Topological aspects and computational approaches for intrinsically disordered protein systems

Intrinsically disordered proteins (IDPs) pose significant challenges for computational modelling due to their conformational flexibility and the complexity of their interaction networks. Their description requires methods capable of capturing structural organization across different spatial scales, from local amino-acid interactions to the collective behaviour of entire protein chains. In this talk, I will focus on topological aspects of IDP systems and numerical methods for their characterization, with particular emphasis on the SPACEBALL algorithm and its applications. I will discuss how mathematical and computational approaches can be used to investigate the structural organization of disordered protein systems and characterize interactions at the residue level. Particular attention will be given to the relationship between local interaction patterns and global structural properties, as well as to the role of these features in protein aggregation and amyloid formation. These phenomena are relevant to understanding neurodegenerative diseases and the formation of membraneless
organelles, in which IDPs often play a central role. The talk will highlight how topological analysis and numerical modelling can contribute to a more systematic understanding of these complex systems, with examples illustrating the application of the SPACEBALL algorithm to their computational investigation.