CONDITIONAL ANTIBODY DESIGN AS 3D EQUIVARI-ANT GRAPH TRANSLATION

Abstract

Antibody design is valuable for therapeutic usage and biological research. Existing deep-learning-based methods encounter several key issues: 1) incomplete context for Complementarity-Determining Regions (CDRs) generation; 2) incapability of capturing the entire 3D geometry of the input structure; 3) inefficient prediction of the CDR sequences in an autoregressive manner. In this paper, we propose Multi-channel Equivariant Attention Network (MEAN) to co-design 1D sequences and 3D structures of CDRs. To be specific, MEAN formulates antibody design as a conditional graph translation problem by importing extra components including the target antigen and the light chain of the antibody. Then, MEAN resorts to E(3)-equivariant message passing along with a proposed attention mechanism to better capture the geometrical correlation between different components. Finally, it outputs both the 1D sequences and 3D structure via a multi-round progressive full-shot scheme, which enjoys more efficiency and precision against previous autoregressive approaches. Our method significantly surpasses state-of-theart models in sequence and structure modeling, antigen-binding CDR design, and binding affinity optimization. Specifically, the relative improvement to baselines is about 23% in antigen-binding CDR design and 34% for affinity optimization.

1. INTRODUCTION

Antibodies are Y-shaped proteins used by our immune system to capture specific pathogens. They show great potential in therapeutic usage and biological research for their strong specificity: each type of antibody usually binds to a unique kind of protein that is called antigen (Basu et al., 2019) . The binding areas are mainly located at the so-called Complementarity-Determining Regions (CDRs) in antibodies (Kuroda et al., 2012) . Therefore, the critical problem of antibody design is to identify CDRs that bind to a given antigen with desirable properties like high affinity and colloidal stability (Tiller & Tessier, 2015) . There have been unremitting efforts made for antibody design by using deep generative models (Saka et al., 2021; Jin et al., 2021) . Traditional methods focus on modeling only the 1D CDR sequences, while a recent work (Jin et al., 2021) proposes to co-design the 1D sequences and 3D structures via Graph Neural Network (GNN). Despite the fruitful progress, existing approaches are still weak in modeling the spatial interaction between antibodies and antigens. For one thing, the context information is insufficiently considered. The works (Liu et al., 2020; Jin et al., 2021) only characterize the relation between CDRs and the backbone context of the same antibody chain, without the involvement of the target antigen and other antibody chains, which could lack complete clues to reflect certain important properties for antibody design, such as binding affinity. For another, they are still incapable of capturing the entire 3D geometry of the input structures. One vital property of the 3D Biology is that each structure (molecular, protein, etc) should be independent to the observation view, exhibiting E(3)-equivariance 1 . To fulfill this constraint, the method by Jin et al. ( 2021) pre-processes the 3D coordinates as certain invariant features before feeding them to the model. However, such pre-procession will lose the message of direction in the feature and hidden spaces, making it less effective in characterizing the spatial proximity between different residues in antibodies/antigens. Further, current generative models (Saka et al., 2021; Jin et al., 2021) predict the amino acids one by one; such autoregressive fashion suffers from low efficiency and accumulated errors during inference. To address the above issues, this paper formulates antibody design as E(3)-equivariant graph translation, which is equipped with the following contributions: 1. New Task. We consider conditional generation, where the input contains not only the heavy-chain context of CDRs but also the information of the antigen and the light chain. 2. Novel Model. We put forward an end-to-end Multichannel Equivariant Attention Network (MEAN) that outputs both 1D sequence and 3D structure of CDRs. MEAN operates directly in the space of 3D coordinates with E(3)-equivariance (other than previously-used E(3)-invariant models), such that it maintains the full geometry of residues. By alternating between an internal context encoder and an external attentive encoder, MEAN leverages 3D message passing along with equivariant attention mechanism to capture long-range and spatially-complicated interactions between different components of the input complex. 3. Efficient Prediction. Upon MEAN, we propose to progressively generate CDRs over multiple rounds, where each round updates both the sequences and structures in a full-shot manner. This progressive fullshot decoding strategy is less prone to accumulated errors and more efficient during the inference stage, compared with traditional autoregressive models (Gebauer et al., 2019; Jin et al., 2021) . We validate the efficacy of our model on three challenging tasks: sequence and structure modeling, antigen-binding CDR design and binding affinity optimization. Compared to previous methods that neglect the context of light chain and antigen (Saka et al., 2021; Akbar et al., 2022; Jin et al., 2021) , our model achieves significant improvement on modeling the 1D/3D joint distribution, and makes a great stride forward on recovering or optimizing the CDRs that bind to the target antigen.

2. RELATED WORK

Antibody Design Early approaches optimize antibodies with hand-crafted energy functions (Li et al., 2014; Lapidoth et al., 2015; Adolf-Bryfogle et al., 2018) , which rely on costly simulations and have intrinsic defects because the inter-chain interactions are complicated in nature and cannot be fully captured by simple force fields or statistical functions (Graves et al., 2020) . Hence, attention has been paid to applying deep generative models for 1D sequence prediction (Alley et al., 2019; Liu et al., 2020; Saka et al., 2021; Akbar et al., 2022) . Recently, to further involve the 3D structure, Jin et al. (2021) proposes to design the sequences and structures of CDRs simultaneously. It represents antibodies with E(3)-invariant features upon the distance matrix and generates the sequences autoregressively. Its follow-up work (Jin et al., 2022) further involves the epitope, but only considers CDR-H3 without all other components in the antibody. Different from the above learning-based works, our method considers a more complete context by importing the 1D/3D information of the antigen and the light chain. More importantly, we develop an E(3)-equivariant model that is skilled in representing the geometry of and the interactions between 3D structures. Note that antibody design assumes both the CDR sequences and structures are unknown, whereas general protein design predicts sequences based on structures (Ingraham et al., 2019; Karimi et al., 2020; Cao et al., 2021) .

Equivariant Graph Neural Networks

The growing availability of 3D structural data in various fields (Jumper et al., 2021) leads to the emergence of geometrically equivariant graph neural networks (Klicpera et al., 2020; Liu et al., 2021; Puny et al., 2021; Han et al., 2022) . In this paper, we exploit the scalarization-based E(n)-equivariant GNNs (Satorras et al., 2021) as the building block of our MEAN. Specifically, we adopt the multichannel extension by Huang et al. (2022) that naturally complies with the multichannel representation of a residue. Furthermore, we have developed a novel equivariant attention mechanism in MEAN to better capture antibody-antigen interactions.

3.1. PRELIMINARIES, NOTATIONS AND TASK FORMULATION

An antibody is a Y-shaped protein (Figure 1 ) with two symmetric sets of chains, each composed of a heavy chain and a light chain (Kuroda et al., 2012) . In each chain, there are some constant

