Kinetic principles of chemical cross-link formation for protein-protein interactions

Proteins play a central role in most biological processes within the cell and deciphering how they interact is key to understand their function. Cross-linking coupled to mass spectrometry is an essential tool for elucidating protein-protein interactions. Despite its importance, we still know surprisingly little about the principles that underlie the process of chemical cross-link formation itself and how it is influenced by different physico-chemical factors. To understand the molecular details of cross-link formation, we have set-up a comprehensive kinetic model and carried out simulations of protein cross-linking on large protein complexes. We dissect the contribution on the cross-link yield of parameters such as amino acid reactivity, cross-linker concentration, and hydrolysis rate. Our model can compute cross-link formation based solely on the structure of a protein complex, thereby enabling realistic predictions for a diverse set of systems. We quantitatively show how cross-links and mono-links are in direct competition and how the hydrolysis rate and abundance of cross-linker and proteins directly influence their relative formation. We show how cross-links and mono-links exist in a “all-against-all” competition due to their simultaneous formation, resulting in a non-intuitive network of inter-dependence. We show that this interdependence is locally confined and mainly limited to direct neighbors or residues in direct vicinity. These results enable us to identify the optimal cross-linker concentration at which the maximal number of cross-links are formed. Taken together, our study establishes a comprehensive kinetic model to quantitatively describe cross-link formation for protein-protein interactions. Significance Statement Cross-linking mass spectrometry is an essential tool for elucidating protein-protein interactions, but to date basic principles of the process of cross-link formation are still not understood. We set-up a comprehensive kinetic model and simulate the process of cross-link formation. We quantitatively show how cross- and mono-links are in direct competition and how hydrolysis, concentration of cross-linker and of proteins influence their formation. Taken together, our study quantitatively describes kinetic principles of chemical cross-link formation and identifies optimal conditions for cross-link formation. ### Competing Interest Statement The authors have declared no competing interest.