BACKGROUND OF THE INVENTION

Field of the Invention

The invention relates to methods and devices for determining reduced ion mobilities Koby trapped ion mobility spectrometry.

Description of the Related Art

Ion mobility spectrometry is an analytical technique which is used to investigate the mobility of analyte ions in a buffer gas. An inherent feature of ion mobility spectrometry is that the ion mobility depends on molecular geometries of the ions such that it is often possible to resolve and thus separate isomers or conformers that cannot be resolved by mass spectrometry.

The reduced ion mobility Korelates to the ion mobility K under the gas pressure P and gas temperature T:

Ko=K⁢PPo⁢ToT
where Toand Poare the standard temperature (273 K) and standard gas pressure (1013 hPa).

The reduced ion mobility Kocan be converted into a momentum transfer cross section Ω (collisional cross section, CCS) via the Mason-Schamp equation:

Ko=3⁢⁢q16⁢⁢no⁢2⁢⁢πμ⁢⁢kB⁢1Ω
where q is the charge of the ion, T is the gas temperature, nois the standard density of the buffer gas, kBis the Boltzmann constant, and μ is the reduced mass of the ion and the drift gas molecules. The reduced ion mobility Koand the collision cross section Ω are equivalent information and are often used interchangeably.

The accuracy of measured values of the reduced ion mobility (collisional cross section) takes on increased significance in a range of applications. For example, the reduced ion mobility which is measured by ion mobility spectrometry-mass spectrometry (IMS-MS) enables to elucidate structures of complex and dynamic biological systems. It is also used to identify metabolites in metabolomics studies and peptides in proteomics studies, in particular by coupling IMS-MS with liquid chromatography (LC).

In trapped ion mobility spectrometry (TIMS), ions are at first trapped along a non-uniform electric DC field (field gradient) by a counteracting gas flow or along a uniform electric DC field by a counteracting gas flow which has a non-uniform axial velocity profile (gas velocity gradient). The trapped ions are separated in space according to ion mobility and subsequently eluted (released) over time according to their mobility by adjusting one of the gas velocity and the electric DC field (U.S. Pat. No. 6,630,662 B1 by Loboda; U.S. Pat. No. 7,838,826 B1 by Park). A TIMS analyzer is commonly operated in the low pressure range of 2 to 500 Pa and uses an electric RF field for radially confining the ions. Regarding the theoretical basis of TIMS, see the article “Fundamentals of Trapped Ion Mobility Spectrometry” by Michelmann et al. (J. Am. Soc. Mass Spectrom., 2015, 26, 14-24).

Ion mobility calibration typically requires a calibration function and calibrants with known reduced ion mobility. An empirical calibration function used in TIMS is known from the article “High Resolution Trapped Ion Mobility Spectrometry of Peptides” by Silveira et al. (Anal. Chem., 2014, 86, 5624-5627):

Ko=a+bVm
where a and b are calibration constants and Vmis approximately the voltage applied across the TIMS analyzer when the ion species is measured at the ion detector. The voltage Vmcan be derived from the measured arrival time of the ion species at the detector. The calibration constants are determined from fitting the known Koof the calibrants and the corresponding voltages Vmof multiple calibrants.

Another calibration procedure is known from the article “A Transferable, Sample-Independent Calibration Procedure for Trapped Ion Mobility Spectrometry (TIMS)” by Bleiholder et al. (Anal. Chem., 2018, 90, 9040-9047).

The calibration strategy by Bleiholder et al. differs from the typical approach in three aspects. First, the calibration function is based on a solution to the Boltzmann transport equation but is not motivated by empirical observations. Second, they separate quantities that depend on the sample from those that depend on the instrument. Third, they perform a Taylor expansion for the instrument-dependent quantities and calibrate the Taylor expansion coefficients. The result is a calibration procedure for a trapped IMS instrument that is stated to be accurate, robust, and transferable.

SUMMARY OF THE INVENTION

In a first aspect, the invention provides a method for determining the reduced mobility Koof an ion species. The method comprises:providing ions of the ion species to a TIMS analyzer;trapping the ions in the TIMS analyzer by setting an electric DC field and gas flow of the TIMS analyzer;adjusting the strength of the electric DC field and/or the velocity of the gas flow in time to release the trapped ions of the ion species;measuring the arrival time tmof the released ions at an ion detector;determining instrumental parameters piof the TIMS analyzer; anddetermining the reduced mobility Koby inverse of the system function: Ko=SYS−1(tm,pi).

The TIMS analyzer may comprise an electric DC field with a field gradient and a gas flow opposing the force of the electric DC field or a gas flow with a velocity gradient and an electric DC field opposing the drag force of the gas flow.

The arrival time tmof an ion species at the ion detector depends on the instrumental parameters and the reduced mobility to be determined: tm=SYS(Ko,pi).

Preferably, the electric DC field of the TIMS analyzer comprises a field gradient and a plateau, which is located downstream of the field gradient and has a substantially constant electric DC field, and the gas flow has a substantially constant velocity at the beginning of the plateau. More preferably, the gas flow is directed downstream towards the ion detector and the electric DC field comprises a rising electric DC field gradient opposing the drag force of the gas flow.

