Mathematics-assisted directed evolution and protein engineering
Yuchi Qiu Guo-Wei Wei
Directed evolution is a molecular biology technique that is transforming
protein engineering by creating proteins with desirable properties and
functions. However, it is experimentally impossible to perform the deep
mutational scanning of the entire protein library due to the enormous
mutational space, which scales as $20^N$ , where N is the number of amino
acids. This has led to the rapid growth of AI-assisted directed evolution
(AIDE) or AI-assisted protein engineering (AIPE) as an emerging research field.
Aided with advanced natural language processing (NLP) techniques, including
long short-term memory, autoencoder, and transformer, sequence-based embeddings
have been dominant approaches in AIDE and AIPE. Persistent Laplacians, an
emerging technique in topological data analysis (TDA), have made
structure-based embeddings a superb option in AIDE and AIPE. We argue that a
class of persistent topological Laplacians (PTLs), including persistent
Laplacians, persistent path Laplacians, persistent sheaf Laplacians, persistent
hypergraph Laplacians, persistent hyperdigraph Laplacians, and evolutionary de
Rham-Hodge theory, can effectively overcome the limitations of the current TDA
and offer a new generation of more powerful TDA approaches. In the general
framework of topological deep learning, mathematics-assisted directed evolution
(MADE) has a great potential for future protein engineering.