Graphical abstract

We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard interaction U . We show that the model becomes exactly solvable for arbitrary U when the BCS pairing amplitude ∆ equals the hopping amplitude t. The nature of the solution is described in detail in this paper. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for S = 1/2 quantum spins and can be viewed as a generalization of Kitaev's construction to S = 1/2 interacting lattice fermions. The BCS-Hubbard model discussed in this paper is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

Many Gram-negative bacteria infect hosts and cause diseases by translocating a variety of type III secreted effectors (T3SEs) into the host cell cytoplasm. However, despite a dramatic increase in the number of available whole-genome sequences, it remains challenging for accurate prediction of T3SEs. Traditional prediction models have focused on atypical sequence features buried in the N-terminal peptides of T3SEs, but unfortunately, these models have had high false-positive rates. In this research, we integrated promoter information along with characteristic protein features for signal regions, chaperone-binding domains, and effector domains for T3SE prediction. Machine learning algorithms, including deep learning, were adopted to predict the atypical features mainly buried in signal sequences of T3SEs, followed by development of a voting-based ensemble model integrating the individual prediction results. We assembled this into a unified T3SE prediction pipeline, T3SEpp, which integrated the results of individual modules, resulting in high accuracy (i.e., ∼0.94) and >1-fold reduction in the false-positive rate compared to that of state-of-the-art software tools. The T3SEpp pipeline and sequence features observed here will facilitate the accurate identification of new T3SEs, with numerous benefits for future studies on host-pathogen interactions. IMPORTANCE Type III secreted effector (T3SE) prediction remains a big computational challenge. In practical applications, current software tools often suffer problems of high false-positive rates. One of the causal factors could be the relatively unitary type of biological features used for the design and training of the models. In this research, we made a comprehensive survey on the sequence-based features of T3SEs, including signal sequences, chaperone-binding domains, effector domains, and transcription factor binding promoter sites, and assembled a unified prediction pipeline integrating multi-aspect biological features within homology-based and multiple machine learning models. To our knowledge, we have compiled the most comprehensive biological sequence feature analysis for T3SEs in this research. The T3SEpp pipeline integrating the variety of features and assembling different models showed high accuracy, which should facilitate more accurate identification of T3SEs in new and existing bacterial whole-genome sequences.