The inverse of the system function SYS can be approximated by:

Ko=1(12⁢βvg⁢2⁢Lpβ+(12⁢βvg⁢2⁢Lpβ)2-βvg⁢(tm-tt-E0β))2⁢PPo⁢ToT
wherein tmis the measured arrival time at the ion detector, β is the scan speed, vgis the gas velocity at the plateau, Lpis the effective length of the plateau, Eois the electrical field strength of the plateau at the start of the scan, ttis the transfer time between the end of the plateau and the ion detector (which can be zero if the detector is located directly at the end of the plateau), P is the gas pressure at the plateau and T is the gas temperature at the plateau. The electric DC field strength of the plateau Ep(t) is preferably linearly decreased in time by the scan speed β:
Ep(t)=E0−βt

In a second aspect, the invention provides a method for determining the reduced mobility Koof an ion species. The method comprises:(a1) providing ions of the ion species to a TIMS analyzer;(a2) trapping the ions in the TIMS analyzer by setting an electric DC field and gas flow of the TIMS analyzer;(a3) adjusting the strength of the electric DC field and/or the velocity of the gas flow in time to release the trapped ions of the ion species;(a4) measuring the arrival time tmof the released ions at an ion detector;(b) repeating the steps (a1) to (a4) for at least two different values of an instrumental parameter x to obtain measured data (tm,x)i=1 . . . nwherein n is the number of measurements; and(c) determining the reduced mobility Koby one of:fitting a system function tm=SYS(x,pi,Ko) to the measured data (tm,x)i=1 . . . nby varying the reduced mobility Ko; andtransforming the measured data (tm,x)i=1 . . . ndetermining polynomial coefficients cjby fitting a polynomial function to the transformed data (tm,x)i=1 . . . nand determining the reduced mobility Kousing the polynomial coefficients cjand inversed coefficient functions Cj(Ko,pi) of a transformed system function SYS:

t_m=S⁢⁢Y⁢⁢S⁡(x¯,pi,Ko)=∑j=1N⁢Cj⁡(pi,Ko)⁢x¯j
Ko=Cj−1(pi,cj)

wherein piare predetermined instrumental parameters which are not varied in the repeated measurements.

The TIMS analyzer may comprise an electric DC field with a field gradient and a gas flow opposing the force of the electric DC field or a gas flow with a velocity gradient and an electric DC field opposing the drag force of the gas flow.

Preferably, the electric DC field of the TIMS analyzer comprises a field gradient and a plateau, which is located downstream of the field gradient and has a substantially constant electric DC field, and the gas flow has a substantially constant velocity at the beginning of the plateau. More preferably, the gas flow is directed downstream towards the ion detector and the electric DC field comprises a rising electric DC field gradient opposing the drag force of the gas flow.

The system function tm=SYS(x,pi,Ko) can be approximated by:

tm⁡(Ko,E0,β,vg,Lp,tt)=E0β-vgβ⁢1K+2⁢Lpβ⁢1K+tt⁢⁢withK=Ko⁢PoP⁢TTo
wherein tmis the arrival time at the ion detector, β is the scan speed, vgis the gas velocity at the plateau, Lpis the effective length of the plateau, Eois the electrical field strength of the plateau at the start of the scan, ttis the transfer time between the end of the plateau and the ion detector, K is the mobility, Kois the reduced mobility, P is the gas pressure at the plateau and T is the gas temperature at the plateau. The electric DC field strength of the plateau Ep(t) is linearly decreased in time by the scan speed β: Ep(t)=E0−βt. The varied instrumental parameter is preferably one of the length of the plateau LP, the scan speed β and the gas velocity vgat the plateau.

Each one of the instrumental parameters pican be directly measured and/or determined from a parameter function pi=Pi(qi) wherein qi(i=1 . . . n, n≥1) is at least one measured instrumental parameter. The instrumental parameter qican be one of the instrumental parameters pior another instrumental parameter. Preferably, the gas pressure Pinat the entrance and/or the gas pressure Poutat the exit of the TIMS analyzer are measured and at least one of the instrumental parameters is determined by a parameter function depending on Pin, Poutor both. More preferably, the gas velocity at the plateau vgand the gas pressure P at the plateau are determined by parameter functions which depend on Pinand Pout. The gas temperature T at the plateau is preferably determined by a parameter function which depends on the gas temperature Tinand the gas pressure Pinmeasured at the entrance of the TIMS analyzer and optionally also on the gas pressure Poutat the exit of the TIMS analyzer.

In all aspects of the invention, ions can be generated using one of spray ionization (e.g. electrospray ESI or thermal spray), desorption ionization (e.g. matrix-assisted laser/desorption ionization (MALDI) or secondary ionization), chemical ionization (API), photo-ionization (PI), electron impact ionization (EI), and gas-discharge ionization. The ionization can take place at or above atmospheric pressure or under vacuum (low, medium or high vacuum).

In all aspects of the invention, ions can be detected by one of a Faraday detector, a secondary electron multiplier (e.g. a microchannel plate) and an image-current detector. Furthermore, the ion detector is preferably a mass analyzer which can for example be one of a time-of-flight mass analyzer (in particular with orthogonal ion injection), an electrostatic ion trap, a RF ion trap, an ion cyclotron resonance analyzer and a quadrupole mass filter.

