Geometric Analysis of Shapes in Ion Mobility–Mass Spectrometry

Abstract

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.

Exploring Isomerism in Isolated Cyclodextrin Oligomers through Trapped Ion Mobility Mass Spectrometry

“…For a perfectly spherical geometry p would be 2/3. 18,46 For Cu-linked β-CD assemblies, we find p = 0.57, i.e., a negative deviation from the ideal spherical/isotropic case. This indicates increasingly closely packed assembly with increasing oligomer size 47 possibly arising from partial inclusion between CD rings.…”

“…Here, normalΩ avg = ( ∑ i = 1 n ′ I i × Ω i ) true/ ( ∑ i = 1 n ′ I i ) where I i and Ω i are the relative intensity and CCS of the i th isomer, respectively, and n ′ is the total number of isomers of all ( n : m ) z + species for a specific size n . Following Haler et al, we fit Ω avg with a function of the form Ω avg = A × n p , where the parameter “ p ” contains the information on the shape of the molecule, and A is a constant (Figure ). For a perfectly spherical geometry p would be 2/3. , For Cu-linked β-CD assemblies, we find p = 0.57, i.e., a negative deviation from the ideal spherical/isotropic case.…”

“…18,20,45 Since the isolated oligomers exist in multiple charge states and exhibit a wide distribution in TIMS CCS N2 , we correlate the weighted average of the CCS distribution (Ω avg ) with the oligomer size (n). Here, where I i and Ω i are the relative intensity and CCS of the ith isomer, respectively, and n′ is the total number of isomers of all (n:m) z+ species for a specific size n. Following Haler et al, 46 we fit Ω avg with a function of the form Ω avg = A × n p , where the parameter "p" contains the information on the shape of the molecule, and A is a constant (Figure 7). For a perfectly spherical geometry p would be 2/3.…”

“…Following Haler et al, we fit Ω avg with a function of the form Ω avg = A × n p , where the parameter “ p ” contains the information on the shape of the molecule, and A is a constant (Figure ). For a perfectly spherical geometry p would be 2/3. , For Cu-linked β-CD assemblies, we find p = 0.57, i.e., a negative deviation from the ideal spherical/isotropic case. This indicates increasingly closely packed assembly with increasing oligomer size possibly arising from partial inclusion between CD rings.…”

Automated Structural Activity Screening of β‐Diketonate Assemblies with High‐Throughput Ion Mobility‐Mass Spectrometry

“…Families of structures differing by n-units often display changes in shape and size proportional to the number of units. [31,35,36] The relationship between changes in mass and shape with similar structures is proportional to the drift time, to the power of an instrument dependant value (Equation 1, where ΔΩ is the change in collision cross section, Δm is the change in mass, K' is the modified mobility, Δt d is the change in arrival time, B is an instrument dependent constant for the TWIMS instrument and z is the charge). [37] In these libraries, multiply charged ions are possible so z must be included.…”