Modeling of the U1 snRNP assembly pathway in alternative splicing in human cells using Petri nets

The investigation of spliceosomal processes is currently a topic of intense research in molecular biology. In the molecular mechanism of alternative splicing, a multi-protein-RNA complex - the spliceosome - plays a crucial role. To understand the biological processes of alternative splicing, it is essential to comprehend the biogenesis of the spliceosome. In this paper, we propose the first abstract model of the regulatory assembly pathway of the human spliceosomal subunit U1. Using Petri nets, we describe its highly ordered assembly that takes place in a stepwise manner. Petri net theory represents a mathematical formalism to model and analyze systems with concurrent processes at different abstraction levels with the possibility to combine them into a uniform description language. There exist many approaches to determine static and dynamic properties of Petri nets, which can be applied to analyze biochemical systems. In addition, Petri net tools usually provide intuitively understandable graphical network representations, which facilitate the dialog between experimentalists and theoreticians. Our Petri net model covers binding, transport, signaling, and covalent modification processes. Through the computation of structural and behavioral Petri net properties and their interpretation in biological terms, we validate our model and use it to get a better understanding of the complex processes of the assembly pathway. We can explain the basic network behavior, using minimal T-invariants which represent special pathways through the network. We find linear as well as cyclic pathways. We determine the P-invariants that represent conserved moieties in a network. The simulation of the net demonstrates the importance of the stability of complexes during the maturation pathway. We can show that complexes that dissociate too fast, hinder the formation of the complete U1 snRNP.