Effective Ion Mobility Calculations for Macromolecules by Scattering on Electron Clouds

Structural studies of supramolecular complexes and assemblies by ion mobility mass spectrometry

Recent advances in instrumentation and development of computational strategies for ion mobility mass spectrometry (IM-MS) studies have contributed to an extensive growth in the application of this analytical technique to comprehensive structural description of supramolecular systems. Apart from the benefits of IM-MS for interrogation of intrinsic properties of noncovalent aggregates in the experimental gas-phase environment, its merits for the description of native structural aspects, under the premises of having maintained the noncovalent interactions innate upon the ionization process, have attracted even more attention and gained increasing interest in the scientific community. Thus, various types of supramolecular complexes and assemblies relevant for biological, medical, material, and environmental sciences have been characterized so far by IM-MS supported by computational chemistry. This review covers the state-of-the-art in this field and discusses experimental methods and accompanying computational approaches for assessing the reliable three-dimensional structural elucidation of supramolecular complexes and assemblies by IM-MS.

Site-Specific Ionization Potentials and Electron Affinities in Large Molecular Systems at Coupled Cluster Level

A many-body expansion of ionization potentials and electron affinities is developed based on a combination of the fragment molecular orbital method and equation-of-motion coupled-cluster (EOM-CC). In addition to site-specific values, obtained as one-body properties, pair and triple corrections are added to account for nonlocal EOM-CC contributions of the molecular environment of a chromophore. The developed method is applied to carboxylic acids, alkyl cations, a protein ubiquitin (Protein Data Bank ID 1UBQ), and a nano ribbon of white graphene elucidating the effect of environment on ionization potential and electron affinity.

The Role of Ion Rotation in Ion Mobility: Ultrahigh-Precision Prediction of Ion Mobility Dependence on Ion Mass Distribution and Translational to Rotational Energy Transfer

The role of ion rotation in determining ion mobilities is explored using the subtle gas phase ion mobility shifts based on differences in ion mass distributions between isotopomer ions that have been observed with ion mobility spectrometry (IMS) measurements. These mobility shifts become apparent for IMS resolving powers on the order of ∼1500 where relative mobilities (or alternatively momentum transfer collision cross sections; Ω) can be measured with a precision of ∼10 ppm. The isotopomer ions have identical structures and masses, differing only in their internal mass distributions, and their Ω differences cannot be predicted by widely used computational approaches, which ignore the dependence of Ω on the ion's rotational properties. Here, we investigate the rotational dependence of Ω, which includes changes to its collision frequency due to thermal rotation as well as the coupling of translational to rotational energy transfer. We show that differences in rotational energy transfer during ion-molecule collisions provide the major contribution to isotopomer ion separations, with only a minor contribution due to an increase in collision frequency due to ion rotation. Modeling including these factors allowed for differences in Ω to be calculated that precisely mirror the experimental separations. These findings also highlight the promise of pairing high-resolution IMS measurements with theory and computation for improved elucidation of subtle structural differences between ions.

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.

Effective collisional cross-section of small ions in the gas phase: Application to ion mobility spectrometry

RATIONALE

The observed drift times of monoatomic ions, including alkali metal ions and halide anions, are not fully consistent with their size. When the effect of mass is included through the Mason-Schamp equation, the deviation gets worse so that the trend of the experimental collisional cross-sections becomes completely opposite to what is expected. This is attributed to the stronger local electric field around smaller ions. The strong electric field in the vicinity of a small ion leads to strong ion-neutral interactions and creates a drag force against ion motion. The smaller the ions, the stronger the interaction, because of the higher charge density.

METHODS

In view of this, a modified equation is introduced to describe the relationship between the observed drift times or ion mobilities and the cross-sections of small ions. Here, for small ions with high charge density, the experimental collision cross-section is expressed as the effective collision cross-section, Ω_eff = σ_i (1 + α/r_i ³ ), that takes into account both intrinsic ion size, σ_i , and the ion-molecule interactions through a correction term of α/r_i ³ , which is proportional to the charge density.

RESULTS

A linear fit of the drift times of alkali metal ions and halide anions to the proposed equation showed relative deviations of <8.2%. The model successfully predicted the drift time of other small diatomic ions with reasonable error.

