Comprehensive Ion Mobility Calibration: Poly(ethylene oxide) Polymer

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Comprehensive Ion Mobility Calibration: Poly(ethylene oxide) Polymer Calibrants and General Strategies Jean R. N. Haler, Christopher Kune, Philippe Massonnet, Clothilde Comby-Zerbino, Jan Jordens, Maarten Honing, Ynze Mengerink, Johann Far, and Edwin De Pauw Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02564 • Publication Date (Web): 24 Oct 2017 Downloaded from http://pubs.acs.org on October 30, 2017

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Analytical Chemistry

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Comprehensive Ion Mobility Calibration: Poly(ethylene oxide)

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Polymer Calibrants and General Strategies

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Jean R. N. Haler1, Christopher Kune1, Philippe Massonnet1, Clothilde Comby-Zerbino2,

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Jan Jordens3, Maarten Honing3, Ynze Mengerink3, Johann Far1, Edwin De Pauw1

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1

Mass Spectrometry Laboratory, University of Liège, Quartier Agora, Allée du Six Aout

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11, B-4000 Liège, Belgium 2

Institut Lumière Matière, Université de Lyon, Université Lyon 1, CNRS, 69100

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Villeurbanne, France 3

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DSM Resolve, Geleen, The Netherlands

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*Corresponding author email address: [email protected]

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Abstract

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Ion Mobility (IM) is now a well-established and fast analytical technique. The IM

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hardware is constantly being improved, especially in terms of the resolving power. The

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Drift Tube (DTIMS), the Traveling Wave (TWIMS), and the Trapped Ion Mobility

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Spectrometry (TIMS) coupled to mass spectrometry are used to determine the Collision

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Cross-Sections (CCS) of ions. In analytical chemistry, the CCS is approached as a

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descriptor for ion identification and it is also used in physical chemistry for 3D structure

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elucidation with computational chemistry support. The CCS is a physical descriptor

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extracted from the reduced mobility (K0) measurements obtainable only from the

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DTIMS. TWIMS and TIMS routinely require a calibration procedure to convert

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measured physical quantities (drift time for TWIMS and elution voltage for TIMS) into

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CCS values. This calibration is a critical step to allow inter-instrument comparisons. The

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previous calibrating substances lead to large prediction bands and introduced rather large

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uncertainties during the CCS determination.

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In this paper, we introduce a new IM calibrant (CCS and K0) using singly charged

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sodium adducts of poly(ethylene oxide) monomethyl ether (CH3O-PEO-H) for positive

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ionization in both helium and nitrogen as drift gas. These singly charged calibrating ions

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make it possible to determine the CCS/K0 of ions having higher charge states. The fitted

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calibration plots exhibit larger coverage with less data scattering and significantly

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improved prediction bands and uncertainties. The reasons for the improved CCS/K0

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accuracy, advantages and limitations of the calibration procedures are also discussed. A

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generalized IM calibration strategy is suggested.

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Introduction

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Ion Mobility spectrometry (IM) provides a fast electrophoretic separation of ions in the

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gas phase. The interest of analytical sciences to couple IM separation, Mass Spectrometry

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(MS; IM-MS) and conventional separation techniques1 (such as Liquid Chromatography,

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LC-MS) has peaked during recent years1–11. IM-MS coupling improves the peak

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capacity12 and raises the confidence level in the identification of compounds and in their

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structural elucidations.

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During a low field IM separation, the measurable quantities are either drift times (dt) or

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elution voltages. They depend on the properties of the ions (charge, mass and shape)13

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and on the buffer gas (pressure, temperature, nature), but they also strongly depend on the

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IM setup and the experimental conditions. In order to compare results between different

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(assumed) low field IM-MS instruments, the raw experimental values have to be

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converted into physical descriptors of the ions such as the Collision Cross-Section (CCS)

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which should be independent of the IM hardware and the experimental conditions, as

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long as the temperature or the drift gas are not changed. In practice, only Drift Tube (DT)

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IM setups allow to directly extract these shape-related descriptors, meaning the Collision

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Cross-Section or the reduced mobility (K0) from drift time measurements14. On other IM

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setups (non-DT setups), a calibration procedure is usually required to convert

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experimental values into ideally instrument-independent physical quantities of the ions,

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i.e. CCS or K0 values15,16. Such calibrations then use reference values obtained from DT-

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based instruments.

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Different IM-fitted instruments such as the Traveling Wave IM (T-Wave), the DT IM,

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the Differential IM (DMS) and the Trapped IM (TIMS) setups are commercially

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available. Their hardware performance boundaries are constantly being pushed further17–

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25

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of ion cloud densities and drift voltages on resolving power are as well being optimized

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in homemade drift tubes26–28. The improvements in resolving power of IM instruments

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lead to better separations of closely eluted compounds and to smaller drift time

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dispersions (i.e. a smaller IM peak width) with regards to the peak apex. While the IM

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measured quantities gain in precision and in accuracy, the calibration processes should

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avoid introducing uncertainties on CCS and K0 values during the calibration procedure.

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Calibrations thus need to rely on highly reproducible and robust calibrating ions, for

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which the CCS and K0 values are insensitive to reasonable changes in experimental

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conditions.

