Geometric Analysis of Shapes in Ion Mobility-Mass Spectrometry

Experimental ion mobility-mass spectrometry (IM-MS) results are often correlated to three-dimensional structures based on theoretical chemistry calculations. The bottleneck of this approach is the need for accurate values, both experimentally and theoretically predicted. Here, we continue the development of the trend-based analyses to extract structural information from experimental IM-MS data sets. The experimental collision cross-sections (CCSs) of synthetic systems such as homopolymers and small ionic clusters are investigated in terms of CCS trends as a function of the number of repetitive units (e.g., degree of polymerization (DP) for homopolymers) and for each detected charge state. Then, we computed the projected areas of expanding but perfectly defined geometric objects using an in-house software called MoShade. The shapes were modeled using computer-aided design software where we considered only geometric factors: no atoms, mass, chemical potentials, or interactions were taken into consideration to make the method orthogonal to classical methods for 3D shape assessments using time-consuming computational chemistry. Our modeled shape evolutions favorably compared to experimentally obtained CCS trends, meaning that the apparent volume or envelope of homogeneously distributed mass effectively modeled the ion-drift gas interactions as sampled by IM-MS. The CCSs of convex shapes could be directly related to their surface area. More importantly, this relationship seems to hold even for moderately concave shapes, such as those obtained by geometry-optimized structures of ions from conventional computational chemistry methods. Theoretical sets of expanding beads-on-a-string shapes allowed extracting accurate bead and string dimensions for two homopolymers, without modeling any chemical interactions.