CONCLUSIONS

The proposed model can be used as a simple and efficient relationship in predicting the effective cross-section of small ions.

Computational Methods for Biochemical Simulations Implemented in GAMESS

Computational methods for modeling biochemical processes implemented in GAMESS package are reviewed; in particular, quantum mechanics combined with molecular mechanics (QM/MM), semi-empirical, and fragmentation approaches. A detailed summary of capabilities is provided for the QM/MM implementation in QuanPol program and the fragment molecular orbital (FMO) method. Molecular modeling and visualization packages useful for biochemical simulations with GAMESS are described. GAMESS capabilities with corresponding references are tabulated for reader's convenience.

Software Requirements for the Analysis and Interpretation of Native Ion Mobility Mass Spectrometry Data

The past few years have seen a dramatic increase in applications of native mass and ion mobility spectrometry, especially for the study of proteins and protein complexes. This increase has been catalyzed by the availability of commercial instrumentation capable of carrying out such analyses. As in most fields, however, the software to process the data generated from new instrumentation lags behind. Recently, a number of research groups have started addressing this by developing software, but further improvements are still required in order to realize the full potential of the data sets generated. In this perspective, we describe practical aspects as well as challenges in processing native mass spectrometry (MS) and ion mobility-MS data sets and provide a brief overview of currently available tools. We then set out our vision of future developments that would bring the community together and lead to the development of a common platform to expedite future computational developments, provide standardized processing approaches, and serve as a location for the deposition of data for this emerging field. This perspective has been written by members of the European Cooperation in Science and Technology Action on Native MS and Related Methods for Structural Biology (EU COST Action BM1403) as an introduction to the software tools available in this area. It is intended to serve as an overview for newcomers and to stimulate discussions in the community on further developments in this field, rather than being an in-depth review. Our complementary perspective (http://dx.doi.org/10.1021/acs.analchem.9b05791) focuses on computational approaches used in this field.

Sodium Coordination and Protonation of Poly(ethoxy phosphate) Chains in the Gas Phase Probed by Ion Mobility-Mass Spectrometry

The two-dimensional shape information yielded by ion mobility-mass spectrometry (IM-MS), usually reported as collision cross section (CCS), is often correlated to the underlying three-dimensional structures of the ions through computational chemistry. Here, we used theoretical approaches based on molecular mechanics (MM), molecular dynamics (MD), and density functional theory (DFT) to elucidate the structures of sodiated poly(ethoxy phosphate) polymer ions at different degrees of polymerization (DP) for three different charge states (1+, 2+, and 3+) by comparing computational results to experimentally obtained CCS values. From the calculated structures, we extract several key interaction distances which merge in clusters for all screened charge states and DPs, independent of the three-dimensional structures and the polymer ion structural rearrangements. These distances were also used to extract the minimum coordination numbers in poly(ethoxy phosphate) and to describe the preferred coordination geometries. When sodiated and protonated polymer ions are compared, the experimental CCS evolutions differ at small DP values and merge at higher DPs. We investigated in more depth this difference for two selected species, namely, [PEtP₅ + 2Na⁺]²⁺ and [PEtP₅ + 2H⁺]²⁺. For the protonated ions, we explored the different protonation sites to extract three-dimensional structure candidates and rationalize the CCS behaviors.

The Fragment Molecular Orbital Method Based on Long-Range Corrected Density-Functional Tight-Binding

The presently available linear scaling approaches to density-functional tight-binding (DFTB) based on the fragment molecular orbital (FMO) method are severely impacted by the problem of artificial charge transfer due to the self-interaction error (SIE), which hampers the simulation of zwitterionic systems such as biopolymers or ionic liquids. Here we report an extension of FMO-DFTB where we included a long-range corrected (LC) functional designed to mitigate the DFTB SIE, called the FMO-LC-DFTB method, resulting in a robust method which succeeds in simulating zwitterionic systems. Both energy and analytic gradient are developed for the gas phase and the polarizable continuum model of solvation. The scaling of FMO-LC-DFTB with system size N is shown to be almost linear, O( N^1.13-1.28), and its numerical accuracy is established for a variety of representative systems including neutral and charged polypeptides. It is shown that pair interaction energies between fragments for two mini-proteins are in excellent agreement with results from long-range corrected density functional theory. The new method was employed in long time scale (1 ns) molecular dynamics simulations of the tryptophan cage protein (PDB: 1L2Y ) in the gas phase for four different protonation states and in stochastic global minimum structure searches for 1-ethyl-3-methylimidazolium nitrate ionic liquid clusters containing up to 2300 atoms.

