On permuted super-secondary structures of transmembrane β-barrel proteins

Transmembrane β-barrel (TMB) proteins constitute a special class of proteins, which are located in outer membranes of Gram-negative bacteria, mitochondria, and chloroplasts. These proteins play diverse important roles in biological organisms. However, only a small number of TMB protein structures are currently known due to difficulties with experimental techniques. Hence, computational structure prediction methods based on learning are poorly tractable for these proteins. We introduce here a graph-theoretic ab initio model for predicting structures of TMB proteins by free energy minimization. TMB super-secondary structures with permuted arrangements are taken into consideration in this model. We show that finding a permuted structure is an NP-hard problem and then analyze the complexity of a tree decomposition-based algorithm to search for the optimal structure of a TMB protein corresponding to a given permutation. The robust performance of the model has been proven in our previously published results.