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In therapeutic antibody design, achieving a balance between optimizing binding affinity subject to multiple constraints, and sequence diversity within a batch for experimental validation presents an important challenge. Contemporary methods often fall short in simultaneously optimizing these attributes, leading to ineffi- ciencies in experimental exploration and validation. In this work, we tackle this problem using the latest developments in constrained latent space Bayesian op- timization. Our methodology leverages a deep generative model to navigate the discrete space of potential antibody sequences, facilitating the selection of diverse, high-potential candidates for synthesis. We also propose a novel way of training VAEs that leads to a lower dimensional latent space and achieves excellent per- formance under the data-constrained setting. We validate our approach in vitro by synthesizing optimized antibodies, demonstrating consistently high binding affini- ties and preserved thermal stability.