On the Computational Complexity of Sequence Design

Inverse protein folding concerns the identification of an amino acid sequence that folds to a given structure. Sequence design problems attempt to avoid the apparant difficulty of inverse protein folding by defining an energy that can be minimized to find protein-like sequences. We evaluate the practical relevance of two sequence design problems by analyzing their computational complexity. Vc' e show that the canonical method of sequence design is intractable, and describe approximation algorithms for this problem. We also describe an efficient algorithm that exactly solves the grand canonical method. Our analysis shows how sequence design problems can fail to reduce the difficulty of the inverse protein folding problem, and highlights the need to analyze these problems to evaluate their practical relevance.