The protein secondary structure (SS) prediction plays an important role in the characterization of general protein structure and function. In recent years, a new generation of algorithms for SS prediction based on embeddings from protein language models (pLMs) is emerging. These algorithms reach state-of-the-art accuracy without the need for time-consuming multiple sequence alignment (MSA) calculations. LSTM-based SPOT-1D-LM and NetSurfP-3.0 are the latest examples of such predictors. We present the ProteinUnetLM model using a convolutional Attention U-Net architecture that provides prediction quality and inference times at least as good as the best LSTM-based models for 8-class SS prediction (SS8). Additionally, we address the issue of the heavily imbalanced nature of the SS8 problem by extending the loss function with the Matthews correlation coefficient (MCC), and by proper assessment using previously introduced adjusted geometric mean metric (AGM). ProteinUnetLM achieved better AGM and sequence overlap score (SOV) than LSTM-based predictors, especially for the rare structures 310-helix (G), beta-bridge (B), and high curvature loop (S). It is also competitive on challenging datasets without homologs, free-modeling targets, and chameleon sequences. Moreover, ProteinUnetLM outperformed its previous MSA-based version ProteinUnet2, and provided better AGM than AlphaFold2 for 1/3 of proteins from the CASP14 dataset, proving its potential for making a significant step forward in the domain. To facilitate the usage of our solution by protein scientists, we provide an easy-to-use web interface under [https://biolib.com/SUT/ProteinUnetLM/](https://biolib.com/SUT/ProteinUnetLM/).

The main problem discussed in this paper concerns the importance of the presence of a hydrophobic core in β-sandwich supersecondary structures. The aim of this research is to propose an alternative structural classification of the relationship between sequence and spatial structure. The set of analyzed proteins contains very diverse examples (taking into consideration source organisms, chain length, domain composition, ligand and metal complexation, quaternary structure), allowing for generalization of conclusions. The biological function of the proteins in question is also fundamentally different. The only common feature of these proteins is the presence of a β-sandwich or β-sandwich-like domain. The data base is taken from alternative classification of secondary and supersecordary of sandwich-like domains. The results show that the secondary and supersecondary despite of high topological similarity represent different forms of hydrophobic core structure. In consequence the stability of sandwich-like domains is differentiated. The local stability/instability has a significant repercussion on biological activity. It is expressed by identified local discordance between idealized and observed hydrophobicity distribution. The closer is the structure of hydrophobic core to the idealized one the higher stability is assumed for the domain under consideration.