Universe of Lasso Proteins: Exploring the Limit of Entanglement of Proteins Predicted by AlphaFold

Knots and lasso topology represent a class of natural motifs found in proteins that are characterized by a threaded structure. Proteins with a lasso motif represent a macroscopic version of the peptide lasso, which is known for its high stability and offers tremendous potential for the development of novel therapeutics. Here, based on AlphaFold, we have shown the limit of topological complexity of naturally occurring protein structures with cysteine bridges. Based on 176 million high confidence (pLDDT > 70) AlphaFold-predicted protein models and a detailed analysis of the conservation of the motif in a family, we found four new lasso motifs, including L₄ and LS₄LS₃ topologies, and the first examples of knotted lasso proteins: L₁K3₁ and L₃#K3₁. We show that in the case of natural proteins, there are no lassos with 5 threadings, but there exist some with 6. Families possessing proteins with more than 6 threadings did not exceed the conservation threshold of 10%. Moreover, we propose a probable folding mechanism for the LS₄LS₃ lasso motif, enhancing our view on protein folding and stability. This work expands the topological space of lasso type motifs in proteins but also suggests that more complex structures could be unfavorable for proteins.