Collidoscope: An Improved Tool for Computing Collisional Cross-Sections with the Trajectory Method

Ion mobility-mass spectrometry (IM-MS) can be a powerful tool for determining structural information about ions in the gas phase, from small covalent analytes to large, native-like or denatured proteins and complexes. For large biomolecular ions, which may have a wide variety of possible gas-phase conformations and multiple charge sites, quantitative, physically explicit modeling of collisional cross sections (CCSs) for comparison to IMS data can be challenging and time-consuming. We present a "trajectory method" (TM) based CCS calculator, named "Collidoscope," which utilizes parallel processing and optimized trajectory sampling, and implements both He and N₂ as collision gas options. Also included is a charge-placement algorithm for determining probable charge site configurations for protonated protein ions given an input geometry in pdb file format. Results from Collidoscope are compared with those from the current state-of-the-art CCS simulation suite, IMoS. Collidoscope CCSs are within 4% of IMoS values for ions with masses from ~18 Da to ~800 kDa. Collidoscope CCSs using X-ray crystal geometries are typically within a few percent of IM-MS experimental values for ions with mass up to ~3.5 kDa (melittin), and discrepancies for larger ions up to ~800 kDa (GroEL) are attributed in large part to changes in ion structure during and after the electrospray process. Due to its physically explicit modeling of scattering, computational efficiency, and accuracy, Collidoscope can be a valuable tool for IM-MS research, especially for large biomolecular ions. Graphical Abstract ᅟ.

Molecular Structures and Momentum Transfer Cross Sections: The Influence of the Analyte Charge Distribution

Structure elucidation by ion mobility spectrometry-mass spectrometry methods is based on the comparison of an experimentally measured momentum transfer cross-section to cross-sections calculated for model structures. Thus, it is imperative that the calculated cross-section must be accurate. However, it is not fully understood how important it is to accurately model the charge distribution of an analyte ion when calculating momentum transfer cross-sections. Here, we calculate and compare momentum transfer cross-sections for carbon clusters that differ in mass, charge state, and mode of charge distribution, and vary temperature and polarizability of the buffer gas. Our data indicate that the detailed distribution of the ion charge density is intimately linked to the contribution of glancing collisions to the momentum transfer cross-section. The data suggest that analyte ions with molecular mass ~3 kDa or momentum transfer cross-section 400-500 Ų would be significantly influenced by the charge distribution in nitrogen buffer gas. Our data further suggest that accurate structure elucidation on the basis of IMS-MS data measured in nitrogen buffer gas must account for the molecular charge distribution even for systems as large as C₉₆₀ (~12 kDa) when localized charges are present and/or measurements are conducted under cryogenic temperatures. Finally, our data underscore that accurate structure elucidation is unlikely if ion mobility data recorded in one buffer gas is converted into other buffer gases when electronic properties of the buffer gases differ. Graphical Abstract ᅟ.

A Priori Intrinsic PTM Size Parameters for Predicting the Ion Mobilities of Modified Peptides

The rising profile of ion mobility spectrometry (IMS) in proteomics has driven the efforts to predict peptide cross-sections. In the simplest approach, these are derived by adding the contributions of all amino acid residues and post-translational modifications (PTMs) defined by their intrinsic size parameters (ISPs). We show that the ISPs for PTMs can be calculated from properties of constituent atoms, and introduce the "impact scores" that govern the shift of cross-sections from the central mass-dependent trend for unmodified peptides. The ISPs and scores tabulated for 100 more common PTMs enable predicting the domains for modified peptides in the IMS/MS space that would guide subproteome investigations. Graphical Abstract ᅟ.

Collision cross sections and ion structures: development of a general calculation method via high-quality ion mobility measurements and theoretical modeling

Theoretical collision cross section calculations revisited for reliable ion structural studies.

