Recommendations for Reporting Ion Mobility
Here we present a guide on ion mobility mass spectrometry experiments, which covers both linear and nonlinear methods: what is measured, how the measurements are done, and how to report the results, including the uncertainties on mobility and collision cross section values. The guide aims to clarify some possibly confusing concepts, and the reporting recommendations should help researchers, authors and reviewers to contribute comprehensive reports, so that the ion mobility data can be reused more confidently. Starting from the concept of the definition of the measurand, we emphasize that (i) mobility values (K0) depend intrinsically on ion structure, the nature of the bath gas, temperature, and E/N, (ii) ion mobility does not measure surfaces directly, but collision cross section (CCS) values are derived from mobility values using a physical model, (iii) methods relying on calibration are empirical (and thus may provide methoddependent results) only if the gas nature, temperature or E/N cannot match those of the primary method. Our analysis highlights the urgency of a community effort towards establishing primary standards and reference materials for ion mobility, and provides recommendations to do so.
I. Introduction<!>II. Definitions<!>II.1. Definition of the measurand in ion mobility<!>II.2. Arrival time distributions (ATD)<!>II.3. Mobility K and reduced mobility K 0<!>𝐾<!>II.4. Collision cross section (CCS or )<!>II.5. Notation for mobilities and collision cross sections<!>II.6. Recommended units and values of constants<!>𝑁 𝑁<!>III. Classification of IM-MS methods<!>III.1.1. Linear methods<!>III.1.2. Nonlinear methods<!>III.2. Types of output: IM-MS data, K 0 values, and CCS values<!>III.3.1. Primary vs. secondary methods<!>III.3.2. Are some secondary methods empirical methods?<!>IV.1. Absence of primary standards for ion mobility<!>IV.2. Uncertainty associated with published values determined by the primary (DTIMS) method<!>IV.2.2. Combined standard uncertainty<!>IV.2.3. How do values obtained from different laboratories currently compare?<!>IV.3. Recommendations for choosing future reference materials<!>V. Reporting ion mobility measurements V.1. Sample preparation and ion preparation (steps 1-2)<!>V.2. Experimental parameters (step 3) for linear methods<!>V.2.1. Electric field<!>V.2.1.1. Drift tube IMS<!>V.2.1.2. Travelling wave IMS<!>V.2.1.3. Trapped IMS<!>V.2.1.4. Differential mobility analyzers<!>V.2.2. Gas nature and pressure (or gas composition and partial pressures)<!>V.2.2.1. Drift tube IMS<!>V.2.2.2. Travelling wave IMS<!>V.2.2.3. Trapped IMS<!>V.2.2.4. Differential mobility analyzers<!>V.2.3. Temperature<!>V.3.1. Gap dimensions<!>V.3.2. Buffer gas properties V.3.2.1. Composition<!>V.3.2.2. Pressure<!>V.3.2.3. Temperature<!>V.3.3. Gas flow and residence time<!>V.3.4. Asymmetric waveform<!>V.3.5. Compensation voltage<!>V.3.6. FAIMS operating modes<!>V.4. Reporting IM-MS data (step 4) V.4.1. m/z range<!>V.4.2. Ion mobility spectra<!>V.4.3.1. Expressing voltages in terms of field strength<!>V.4.3.2. Complete E C (E D ) curves<!>V.4.3.3. Extracting a(E) functions from FAIMS data<!>V.4.3.4. Using FAIMS data to reconstruct absolute K(E) functions<!>V.4.3.5. Ion types<!>V.4.3.6. Relating ion types to K(E) functional forms<!>V.5.2. Primary (DTIMS) method<!>V.5.2.1. K 0 values<!>V.5.2.2.1. Propagation of uncertainty on K0 from the linear regression<!>V.5.2.2.2. Standard deviation from technical replicates (independently repeated experiments)<!>V.5.2.2.3. Estimation of the uncertainty associated with a single measurement<!>V.5.2.3. CCS values and their uncertainties<!>V.5.3.2. Calibration curves<!>V.5.3.3. Quality control after calibration<!>V.5.4.2. Evaluation of uncertainty<!>V.5.5.2. Calibrant choice for TWIMS<!>V.5.6. TIMS<!>V.5.6.1. Calibration from experiments at different scan rates<!>V.5.6.2. First order calibration<!>Transferrable calibration<!>V.5.7. DMA<!>VI. Conclusions and outlook
<p>The ion mobility spectrometry (IMS) technique measures how ions drift through a region filled with a buffer gas, under the influence of an electric field. IMS was first reported in 1898 (Zeleny, 1898), approximately 15 years before mass spectrometry (MS) (Thompson, 1912), with both analytical methods originating in the Cavendish laboratory at Cambridge University. The coupling of IMS to MS for analytical purposes dates back to 1970 (Cohen & Karasek, 1970). In IMS-MS, the ions are detected at the end, but are successively separated by two different principles: IMS then MS. IMS is often presented as an additional dimension of separation added to MS. The abbreviation "IM-MS" (ion mobility mass spectrometry) is also commonly encountered; it is equivalent to "IMS-MS" and both are acceptable.</p><p>In 2006, the availability of IM-MS instrumentation from a major MS manufacturer marked the onset of a growing use of IM for the separation, identification, and structural characterization of analytes across diverse fields of science. These include: ionic clusters (Bowers et al., 1993;Von Helden et al., 1993;Dugourd et al., 1998;Hudgins et al., 1999;Gilb et al., 2002), catalysts (Czerwinska et al., 2016;Greisch et al., 2018), supramolecular complexes (Li et al., 2011;Ujma et al., 2012;Warzok et al., 2018;Wollschlager et al., 2018), small organic molecules including drugs (Campuzano et al., 2012;Hines et al., 2017), lipids (Hinz, Liggi & Griffin, 2018;Zheng, Smith & Baker, 2018) and other metabolites (Far et al., 2014;Mairinger, Causon & Hann, 2018;Zhang et al., 2018), glycans (Hofmann & Pagel, 2017;Chen, Glover & Li, 2018;Morrison & Clowers, 2018), peptides (Valentine et al., 1998;Wu et al., 2000;Harvey, Macphee & Barran, 2011), proteins (Clemmer, Hudgins & Jarrold, 1995;Jarrold, 1999;McLean et al., 2005), synthetic polymers (Trimpin & Clemmer, 2008;Morsa et al., 2014;Wesdemiotis, 2017), biomolecules (Clemmer & Jarrold, 1997;Fenn & McLean, 2008) and biomolecular complexes (Benesch & Ruotolo, 2011;Liko et al., 2016;Ben-Nissan & Sharon, 2018). However, as IM-MS instruments now commercially available from different manufacturers operate according to different principles of ion mobility separation (May & McLean, 2015), this introduces complexity-and potentially confusion-amongst practitioners and readers. The increasing rate at which IM data are being generated has established the need for a community-coordinated set of recommendations to report IM-MS results. The present article is a first step to unify the community support in this respect.</p><p>In IM separations, mobility values (K or K0) can be used akin to retention times in chromatographic analyses (with K0 being more invariant). Today, standalone IMS is widely used for defense (Eiceman & Stone, 2004), security (Ewing et al., 2001) and environmental (Zheng et al., 2017) applications. Further, thanks to the availability of IM-MS instruments, scientists active in the fields of "omics" have also begun to adopt IMS as an additional separation dimension (May, Gant-Branum & McLean, 2016;Barran & Baker, 2018). Furthermore, mobility values, or a derived property such as the ion-neutral collision cross section (CCS) can be calculated from structural models of ions. Ion mobility measurements can hence serve a two-fold purpose; they can add a separation dimension that is partly orthogonal to mass spectrometry, and can be used for structural elucidation. Structural inferences based on comparing experimental CCS values with those calculated from 3D models have become increasingly prominent in structural biology (Politis et al., 2010;Konijnenberg, Butterer & Sobott, 2013;Thalassinos et al., 2013;Marklund et al., 2015;Ben-Nissan & Sharon, 2018), structural chemistry (Ujma et al., 2012;Surman et al., 2016) and physical chemistry (Wyttenbach et al., 2014), For these reasons, we devoted special attention to define K0 and IM-derived CCS values, and to clarify their influence quantities. There are other methods than ion mobility spectrometry to determine experimental collision cross sections in a more direct way, for example by monitoring the loss of ion signal due to collisions (Covey & Douglas, 1993;Chen, Collings & Douglas, 1997;Anupriya, Jones & Dearden, 2016;Anupriya et al., 2017;Dziekonski et al., 2017;Elliott et al., 2017;Sanders et al., 2018).</p><p>However, these methods to determine collision cross sections are not based on ion mobility measurements, and will not be covered here.</p><p>Ion mobility spectrometry is a measurement science, and should thus be performed and reported according to the internationally recognized best practices in metrology, including traceability to the international systems of units, use of standards, and evaluation of measurement uncertainty. This critical review devoteds particular attention to the uncertainty (JCGM, 2008; EURACHEM/CITAC, 2012) associated with K0 and CCS values. Over the years, several groups have published tables of CCS values (Wyttenbach, Von Helden & Bowers, 1996;Hoaglund et al., 1997;Shelimov et al., 1997;Valentine et al., 1997;Valentine, Counterman & Clemmer, 1997;Counterman et al., 1998;Hoaglund et al., 1998;Wyttenbach, Bushnell & Bowers, 1998;Henderson et al., 1999;Henderson et al., 1999;Valentine, Counterman & Clemmer, 1999;Fenn et al., 2009;Bush et al., 2010;Bush, Campuzano & Robinson, 2012;Campuzano et al., 2012;Salbo et al., 2012;Forsythe et al., 2015;May, Morris & McLean, 2017), which are widely used as input values for calibrating instruments from which CCS values cannot be obtained directly.</p><p>One significant source of confusion is that it is difficult to interpret differences in output values obtained on different instrumental platforms or when using different sets of calibrants, or different sets of values for the same calibrant. To establish whether differences are within the uncertainty of the measurement, or have a physical meaning (e.g., temperature or field effects) or a chemical meaning (e.g., different ion structures), one must first know the uncertainty associated with the calibrant values. Unfortunately, the lack of a common approach in reporting all details associated with values makes it difficult to establish the appropriate level of confidence in each value. Here we used international guidelines (Guideline to the expression of Uncertainty in Measurement or "GUM" (JCGM, 2008) and Quantifying Uncertainty in Analytical Measurement or "QUAM" (EURACHEM/CITAC, 2012)) to provide recommendations on how to report values and their associated uncertainty.</p><p>Another objective of this document is to clarify the data reporting across different instrumental platforms, with the aim of harmonizing them and enable cross-platform comparisons. The metrology considerations will lead us to underline a few "do's and don'ts", but besides these, the recommendations will focus on how to report the data, rather than on how to obtain and treat the data. For the latter, consult the primary literature and reviews cited throughout the paper. We will however outline the scientific rationale that underlies the recommendations, and should underlie any future effort towards establishing minimum information standards, data formats which would update the JCAMP-DX format proposed for standalone IM (Baumbach et al., 2001), and shared databases of experimentally derived values related to IM. Finally, we aim to guide authors, readers and reviewers on how to prepare comprehensive supporting information for IM-MS reports.</p><!><p>The present guidelines are intended to be applied primarily to the determination of ion mobility values and of CCS values from IM-MS experiments. It should be noted that there are other ways to determine collision cross sections, for example using single-collision scattering experiments, but that the definition of these collision cross sections is slightly different (see below). The present recommendations focus exclusively on IM experiments, wherein ions are directed by an electric field and experience many collisions with a background gas.</p><!><p>Incomplete definition of the measurand (i.e. what is measured) is itself a source of uncertainty.</p><p>Unlike mass, which is a unique property of a molecule, an ion's mobility and the ion-neutral CCS depend not only on the composition and structure of the analyte, but also on other factors.</p><p>For example, "the CCS of aniline" is vague and does not fully convey the context and conditions under which a measurement is made, such that many values can match this definition of the measurand. In contrast "the ion-neutral CCS determined from the position of the apex of the most intense mobility peak of the [M+H] + ion generated by electrospray ionization of aniline prepared at 50 ppm in a 49.5/49.5/1 (v:v) water/acetonitrile/formic acid solution in the softest possible source conditions (sampling cone of 10 V on instrument X), and measured in 4 mBar nitrogen drift gas at 298 K under an electric field of 13 V/cm" is more precise and useful for interpreting the reported value. For aniline (Attygalle, Xia & Pavlov, 2017) and other small molecules that can form protonation isomers (tautomers), all these details matter (Steill & Oomens, 2009;Warnke et al., 2015;Boschmans et al., 2016;Xia & Attygalle, 2016;Xia & Attygalle, 2017). However, such textual description would be unpractical to implement in papers reporting ion mobility mass spectrometry measurements. We will thus provide here a concise notation, and a list of relevant parameters to report in the supplementary information of papers.</p><p>First, this example highlights that the property being measured is not an absolute, constant attribute of the analyte, but refers to a population of ions coming from a sample containing the analyte. The whole chain of events from the original sample to ion detection could potentially influence the result. These guidelines also recommend documenting the sample preparation, ion preparation (ion formation and desolvation/declustering, typically done in the source region of the spectrometer), ion transfer conditions (to account for all post-ionization transformations due to ion-molecule reactions and/or to ion activation), ion packet preparation before introduction into the IM device, and ion transfer conditions from the IM device to the detector at which the arrival time is measured.</p><p>Second, the measurement is not made on a single ion, but on an ensemble (population) of ions.