Protein designability analysis in sequence principal component space using 2D lattice model

The number of proteins that fold into a certain structure differs drastically. The designability of a protein structure, which is defined as the number of sequences that have that structure as their unique lowest energy state, is studied in this paper using a simplified lattice model. The two-letter (HP) code and the pair-contact energy model are employed in the formulation of the relationship between the protein sequences and the compact structures. Due to the correlations between different dimensions, principal component analysis (PCA) is carried out to remove these correlations and develop reliable approximations of probability density functions of the protein sequences and the compact structures. An estimation of designability is derived using these probability density functions. Good correlation between estimated designabilities and those obtained through enumerative calculations is successfully achieved.