Proteinsin vacuo. A connection between mean overcrossing number and orientationally-averaged collision cross section

Abstract

Recently, the structure of protein ions in vacuo has received a lot of interest. Experimentally, such structures can only be characterized by global, low-resolution descriptors like the orientationally-averaged collision cross section . An alternative descriptor of chain entanglement, the mean overcrossing number , is a very useful tool because it can distinguish sensitively between different conformations based on aspects of their geometry and topology. An overcrossing number distribution arises from an ensemble of different projections of the protein structure onto a viewing plane, where for each projection, the number of crossings by the set of line segments joining sequence-adjacent C_α atoms is computed. is the mean of this distribution. Despite their usefulness, overcrossing numbers depend on the atomic coordinates and thus cannot be measured for protein ions in vacuo as can collision cross sections. In this work, we explore theoretically whether collision cross sections are correlated with overcrossing numbers. Using a group of diverse proteins with the same chain length as lysozyme and known X-ray structures, we find a weak correlation between and . Thus, a nontrivial range of orientationally-averaged cross section values can be consistent with the same mean overcrossing number. Since comprises a very sensitive tool for the study of conformational rearrangements, we checked also for correlations between and during molecular dynamics simulated unfolding and relaxation pathways of lysozyme in vacuo. For a given pathway, the two quantities are found to be highly correlated. Although neither nor maps one-to-one onto a particular tertiary fold, they are both sensitive descriptors to monitor the conformational state of a protein along a pathway of dynamical change.