</p><p>Depending on the ion preparation, on the temperature in the IMS device and on the time spent in the device, the mobility and CCS properties of the ensemble can vary. The arrival time distribution (ATD) conveys information on how homogeneous or heterogeneous the ensemble is.</p><p>Section II.2 further elaborates on the importance of ATDs for the definition of the measurand.</p><p>Finally, the gas composition, temperature, pressure and field strength also influence the mobility of an ion, as explained in sections II.3 and II.4. Table 1 clarifies the parameters that should be part of the definition of the measurand.</p><!><p>Each ion takes a defined time to traverse the mobility region and, because the measurement is performed on a population of ions, a distribution of arrival times is obtained. The "arrival time distribution" (ATD) is defined as a 2D graph of the number of counts detected as a function of the time at which they arrive at a specific location in the instrument (comprising a drift time plus a time spent outside the drift region). Drift tube and travelling wave IM devices are time dispersive. In scanning devices (e.g. TIMS and DMA), a voltage is ramped as a function of time and the analyzer primarily measures the number of ion counts as a function of a time or scan number. We define ATDs in this broader sense. The term "mobilogram" is sometimes encountered in the literature reporting TWIMS data; but the terminology is not widely adopted and "arrival time distribution" or "ion mobility spectrum" should be preferred.</p><p>For a homogeneous population of ions, the width of ATD is primarily controlled by ion diffusion, Coulomb repulsion (space charge), the (temporal or spatial) width of ion injection pulse, the (temporal or spatial) width of detector acquisition window, and electric field homogeneity. This nominal width can be predicted theoretically (Siems et al., 1994;Wyttenbach, Von Helden & Bowers, 1996;May et al., 2015), or determined experimentally from structurally rigid (e.g., C60) or homogeneous ions (Jeanne Dit Fouque et al., 2015;Kune, Far & De Pauw, 2016), although this can be hard to achieve for large ions. However, the experimental ATD can be broader than predicted. Provided that the contribution of instrumental factors to the ATD has been properly established, additional information may be cautiously inferred from ATD widths that significantly deviate from the ideal. One reason is that the ion population comprises multiple structures (in the broad sense, i.e. different shapes, different charge isomers, and/or different charges), each having different mobility and CCS values. In some cases, multiple peaks are discernable. Alternatively, the ATD width can be increased by space charge (in instances where the ion concentration is sufficiently high) as well as by structural dynamics and reactions of the ions during transit in the gas phase.</p><p>If the measurand is defined as the entire population of ions generated from the sample in given conditions, if the peak is broader than predicted for a population of ions with a single structure, then the distribution of values satisfying this definition of the measurand is also broad. For proteins, the full-width at half-maximum of the ATDs can be 10% of the centroid value (Uetrecht et al., 2010;Laszlo, Munger & Bush, 2016), and up to 20% for intrinsically disordered proteins (Beveridge et al., 2014). However, if the measurand is defined as "the mobility or CCS associated with the centroid of the ATD of the ion population" (or any other precisely defined attribute of the distribution), the uncertainty on that value will be smaller.</p><p>The present recommendations for reporting mobility and CCS values, and their associated uncertainty, will here focus on reporting the values associated with the centroid of each distinguishable peak of the ATD. However, the above examples illustrate that, for structural characterization, both the representative value and the shape and width of the ATD are worth reporting. We will provide specific guidance accordingly.</p><!><p>In a device filled with a homogeneous gas and under the influence of a weak electric field E (E = ΔV/L), the ion's mobility (K) is defined as the ratio between the steady-state net ion/gas relative velocity (vd = L/td) and the applied electric field E (Eq. 1).</p><!><p>(1)</p><p>The mobility K provides information on the range of ion-neutral interactions experienced by an ion as it traverses through a buffer gas. In a highly simplified definition, K thus depends on the collision frequency of the ion with gas molecules. This frequency depends on the gas numberdensity (N = number of gas molecules per unit volume), and is thus related to the gas pressure (p)</p><p>and temperature (T). For this reason, more useful for inter-laboratory comparisons is the reduced mobility (K0), which is calculated from K by applying the following correction factor:  , 1997). This illustrates that specifying the constants and conventions used is also crucial for data reuse: failing to specify whether STP or NTP was used (i.e., which value of p0 was used) introduces an uncertainty of 1.3 % in the definition of K0.</p><p>It is important to note that K0 still depends on the temperature T, on E/N, and on the nature of the buffer gas:</p><p>1) The temperature influences the nature of the ion-neutral interaction (long-range interactions vs. hard-spheres collisions), which can be approximated using Lennard-Jones potential functions (Wyttenbach et al., 1997) and the structure (or conformational ensemble) of the ion (Mao et al., 1999;Kinnear, Hartings & Jarrold, 2001;Gidden & Bowers, 2002;Kinnear, Hartings & Jarrold, 2002). In polarizable gases (CO2, SF6, air,…), the temperature influences the formation of transient clusters and hence the reduced mobility as well (Karpas, Berant & Shahal, 1989).</p><p>2) The reduced ion mobility also depends on the ratio E/N:</p><p>Linear methods in the low-field limit assume that E/N is low enough so that K0 = K0(0), whereas nonlinear methods exploit the E/N dependence (see section III). It is presently unclear how low E/N must be for the linear regime to remain valid (Hauck et al., 2017), but because for future data exploitation it is better to err on the side of providing too many details than too few, it is recommended to report an estimate of E/N (or more conveniently, E, p and T) at which the experiments were carried out, even if it is thought to be in the low-field limit.</p><p>3) Finally, the nature of the buffer gas influences the resisting force because it influences the nature of the ion-gas interaction (gas size and polarizability) and the elasticity of collisions.</p><p>In summary, the temperature, the gas composition, and E/N should be part of the definition of the measurand in ion mobility. In practice, the level of detail and precision to which the measurand should be defined depends on whether the definition of the measurand is the limiting factor, compared to measurement uncertainty. For example, Hill's group recently reported on an instrument capable of measuring K0 values with 0.1% precision (Hauck et al., 2017), which revealed the necessity of defining the measurand more precisely in terms of temperature range, gas composition (in particular, water humidity) and E/N range (Hauck et al., 2018). The gas composition was the major contributor to changes in K0. For many applications, it will probably be sufficient to state the gas identity and purity, a temperature range spanning no more than a couple of Kelvin (achievable in a temperature-controlled laboratory), and to assume that K0 is independent of E/N. Providing the actual ranges and values will further help the reader to assess and interpret the results in light of the above discussion.</p><!><p>To calculate the experimental CCS value from the mobility K or reduced mobility K0, most procedures use the mathematical function provided by the fundamental low-field ion mobility equation (Revercomb & Mason, 1975):</p><p>µ is the reduced mass of the ion-gas pair: µ = mimg/(mi+mg), where mi is the mass of the ion and mg is the mass of the gas. The relationship between CCS and K0 depends on the temperature. To</p><p>give an idea of order of magnitude of the combined effect of the ion-neutral interactions plus the temperature dependence of Eq. ( 4), we can examine the trajectory model calculations for C60 (no possible conformational change) (Young & Bleiholder, 2017). The simulations give a relative CCS change of 0.13% per Kelvin around 300 K for C60 + in nitrogen (0.07% in helium).</p><p>Because Eq. ( 4) is derived from the equilibrium of forward acceleration of the ion in the electric field and the opposing resisting force due to collisions with the buffer gas (momentum transfer to the buffer gas), CCS represents a momentum transfer cross section Ω. Historically, the term collision cross section was used in the context of a hard sphere collision model (Millikan, 1923) and is strictly speaking not entirely appropriate for the mobility-derived cross section. The cross section based on the size of colliding spheres can differ from Ω by a factor of up to 1.4, or be identical to Ω in other cases, depending on the nature of the collisions (Wyttenbach, Bleiholder & Bowers, 2013). Nevertheless, CCS is now routinely used to describe the quantity obtained in Equation ( 4). Thus, although the term collision cross section (symbol: CCS) is accepted, it should however be understood that it reflects a momentum transfer cross section (symbol: Ω).</p><p>Both symbols are acceptable. We will use CCS in the remainder of the text.</p><p>It is important to note that the primary output of the measurement is the mobility (K), that the experimental CCS is a quantity derived from K via a mathematical model. In other words, ion mobility measures mobilities, not surfaces. A mathematical model such as Eq. ( 4) is a compromise based on our best understanding of the physics of the phenomenon, and on some simplifications. Approximations underlying Eq. ( 4) include that the electric field is zero (i.e. the kinetic energy imparted by the field is negligible compared to the thermal kinetic energy), which is fundamentally not the case in a real IM experiment (Siems, Viehland & Hill, 2016). Thus, the use of Eq. ( 4)-or any mathematical model-in the data treatment procedure constitutes also a possible source of bias. At the current state-of-the-art we do not yet know the sign and magnitude of the correction factor that could improve the accuracy of the estimated value, although progress is being made in this respect (Siems, Viehland & Hill, 2016). In principle both signs may be encountered, as the K values increase with increasing E/N for some ion/gas combinations (type A or B in FAIMS, see below) and decrease for others (type C) (Barnett et al., 2000;Shvartsburg, 2009). We recommend that every equation and mathematical model used in the data treatment procedure should be stated clearly. If a mathematical model other than Eq. ( 4) is used, it must be fully described.</p><p>Another consequence of the above is that, while ion mobility (K or K0) values can be traced back to the SI (its SI base unit is the A s² kg -1 , see</p><!><p>As discussed above, for a given ion structure, K0 (and thus the CCS derived from it) depends on the gas composition, on the temperature, and on E/N. Besides a full description in the materials and methods section, it is desirable to include some metadata about gas, temperature and E/N in the K0 and CCS notation themselves. It is also desirable to have an explicit notation for values obtained by the primary method, versus from secondary methods or empirical methods. As discussed elsewhere (Gabelica & Marklund, 2018), the range of fields used in so-called linear methods can differ enough so that effective temperatures higher than the gas temperature may be reached in TWIMS, TIMS, or in DTIMS at high fields. Further, K0 and CCS depend on the population distribution of ion structures sampled in the experiment, which can be different for different experimental setups. Thus, although the principle of the measurement technique should not have an effect on the CCS per se (see also section III.3.2), specifying the instrument used currently makes sense. In a compendium of collision cross section values, the McLean group (May, Morris & McLean, 2017) recommended using the nomenclature introduced by the Barran group (Pacholarz & Barran, 2015), which includes the method type as a superscript and the drift gas, or drift gas equivalent for calibrated values, as subscript, giving notations such as DT CCSN2</p><p>and TW CCSN2, for CCS values obtained using a drift tube instrument with nitrogen gas and a traveling wave instrument using nitrogen gas, respectively.</p><p>Furthermore, we recommend an explicit notation to distinguish primary values (obtained without calibration) and secondary values (obtained following calibration). This is important because on the one hand not all DT measurements have the qualities of a primary method, and on the other hand attempts to determine CCS values directly (without calibration) from TWIM data are emerging (Mortensen, Susa & Williams, 2017;Richardson, Langridge & Giles, 2018). One way to specify this in the notation is to include the notation "1ry" (primary) explicitly when appropriate, e.g. DT,1ry CCSHe. This would single out the primary values, which are of special interest for calibrating secondary methods. For secondary methods, if gas 1 is the (predominant) drift gas in which the measurement was made, and gas 2 is the drift gas in which the calibrant values were obtained, we suggest using the notation: TW CCSgas1→gas2. It should also be noted that mobility values for gas mixtures can be determined and related to the partial pressures of the individual gases comprising the mixture and can be related through Blanc's Law (Revercomb & Mason, 1975).</p><p>For DT data, the buffer gas temperature is at present not included in the notation. Most measurements are performed in ambient conditions, i.e. usually between 298 and 300 K. If temperature-variable instruments (von Helden, Wyttenbach & Bowers, 1995;Dugourd et al., 1997;Mao et al., 1999;Wyttenbach, Kemper & Bowers, 2001;May & Russell, 2011;Ujma et al., 2016) become more widespread, or if measurement uncertainty becomes small enough that the exact temperature matters and the notion of "ambient conditions" is no longer sufficient, then introducing the temperature in the notation will become useful. This could come as an index next to the gas, e.g.: DT,1ry CCSHe,298.</p><!