, especially in terms of resolving power. Fundamental parameters such as the influence

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Experimental IM data are related to a three-dimensional shape-dependent property of the

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ions, reduced to a two-dimensional value. Given that IM measurements convert

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measurable quantities (drift times, elution voltages) into CCS or K0 values related to the

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shape of the ions, each calibrating ion needs to have one unique shape which is retained

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in all IM(-MS) instruments and experimental conditions.

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Here we suggest synthetic homopolymers, using poly(ethylene oxide) monomethyl ether

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(CH3O-PEO-H) for proof of concept, as calibrating ions for CCS and K0 measurements in

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positive ion mode with commercial instruments using N2 as a drift gas. For sake of

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completeness, the DT-obtained values in He are also provided. The advantages of using

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synthetic homopolymers are discussed. Their known and constant shapes when

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increasing the polymer chain length (excluding the zones of structural rearrangements29)

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stand in contrast to peptide or protein structures which often show multiple

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conformations upon ion heating30,31. We show that IM calibrations using synthetic

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homopolymers result in accurate CCS-deduced values for each benchmarked instrument

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and decreased errors (uncertainties) on the calibrated measurements. The calibration is

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applied to CCS and K0 measurements on the widely used Synapt G2 HDMS T-Wave

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(Waters, UK) and the recently developed high-resolution TIMS (Bruker Daltonics, USA)

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instruments.

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Experimental

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All presented data and plots compare measurements taken at room temperature in N2 as

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drift gas. Drift Tube-obtained CCS and K0 values in N2 and in He used as drift gases are

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given in the dedicated table in the Supporting Information (Table SI1).

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Sample Preparation

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Poly(ethylene oxide) monomethyl ether (CH3O-PEO-H) 750 g/mol (ref. 202495) and

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2000 g/mol (ref. 202509) samples were bought from Sigma-Aldrich. The samples were

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diluted to 5 × 10-6 M in pure methanol (Biosolve) spiked with 10-5 M Na+ cations (NaCl

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salt prepared in pure methanol) for injection. The calibrating substances used in this study

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are contained in the 750 g/mol sample.

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Ion Mobility-Mass Spectrometry: Drift Tube IM (DT)

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The samples were infused at a flow rate of 150 µL/h into a homemade Ion Mobility-Mass

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Spectrometer fitted with an Electrospray Ionization source (ESI). The instrument is a

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Drift Tube-modified Maxis Impact (Bruker, Germany) Quadrupole Time-of-Flight mass

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spectrometer (Q-ToF). The setup is described in detail elsewhere14. In brief, it contains

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two 79 cm-long drift tube separated by a dual-stage ion funnel assembly. Both

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extremities of both drift tubes are fitted with grids, precisely defining the drift distance.

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After the IM separation, the ions pass through another dual funnel assembly which is

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followed by a stacked-ring radio-frequency ion guide before entering the original transfer

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optics of the Maxis Impact Q-ToF. The drift time measurements leading to the CCS and

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K0 calculations reported in this article were obtained using the second drift region only.

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The He and N2 DT reference values provided in Table SI1 were taken as 3 replica

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measurements on 3 different days by 3 different operators. The first and last

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measurements were spaced by 10 months. For more details on the experimental

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parameters and on the CCS and K0 calculations, see the Supporting Information. Data

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processing was performed using Excel 2011 and IgorPro 6.34A.

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Ion Mobility-Mass Spectrometry: Trapped IM (TIMS)

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For details on the TIMS-TOF (Bruker Daltonics, USA) parameters, see the Supporting

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Information. The interpretation of the TIMS data was performed using a beta version of

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Bruker’s DataAnalysis 5-0 software and the UIMF_Viewer software. Data processing

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was performed using Excel 2011 and IgorPro 6.34A.

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Ion Mobility-Mass Spectrometry: Traveling Wave IM (T-Wave)

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For details on the T-Wave SYNAPT G2 HDMS (Waters, UK) parameters, see the

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Supporting Information. The interpretation of the T-Wave data was performed using

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Waters’ MassLynx 4.1 software. ATD peaks were fitted using PeakFit v.4.11 to

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determine accurate drift times. Data processing was performed using Excel 2011 and

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IgorPro 6.34A.

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Calibration procedure: T-Wave

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Ruotolo and coworkers described the Collision Cross-Section (CCS) calibration

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procedure for Traveling-Wave-based instruments (T-Wave)15. The detailed protocol with

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all necessary equations can be found in the Supporting Information.

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In short, equation 1 represents the calibration curve fit. The reduced DT-measured CCS

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values (Ω’; charge and reduced mass correction, see equation SI3) are plotted as a

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function of the corrected drift times (dt”; see equation SI2), measured on the T-Wave

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instrument. The two fit parameters a and b depend on the experimental conditions.

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Ω' = a ⋅ ( dt '')

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, Ω’ is the DT-obtained reduced CCS (see equation SI3), dt” is the corrected T-Wave-

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obtained drift time (see equation SI2) and a and b are the fitting parameters of the

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calibration equation depending on the experimental conditions.

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Calibration procedure: TIMS

b

(1)

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The TIMS calibration procedure was detailed by the groups of Fernandez-Lima16 and

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Park32. The detailed protocol with all necessary equations can be found in the Supporting

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Information.

