Knots and $theta$-curves identification in polymeric chains and native proteins using neural networks

Entanglement in proteins is a fascinating structural motif that is neither easy to detect via traditional methods nor fully understood. Recent advancements in AI-driven models have predicted that millions of proteins could potentially have a nontrivial topology. Herein, we have shown that long short-term memory (LSTM)-based neural networks (NN) architecture can be applied to detect, classify, and predict entanglement not only in closed polymeric chains but also in polymers and protein-like structures with open knots, actual protein configurations, and also ▫$theta$▫-curves motifs. The analysis revealed that the LSTM model can predict classes (up to the ▫$6_1$▫ knot) accurately for closed knots and open polymeric chains, resembling real proteins. In the case of open knots formed by protein-like structures, the model displays robust prediction capabilities with an accuracy of 99%. Moreover, the LSTM model with proper features, tested on hundreds of thousands of knotted and unknotted protein structures with different architectures predicted by AlphaFold 2, can distinguish between the trivial and nontrivial topology of the native state of the protein with an accuracy of 93%.