  Therapeutic antibodies have been extensively studied in drug discovery and
development in the past decades. Antibodies are specialized protective proteins
that bind to antigens in a lock-to-key manner. The binding strength/affinity
between an antibody and a specific antigen is heavily determined by the
complementarity-determining regions (CDRs) on the antibodies. Existing machine
learning methods cast in silico development of CDRs as either sequence or 3D
graph (with a single chain) generation tasks and have achieved initial success.
However, with CDR loops having specific geometry shapes, learning the 3D
geometric structures of CDRs remains a challenge. To address this issue, we
propose AntibodyFlow, a 3D flow model to design antibody CDR loops.
Specifically, AntibodyFlow first constructs the distance matrix, then predicts
amino acids conditioned on the distance matrix. Also, AntibodyFlow conducts
constraint learning and constrained generation to ensure valid 3D structures.
Experimental results indicate that AntibodyFlow outperforms the best baseline
consistently with up to 16.0% relative improvement in validity rate and 24.3%
relative reduction in geometric graph level error (root mean square deviation,
RMSD).