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In short, equation 2 represents the calibration curve fit. The DT-measured reduced

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mobility K0 values are plotted as a function of the inverse elution voltage (1/Ve; see

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equation SI5 and equation SI6), obtained from the TIMS measurement. The two fit

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parameters a and b depend on the experimental conditions (equation 2). Using equation 3

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(derived from the Mason-Schamp equation13), the CCS values can be recalculated from

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the K0 values.

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 1 K0 = a + b ⋅    Ve 

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, K0 is the reduced mobility, a and b are the fitting parameters of the calibration equation

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depending on the experimental conditions, Ve is the elution voltage.

Ω = c⋅ 150

z 1 ⋅ µT K 0

(2)

(3)

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, Ω is the Collision Cross-Section (CCS), c is a constant derived from the Mason-Schamp

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equation (c = 18500 at 305 K), z is the charge of the ion, µ is the reduced mass of the drift

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gas and the ion, T is the temperature (assumed to be 305 K) and K0 is the reduced

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mobility.

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Results and Discussion

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The calibration process is meant to convert low field (small E/N) IM setup-dependent

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measured drift times (or its equivalent) into invariant CCS or K0 values (if not changing

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the temperature or the drift gas). Once the IM calibration is performed, the plot of the

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CCS as a function of the mass (or mass-to-charge ratio; m/z) for a series of homologous 7 /32



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molecules should be identical for all IM setups. Such plots constitute the repeatability

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tests (quality control) of the robustness of the calibration. Discrepancies could be

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assigned to poor calibration fits originating from a temperature-dependent three-

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dimensional structure of the calibrating substances, a strongly temperature-dependent

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interaction between the drift gas and the calibrating substances, from a too small number

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of calibrating points and/or from intrinsic errors in the calibration procedure due to

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poorly defined ion trajectories. Before presenting the experimental results, the classical

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(established) calibrating substances of the two non-DT IM setups used in this paper are

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presented (T-Wave and TIMS).

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Classical calibrating substances.

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Biomolecules. The choice of the calibrating ions was up to now guided by equation 4. If

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the CCS values of biomolecules are plotted as a function of their mass and fit with a pow

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parameter of ~0.66, then their shapes were postulated to be globular in the gas phase15.

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Different charge state ions were thus mixed in the calibration plots. However, when

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fitting polymer-cation CCS evolutions, pow parameters near 0.66 can be found for non-

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globular shapes. Figure SI1 illustrates such fits for the [PEO + 1Na+]1+ and the [PEO +

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3Na+]3+ charge states. The globular shapes of [PEO + 1Na+]1+ (no Coulomb repulsion;

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‘Fit 1+’ in Figure SI1) correlate with pow=0.61 whereas the elongated shapes33 of [PEO

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+ 3Na+]3+ fit with pow=0.65 (‘Fit 3+’ in Figure SI1). The 0.66 criterion is thus not

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sufficient to attribute shapes to ions.

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Ω = A ⋅ mass pow

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, Ω is the CCS, A and pow are two fitting parameters and mass represents either the mass

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of the ion or the Degree of Polymerization (DP) of polymer ions.

(4)

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Additionally, Waters’ T-Wave and Bruker’s TIMS instruments are mainly operated using

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N2 as drift gas. In contrast, most of the DT-obtained reference values of calibrating

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substances are published mainly for He as drift gas. The range of calibrating substances

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available in N2 is drastically reduced34,35.

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Moreover, multiple conformation peaks are often observed in the ATD for one given

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mass-to-charge ratio (m/z) of biomolecules36–39. Each of these peaks would have to be

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annotated in literature (DT reference measurements) in order to be able to correlate the

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reference peaks to the observed peaks in the IM setup needing calibration. However, such

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multi-peak annotations are barely the case in literature.

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Above all, in addition, these multi-peak ATDs obtained from the DT (reference)

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instruments would have to be reproduced on the other IM-MS setups. Otherwise, the

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assignment of each drift time peak is almost unachievable with a high level of

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confidence. Even if performing such drift time assignments, the question of the

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unambiguously invariant shape attributions to each conformation would nevertheless still

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be unsolved. Indeed, ion temperature25,40–42 and ion dynamics43 studies showed that ion

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history (ionization source, ion optics…) in different IM setups can differ from instrument

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to instrument, making multi-peak ATD reproducibility for biomolecules nearly

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impossible44.

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Homopolypeptides such as poly(alanine), poly(glycine)34 and poly(proline)45,46 also

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suffer from multiple conformations depending on the charge state and ion

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temperature30,31,47.

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All in all, the uncertainty of reproducible and invariant ATDs or CCS values (i.e. shapes)

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of biomolecule-based calibrating substances or even of homopolypeptides could lead to

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skewed IM values, misinterpretations and low-quality calibration fits (Figure 1.a.).

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Figure 1

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Agilent Tune Mix. On the TIMS instrument, the usual calibrating substances originate

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from the Agilent Tune Mix48. They act as both a mass and a mobility calibrating

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substance in one sample injection. Nevertheless, the limited number of the Agilent Tune

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Mix48 calibrating points provides a non-negligible downside due to the operational mode

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of the TIMS itself. Even when using long TIMS voltage ramps, only a few calibrating

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ions elute during a TIMS experiment (Figure 2.a.). However, large TIMS ramps prevent

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attaining the advertised high resolving power32. In order to improve the resolving power

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and thus the separation of given ions, different TIMS parameters can be changed and

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optimized. Rather rarely, the gas pressure in the TIMS cell is adjusted. Regularly, the

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scan rates of the voltage ramp can be changed, but the TIMS ramp itself can as well be

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changed, meaning shortened. If the elution voltage window is thus shortened, not enough

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calibrating points of the Agilent Tune Mix can be extracted from the data. This affects the

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calibration curve accuracy or may even prevent any calibration fit.

