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

TL;DR

The paper tackles two main challenges in computational antibody design: lack of dynamical consistency in generated structures and limited generalization under data bias. It introduces FP-AbDiff, a diffusion-based generator that enforces Fokker–Planck Equation residuals on the mixed geometry $\mathbb{R}^3 \times SO(3)$, integrating SE(3)-equivariant biological priors. By coupling translational variance-preserving diffusion with rotational variance-exploding diffusion and adding a dedicated FPE regularizer, the approach yields globally coherent probability flows and dynamically plausible trajectories. On the RAbD benchmark, FP-AbDiff delivers state-of-the-art performance across de novo CDR-H3 design and six-CDR co-design, with notable gains in RMSD, amino acid recovery, and functional docking metrics, while ablations confirm the regularizer’s critical role. This physics-powered framework enhances robustness and generalization, reducing reliance on costly MD refinement and advancing practical, physically faithful antibody design.

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 Å 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.

Figures (3)

• Figure 1: Motivating FPE-Regularized Antibody Design: Gaps, Failures, and Inspirations. (a) Core flaws in current models, such as biased data and time-agnostic objectives, lead to (b) catastrophic failures in generalization and structural integrity. (c) Inspired by successes in computer vision, we address this by enforcing physical laws through Fokker-Planck Equation regularization to ensure a physically consistent generative path.
• Figure 2: Overview of FP-AbDiff. FP-AbDiff leverages a Continuous Time Markov Chain (CTMC) for CDR sequence modeling and a score-based diffusion framework for CDR structure generation. It incorporates physical and geometric constraints via a physics-informed loss derived from the Fokker–Planck Equation and applies evolutionary priors within the model architecture. The grey regions indicate the antigen and antibody framework, while the red regions highlight the designed CDRs in the antibody.
• Figure 3: Binding affinity comparison and representative structure design. (a) Predicted binding energy change ($\Delta\Delta G$) for all designs after full-CDR relaxation. Cyan quadrant: designs with $\Delta\Delta G<0$ for both FP-AbDiff and AbX. (b) Zoomed view of (a), highlighting co-successful cases. (c) Representative example on PDB: 1OSP.