><p>Table 2 gives the units of each term used in Eqs. (14), in SI base units, in derived SI units, and in commonly used non-SI units, as well as the values of the constants used in Eqs. (14)</p><p>according to the 2014 CODATA (Mohr, Newell & Taylor, 2016). Although these are not SI units, it is customary to report K0 values in cm² V -1 s -1 and CCS values in Å² or nm². For practical reasons, using these units will be continued. Every report should specify the unit associated with each value.</p><p>Literature values may sometimes have been determined using older values of constants, or using fewer significant digits. Note also that a revision of the international system of units (SI) will take place in 2018 (BIPM, 2018)</p><!><p>, see T, p and N0</p><!><p>Workflows differ according to the principle of measurement, linked to the type of instrument hardware (see Figure 1), and according to the objective of the measurement.</p><!><p>In linear methods, K0 is assumed to be independent of the electric field. The measured property (usually the transit time) is thus assumed to be linearly proportional to the field. Linear methods include:</p><p>-DTIMS (drift tube ion mobility spectrometry) in which ions are directed through a stationary gas by a constant and homogeneous electric field E (Eiceman & Karpas, 2005). Radiofrequency fields can be superimposed on the drift field to confine ions along the axis separation, which is used in radio-frequency confining drift cells (Allen & Bush, 2016;Allen et al., 2016). E/N values for drift tube typically vary from 1 to 15 Td (1 Td = 10-21 V m²).</p><p>-TWIMS (travelling wave ion mobility spectrometry), in which ions are directed through a stationary gas by a sequence of symmetric potential waves continually propagating through the drift region (Giles et al., 2004). In TWIMS, the ions are subjected to varying E/N, with peak values reaching 50 to ~160 Td (Giles et al., 2010;Gabelica & Marklund, 2018).</p><p>Structures for lossless ion manipulation (SLIM) can be used to implement travelling waves (Tolmachev et al., 2014) and thus perform TWIMS separations (Deng et al., 2017;Ibrahim et al., 2017).</p><p>-TIMS (trapped ion mobility spectrometry), in which ions are held in place against a moving gas with an electric field (Fernandez-Lima et al., 2011). In TIMS operation, multiple isomers/conformers are trapped simultaneously at different E values resulting from a voltage gradient applied across the IMS tunnel region. In TIMS, the typical E/N is 45-85 Td (Gabelica & Marklund, 2018). Ions are then released by decreasing the electric field in stepwise decrements. Each isomer/conformer eluting from the TIMS cell can be described by a characteristic elution voltage (Ve), which is connected to the 1/K0 value (see section V.5.4).</p><p>-DMA (differential mobility analyzers) in which ions are separated spatially based upon electrophoretic migration in one direction (at mobility dependent speeds) and fluid flow driven migration in an orthogonal direction (with all ions at the same speed) (Reischl, 1991).</p><p>Only ions of a prescribed mobility traverse from the inlet to the outlet of a DMA. DMA is operated in the low-field limit only (typical E/N below 20 Td (Hogan & Fernandez de la Mora, 2009)), which differentiates it from all nonlinear methods described below.</p><!><p>Differential Ion Mobility Spectrometry (DIMS) exploits the fact that the mobility (K) of any ion in any gas depends on the electric field intensity (E) to identify chemical species and separate their mixtures based on the difference between K values at two or more E levels (or ranges thereof) (Guevremont, 2004). It is a nonlinear IMS method in the sense that the measured perturbation in media (dynamics of the ion swarm) is not linear with respect to the magnitude of perturbing force (applied field), (Shvartsburg, 2009).</p><p>Except for the cases of electric dipole alignment, the K values depend on E via normalized mobility (E/N), see Equation (3). As varying E is a lot more practical, precise, and rapid than varying N, all present systems involve varying E. Experimentally, E is temporally varied in a periodic asymmetric waveform (i.e., the segments of opposite polarity are not mirror images).</p><p>Hence the technique is alternatively called Field Asymmetric Waveform Ion Mobility Spectrometry (FAIMS). The shape of the enclosure (gap) where the field is established and separation is performed affects the field homogeneity, which is critical to DIMS system performance (Guevremont & Purves, 1999). For historical reasons, the systems with planar and curved gaps have preferentially been called Differential IMS and FAIMS, respectively. That distinction has no basis outside of dated historical context and is discouraged. To unify the associated literature and simplify its search, we suggest mentioning both Differential IMS and FAIMS in the abstract and/or introduction of publications as an interim measure until one term is settled upon. The term Differential Mobility Spectrometry (DMS) is often encountered too, primarily by users of the commercial SCIEX SelexION® (Campbell, Le Blanc & Kibbey, 2015).</p><p>A further term "Ion Mobility Increment Spectrometry" (IMIS) is common in the Russian-origin literature (Buryakov, 2004). Thus, the four acronyms (DIMS, DMS, FAIMS and IMIS) designate the same principle of measurement. Below we will use "FAIMS" for conciseness.</p><!><p>A typical ion mobility mass spectrometry experiment involves up to six steps (Figure 2): (1) sample preparation, (2) ion preparation (i.e., ionization, transfer and storage), (3) IM-MS measurement, (4) peak attribution, (5) mobility (K or K0) determination and (6) CCS determination. Steps 1-3 involve carrying out the experiments and steps 4-6 involve data processing.</p><p>Steps 1, 2 and 4 are common to all mass spectrometry experiments. Their reporting guidelines are thus largely inspired by similar guidelines for reporting proteomics experiments or mass spectrometry data in proteomics (Taylor et al., 2007) and glycomics (Struwe et al., 2016).</p><p>Step 3 is common to all ion mobility principles outlined above. For many applications which do not need mobility or CCS values, for example in separation sciences or discussion of changes in ion structure (rather than absolute values), reporting IM data consists of steps 1 to 4. We thus include specific guidelines for reporting either linear or nonlinear (differential) mobility experiments, for example in the form of arrival time distributions. The determination of mobility values (step 5) can be done at any electric field, but only via direct (not differential) methods. The CCS values (step 6) can only be determined from experiments operating-or assumed to be operatingwithin the low-field limit, i.e. with the linear methods.</p><p>We thus distinguish three types of reports, each having different scopes and constraints:</p><p>reporting IM-MS data (steps 1 to 4), reporting K0 values (steps 1 to 5) and reporting collision cross section values (steps 1 to 6). III.3. K 0 and CCS determination: methods of measurement</p><!><p>A primary method of measurement is defined (BIPM, 1995;Quinn, 1997;Milton & Quinn, 2001;Taylor, Kipphardt & De Bièvre, 2001) as "a method having the highest metrological qualities, whose operation can be completely described and understood, for which a complete uncertainty statement can be written in terms of the SI, and whose results are, therefore, accepted without reference to a standard of the quantity being measured" (BIPM, 1995). To be able to write a complete uncertainty statement, the operation of the method should be represented by a measurement equation. The determination of K0 by DTIMS satisfies this definition with the least uncertainties: the constant field makes it straightforward to calculate E from V/L (V m -1 ) and vd from td/L (s m -1 ) to obtain K0 (m² V -1 s -1 ). Only few instruments are conceived to measure drift times td directly (Hauck et al., 2018). However, most instruments measure the arrival time (tA) at a location further away from the end of the drift region. Additional mathematical operations are required to obtain td from the measured arrival time tA, but these are also traceable (see an example in section V.5.2.1). Thus, K0 determined using DTIMS from first principles are today considered as primary standards. The CCS (SI unit: m²) is then derived from K0 with a mathematical model such as Eq. ( 4), but the CCS is not what is primarily measured by DTIMS.</p><p>Secondary methods use calibration against some primary standards or primary methods. It is important to underline that not all DTIMS measurement methods are primary methods. Working with a reference compound in DTIMS is preferable if the accuracies of E, L, T and p needed to implement the primary method are insufficient, while high-quality reference values are available.</p><p>The DTIMS methods include (I) a direct measurement of drift time (the method is more common in portable IM instruments with 63 Ni radioactive ionization sources), (II) multi-field measurement of arrival times to deduce the drift time from a linear regression and determination of the pressure from an instrument reading, (III) multi-field measurement of arrival times and determination of the pressure using at least one reference compound, or (IV) single-field measurement of arrival time, which is then converted to K0 with a calibration function f determined using several reference compounds of known K0 (or, more generally, K0, mass and charge). Thus, DTIMS methods (I) and (II) are primary methods, whereas DTIMS methods (III) and (IV) require reference compounds.</p><p>For TWIMS and TIMS, in practice the K0 and CCS values are determined via an instrumental calibration function f determined using reference compounds. With TIMS (Bleiholder, 2016) and TWIMS (Giles et al., 2010;Mortensen, Susa & Williams, 2017;Richardson, Langridge & Giles, 2018), obtaining K0 without calibration may be achievable in principle, but the uncertainty associated with such approaches in development have not yet been fully evaluated. In DMA measurements, precise knowledge of the applied voltage, DMA dimensions, and fluid flow rates into the device can yield K0 values without the need for calibration. DMAs can be thus be used as a primary method of measurement; this approach has been shown accurate enough to examine the sizes of NIST certified polystryene latex size standard particles (Mullholland et al., 2006).</p><p>For extremely large, spherical ions, the CCS can be linked to the diameter. However, higher resolving power DMAs utilize high sheath flows (hundreds of liters per minute), hence in many instances reference compounds are used in DMA calibration (Ude & Fernández de la Mora, 2005), particularly for DMAs interfaced with mass spectrometers.</p><p>To summarize, in Figure 2, the gold color indicates the workflow allowing one to estimate K0</p><p>values and CCS values without using any reference compound (primary method of measurement). This workflow is currently routine in DTIMS only. The green color indicates the workflows using reference compounds (compounds of known K0 measured across multiple instruments and laboratories) to verify and/or calibrate the instrument. The calibration procedure differs for DTIMS, TWIMS or TIMS in the sense that the function f differs, but common principles can be applied.</p><!><p>An empirical method (EURACHEM/CITAC, 2012) is a method in which the measurand is defined by the measurement method. The measurand in ion mobility is defined by the ion structure, the gas, the temperature, and E/N. For a particular secondary method, if it is possible to place oneself in the exact same conditions of ion structure, gas, temperature and E/N as the primary method, then it is not an empirical method. However, this may not always be possible. If we take the example of TWIMS, although efforts have been made to construct RF-confining drift cells and fit them in a SYNAPT G1 (Bush et al., 2010) and G2 (Allen et al., 2016) to reproduce ion structures, gas and temperature conditions, TWIMS operates with inherently different E/N conditions than the RF-confining drift cell. Thus, the TWIMS measurement method is empirical, and may thus produce method-dependent results (the calibrant choice being part of the method) even after partial correction through calibration. The accuracy of calibrated mobilities and dependence on the travelling-wave method have been characterized for peptides (Bush, Campuzano & Robinson, 2012) and protein complexes (Zhong, Hyung & Ruotolo, 2011).</p><!><p>Primary measurement methods can serve to determine the values associated with primary standards (BIPM, 1995;Quinn, 1997), defined as "a standard that is designated or widely acknowledged as having the highest metrological qualities and whose value is accepted without reference to other standards of the same quantity" (BIPM, 1995) Primary standards serve to prepare certified reference materials (CRM). Then, according to recommended practice (EURACHEM/CITAC, 2012), any additional bias associated to another method should be estimated by comparing the results with those of a reference method or by analyzing an independent CRM as quality control. Unfortunately, there is not presently consensus for a primary standard compound and thus no reference material is currently available.</p><p>The initiation of a certification study on materials proposed as primary standards and on their associated mobility values is therefore urgent for our field. Meanwhile, we shall provide practical advice and recommendations in using the data currently available from the literature.</p><!><p>Multiple papers have reported CCS values determined with the primary method (reviewed for</p><!><p>A few studies provide a more detailed assessment of the combined standard uncertainty (Crawford et al., 2012;Stow et al., 2017;Hauck et al., 2018), based on proper propagation of the standard uncertainties on t, E (V/L), p and T. The work referenced above also devoted particular care to characterize V, L, p and T and their uncertainties with the appropriate technologies and measurement methods, not just by using instrument settings or read backs and ballpark estimates of the associated errors.</p><!