The design of novel protein sequences with targeted functionalities underpins a central theme in protein engineering, impacting diverse fields such as drug discovery and enzymatic engineering. However, navigating this vast combinatorial search space remains a severe challenge due to time and financial constraints. This scenario is rapidly evolving as the transformative advancements in AI, particularly in the realm of generative models and optimization algorithms, have been propelling the protein design field towards an unprecedented revolution. In this survey, we systematically review recent advances in generative AI for controllable protein sequence design. To set the stage, we first outline the foundational tasks in protein sequence design in terms of the constraints involved and present key generative models and optimization algorithms. We then offer in-depth reviews of each design task and discuss the pertinent applications. Finally, we identify the unresolved challenges and highlight research opportunities that merit deeper exploration.
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