ForceFlowAb: physics-aware mixture-of-experts flow matching model for antibody CDRs design

Abstract Motivation: Antibodies are a major class of therapeutic molecules, and their recognition of target antigens is largely mediated by complementarity-determining regions (CDRs), making antigen-conditioned CDR design a central problem in antibody engineering. Recent generative methods have enabled antigen-conditioned co-design of CDR sequences and structures, but their limited capacity to capture local interface heterogeneity and lack explicit energy-based guidance during sampling, which may result in unfavorable antibody-antigen interaction energies. Overcoming these limitations requires methods that better represent diverse interface environments via adaptive routing and incorporate physical guidance to steer sampling toward energetically favorable conformations. Results: We present ForceFlowAb, a physics-aware mixture-of-experts flow-matching framework for antigen-conditioned CDR sequence-structure co-design. The framework models heterogeneous interface environments through specialized expert routing and applies differentiable force-field guidance during sampling to guide CDR generation toward energetically favorable conformations. For CDR-H3 design, ForceFlowAb achieved more favorable antibody-antigen interaction energies than FlowDesign and Diffab, with improvement rates (IMP) of 46.5% versus 35.0% and 35.5%, respectively. For simultaneous six-CDR design, ForceFlowAb also outperformed Diffab, with IMP values of 16% versus 9%. These results suggest complementary roles for interface-adaptive modeling and energy-based guidance, with the former capturing binding-mode diversity and the latter leveraging physical constraints to ensure biophysical feasibility. Availability and implementation: The web server is freely available at http://zhanglab-bioinf.com/ForceFlowAb. The source code and implementation are available at https://github.com/iobio-zjut/ForceFlowAb. Contact: zgj@zjut.edu.cn Supplementary information: Supplementary data are available at Bioinformatics online.