><p>However, these approaches do not include an analysis of bias. The most appropriate way to assess trueness is to carry out a round robin test (an interlaboratory test performed independently-i.e., without knowledge of any expected value before submitting the resultsseveral times). After discussion to define consensus values, the compounds could then be used to manufacture reference materials, having fixed reference CCS values accepted by the entire IMS community ("IUPAC compliant"). However, such interlaboratory study has not been reported to date.</p><p>Meanwhile, information can be gleaned by comparing values obtained by different groups. For this paper, the groups of Bowers, Clemmer and Bush shared their experience in comparing CCS values obtained independently (Dugourd et al., 1997;Counterman et al., 1998;Bush et al., 2010;Dilger et al., 2012;Allen et al., 2016). The values found on different tube designs had a relative span most of the time of no more than 2%, and only in a few exceptions was 3%. The consensus is thus that primary values measured on different DTIMS platforms have a distribution characterized by a relative standard deviation (s.d.) of 0.5% (see Figure 3A). Note that the labs may have operated at slightly different ambient temperatures. Importantly, this distribution held true only provided that the same ion structures were measured. In practice, in individual publications, values are reported for a single instrument platform. In such case, the combined uncertainty can be evaluated by a type B approach (JCGM, 2008). Figure 3B shows that assuming for example triangular distributions with a 2% margin on each side is reasonable. With these assumptions, one can assign to published values a combined standard relative uncertainty of ≈0.8% (expanded uncertainty with a 95% level of confidence: ≈1.6%). This is the best estimate of the level to which measurements across instrument platforms with different designs and in "ambient" conditions can compare today. Reducing this contribution to uncertainty will require the community to agree on at least one reference value to which all measurements could be traced.</p><!><p>Reference compounds for calibration should be primary standards that are the least susceptible to sample manipulation (chemically stable upon long-term storage and dilution in different solvents), to ionization (the same ions should be produced independently of the ionization method, solvent used, flow rate,…), to ion-molecule reactions in the source or transfer regions, and to ion activation. Ideally all users should measure the same ion structures, independently on what instrument types and instrument settings they choose to work with. The reference compounds should thus produce ion structures that are identical over a broad range of instrumental conditions. Further, the reference compounds should ideally be robust in terms of variations in influence quantities that affect the definition of the measurand (temperature, moisture, and field) (Kaur-Atwal et al., 2009;Hauck et al., 2018), or have characterized dependencies that can be used to determine correction factors and their associated uncertainty.</p><p>In MALDI-IMS, a commonly used reference compound was C60 •+ (Von Helden et al., 1993;Dugourd et al., 1997), but unfortunately this ion is not particularly suitable for analysis in common ESI solvents. For ESI, other calibrants were thus used (Wyttenbach, Von Helden & Bowers, 1996;Hoaglund et al., 1997;Shelimov et al., 1997;Valentine et al., 1997;Valentine, Counterman & Clemmer, 1997;Counterman et al., 1998;Hoaglund et al., 1998;Wyttenbach, Bushnell & Bowers, 1998;Henderson et al., 1999;Henderson et al., 1999;Valentine, Counterman & Clemmer, 1999;Fenn et al., 2009;Bush et al., 2010;Bush, Campuzano & Robinson, 2012;Campuzano et al., 2012;Salbo et al., 2012;Forsythe et al., 2015;May, Morris & McLean, 2017). The hexakis-fluoropropoxyphospahzines (Agilent Tunemix calibration standard (Stow et al., 2017)) and polyalanine (Allen et al., 2016) satisfy the criteria and are compatible with ESI. Several other synthetic polymers (Duez et al., 2017;Haler et al., 2017;Haler et al., 2017) or supramolecular assemblies (Hupin et al., 2018) have recently been proposed as alternative calibrants. Finding new reference materials is currently a very active area of research, and it is expected that a few more years of testing will be necessary to reach consensus on widely accepted materials and their values. It is also likely that different chemical classes of reference materials will have to be developed, depending on the analyte (for example, to ensure interpolation in the K0 domain (Shvartsburg & Smith, 2008), and for TWIMS, to have similar K0=f(m/z) dependencies (Richardson, Langridge & Giles, 2018)).</p><p>Besides a set of compounds for calibration, an independent quality control should be used.</p><p>Regularly monitoring the value of its estimated CCS within a specified uncertainty window, with the same experimental settings than the calibration and CCS determination, will unveil systematic deviations with time, and indicate when recalibration is necessary. A QC reference compound is also used to estimate the trueness of the method when necessary (when absolute values are the goal).</p><p>In addition, the community would also benefit from having reference compounds for instrument performance evaluation, i.e. compounds which would be sensitive to some particular aspects of the measurement, such as the pre-IM activation (for example, native ubiquitin 7+ is frequently used to gauge instrument softness (Wyttenbach & Bowers, 2011;Chen & Russell, 2015;Gabelica, Livet & Rosu, 2018)), post-IM activation (a fragile compound), sensitivity to gas purity (in particular, sensitivity to moisture), temperature, or E/N. Periodic monitoring of one or more reference compounds may be used to correct small deviations in measured drift times (or equivalent quantities) during long experiments (e.g. LC-MS analyses), in a similar way as when correcting the mass bias using a lock-mass strategy for TOFMS.</p><!><p>These steps influence the nature of the ion population that is subjected to measurement from a given analyte (see Section II.1). The different charge isomers (e.g., protonation isomers), the different adducts, the ions of different polarities and charge states, and the conformers introduced into the mobility cell must be considered as different ions produced from the same analyte in the sample, each potentially having different mobilities. It is thus normal that databases contain CCS and K0 values for different ions corresponding to a same analyte entry. If there is mass selection or significant discrimination in transmission (e.g., quadrupole cut-off) of the ion population admitted into the IMS separation region, the m/z range must be indicated (this is different from the m/z range selected during data processing, i.e. step 4).</p><p>In turn, the nature and relative abundance of the adduct(s) or charge isomers can depend on the sample preparation and ionization/ion transfer conditions. Similarly, ion activation (i.e., internal energy) history prior to the mobility measurement can potentially influence the nature of the charge isomer or adduct, its conformation, or both because they are linked. This justifies the importance of reporting as many instrumental parameters as possible (source conditions, solvent and flow rates, voltages, pressures, temperatures, transit times, accumulation times and trapping times, bias voltages for ion injection in the IM) along with the exact instrument type and geometry.</p><!><p>The measured output X may differ depending on the measurement principle, but in all linear methods, the output X is linked to the ion drift velocity vd. The following sections discuss the experimental parameters that must be described to proceed towards steps 5 and 6. The necessary information differs for the first principle determination and for calibrated measurements. For first principles, the minimum is to report all variables and constants involved in Equations 1-4, i.e., E, T, p, and gas composition which will define M. For calibrated methods, the report should focus on the consistency of the conditions between the calibrants and analytes, and on providing all necessary information to reproduce the results.</p><!><p>Because E = V/L, the general principle is to report instrument design and voltages. For the instrument design, if a primary article has described the instrument in detail, a citation suffices.</p><p>Voltages should be specified in every report for clarity.</p><!><p>The electric field is linear and constant. E is characterized by the voltage difference (ΔV) and the length L of the drift region, (E=ΔV/L). Possible sources of bias may occur if the voltage difference is not monitored during the measurement. Other possible sources of bias are field inhomogeneity, and difference between the geometric length of the drift tube and the effective length on which ΔV is applied (Hauck et al., 2017) (this effective length may depend on ΔV and on the field in the optics entering and exiting the drift tube), and gas dynamics. To minimize additional errors, it is imperative that users, when measuring the high voltage found in many drift tube IMS systems, correct for the degree to which the high voltage probe alters the observed voltage.</p><!><p>For TWIMS, name the specific instrument model if commercial (G1, G2, G2-S, etc., which will specify the wave shape), and give the entered "wave height" (in volts) and "wave velocity" (in m/s). Descriptions of the typical wave shapes have been published for the first-generation SYNAPT (Giles et al., 2004), and the SYNAPT G2/G2-S/G2-Si (Giles, Williams & Campuzano, 2011) series. For home-made instruments (e.g., SLIM-based), specify the electrode dimensions, inter-surface gap, and all wave attributes (shape, height(s), velocity,…) (Hamid et al., 2018).</p><!><p>In a TIMS analyzer, the axial electric field E varies both temporally and spatially (Fernandez-Lima et al., 2011;Michelmann et al., 2015;Bleiholder, 2016). Spatially, the electric field strength increases over the length of the ion storage region up to a value E0 in the first half of the analyzer ("ramp") whereas it remains constant at E0 in the second half of the analyzer ("plateau"). Temporally, this electric field profile is controlled by the rate  at which the plateau height E0 is decreased ("ramp rate"). Mathematically, the electric field strength at axial location z in the analyzer at time t is given by (Michelmann et al., 2015;Bleiholder, 2016): pressure in the entrance and exit (P1 and P2), and the scan rate (Sr= Vramp/tramp). (Hernandez et al., 2014) In the case of nonlinear scan operation of the TIMS device, the Vramp(t) profile should be reported (Silveira et al., 2016;Benigni et al., 2018).</p><!><p>DMAs can be found in parallel plate (Hogan & Fernandez de la Mora, 2009), concentric cylinder (Fernandez de la Mora et al., 1998), and radial geometries (Zhang et al., 2007). Ion motion is driven electrostatically in one direction, while a clean gas sheath flow drives ion motion in an orthogonal or near orthogonal direction, such that only ions of a specific mobility traverse the instrument from inlet to outlet. DMA operates with similar instrument geometries as nonlinear (FAIMS) methods, and section V.3 can be consulted for the geometric details to be reported.</p><p>Irrespective of geometry, the mobility of the transmitted ions is proportional to the product instrument geometry constant and the sheath flow rate, and inversely proportional to the voltage difference between the inlet and outlet electrodes. For IMS measurements the following items should be reported: (i) the DMA classification region dimensions (or the commercial model specified, along with the DMA geometry), (ii) the voltage range applied in measurement, and the dwell time at each voltage.</p><!><p>Gas compositions should be reported as volume fractions (see also V.3.2.1). For the pressure, the principle is to specify how, where, and when the pressure is measured. Theoretically it is the pressure inside the drift region during the measurement (or the pressure drop along the analyzer in TIMS). It is recommended to specify how and where the pressure was determined, the type of gauge used and the model (remember that gauge specifications are gas and pressure-dependent;</p><p>for example, Pirani gauges are very gas-dependent, whereas capacitance manometers are gasindependent and should thus be preferred). Furthermore, different instruments may suffer from different biases or fluctuations related to gas flows, and for this reason the verification of an instrument with a reference compound is often carried out instead of-or in addition to-the pressure measurement. Leakage of gas or moisture from the source to the drift region is a main source of contamination, and in this context, reporting the source and ion transfer parameters is also relevant to the characterization of the gas composition in the drift region.</p><!><p>The measurements are carried out in pure gases for CCS determinations, but K0 determinations are possible in gas mixtures. Note that ensuring the gas purity can be challenging depending on the instrument geometry and isolation of source and mobility regions. For example, if the tube must operate in 100% helium at sub-ambient pressures, pressure differentials must be carefully controlled to avoid that nitrogen or air from the source penetrates into the drift region.</p><p>Furthermore, pressure homogeneity and absence of net gas flow is often assumed, but difficult to achieve in practice.</p><!><p>In Synapt G1 instruments, the TWIMS region contains only one gas, usually nitrogen (assuming that argon does not leak from the trap and transfer cells). In Synapt G2 and G2-S instruments, however, a helium cell immediately precedes the nitrogen-containing TWIMS region. As a consequence, the TWIMS region actually contains a mixture of helium and nitrogen. The report should specify how the pressure was regulated: either by fixing the gas flow rates (provide the flow rate settings in mL/min and the range of pressure readbacks from the He and N2 cells) or by varying the flow rates so as to have a narrow range of pressure readbacks (Morsa, Gabelica & De Pauw, 2011;Morsa, Gabelica & De Pauw, 2014) (provide the measured pressures, specify the gauges used, and provide the typical range of gas flow rates used to achieve these readings).</p><!