Gas molecule scattering & ion mobility measurements for organic macro-ions in He versus N2 environments

A pending issue in linking ion mobility measurements to ion structures is that the collisional cross section (CCS, the measured structural parameter in ion mobility spectrometry) of an ion is strongly dependent upon the manner in which gas molecules effectively impinge on and are reemitted from ion surfaces (when modeling ions as fixed structures). To directly examine the gas molecule impingement and reemission processes and their influence, we measured the CCSs of positively charged ions of room temperature ionic liquids 1-ethyl-3-methylimidazolium dicyanamide (EMIM-N(CN)2) and 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF4) in N2 using a differential mobility analyzer-mass spectrometer (DMA-MS) and in He using a drift tube mobility spectrometer-mass spectrometer (DT-MS). Cluster ions, generated via electrosprays, took the form (AB)N(A)z, spanning up to z = 20 and with masses greater than 100 kDa. As confirmed by molecular dynamics simulations, at the measurement temperature (∼300 K), such cluster ions took on globular conformations in the gas phase. Based upon their attained charge levels, in neither He nor N2 did the ion-induced dipole potential significantly influence gas molecule-ion collisions. Therefore, differences in the CCSs measured for ions in the two different gases could be primarily attributed to differences in gas molecule behavior upon collision with ions. Overwhelmingly, by comparison of predicted CCSs with selected input impingement-reemission laws to measurements, we find that in N2, gas molecules collide with ions diffusely--they are reemitted at random angles relative to the gas molecule incoming angle--and inelastically. Meanwhile, in He, gas molecules collide specularly and elastically and are emitted from ion surfaces at determined angles. The results can be rationalized on the basis of the momentum transferred per collision; in the case of He, individual gas molecule collisions minimally perturb the atoms within a cluster ion (internal motion), while in the case of N2, individual gas molecules have sufficiently large momentum to alter the internal motion in organic ions.

On the structural denaturation of biological analytes in trapped ion mobility spectrometry – mass spectrometry

Trapped ion mobility spectra recorded for ubiquitin are consistent with structures reported for the native state by NMR.

EM∩IM: software for relating ion mobility mass spectrometry and electron microscopy data

We present EM∩IM, software that allows the calculation of collision cross-sections from electron density maps obtained for example by means of transmission electron microscopy. This allows the assessment of structures other than those described by atomic coordinates with ion mobility mass spectrometry data, and provides a new means for contouring and validating electron density maps. EM∩IM thereby facilitates the use of data obtained in the gas phase within structural biology studies employing diverse experimental methodologies.

Linking molecular models with ion mobility experiments. Illustration with a rigid nucleic acid structure

Ion mobility spectrometry experiments allow the mass spectrometrist to determine an ion's rotationally averaged collision cross section Ω(EXP). Molecular modelling is used to visualize what ion three-dimensional structure(s) is(are) compatible with the experiment. The collision cross sections of candidate molecular models have to be calculated, and the resulting Ω(CALC) are compared with the experimental data. Researchers who want to apply this strategy to a new type of molecule face many questions: (1) What experimental error is associated with Ω(EXP) determination, and how to estimate it (in particular when using a calibration for traveling wave ion guides)? (2) How to generate plausible 3D models in the gas phase? (3) Different collision cross section calculation models exist, which have been developed for other analytes than mine. Which one(s) can I apply to my systems? To apply ion mobility spectrometry to nucleic acid structural characterization, we explored each of these questions using a rigid structure which we know is preserved in the gas phase: the tetramolecular G-quadruplex [dTGGGGT]4, and we will present these detailed investigation in this tutorial.

A local collision probability approximation for predicting momentum transfer cross sections

The local collision probability approximation (LCPA) method is introduced to compute molecular momentum transfer cross sections for comparison to ion mobility experiments.

Advances in ion mobility-mass spectrometry instrumentation and techniques for characterizing structural heterogeneity

Enabling IM-MS instrumentation and techniques for characterizing sample structural heterogeneity have developed rapidly over the last five years.

Modeling vapor uptake induced mobility shifts in peptide ions observed with transversal modulation ion mobility spectrometry-mass spectrometry

Adsorption models are used to explain vapor dopant facilitated mobility shifts for peptide ions.