FP-AbDiff: Improving Score-based Antibody Design by Capturing Nonequilibrium Dynamics through the Underlying Fokker-Planck Equation

2025-11-05

AI Summary

Existing antibody generation models suffer from two key limitations: dynamic inconsistency—leading to physically implausible structures—and poor generalization—constrained by data scarcity and structural bias. To address these, this work introduces the Fokker–Planck equation (FPE) into antibody generative modeling for the first time, proposing an FPE-based residual loss that enforces globally consistent probability flows on the hybrid manifold ℝ³×SO(3), ensuring physically interpretable and dynamically coherent generation trajectories. The method integrates SE(3)-equivariant diffusion, Cα–Cβ backbone representation, and geometric constraints on complementarity-determining regions (CDRs). On the RAbD benchmark, it achieves a CDR-H3 RMSD of 0.99 Å and 39.91% contact residue recovery. In six-loop co-design tasks, it attains state-of-the-art full-chain and CDR-H3 functional-region recovery rates. These results demonstrate simultaneous advances in physical plausibility and generalization capability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Computational antibody design holds immense promise for therapeutic discovery, yet existing generative models are fundamentally limited by two core challenges: (i) a lack of dynamical consistency, which yields physically implausible structures, and (ii) poor generalization due to data scarcity and structural bias. We introduce FP-AbDiff, the first antibody generator to enforce Fokker-Planck Equation (FPE) physics along the entire generative trajectory. Our method minimizes a novel FPE residual loss over the mixed manifold of CDR geometries (R^3 x SO(3)), compelling locally-learned denoising scores to assemble into a globally coherent probability flow. This physics-informed regularizer is synergistically integrated with deep biological priors within a state-of-the-art SE(3)-equivariant diffusion framework. Rigorous evaluation on the RAbD benchmark confirms that FP-AbDiff establishes a new state-of-the-art. In de novo CDR-H3 design, it achieves a mean Root Mean Square Deviation of 0.99 {AA} when superposing on the variable region, a 25% improvement over the previous state-of-the-art model, AbX, and the highest reported Contact Amino Acid Recovery of 39.91%. This superiority is underscored in the more challenging six-CDR co-design task, where our model delivers consistently superior geometric precision, cutting the average full-chain Root Mean Square Deviation by ~15%, and crucially, achieves the highest full-chain Amino Acid Recovery on the functionally dominant CDR-H3 loop (45.67%). By aligning generative dynamics with physical laws, FP-AbDiff enhances robustness and generalizability, establishing a principled approach for physically faithful and functionally viable antibody design.

Problem

• Addresses physically implausible antibody structures through dynamical consistency
• Overcomes poor generalization from data scarcity and structural bias
• Aligns generative dynamics with Fokker-Planck Equation physics

Innovation

• Enforcing Fokker-Planck Equation physics in generative trajectory
• Minimizing FPE residual loss over mixed manifold geometries
• Integrating physics-informed regularizer with SE(3)-equivariant diffusion