><p>In TIMS, the buffer gas is forced to stream through the analyzer and exert the force that pushes the analyte ions towards the exit of the analyzer. The buffer gas velocity profile is nearly homogenous in the central region (typically, tens to hundreds of m/s) and that the gas velocity decreases in magnitude near the walls of the TIMS tunnel region due to friction. (Hernandez et al., 2014) The resulting parabolic flow profile determines the trapping conditions during TIMS operation; that is, in a TIMS device the basis for the mobility separation lies in the compensation of the drag force (proportional to the gas velocity vg) with the electric force (increasing in magnitude from the entrance to the exit with the electrode positions). The operator modulates the velocity at which the gas streams through the TIMS analyzer (corresponding to the volumetric flow rate of the gas divided by the cross section area of the TIMS analyzer) by setting a pressure difference between the entrance and the exit of the analyzer (P1 and P2, respectively, which should be reported). More details can be found in (Hernandez et al., 2014;Michelmann et al., 2015;Silveira et al., 2016).</p><!><p>As DMAs require use of a controlled, steady, laminar flow (often at atmospheric pressure), reporting on gas composition and flow conditions is essential. Specifically, the gas composition, temperature, and relative humidity need to be specified as precisely as possible, and sheath flow rate or the voltage required to transmit a calibration ion needs to be reported. DMA hardware bears resemblance to nonlinear designs (though the manner of operation is quite distinct), and the reader can consult sections V.3.1 to V.3.3. for more detailed guidelines.</p><!><p>This parameter is essential for DTIMS and DMAs, and for a determination of K0 and CCS from first principles. The report should specify how, where and when the temperature is measured.</p><p>Theoretically one should determine the temperature of the gas inside the drift region during the measurement. Temperature measurements made outside and inside the drift region may not exactly reflect the actual temperature ions experience. The temperature is one of the most difficult parameters to control and measure, and is possibly a major source of bias and fluctuations. When using "ambient" conditions, the actual laboratory temperature should be reported (ideally, the laboratory should be thermostated).</p><p>On the SYNAPT (commercial TWIMS) instruments, the temperature is not measured, and since measurement of both calibrants and analytes will be affected, only differential effects will appear in the calibrated results. Furthermore, in TWIMS and TIMS, the ions may encounter collisions at a higher relative velocity than the corresponding thermal velocity. The extent to which these effects affect the results is not yet clear. Because it is preferable to err on the side caution, by reporting rather too many details than too few, all parameters influencing the ion-gas relative velocity should be mentioned. In TIMS this is directly dependent on the gas velocity vgas. In TWIMS, the relevant instrumental parameters are the wave height, wave speed, and gas pressures. The mass of the gas, of the ion, and the ion charge will also influence the effective temperature (Morsa, Gabelica & De Pauw, 2011;Morsa, Gabelica & De Pauw, 2014).</p><!><p>The FAIMS gap is between a pair of electrodes carrying the asymmetric waveform (Guevremont, 2004). Ions are filtered by motion perpendicular to the gap (along the field direction) while pulled through it by gas flow. The metrics of the gap are width g (the distance between opposite electrodes), length L (the shortest distance along the median traversed by ions from entrance to exit), and span s (the lateral dimension perpendicular to width and length), typically specified in mm or μm (g) and cm or mm (L and s) (Shvartsburg, 2009). With nonplanar gaps, the curvature is specified by shape (cylindrical or spherical) and electrode diameters (outer for internal electrode and inner for external electrode, typically in mm) (Guevremont & Purves, 2005). More complex gap shapes require further dimensions, e.g., the length of cylindrical section and range of g in the hemispherical section of "dome" geometry (Tang et al., 2005).</p><!><p>The buffer gases often comprise two gases or a vapor doped into a gas (especially for higher FAIMS resolution, exploiting chemical interactions between these gases and ions or deviations from the Blanc law for gas mixtures in high electric fields). The composition should be specified in volume fractions (typically percentages for gases (Shvartsburg, Tang & Smith, 2004) and ppm for the vapors (Krylova et al., 2003)). Specifying the partial vapor pressure is discouraged, as the associated fraction depends on the temperature and total pressure.</p><!><p>Historically, FAIMS operated at ambient pressure, including with defined gas compositions (rather than ambient air). The separation parameters scale roughly as the inverse pressure squared (Shvartsburg, 2009), and large pressure variations that can be caused by difference in altitude above the sea level and weather conditions and/or laboratory setup have resulted in major discrepancies between the parameters measured in different settings or at different times.</p><p>Indicating the ambient pressure (obtained using a barometer near the FAIMS device, usually in Torr) is advised for future work (Canterbury et al., 2008), unless the pressure is controlled (as in some recent studies (Nazarov et al., 2006;Shvartsburg et al., 2018)), in which case the measured pressure in the gap should be stated. The variation of pressure can to some extent be offset by using calibrations (below). Some commercial FAIMS offerings, such as those by SCIEX and Heartland MS, account for such environmental variations in ambient pressure.</p><!><p>The gas temperature is crucial. Historically, FAIMS was operated at ambient temperature, and its variations contribute to the discrepancies between analyses made in different places or times (Krylov, Coy & Nazarov, 2009). Less preferably, in arrangements where the temperature of the FAIMS cell is controlled by heating the supplied carrier gas, the temperature measured near the unit inlet may be reported (Robinson et al., 2008). The temperature should be ideally measured on electrode surfaces facing the gap (e.g., using a thermocouple with the waveform off), or in close proximity to the cell unit but not in direct contact with the electrode itself (i.e., no electrical contact or influence on the thermocouple by the waveform) (Schneider et al., 2010). Some systems employ a thermal gradient between electrodes to create ion focusing in the gap (Barnett et al., 2007), and in such case the temperature of each electrode should be specified.</p><!><p>The residence time in the gap t (or filtering time) is proportional to the width and inverse volume flow rate (Qgap, normally in L/min). However, the often used (Canterbury et al., 2008) t = gLs/Qgap is only an approximation because of the gas flow gradient across the gap forced by boundary conditions on the electrodes (Shvartsburg, Tang & Smith, 2005). As ions exiting the gap have traversed it near the median where the gas flow is faster than the average, the above is an upper limit and actual values are substantially lower. Accurately, there is a distribution of t due to the longitudinal diffusion and inequivalent paths through the gap traversing regions with different gas flow speeds.</p><p>In most FAIMS instrument designs, the measured gas flow to the device (Q) splits between those to the source (for ion desolvation) and the gap (Qgap), hence Qgap is not accurately known, although it can be estimated based on the calculated conductance limits along the two paths (Shvartsburg et al., 2006). In other systems (sealed to a mass spectrometer) with gas flow drawn by MS vacuum suction, attaching the FAIMS device affects the conductance into the mass spectrometer and actual Q is below that for the underlying MS system. Some systems of this type also add (pull) a measurable gas flow to (from) the FAIMS/MS interface (Shvartsburg et al., 2009), which must be accounted for when calculating Q.</p><p>Hence we recommend reporting Q and (if desired) Qgap and t estimated as above with proper clarifications, unless it was directly measured -e.g., using a shutter (Shvartsburg et al., 2018). In the latter case, the actual t (preferably with the distribution) should be stated.</p><!><p>As with any periodic function, the first key metric of FAIMS waveform is frequency, to be specified in Hz (kHz, MHz). The waveform is often synthesized from individual (in particular, two) harmonics, and its frequency should not be confused with those of individual harmonics (Shvartsburg, Tang & Smith, 2004;Shvartsburg, 2009). The second key metric is the peak amplitude termed Dispersion Voltage (DV), expressed in V (kV). To avoid confusion, DV should not refer to the waveform itself, and the peak-to-peak amplitude (common in electrical engineering literature) should not be given; instead, the zero-to-peak amplitude of the waveform should be stated.</p><p>Unlike with symmetric (harmonic) waveforms, defining an asymmetric waveform also requires specifying the profile. In general, the profile must be specified numerically via a graphic or table (Shvartsburg et al., 2009). However, the waveforms resulting from superposition of harmonics can be described analytically in their terms. For example, the common bisinusoidal waveform comprises two harmonics with fixed 1:2 frequency ratio and can be specified via their amplitude ratio (commonly 2:1). A nominally rectangular profile can be defined in these terms (as "high-tolow ratio" of maximum absolute voltages in opposite polarities), but the rise and fall times must be given (Shvartsburg et al., 2018). The key metrics of waveform profile are its moments <Fn> that control the FAIMS separation parameters and resolution. Their number is theoretically infinite, but most important are those for n = 2 -7 and especially 2, 3, 5 (Shvartsburg, 2009).</p><p>Moreover, an asymmetric waveform has a specific polarity, defined by the sign of DV. This polarity is critical to analyses in curved gaps and must be reported.</p><p>In summary, the waveform is defined by frequency, DV (including sign), and profile specified directly (analytically or numerically) and/or indirectly via the set of relevant moments. Both profile descriptions are advisable for redundancy and higher accuracy (given the infinite number of <Fn> moments and inherent inaccuracy of numerical definitions).</p><!><p>While the waveform disperses ions along different trajectories inside the enclosure, those allowed to exit to the detector are selected by Compensation Voltage (CV), expressed in V (Guevremont, 2004). With FAIMS operated in the prevailing scanning mode, CV should be specified via range (initial and final values) and scan rate (V/min or V/s). With operation in the fixed-or stepped-CV modes (parallel to SIM and MRM in mass spectrometry), each CV and step duration (in min or s) should be specified (Canterbury et al., 2008). With equal steps, one can state the CV range and increment instead of each CV (Tang et al., 2005).</p><p>As with DV, the sign of CV is critical. The physical sign of CV depends on whether it is superposed on the waveform on same electrode or applied to the other electrode with fields superposed in the gap (Shvartsburg et al., 2006). The two arrangements (adopted in different instruments) formally yield opposite CV signs for identical separations. To address this problem, we propose the sign convention where CV is assumed superposed on the waveform regardless of the actual implementation. This yields CV > 0 for ions with K values decreasing at higher E/N and CV < 0 for those with K increasing at higher E/N (Kaszycki, Baird & Shvartsburg, 2018;Shvartsburg et al., 2018).</p><!><p>The combinations of positive and negative ion charges and two signs of K(E) or K(E/N) derivative results in four useful FAIMS modes as defined by (Purves et al., 1998): P1 (cation with positive derivative), P2 (cation with negative derivative), N1 (anion with positive derivative), N2 (anion with negative derivative). We recommend summarizing the operating mode in those terms, even if the information involved is separately stated. Those modes define the correct waveform polarity for ion focusing in curved gaps with inhomogeneous electric fields: positive for P1 and N2 and negative for P2 and N1. The opposite polarities cause ion defocusing and are thus not analytically useful (Purves et al., 1998). Hence the above indication of FAIMS mode essentially contains the information about waveform polarity in curved-gap systems (that in planar-gap systems with homogeneous fields is immaterial).</p><!><p>We recommend reporting the extracted mass range [(m/z)1, (m/z)2] corresponding to a particular IMS or FAIMS feature extracted during data processing, in order to allow the reader to understand which isotopologues (relevant to smaller molecules) or adducts (relevant to large biologically relevant complexes) are averaged in.</p><p>In linear IMS, the isotopologue effects come from a reduced mass effect (which is removed when converting mobilities to CCS). Any validated difference in CCS (not reported thus far) would indicate other effects, primarily the isotopic impact on the ion geometry that could be structurally informative. The isotopic effects in FAIMS are now proven to be highly structurally specific (allowing robust isomer differentiation) and not substantially mass-dependent. The specification of isotopic envelopes was not considered in IMS until very recently (Valentine & Clemmer, 2009), as all isotopologues were previously indistinguishable because of limited resolution. With the improvements in resolving power both in linear IMS and FAIMS, separation of isotopologues is now possible (Shvartsburg, Clemmer & Smith, 2010;Kaszycki, Bowman & Shvartsburg, 2016;Kirk, Raddatz & Zimmermann, 2017), and necessitates defining the isotopic composition of species in question. By analogy to MS, we propose in linear IMS the monoisotopic ion mobility (raw or reduced) for the monoisotopic species, average mobility for the integral over full mobility distribution for all natural isotopologues, and most probable mobility for the most abundant isotopologue. In FAIMS, we would respectively have the monoisotopic, average, or most probable compensation field (raw or normalized).</p><!