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Figure 2

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Proposing new calibrating substances: Synthetic homopolymers.

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Using synthetic homopolymers as calibrating substances presents several advantages

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compared to biomolecules and to the Agilent Tune Mix. First, synthetic homopolymers

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such as PEO (poly(ethylene oxide) monomethyl ether) are low-priced, storable at room

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temperature, and easy to handle compared to biomolecules. Second, many synthetic

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polymers such as PEO are not subjected to sample degradation or alteration over time.

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Also, the large mass dispersities of polymer samples lead to a large mobility dispersity.

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This results in the large coverage of dt”, Ω’, 1/Ve and K0 in the calibration plots by the

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homopolymer calibrating substances (equation 1 and equation 2) whatever the chosen

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instrument settings. Polymer samples will yield one-shot easy-to-handle calibrations (e.g.

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CH3O-PEO-H 750 g/mol sample). This one-shot calibration then reduces the analysis

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time for any commercially available ion mobility-mass spectrometer (T-Wave, TIMS…).

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Finally, as we will discuss now, single-cation adducts such as sodium adducts of PEO

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have an easily predictable shape (spherical shape) which was additionally established to

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be temperature independent49,50. Their CCS also monotonically depends on the degree of

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polymerization. These features enable easier troubleshooting detection and last but not

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least a straightforward interpolation and extrapolation of the calibration curves.

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Robustness and reproducibility. PEO does not have strong intramolecular interactions,

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contrary to structured peptides or DNA. PEO-cation complexes provide single and unique

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ATD peaks for all considered charge states and polymer chain lengths (see Figure 3.a.),

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as opposed to other polymer ions being much stronger influenced by Coulomb

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repsulsions51. Using PEO calibrating ions hence seems robust and reproducible, tackling

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the issue of multi-peak ATD assignments of many biomolecules or synthetic

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homopolypeptides.

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Figure 3

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Moreover, PEO polymer-cation complexes have robust shapes and do not exhibit any

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change in conformations or any appearance of new stable shapes upon ion heating49,50.

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Conformational changes crossing large energy barriers and trapping ions in new

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geometries do not occur. The assignments of the PEO IM peaks therefore provide

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unambiguous CCS or K0 values. Such synthetic homopolymer calibrations should then

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even be usable throughout a large range of experimental temperatures in new non-DT-

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based Variable Temperature IM-MS setups25 (VT-IM-MS), limiting the requirement of

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recalibration of the IM cells for each effective temperature.

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Calibration plots, improved error bars and accuracy. Table SI1 provides the DT-

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obtained CCS and K0 values of the [PEO + 1Na+]1+ calibrating substances measured in

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N2 and He at room temperature. The replica measurements were performed on 3 separate

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days by 3 different operators. The first and last measurements were spaced in time by 10

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months. Relative Standard Deviations (RSD), 95% confidence intervals (2SD) and the

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exact number of replica measurements (n) are provided for each calibrating ion, as well

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as the theoretical masses of the [PEO + 1Na+]1+ complexes, i.e. the theoretical m/z values.

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Figure 1.a. and Figure 1.b. represent the CCS calibration curves of a T-Wave instrument

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(according to equation 1). Figure 1.a. uses the published N2 tryptic digest of BSA

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values34 whereas Figure 1.b. uses our new DT-obtained [PEO + 1Na+]1+ calibration

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values. Figure 2.a. and Figure 2.b. represent the K0 calibration curves of a TIMS

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instrument (according to equation 2). Figure 2.a. uses the published N2 Agilent Tune Mix

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substance values16 whereas Figure 2.b. uses our new DT-obtained [PEO + 1Na+]1+

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calibration values. The four plots contain the calibration curve fits described in equation 1

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and equation 2, the 95% confidence bands and the 95% prediction bands of the fit curve.

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The comparisons of Figure 1.a. and Figure 1.b. as well as of Figure 2.a. and Figure 2.b.

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reveal major improvements with respect to the prediction bands, i.e. the greatest

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estimated interval of uncertainty on a calibrated value (‘worst case’ error), when using

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PEO as calibrating substance.

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The PEO calibrants [PEO + 1Na+]1+ also increased the number of calibrating points and

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extends the ranges of the calibration plot axes, especially compared to the tryptic digest

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of BSA calibration (T-Wave). Compared to the Agilent Tune Mix calibration (TIMS), the

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synthetic homopolymer calibration improves the correlation coefficient (R²) especially in

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cases of narrow TIMS ramp voltage conditions.

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In order to further illustrate the enhanced quality of the calibration fits, i.e. the

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improvement in the IM error bars (or interval of uncertainty) yielded only by the

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calibration process, Figure 1.c. and Figure 2.c. plot the CCS and K0 errors calculated

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from the 95% prediction bands of both the established calibrations and the new synthetic

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homopolymer calibration. The evolution of these error bars are illustrated on the drift

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times (or elution voltages) measured for PEO complexes bearing 1 to 4 sodium cations

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and covering a mass range from ~0 to 4000 Da.

