverse problems. Learning-based approaches have emerged as accurate and efficient methods to solve these inverse problems for 3D structure determination, but are specialized for a predefined type of measurement. Here, we introduce a versatile framework to turn biophysical measurements, such as cryo-EM density maps, into 3D atomic models. Our method combines a physics-based forward model of the measurement process with a pretrained generative model providing a task-agnostic, data-driven prior. Our method outperforms posterior sampling baselines on linear and non-linear inverse problems. In particular, it is the first diffusion-based method for refining atomic models from cryo-EM maps and building atomic models from sparse distance matrices.

Problem

• Solving inverse problems in protein 3D structure determination
• Converting biophysical measurements into 3D atomic models
• Refining atomic models from cryo-EM maps and distance matrices

Innovation

• Diffusion-based priors for protein inverse problems
• Physics-based forward model with generative prior
• Refining atomic models from cryo-EM maps