><p>These data are the relevant output when ion mobility is exploited for separation sciences. The measurable X is usually an arrival time distribution (see Section II.2). ATDs should be presented as follows: the y-axis is the ion signal (number of counts or relative intensities), and the x-axis is the time (usually labeled tA for "arrival time"). Don't label the axis "drift time" if what is measured is an "arrival time". Alternate graphs are possible, for example by converting arrival times to drift times (time spent in the drift region, td), to the voltage of elution (Ve) in TIMS, or to compensation voltage (CV) in FAIMS.</p><p>For structural studies, ATDs are also important to reveal peak width, peak shapes, and the time the ions spent in the separation region (which can influence the result in case isomerization can occur during the separation (Laszlo, Munger & Bush, 2017;Poyer et al., 2017)). In the framework of structural studies, reporting collision cross section distributions (CCSD) becomes increasingly popular, but unfortunately the detailed procedure used to construct these plots is not always reported. A outline and discussion of the different procedures possible for drift tube ion mobility is provided by Marchand et al. (2017). It should also be noted that the procedure introduce additional uncertainty and biases depending on the data processing method (using the term "apparent CCSD" would convey this notion), and should not be used when ions of different charges coexist within the given m/z range. The principle is to report all information required for traceability, i.e. to enable the user to convert back and forth between CCSD and the primary data.</p><p>Reports focused on K0 and CCS values should preferably include representative arrival time distributions as supporting information, for example to show the peak width, the peak shape, and absence/presence of distinguishable minor contributions. If a peak fitting software was used to distinguish contributions, all details should be given so that the reader could reproduce the data processing. Mass-to-charge/drift time heat maps wherein the intensity is represented by a color code are useful for visualization, but should be accompanied by the extracted ATD and mass spectra to give a better sense of the relative abundances. In the case of CCS reports, the charge assignment for each mobility peak should be specified, and supporting evidence for this assignment should ideally be documented (for example, with an extracted mass spectrum showing the isotopic distribution).</p><!><p>Reported FAIMS systems have gap widths varying by >100-fold (from 0.035 to 5 mm). As a result, dramatically different DV and CV values can provide similar separations (Shvartsburg et al., 2009;Shvartsburg et al., 2018). DV and CV can be employed in the reports only provided that FAIMS cell dimensions are also clearly stated (such that ED and EC could be calculated).</p><p>However, to help compare the FAIMS spectra across systems with different g, we recommend converting DV and CV (via dividing by g) into Dispersion Field (ED) and Compensation Field (EC), typically in V/cm (Kaszycki, Baird & Shvartsburg, 2018). These quantities carry the signs of DV and CV. One can further convert ED and EC into normalized dispersion and compensation fields ED/N and EC/N expressed in units of Townsend (Td) (Shvartsburg et al., 2018). These units may find greater use to compare results across pressures, owing to the emergence of FAIMS units capable of operation above and below 1 atm. However, proteins and perhaps other macromolecules with strong macrodipoles may be reversibly aligned by strong field in FAIMS, a process governed by E (rather than E/N as other high-field effects underlying FAIMS) (Shvartsburg et al., 2009). Hence separations may be controlled by a combination of E and E/N, and reporting just E/N is insufficient in those situations. As an interim solution, we propose reporting ED and EC for analyses at ~1 Atm (that so far dominate FAIMS applications) and ED/N and EC/N for substantially different pressures.</p><!><p>Many FAIMS analyses employ a single ED value, either the highest allowed by the hardware or the ED value that provides optimal separation of ions balanced with concomitant signal attenuation. This generally maximizes resolution, but may limit the analytical information as (i) fragile species may not survive to the maximum ED because of dissociation or isomerization upon field heating and (ii) certain species may be better resolved at lower ED (Shvartsburg et al., 2012). Also, the full EC(ED) curve allows extracting the (E) function (below) that most specifically identifies any ion (Guevremont et al., 2001). Hence, we recommend presenting in graphic or tabulated form the EC(ED) or EC/N(ED/N) curves over the whole experimental ED range rather than single ED values.</p><!><p>The ultimate way to catalog FAIMS data is via its alpha-function as a function of E (or E/N):</p><p>where K( 0) is the zero-field mobility (Guevremont et al., 2001).</p><p>This most universal representation allows comparing the results independently of the gap width, gas pressure, and, most importantly, waveform profile inherent in the EC(ED) curves. Extracting the a(E) functions requires deconvoluting EC(ED) curves for the known waveform profile (Schneider et al., 2016), which appears to produce unique results for practical profiles (Shvartsburg, 2009). The resulting a(E) or a(E/N) functions could be reported in graphic forms or as tables. While this deconvolution involves significant effort, it is recommended because it produces more transferable data for comparisons across systems and laboratories, especially with the proliferation of different FAIMS systems employing diverse waveform profiles.</p><!><p>No information on absolute mobility is obtainable from FAIMS data. However, they can be combined with linear IMS measurements providing K(0) to construct the absolute K(E) or K(E/N) curves. Then the error margins of the K(0) point translate into resulting curves and its source should be verified and reported.</p><!><p>All ions have been phenomenologically grouped into three types by FAIMS separation properties (Levin et al., 2006;Shvartsburg, 2009;Rorrer & Yost, 2011). These types are handy to concisely describe the ion behaviors and associated FAIMS regimes, because they can be readily visualized from the experimental data (Levin et al., 2006;Rorrer & Yost, 2011). The type A and C ions were defined to have EC(ED) functions uniformly increasing and decreasing at higher absolute ED, respectively. For type B ions, EC would first increase and then decrease with increasing absolute ED. These definitions were made with an early sign assumption for EC. With the present uniform sign convention, these definitions are amended to those listed in Table 3:</p><p>These definitions naturally expand to EC and ED expressed as EC/N and ED/N. The development of FAIMS science since the introduction of these ion types in early work by Guevremont has brought forward a deeper understanding and re-evaluation of these definitions in several aspects.</p><p>First, All "ion types" are actually "ion-gas pair" types-the same ions can assume different types in different gases based upon the ion/molecule interactions between these species (Barnett et al., 2000;Levin et al., 2006;Campbell, Zhu & Hopkins, 2014;Liu et al., 2015;Liu et al., 2017).</p><p>Generally, increasing the mass and polarizability of gas molecules shifts ions from type C to B to A. Hence, the ion type should be reported only with reference to the gas as "species X + has behaved as a type C ion in N2". Second, since all type A ions will eventually turn into type B at higher ED (Shvartsburg, 2009;Shvartsburg et al., 2009), the existence of type A ions is an artifact of ED range limited by hardware (arc breakdown in gas or waveform generator constraints), fragmentation of precursor or other loss (e.g. scattering), or just explored experimental range.</p><p>Hence, the type A should be reported only in conjunction with the covered ED (or ED/N) range as "species X + has behaved as type A ion in N2 up to ED of 30 kV/cm explored here".</p><p>Similarly, the conversion of type C ions to a new type (EC become more positive with increasing absolute ED up to certain point, then less positive at higher ED) was recently encountered in He/N2 mixtures with high He content (Shvartsburg, Ibrahim & Smith, 2014) and, by analogy to type A transitioning to type B, may be termed type D. This type appears much less common than B, as all type A ions must turn into B but not all type C ions turn into D. Possibly type D only occurs in certain gas mixtures due to non-Blanc (Biondi & Chanin, 1961) effects.</p><p>Finally, large macromolecular ions (including proteins above ~30 kDa) exhibit extremely negative EC at high ED (Shvartsburg et al., 2009). This effect must be due to electric dipole alignment during the high-field waveform segment dramatically raising the K value in that segment relative to low-field segments with weaker or no alignment. While this behavior superficially resembles the type D, it manifests much more dramatically with EC becoming negative (not just decreasing from a maximum), has unrelated physical cause, and emerges for much larger ions. Hence we propose assign such species to a new type E.</p><!><p>While the ion types were defined in terms of EC trends depending on ED, they were related to K(E) forms. The types A and C correspond to K increasing and decreasing as a function of E or E/N, respectively. The type B was ascribed to K rising to a maximum and then dropping at higher E. That is not necessarily true: a K(E) function that continues increasing with decreasing slope (i.e., negative second derivative) can yield type B behavior as the absolute difference between K values at two ED with fixed ratio decreases (Shvartsburg, 2009). Similarly, a K(E)</p><p>function that continues decreasing with decreasing slope (i.e., positive second derivative) can yield type D behavior as the absolute difference between K at two ED with fixed ratio decreases.</p><p>We advise making no conclusions about the K(E) functions for type B and D ions, unless upon quantitative extraction as discussed above.</p><p>Table 3: Definition of ion types in nonlinear methods.</p><p>Type A EC is negative and becomes more negative with increasing absolute ED, up to the maximum ED employed Type B EC is initially negative and becomes more negative with increasing absolute ED up to certain ED (as in type A), then becomes less negative at higher ED (with or without becoming positive)</p><p>Type C EC is positive and becomes more positive with increasing absolute ED, up to the maximum ED employed Type D EC is initially positive and becomes more positive with increasing absolute ED up to certain ED (as in type C), then becomes less positive at higher ED (without becoming negative) up to the maximum ED employed Type E Macromolecular ions with negative EC at any ED V.5. Determination of K 0 (step 5) and CCS (step 6)</p><p>V.5.1. Definition of the representative X from a distribution of X</p><p>The primary measurable X is often the arrival time tA, and the distribution is the ATD. The first step is to determine the centroid arrival time for the ion population of interest, at each voltage. A comprehensive report should document (i) the definition of the centroid (e.g., apex, center of a Gaussian,…), (ii) the procedure (e.g., smoothing, fitting by a specified function, fixed parameters such as peak width and justification of the choice,…), (iii) the software or script used (name, version, provider) and (iv) the resulting centroid values and their uncertainties.</p><!><p>Even when the final aim is to obtain CCS values, we recommend that K0 values are also explicitly included in the data report. The reasons are: (1) Instrument calibrations should be carried out in the K0 domain to avoid undue extrapolation, (2) K0 values can be determined in gas mixtures without introducing error, but not CCS values, (3) the combined uncertainty on CCS differs from that on K0.</p><!><p>Most instruments do not measure directly the time the ions take to traverse the drift region (td), but measure a total time (arrival time tA, which is the sum of td plus a time t0 spent outside the drift region). Multi-field experiments involve measuring arrival times as a function of the inverse of the drift voltage, making a linear regression, and obtaining t0 from the intercept and K0 from the slope (Equation 6). The procedure thus assumes that K0 does not change with E/N over the range of fields defined by the different ΔV values. Some bias (thus, uncertainty) is thus associated with this assumption.</p><p>The software and procedure used for the linear regression should be specified and the uncertainty on the intercept and slope (and how it was determined) should be documented. Note that a regression by least squares minimization correctly estimates the uncertainty on the slope if the data points are equally spaced on the x-axis and if the variances are similar over the entire range.</p><p>In that sense, the linear regression procedure itself contributes some uncertainty.</p><p>In addition to providing a graph of the linear regression and indication of its quality (for example, via r²), providing a plot of residuals can be informative: curvature may indeed indicate either that effective drift length varies as a function of the field, or that the mobility depends on E/N on the measurement range (Kemper, Dupuis & Bowers, 2009;Allen & Bush, 2016;Hauck et al., 2017). Nonrestrictive examples are given below.</p><!><p>The combined standard uncertainty uc on each K0 value can be estimated from the propagation of the standard uncertainties u on each component (L, p and T from the experimental parameters in step 3, standard error on the slope from the linear regression in step 5), which is given by Equation ( 8), assuming that the uncertainties are uncorrelated:</p><p>This uncertainty evaluation is quick, and takes into account how K0 may fluctuate with ΔV, than thus on E/N over the chosen field range. Usually, the contributions of the uncertainties on T and p dominate in the combined uncertainty. Whether the uncertainty on the slope takes into account the uncertainties on tA and ΔV depends on how it was determined (i.e. whether the linear regression software uses the data points only, or whether the regression parameters and their uncertainty was weighted using vertical and horizontal error bars on each data point).