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Figure 1.c. and Figure 2.c show that the synthetic homopolymer calibration yields

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constant errors throughout the whole drift time (or elution voltage) and mass range. In the

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case of the T-Wave, the tryptic digest of BSA calibration yields errors of up to 55 Å2

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whereas the PEO calibration only yields errors of up to 15 Å2 (up to 73% decrease in

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error for e.g. m/z ~3500, z = 4+, CCS ~1200 Å2). Moreover, both calibration errors

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increase when the charge states of the calibrated analytes increase. For the [PEO +

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1Na+]1+ calibration, however, this error is still constant within each investigated charge

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state throughout the whole mass range. In the case of the TIMS, the Agilent Tune Mix

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almost yields a constant error throughout all the different charge states, reaching error

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values up to 0.050 cm2V-1s-1 while the PEO calibration reaches a constant average error

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value of around 0.008 cm2V-1s-1 (84% decrease in error for e.g. m/z ~1500, z = 1+, K0

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~0.49 cm2V-1s-1), identical for all investigated charge states.

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In order to establish the accuracy of the PEO-calibrated values, the resulting CCS (T-

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Wave and TIMS) or K0 (TIMS) values are compared to the reference DT-obtained values

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in Figure 4.a. and Figure 5.a., and in the Supporting Information (Figure SI5 and Figure

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SI6). The TIMS comparisons also include the values obtained through the established

302

calibrating substances (Agilent Tune Mix). In order to better visualize these differences

303

between the DT reference values and the calibrated CCS or K0 values, percentage

304

deviations of the calibrated values are calculated using equation 5. These plots are shown

305

in Figure 4.b. and Figure 5.b.

306

%( CCS or K 0 ) =

DT − Calibrated × 100 DT

(5)

307

, DT is the Drift Tube-obtained CCS or K0 value and Calibrated is the TIMS or T-Wave

308

CCS or K0 value after calibration.

309

Figure 4

310

Figure 5

311

Figure 4.a. exhibits that the TIMS and T-Wave CCS experimental values of the BSA

312

peptides are in better agreement with the DT-obtained reference values when using the

313

PEO calibration. According to Figure 4.b., the PEO-calibrated CCS values for 1+ and 2+

314

peptides are slightly more accurate than the Agilent Tune Mix-calibrated TIMS CCS

315

values. Figure 5.a. exhibits an overall better TIMS K0 accuracy for the different charge

316

states of PEO-sodium complexes using the PEO calibration instead of the Agilent Tune

317

Mix calibration. Figure 5.b. more clearly leads to the same conclusion, especially

14 /32


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318

considering the PEO ions carrying 4 charges, and keeping in mind that the [PEO +

319

1Na+]1+ complexes’ deviation for the PEO calibration should not be taken into account

320

because they constitute the calibrating ions (reference). Figure SI3 and Figure SI4 in the

321

Supporting Information show the same plots for CCS values of PEO complexes and K0

322

values of the tryptic digest of BSA peptides. Figure SI5 and Figure SI6 show the

323

correlations between the CCS or K0 values from a T-Wave or a TIMS after the

324

calibration procedure (i.e. using [PEO + 1Na+]1+, a peptide digest from BSA with

325

trypsin34, or the Agilent Tune Mix16 as calibrating points) and the CCS or K0 values

326

obtained from the drift tube instrument used as reference. The slope of the linear

327

regressions and the statistical evaluators (correlation coefficient (R2), residual sum of

328

squares (RSS), F statistic (F-stat) and p-value) provided in these plots lead to the same

329

conclusions as Figure 4, Figure 5, Figure SI3 and Figure SI4, i.e. an overall improvement

330

of the CCS or K0 value accuracy. An important conclusion of those figures is that the

331

calibrating process based on solely the singly charged PEO complexes [PEO + 1Na+]1+ as

332

calibrants yields more accurate CCS (or K0) values even for the CCS or K0 determination

333

of multiply charged ions (e.g. PEO carrying 2 to 4 sodium cations).

334

All in all, improvements in accuracy and in the interval of uncertainty of the calibrated

335

values are obtained when using the synthetic homopolymer complexes ([PEO + 1Na+]1+)

336

as calibrating substances compared to the established calibrating substances.

337

Discussion on the origins of the improved calibration using synthetic homopolymers.

338

The improved calibration plots can be explained by several different considerations. As

339

already mentioned earlier, there are the robust shapes due to the temperature

340

independence of synthetic homopolymers.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

341

Then, the choice of the singly charged polymer ions bears further significant

342

improvements because all the calibrating points share the same shape. Figure SI7 and

343

Figure SI8 illustrate the reproducibility and insensitivity of the [PEO + 1Na+]1+ calibrants

344

when calibrating in different T-Wave wave parameters. Lastly, the choice itself of

345

synthetic homopolymer ions used as calibrating substances plays an important role in

346

enhancing the calibration plots by mimicking the IM behavior of the ions to be measured.

