The transmembrane β-barrel proteins (TMBs) are found in the outer membrane of Gram-negative bacteria, mitochondria and chloroplasts. They entirely span the biological membrane and perform a wide range of important functions. As the number of TMB structures known today is very limited, due to difficulties in experimental methods, it is arguable whether the learning-based prediction methods could work well for recognizing and folding TMBs which are not homologous to those currently known. We present a novel graph-theoretic model for classification and prediction of permuted super-secondary structures of TMBs from their amino acid sequence, based on energy minimization. The model does not essentially depend on learning. The algorithms are fast, robust with comparable performance to the best currently known learning-based methods. This method can be thus a useful tool for the genome screening. Besides the performance on prediction and classification, this study gives an insight into TMB structures regarding the physicochemical constraints of biological membranes. The predicted permuted structures can also enhance the understanding on the folding mechanism of TMBs.
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