</p><p>Other methods of uncertainty evaluation exist, such as Monte Carlo simulations. With that approach, the relative standard uncertainty on the drift time (hence, on 1/K0 or on CCS) was estimated at 0.27% on an Agilent 6560 IMS-Q-TOF modified by the manufacturer to make more accurate measurements (Stow et al., 2017). With that instrument, DT CCSN2 values for the Agilent tunemix ions in positive and negative mode were determined (Stow et al., 2017).</p><!><p>When reporting average values from multiple independent measurements, in case a quality criterion (for example on r² or residuals of the linear fit) was used to accept/reject values, it should be specified. The entire procedure, including the gas equilibration in the tube, should be replicated. This standard deviation thus gives a sense of the precision under repeatability conditions. The standard deviation (u) and number of independent replicates (n) should be mentioned. For data intended to be used as primary standards, we recommend n ≥ 6, in order to minimize the expanded uncertainty for a certain level of confidence.</p><!><p>For rare samples, replication is not always possible. One may then (i) propagate uncertainty from the linear regression, (ii) use one's knowledge of uncertainties determined previously for similar analytes with the same procedure in the same lab, (iii) use published values of uncertainties evaluated thoroughly on the same instrument model, and justification of how closely comparable the procedures are (for example, use the interlaboratory precision values reported for the stepfield procedure on the Agilent 6560 IMS-Q-TOF (Stow et al., 2017)), or (iv) invoke the conservative value of 0.8% s.d. discussed in section IV.1 for previously published values coming from different DTIMS instrument designs. All are acceptable if properly justified so that the meaning is clear to the reader.</p><!><p>Combining the expression of K0 coming from the slope with Equation (4) gives:</p><p>The combined uncertainty on the CCS determined from a single experiment (single regression) is</p><p>given by:</p><p>Compared to K0, the temperature weights differently on the uncertainty. Simple propagation of error from K0 would ignore the (negative) correlation between the temperature effects. As for z and µ, the peak assignment (step 4) plays a role. If one assumes that the uncertainty on the ion charge is zero, proper justification should be given. Note that automatic assignment of charge states may fail in some cases, especially as z becomes large. One often assumes that the relative error on µ is negligible, but a word of caution is warranted. Indeed the ion mass mi (provided that z is certain) and gas mass mg can be known with a very high precision and accuracy, the gas purity plays a role here: traces of other gases will also contribute to an uncertainty on µ. Note that this effect involves not only the purity of the gas intentionally introduced inside the IMS, but also the nature of the gases present outside the IMS and that may be leaking inside the tube.</p><p>These effects may thus be far from negligible, and one of the major contributors for differences observed with different drift tube designs (see section IV.1). This is the main reason for which not only the purity of the gas introduced in the drift tube, but also all information on pressure differentials between the tube and neighboring zones, especially if the nature of the gas in the neighboring zone(s) is(are) different, should be included in the experimental details of step 3. In a similar way as for K0, repeated experiments give a sense of the precision under repeatability conditions. Again, the whole procedure has to be repeated, including gas equilibration. This is a better way than Eq. ( 10) to account for fluctuations in gas purity.</p><p>If any equation other than Eq. ( 4) is used, the mathematical function and all input parameters should be fully documented, based on the same principles: the users should have all information to link CCS values to K0 values, and calculate the uncertainties.</p><p>V.5.3. Secondary methods: general recommendations.  the list of calibrant ions, with motivation of the choice (specific recommendation for the different methods will be given in the following sections),</p><p> the DT K0 or DT CCS values used for calibration (e.g., from references to the primary literature), with specification of the gas and temperature at which these were determined,  the uncertainties attributed to these DT K0 or DT CCS values (if not provided according to the recommendations of section V.5.2.2, see section IV.1), either expressed as standard uncertainties or as 95% confidence interval. Obviously these will put a lower limit on the uncertainty of the results obtained following calibration.</p><p> documentation of steps 1-4 for the calibrants.</p><!><p>The calibration gives the instrumental function that relates the measurable X to K0. Alternatively, a parameter directly proportional to K0 (thus assumed to be the same for all calibrants and analytes) can be calculated from DT CCS values and used instead of K0. If the analyst intends to assess and report the uncertainty of measurement following the (so-called bottom-up) procedure outlined in the ISO Guide for the Expression of Uncertainty in Measurement and in QUAM (Chapter 4) the uncertainty of CCS calibrants is an important component contributing to the total combined uncertainty of the measurand (see Figure 4). We recommend to show representative calibration curves, and to provide the calibration equation(s) relating X to K0 (typical equations for the different methods will be given in the following sections). To estimate the value of the analyte, it does not matter whether the x-axis is X or K0. However, to estimate the uncertainty on the value, the measured value X should be on the x-axis and the calibration/predicted value K0 (or the value proportional to K0), because regression analysis is designed to determine y from a given x, and several software packages (e.g., SigmaPlot, Origin) can provide prediction bands alongside with predicted values. Such prediction bands take into account the number of degrees of freedom of the calibration curve (number of calibration points minus the number of fitted parameters; the prediction band narrows when the number of degrees of freedom increases), and the spread of the calibration points.</p><p>Prediction bands are very useful to compare the figures of merit of different calibration strategies (Haler et al., 2017). Further, although it is not common practice today, it would be useful to display the uncertainty on both X and K0 (or the value proportional to K0) as error bars, and to use a software able to weight the regression and its prediction band according to these error bars.</p><p>Figure 4: Exemplary calibration curve (measured X as x-axis, calibrant inverse mobility or parameter proportional thereto as y-axis), wherein the uncertainty on the mobility of the calibrants is displayed as error bar. The prediction band gives the interval in which there is 95% likelihood to make one or more future observations.</p><!><p>Calibration is a well-known analytical procedure and, for CCS measurements, we can apply standard quality control schemes and measures. Accordingly, we also recommend including QC injections after the calibration process, during the sequence of experiments. The QC should be an independent material (i.e., one not used to calibrate the instrument at the time of the experiment).</p><p>This QC is to check the trueness of the experimental CCS with regards to the calibration procedure. Replicates of this(ese) QC point(s) should also provide a good estimation of the precision under repeatability conditions of measurement, which can be used to estimate that of the experimentally determined CCS. In DTIMS, instead of the multi-field primary measurement method, a convenient method (especially for LC-MS) is to use a single field strength for measurements of both established calibrant ions and unknown ions (Mordehai et al., 2015;Stow et al., 2017). To find the relationship between the measured arrival time tA and K0, one starts from Eq. ( 7). By expressing 1/K0 as a function of CCS (Eq. 11),</p><p>t0 is assumed to be the sum of a fixed term tfix and a mobility-dependent term:</p><p>Where  = [mi/(mg+mi)] 1/2 /z and must be calculated for each calibrant and analyte ion, and 1 is a constant derived from Equation (4) depending on the drift gas employed and the ion transfer settings outside of the drift region. By replacing in Eq. ( 7), one obtains:</p><p>where 𝛽 • 𝛾 𝐶𝐶𝑆 is the true drift time (td) derived from Equation (4), and β2 is a coefficient dependent on the experimental gas pressure, temperature, electrical field (actually E/N), and geometry of the drift cell. The term β thus reflects the aggregate of experimental conditions experienced by the ion (i.e. temperature, pressure, field strength) and is directly taken from the slope of a calibration curve of γ DT CCS values of reference calibrant ions. This is a linear function defined by two parameters, β and tfix.</p><p>The underlying assumptions are thus:</p><p> that tfix is the same for the calibrant and analytes (i.e. that m/z dependent, TOF-like effects are negligible (Mordehai et al., 2015;Stow et al., 2017)),</p><p> that the CCS is the same inside the drift region and outside the drift region, and thus equal to the DT CCS measured by the step-field method. Most of the drift contributing to t0 occurs in the ion funnel containing the same gas as the drift region, but drift occurs in the collision cell as well. Small analyte-dependent effects on t0 were found when a different gas was used in the collision cell compared to the drift region (Marchand et al., 2017). If the same gas is used (typically N2), then the calibrant and analyte need not be of the same chemical class.</p><p>The calibrant and analyte have to be acquired with the same IM settings (so that 2 is constant)</p><p>and the same MS settings (so that 1 and tfix are constant). Also, if the drift gas and its temperature are the same as in the primary method, and if the E/N falls within the range used in the primary method, the measurand has the same definition as in the primary method. If, for example, the gas or temperature is different, the single-field method becomes an empirical method.</p><p>Routine single-field operation should report key experimental IM-MS variables (drift gas, temperature, pressure, field strength, calibrant ions, and MS voltages that can affect tfix or 1)</p><p>which can assist in assessing potential analyte dependencies on such factors. Ideally, routine collection of single-field data needs to be controlled in terms of accuracy by comparison to multi-field results utilizing independent (non-calibrant) compound sets.</p><!><p>The nature of the calibrant ions does not need to match that of the unknown ions (i.e. molecular class, charge state), but precise and reproducible measurement conditions as well as agreement on a unified single-field calibration approach are critical for providing the most accurate DT CCS values with the single-field method. A recent interlaboratory study (Stow et al., 2017) demonstrated extremely low bias between multi-and single-field measurement modes on the same instrument platform (average absolute bias of 0.54%, details per chemical class can be found in the paper (Stow et al., 2017)) for more than 90 different ion species. This was achieved by ensuring inter-instrument compliance regarding the DT CCS values of the calibrant set determined in the multi-field approach.</p><p>If using different conditions (empirical method), the bias should be studied for some primary standards to evaluate the uncertainty.</p><p>V.5.5. TWIMS V.5.5.1. Procedure CCS values cannot currently be derived from first principles for the TWIMS device, but presently must be obtained following calibration with standards of known CCS value, primarily derived from DTIMS measurements. To generate TW CCS values, standards of known DT CCS value must be measured to generate a calibration curve (Ruotolo et al., 2008;Smith et al., 2009;Thalassinos et al., 2009;Bush et al., 2010). Published DT CCS values (He or N2) are converted to a value CCS', which according to Eq. ( 4) is proportional to 1/K0:</p><p>μ is the reduced mass of the neutral gas (typically N2) and analyte and z is the charge state.</p><p>Whilst it is noted here that the neutral gas in TWIM cells (for Synapt G2 and later) is a mixture of He and N2, CCS values measured in each gas are highly correlated for a given charge state. (Bush, Campuzano & Robinson, 2012) Helium reference values have been used previously to calibrate N2 measurements (i.e. TW CCS N2->He experiments) and the discrepancies introduced by measuring in N2 with a limited admixture of He will be proportionally smaller. Direct comparisons of CCS values measured on various DTIM and TWIM instruments (Giles et al., 2015) show that Synapt G2-Si data fall within the range of measurements with the other instruments.</p><p>X is an instrumental constant containing the effective temperature of the ion-buffer gas collisions. An assumption for the following procedure is thus that X is the same for the calibrant ions and for the ion of interest. This assumption warrants discussion. The effective temperature</p><p>Teff is equal to the bath gas temperature Tgas only in the low-field limit. According to the twotemperature treatment, Teff = Tgas + mgasvd²/3kB for non-negligible but low E/N (Siems, Viehland & Hill, 2016). vd is the drift velocity defined by Equation (1). However, in TWIMS the field 𝐷𝑇 applied to the ions is changing over time, and it is possible that Equation ( 1) is not satisfied at all times because of velocity relaxation effects (the ions need time to reach the steady state defined by Equation ( 1)) (Richardson, Langridge & Giles, 2018). Empirically, ion effective temperatures were found to be significantly higher than bath gas temperatures (Morsa, Gabelica & De Pauw, 2011;Morsa, Gabelica & De Pauw, 2014), so these effects are significant. It is thus plausible that the necessity for X to be the same for the calibrant and analyte is one of the reasons why chemical classes and charge states must be matched. The magnitude of the correction factor that would be needed to correct for this calibrant-related bias has not yet been established, and progress is expected in that direction. Meanwhile, it is crucial to report the full list of calibrant ions and their associated DT CCS values used for the calibration.