347

Choosing the singly charged calibrating substances. The choice of using only one given

348

charge state over the whole mass range, namely the 1+ charge state [PEO + 1Na+]1+,

349

prevents any shape bias during the calibration. Indeed, 1+ complexes have intrinsically

350

spherical shapes due to the dominant entropic contribution in the absence of strong

351

intramolecular interactions and of Coulomb repulsion (i.e. maximized charge screening

352

of the cation). This eliminates potential biases caused e.g. by concavities and harmonizes

353

the specific interactions of all the [PEO + 1Na+]1+ calibrants with the drift gas particles as

354

revealed by Siems and coworkers52. Indeed, these authors improved the description of

355

hard sphere interactions for the Mason-Schamp equation and identified increasingly

356

disruptive CCS calibration inaccuracies due to differing interaction potentials with the

357

drift gas.

358

Furthermore, the singly charged homopolymers cover larger ranges of the calibration plot

359

axes. This increased number of calibrating points constitutes a significant advantage for

360

TIMS calibrations. Indeed, the TIMS voltage ramp settings dictate the window of

361

measurable K0 ranges. The numerous available calibrating points from [PEO + 1Na+]1+

362

will allow to perform calibrations whatever the ramp settings.

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363

Finally, being able to cover large ranges of the calibration plots by using only the [PEO +

364

1Na+]1+ calibrant ions, avoids the requirement of higher charge state ions to extend the

365

CCS range, which can introduce biases during the calibration (see Table SI2).

366

Identifying uncorrected instrumental biases. Even if calibration procedures should be

367

entirely independent of the instrumental setups (mathematical data transformations),

368

empirical evidence of inaccurate calibrated values depending on the calibrating

369

substances is mounting in literature53,54. Such observations result in the conclusions that

370

analyte-homologous calibrating substances should be used for calibration.

371

Hines and coworkers53 analyzed different calibrating substances for yielding reproducible

372

and accurate calibrated CCS values of phospholipids. They found that only lipid

373

calibrating substances were able to yield satisfying accuracies when CCS determination

374

of lipids was performed. Such issues were also observed when analyzing other

375

biomolecules. Because of their inherent sequence differences, inherent shape differences

376

translate into inherent potential energy surface (CCS) dispersities55. These CCS

377

dispersities are reflected in calibration plot dispersities. Despite the introduction of new

378

calibrating substances, calibrating substances which are too different from the chemical

379

nature of the analytes could yield inaccurate calibrated values (affected trueness). Owing

380

to the identical building blocks of given synthetic homopolymers, no CCS dispersities are

381

observed for synthetic homopolymer complexes in restrained mass ranges (see Figure

382

5.a. 2+ ions: DP 13-30, 31-42, 43-49). This results in greatly decreased dispersities on the

383

calibration plots, yielding greatly decreased error bands. The 95% prediction band fits

384

yielded by the PEO calibration are indeed well below (almost up to one order of

17 /32



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

385

magnitude) the ones obtained for the established calibrating substances (Figure 1.c. and

386

Figure 2.c.).

387

This issue of CCS dispersities being reflected in the calibration plots has its origins in

388

flawed drift time (or equivalent) corrections during the calibration process (equation SI2

389

and equation SI6). If the drift time measurements were performed exactly between the

390

beginning and the end of the ion mobility cells and if the ions did not pass through any

391

different pressure/vacuum interfaces or ion optics devices, then one set of calibrating ions

392

would yield satisfying accurate results for all analytes (peptides, lipids, carbohydrates…)

393

as soon as the calibrating ion shapes are not affected by e.g. heating effects. Nevertheless,

394

the drift time measurements are only stopped later in the instruments. The ions have

395

undergone several ion optics and pressure changes. These stages in the IM-MS setups

396

induce in fact additional, presumably non-constant, and uncontrolled IM separations due

397

to variable drag forces. These variable drag forces depend on the different CCS values of

398

the ions at given kinetic energies. The kinetic energies are provided by the acceleration

399

voltages of ion optics, directly related to the mass of the ions. These additional,

400

interfering IM separations are not taken into account when correcting the drift times or

401

elution voltages for calibration (see equation SI2 and equation SI6). These performed

402

drift time (or equivalent) corrections are indeed purely mathematical (equation SI2) or

403

constant (equation SI6), meaning that they do not consider the interfering drifts according

404

to the CCS/mass ratio which occur in the ion optics after the IM cells. The interfering

405

CCS/mass ratio reflects a density parameter of the ions.

406

The corrections (t0) to the drift times of a DT setup are extracted experimentally when

407

performing the linear regressions for CCS determinations. The plots of the drift time

18 /32


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408

evolutions of PEO, as well as the experimental DT corrections (t0) and the

409

mathematically calculated T-Wave drift time corrections (t0; equation SI2) are

410

represented in Figure 3. The difference between the DT and T-Wave t0 evolutions

411

represented in Figure 3.b. highlights the interfering and uncontrolled IM separations

412

occurring within the IM-MS instruments. As it is clearly observed for the [PEO + 2Na+]2+

413

complexes, the drift time evolution (Figure 3.a.) is very similar to their DT t0 evolution

414

(Figure 3.b.). However, the T-Wave t0 evolution (Figure 3.b.) of [PEO + 2Na+]2+ does

415

not reflect its drift time evolution. The interfering drifts according to the CCS/mass ratios

416

are hence not taken into account by the mathematical corrections (t0) in the T-Wave

417

calibration procedure.