</p><p>where c is a constant depending on the voltages used in the transfer optics (obtained from the MassLynx software; note that the resulting corrections are typically of the order of 100 μs in measured drift times of several ms, and uncertainties in the determination of c therefore have a small effect on the final measurement). The derived CCS′ versus t′ data are fitted using an empirically determined power law (Wildgoose et al., 2006),</p><p>its linearized version (Ruotolo et al., 2008),</p><p>or a polynomial (Bush, Campuzano & Robinson, 2012):</p><p>The calibration curve derived in this way is subsequently used to calculate the TW CCS of the ions of interest from their measured t values, obtained under identical operating conditions to those of the calibrant species. An undetermined time offset, t0, intended to capture any additional timing delays in the system (assumed constant for all ions) may also be introduced into the calibration for improved accuracy. The power law calibration then becomes:</p><p>Equation ( 19) is the one currently adopted by Waters' to calibrate data from the Synapt G2-S, G2-Si and VION instruments using the MassLynx/UNIFI software platform.</p><!><p>Precise measurements revealed that, for current TW calibration procedures, matching the charge state (singly versus multiply charged) and chemical class of calibrant provides calibrated data that agree better with drift tube data (Thalassinos et al., 2009;Bush, Campuzano & Robinson, 2012;Wright et al., 2013;Gelb et al., 2014). TWIMS is an empirical method relying on calibration, because at this point in time it not fully understood how to quantitatively account for both the velocity relaxation and the oscillatory field for all ion types. For TIMS, which works at similar E/N than TWIMS but with non-oscillatory fields, the compound class has no influence on the calibration at the current level of precision, so the compound-class effects in TWIMS are most probably due to velocity relaxation. Compound class matching to have similar velocity relaxation effects means that the analyte and calibrant should have similar K0=f(m/z) dependencies (Richardson, Langridge & Giles, 2018), and these dependencies segregate with the compound class (lipids, peptides, carbohydrates, nucleic acids, folded proteins, unfolded proteins,…) (McLean, 2009). Alternatively, the calibration method may be generalized to explicitly account for velocity relaxation (Richardson, Langridge & Giles, 2018). Further, if one is using DT CCSHe values to calibrate TWIMS instrument working mainly in nitrogen (which was frequent in the early days, as mostly only DT CCSHe values were available), this adds other compound-class effects (Gabelica & Marklund, 2018), related to the interaction potentials of nitrogen and helium with the exposed surface groups (Bleiholder et al., 2015). Here, the charge density will play the largest role (Young & Bleiholder, 2017), and for multiply charged proteins these effects become significant (Canzani, Laszlo & Bush, 2018) compared with measurement precision. For small molecules, dipole moments play a much larger role in N2 than in He (Warnke et al., 2015), and it is thus recommended to use DT CCSN2 values to calibrate TWIMS. Some groups have proposed using calculated CCS values to calibrate TWIMS because DT CCS values were unavailable for their molecular classes (phosphoric acid clusters (Lavanant, Tognetti & Afonso, 2014), large protein complexes (Marklund et al., 2015), nucleic acids (Lippens et al., 2016)). However, in the framework of measurement sciences, calculating theoretical CCS values is not equivalent to an independent primary method for ion mobility measurements, for three main reasons. First, ion mobility spectrometry primarily measures mobilities (K, in m² V -1 s -1 ), not surfaces (CCS, in m²). Collision cross section values are not directly traceable to the SI (the meter). Second, the uncertainty is higher, and a large component of it comes from uncertainties about the gas-phase geometries assumed by the ions. Third, even in the most physically accurate calculation method (trajectory model), the Lennard-Jones parameters have been themselves parameterized against DTIM measurements (e.g., for carbon, on values measured for C60 + ) (Mesleh et al., 1996)), so the method is not independent. Thus, calculated values cannot be traced to the international system of units, and thus using calculated values for calibrating instruments is in contradiction with the fundamental principles of metrology. What is encouraged is to collect more high-quality DT CCS data.</p><p>Empirical methods, by definition, assume that there is no bias (if the bias was known, it should be corrected for). It thus means that the output result will depend on the choice of the calibrants.</p><p>Thus, given the empirical nature of TWIMS, it is of utmost importance to provide the full list of calibrant ions and the values used for the calibrants.</p><!><p>The separation in a TIMS device can be described in the center of mass frame, and is therefore based on the same principles as in DTIMS. The mobility separation in a TIMS device depends on the bath gas drift velocity, ion confinement and ion elution parameters. The primary measurand in a TIMS experiment is the scan number, which is related to its corresponding ion trapping and elution voltage parameters. Absolute ion mobilities K0 or cross sections Ω of the analyte ions are currently not directly amenable. Hence, currently, ion mobilities and cross sections are determined by a calibration procedure with standards of known mobilities. The calibration can be performed internally or externally.</p><p>TIMS separation depends on the gas flow velocity (vg), elution voltage (Ve), ramp time (tramp) and base voltage (Vout). The reduced mobility, K0, is defined by,</p><p>where A is a constant related to the instrument. Three different calibration procedures have been described.</p><!><p>Running the TIMS experiment at different scan rates allows one to determine the time outside of the TIMS (to), followed by the determination of the elution voltage and the calibration constant (Hernandez et al., 2014). The total analysis time (tTotal) is given by:</p><p>where, ttrap is the thermalization/trapping time, tof is the time after the ion mobility separation, and Vramp and tramp are the voltage range and time required to vary the electric field, respectively.</p><p>The elution voltage (Ve) is experimentally determined by varying the ramp time for a constant ramp voltage. A linear dependence of tTotal with tramp for all the investigated m/z was obtained.</p><p>From the slope and the intercept of this graph, the to and Ve can be determined for each m/z range of interest.</p><!><p>Alternatively, a first order calibration is possible for an acquisition at a single scan rate, using known mobility peaks. This approach is based on the empirically made observation that the "elution voltage" Ve is strongly linearly correlated to the reduced mobility of the ions (Silveira, Ridgeway & Park, 2014;Liu et al., 2018). This approach employs the following empirical calibration function:</p><p>where a and b are calibration constants and the elution voltage Ve is approximately the voltage across the TIMS analyzer when the ion is measured. In commercial versions of the software, the calibration from scan number to 1/K0 is performed automatically using a linear regression of K0 as a function of 1/Ve. Note that in this approximation, an average tof is considered.</p><p>Eq. ( 22) has been successfully used to calibrate TIMS spectra. For example, cross sections calibrated for ubiquitin (Liu, Kirk & Bleiholder, 2016) or cytochrome c (Molano-Arevalo et al., 2017) agree well with the corresponding drift tube values (Bleiholder et al., 2015). More recently, a tandem-TIMS device was constructed from coupling two TIMS analyzers and calibrated tandem-TIMS spectra according to Eq. ( 22) (Liu et al., 2018). Cross sections calibrated for ubiquitin spectra obtained by tandem-TIMS also closely match the corresponding drift tube values. Overall, this calibration scheme reproduces drift tube ion mobilities to within less than 1% (Chai et al., 2018).</p><p>Importantly, the constants a and b depend highly, and in an unknown manner, on the TIMS operating settings. This is a consequence of the empirical nature of the calibration function.</p><p>Hence, the calibrated coefficients are only valid for the exact TIMS settings (scan rate, range and pressure) that were used for their determination (Chai et al., 2018).</p><p>V.5.6.</p><!><p>More recently, a transferable and sample-independent calibration procedure was reported for TIMS based on a Taylor expansion of instrument properties (TEIP) (Chai et al., 2018). The TEIP calibration is based on a calibration function that is derived from a solution to the Boltzmann transport equation but not motivated by empirically observed correlations. TEIP then separates those quantities that depend on the sample (m/z, K0) from those that depend on the TIMS instrument (, vg, etc). Finally, a Tayler-expansion is performed for the instrument-dependent quantities and the Taylor expansion coefficients form the basis for the calibration coefficients.</p><p>These calibration coefficients were found, to a good approximation, constant over time and independent of instrument settings or sample properties (Chai et al., 2018).</p><p>V.5.6.4. Calibrants for TIMS</p><p>The only significant difference between the definition of the measurand in TIMS and in DTIMS is the magnitude of E/N. Currently, it is assumed that the E/N in TIMS is low enough that the definitions of the measurand are equivalent. The level of measurement precision and accuracy that has to be reached to invalidate this assumption is not yet documented, and with the current level of precision/accuracy, the assumption seems valid. Thus, a single compound class is assumed to suffice for calibration. Commercial instruments use the Agilent tuning mixture as calibrants. However, it must be noted that the values currently embedded in the calibration files differ (Chai et al., 2018) from the values reported by Stow et al. from DTIMS (Stow et al., 2017), and used to calibrate the single-field measurement in Agilent instruments. The values differ by 0.75% on average. Thus, a significant bias between two methods (DTIMS vs. TIMS) is directly attributable to the choice of primary values for the calibrant ions, rather than to the measurement principle or instrument design. This illustrates how important and urgent it is for the community to agree on values for a set of primary standards.</p><!><p>Absolute K0 determination is possible, by precise measurement of the sheath flow rate, gas composition, temperature, pressure, and DMA geometry (with uncertainties reported). However, as noted earlier in this document, it is often much easier to proceed via a calibration using compounds which had their K0 determined previously with low uncertainty. While the former is preferred, the latter is commonly utilized for DMA measurements made in environmental settings, where instruments are operated remotely and broad mobility distributions are of interest.</p><p>Tetra-alkylammonium ions are popular calibrants for DMA (Ude & Fernández de la Mora, 2005).</p><p>In the case of known mobility analyte calibration, for a fixed sheath flow rate, a plot of the known ion inverse mobility versus the applied voltage where the ion is maximally transmitted should yield a linear relationship (for all DMA geometries), which can be used to subsequently link applied voltage to mobility.</p><!><p>We presented here a concerted effort to outline the fundamental principles underlying ion mobility measurements, with the aim to reduce the confusion among users. Reflecting on how the GUM (JCGM, 2008) and QUAM (EURACHEM/CITAC, 2012) guidelines apply to ion mobility measurements gives important insight (i) about the definition of the measurand (what we measure in ion mobility), (ii) about the distinction between primary methods of measurements and secondary or empirical methods, and (iii) about the sources of uncertainty of ion mobility measurements.</p><p>Ion mobility measures the ions' mobilities (K), not surfaces (CCS). Reduced mobility (K0) and CCS values depend solely on the ion structure, the gas nature, the temperature and E/N, but not per se on the method of measurement. However, a distinction must be made between a primary method of measurement (DTIMS), wherein the mobilities are traceable to the SI, and secondary methods, wherein the mobilities are traceable to those of the reference compounds used for calibration. Here we provide recommendations to make this traceability possible.</p><p>We also highlight the difficulties and confusion caused by the absence of commonly agreed upon reference materials and consensus values for primary standards for ion mobility spectrometry.</p><p>Several sets of compounds and several sets of values currently coexist. This situation is akin to that of mass spectrometry before having agreed on the mass of carbon 12 (Cameron & Wichers, 1962). Progress towards agreeing on values of the highest metrological quality for primary standards is urgent, to fully take advantage of the recent progress made in ion mobility measurement precision and speed. To determine the best standards and their values, the community would benefit from a round robin study using exclusively the primary method, and to compare values obtained with drift tube instruments having different designs. These standards and their reference values shall eventually be used to assess the merits of secondary methods of measurements, or compare the merits of different calibration procedures. Meanwhile, when comparing secondary methods or calibration procedures, it is very important that the study design eliminates as far as possible the variabilities related to the effects of ion structures, as well as the effects of unrecognized biases in the calibration input values.</p><p>Although the present article was conceived as a guide and provides recommendations rather than strict guidelines, we anticipate that in the future one may need such guidelines, for example to establish data standards, reporting standards, data processing software packages, data formats and databases. Common databases of CCS and K0 would need to include all information about the methods used for data acquisition (steps 1-3) and for data processing (steps 4-6) to obtain the values and their associated uncertainties. The present recommendations should constitute the foundation for future guidelines and standards in ion mobility.</p>