418

The magnitude of the interfering drifts can nevertheless be estimated through the quality

419

control plot of a CCS calibration, namely the CCS versus mass plots. Indeed May and

420

coworkers9 established categorizations of CCS spaces as a function of the mass for

421

different analyte families such as lipids, peptides and carbohydrates. These uncontrolled

422

interfering IM separations will increasingly differ for analytes and calibrating substances

423

in increasingly differing CCS spaces. Indeed, isobaric ions can have different volumes,

424

resulting in different CCS/mass ratios, i.e. different density parameters of the ions.

425

Detailed discussions on the effect of the ion density parameter during ion mobility

426

experiments will be the focus of a future paper. Regarding the calibration process, it

427

affects the trueness of the drift times (or elution voltages).

428

Regrouping different biomolecules (enzymatic digests of proteins, proteins or other

429

biomolecules) in the same calibration plots (see Figure 1.a.) therefore prevents producing

430

high quality calibration plots, especially when using even several charge states of

19 /32



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

431

biomolecules or polymers because it further increases the inevitable shape differences

432

incorporated in the IM calibration process54.

433

Remedying uncorrected instrumental biases: General concept of IM calibrations and

434

prospects. In general, singly charged synthetic homopolymer complexes constitute a

435

known, external and independent reference of known spherical shapes. All synthetic

436

homopolymers which do not exhibit multiple conformations or conformational changes

437

dependent on the experimental conditions, will lead to robust and reproducible calibrating

438

substances with high quality calibration fits.

439

Figure SI9 illustrates the close correlation of the CCS spaces (i.e. comparable density

440

parameters) of peptides and of PEO-sodium complexes. The PEO calibrating ions appear

441

to fulfill the calibration requirements for accurate peptide CCS determinations9,56. The

442

correlation of their CCS evolutions as a function of the mass can be described by their fit

443

parameters A from equation 4. The choice of the appropriate calibrating substance for

444

different analytes should thus be based on similar fit parameter A values between the

445

calibrants and the ions of interest.

446

As a general concept, the analyte CCS value has to be probed by an iterative calibration

447

procedure or by selecting tabulated ‘parameter A’ values of calibrants (see equation 4).

448

Indeed, after initial calibration, the CCS or K0 values can to be reevaluated using the

449

appropriate calibrants having the parameter A that matches the parameter A of the ions

450

being measured. This should thus improve the accuracy and the trueness of the measured

451

CCSs. Future efforts in IM calibrations should also go into instrumental developments

452

where the drift time measurements will have to be restricted to solely the IM cells,

453

eliminating the interfering drifts in ion optics, or to calibration databases of singly

20 /32


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454

charged synthetic homopolymers sampling the different parameter A values (CCS

455

spaces), allowing an (automated) iterative calibration procedure.

456 457

Conclusions

458

We proposed a new calibrating substance for Ion Mobility calibrations based on synthetic

459

homopolymers, namely poly(ethylene oxide) monomethyl ether (CH3O-PEO-H). We

460

provided DT-obtained CCS and K0 calibrating points ([PEO + 1Na+]1+) in N2 and He

461

obtained from an electrospray ionization source operated in positive ion mode. The

462

provided values are average values of 3 replica measurements taken on 3 different days

463

by 3 different operators, with 10 months between first and last measurements. We tested

464

the IM calibrations on a T-Wave and a TIMS instruments.

465

The presented IM calibration strategy was based on singly charged synthetic

466

homopolymer [PEO + 1Na+]1+ complexes leading to unambiguously known, spherically

467

shaped calibrating substances. These singly charged calibrating ions are able to provided

468

improvements on prediction bands and uncertainties during the CCS determination of

469

singly charged and multiply charged ions. [PEO + 1Na+]1+ calibrating ions allowed a

470

controlled calibration procedure of the measured values into CCS or K0 values, that

471

ideally should be independent of the density parameter of the calibrating ions.

472

The increased number of calibrating substances is spread over a large range of the

473

calibration plot axes. This avoids the requirement of higher charged species as calibrating

474

substances which increase the error bars on the calibrated values. Additionally, in the

475

case of the TIMS setup, the calibration procedure can now be performed regardless of the

476

TIMS voltage ramps to improve the instrumental resolving power.

21 /32



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

477

Given the little CCS or K0 value dispersity of synthetic homopolymers, the calibration fit

478

quality improved when using synthetic homopolymer calibrants and yields largely

479

decreased 95% prediction bands. This translates into diminished CCS or K0 errors due to

480

the calibration process, i.e. the interval of uncertainty on the calibrated values. This

481

allows for the first time to confidently extract CCS values extrapolated beyond the

482

calibration fit range.

483

Consequently, the focus of IM analyses on improved higher resolution commercial

484

instruments can now shift towards measuring the actual CCS or K0 errors, meaning the

485

peak width of an IM measurement57.

486

The more general concept of calibrating substance choices in real-world context was

487

discussed as well. In reality, the calibration plots are not fully independent of the nature

488

of the calibrating substances. Singly charged PEO homopolymers constitute appropriate

489

calibrating substances for peptide analyses, providing improved accuracy and trueness of

490

the measured CCS values because their density parameters (CCS/mass ratios) matched

491

very well. The choice of the appropriate singly charged synthetic homopolymer to be

492

used as calibrating substance should in fact be based on the density parameter which can

493

be extracted by fitting CCS versus mass plots and will be the subject of a future paper.

494

The general concept of an iterative calibration procedure based on singly charged

495

homopolymer calibrating substances, sampling the density parameters with e.g. pre-

496

established tabulated density values, was suggested.

497 498

Acknowledgments

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499

The authors thank the F.R.S.-FNRS for the financial support (Jean R. N. Haler and

500

Philippe Massonnet are F.R.I.A. doctorate fellows). Prof. Philippe Dugourd, Dr. Fabien

501

Chirot and Dr. Luke MacAleese (Université de Lyon) are thanked for the access to the

502

drift tube instrument and for the helpful discussions on this paper. Bruker is

503

acknowledged for their TIMS instrument and software support.

504 a.

b.

c.

505 506

Figure 1: 1.a. and 1.b. represent the Collision Cross-Section (CCS) calibration curves

507

generated for a T-Wave IM setup (equation 1). The reduced N2 CCS (Ω’) values are

508

plotted as a function of the corrected drift time (dt”) values measured in N2 on the T-

509

Wave instrument. Figure 1.a. uses the tryptic digest values of BSA described in

510

literature34 to calculate Ω’ values. Figure 1.b. uses DT-measured values of [PEO +

23 /32



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

511

1Na+]1+ as Ω’ reference values. In both plots, the calibration fits are represented in black,

512

the 95% confidence bands are shown in blue and the 95% prediction bands are

513

represented in red. The calibration equations with their respective fit parameters and their

514

95% prediction band-deduced errors on the coefficients are depicted in each figure.

515

Figure 1.c. plots the largest expected CCS errors as a function of the Degree of

516

Polymerization (DP, number of polymerized monomer units in the polymer chain) of

517

PEO complexes (1 to 4 sodium cations). The largest expected errors are calculated from

518

the 95% prediction bands yielded from the tryptic digest of BSA calibration (in red) and

519

the [PEO + 1Na+]1+ calibration (in red).

520 a.

b.

c.

521

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Page 24 of 32

Page 25 of 32

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522

Figure 2: 2.a. and 2.b. represent the reduced mobility (K0) calibration curves generated

523

for a TIMS setup (equation 2). The N2 reduced mobility (K0) values are plotted as a

524

function of the inverse of the elution voltage (1/Ve) values measured in N2 on the TIMS

525

instrument. Figure 2.a. uses the Agilent Tune Mix substances16 to calculate K0 values.

526

Figure 2.b. uses DT-measured values of [PEO + 1Na+]1+ as K0 reference values. In both

527

plots, the calibration fits are represented in black, the 95% confidence bands are shown in

528

blue and the 95% prediction bands are represented in red. The calibration equations with

529

their respective fit parameters and their 95% prediction band-deduced errors on the

530

coefficients are depicted in each figure. Figure 2.c. plots the largest expected K0 errors as

531

a function of the Degree of Polymerization (DP, number of polymerized monomer units

532

in the polymer chain) of PEO complexes (1 to 4 sodium cations). The largest expected

533

errors are calculated from the 95% prediction bands yielded from the Agilent Tune Mix

534

calibration (in red) and the [PEO + 1Na+]1+ calibration (in red).

535 a.

b.

536 537

Figure 3: 3.a. represents the DT N2 drift time evolutions of PEO-sodium complexes

538

bearing 1 to 4 cations for several polymer chain lengths (~DP 8 to 70). Figure 3.b.

25 /32



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

539

represents the comparison of the drift time corrections (t0) of a DT (black markers) and a

540

T-Wave (red markers) IM setup. The DT t0 values are obtained experimentally whereas

541

the T-Wave t0 values are obtained mathematically (see equation SI2).

542 a.

b.

543 544

Figure 4: 4.a. represents N2 Collision Cross-Sections (CCS) of peptides provided by a

545

tryptic digest of BSA plotted as a function of the mass. The DT-obtained reference values

546

are represented in gray, the TIMS PEO-calibrated values in red and the Agilent Tune

547

Mix-calibrated16 values in blue. The T-Wave values calibrated by the PEO complexes are

548

represented in green. Figure 4.b. plots the relative percentage of the difference between

549

the DT CCS reference values and the TIMS calibrated CCS values (equation 5; PEO

550

calibration in red and Agilent Tune Mix calibration16 in blue). The dotted lines represent

551

the average percentages for the different charge states for each of the calibrations (color-

552

coded).

553

26 /32


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a.

b.

554 555

Figure 5: 5.a. represents N2 reduced mobilities (K0) of PEO-sodium complexes bearing 1

556

to 4 cations plotted as a function of the Degree of Polymerization (DP, number of

557

polymerized monomer units in the polymer chain). The DT-obtained reference values are

558

represented in gray, the TIMS PEO-calibrated values in red and the Agilent Tune Mix-

559

calibrated16 values in blue. Figure 5.b. plots the relative percentage of the difference

560

between the DT K0 reference values and the TIMS calibrated K0 values (equation 5; PEO

561

calibration in red and Agilent Tune Mix calibration16 in blue). The dotted lines represent

562

the average percentages for the different charge states for each of the calibrations (color-

563

coded).

564 565 566

For TOC only CCS error

K0 error

cm2V-1s-1

Å2

Other Calibrations Polymer IM Calibration DP

DP

567 568

27 /32



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Comprehensive Ion Mobility Calibration: Poly(ethylene oxide) Polymer

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