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OVERVIEW

PURPOSE: Further investigation of the physics of Travelling

Wave Ion Mobility (TWIM) to inform best experimental

practice, improve calibration methodology and guide future

instrument design.

METHODS: A generalised theoretical approach to TWIM is

presented. Numerical simulations were carried out in SIMION

8.1 and experimental measurements were taken for a diverse

range of species over a wide range of TWIM conditions.

RESULTS: In order to accurately describe TWIM

measurements, the effects of velocity relaxation should be

properly taken into account. We introduce a generalised

calibration method that can accommodate these effects and

demonstrate its performance on experimental data.

INTRODUCTION

Travelling Wave Ion Mobility (TWIM) has been in use since

around 20041. Ions are separated by a series of DC waves of

wavelength λ moving with velocity v (Figure 1) which

overtake them and push them through a gas-filled RF ion

guide. Less mobile species are overtaken more frequently

than highly mobile species, producing a mobility dependent

average ion velocity v̅ion. Owing to the relatively complicated

motion of ions in a TWIM device, these are typically calibrated

using standards whose collisional cross section (CCS) has

been measured by drift tube ion-mobility.

Routine TWIM CCS measurements of singly charged species

is supported in commercially available software, giving

accurate CCS between 1-2%2. In this poster we address the

problem of deriving a robust calibration method that is valid

over a wide range of charge states, mobilities and instrument

conditions.

FUNDAMENTALS OF TRAVELLING WAVE ION MOBILITY REVISITED: TOWARDS UNIVERSAL CALIBRATION

Keith Richardson1, David Langridge1, Kevin Giles1, Sugyan Dixit2, Brandon Ruotolo2 1Waters Corporation, Altrincham Road, Wilmslow, UK; 2Department of Chemistry, University of Michigan, University Ave., Ann Arbor, MI, USA

Figure 1. Simulated electrical potential in the TWIM ion guide configura-

tion used in the Waters Synapt G2-Si and VION instruments. On these

instruments the wavelength λ = 12mm and v is typically between 300 and 1000 ms-1. Along the axis of the device the waveform is approximately sinusoidal.

METHODS

Basic TWIM Theory

References

1. K. Giles, S.D. Pringle, K.R. Worthington, D. Little, J.L. Wildgoose, R.H. Bateman, Rapid Commun.

Mass Spectrom. 18, 2401-2414 (2004)

2. M. Bush, I. Campuzano, C. Robinson, B. Ruotolo, Anal. Chem. 82, 9557-9565 (2010)

3. K. Richardson, D. Langridge, K. Giles, Int. J. Mass Spectrom. 428, 71-80 (2018)

4. A.A. Shvartsburg, R.D. Smith, Anal. Chem. 80 (24), 9689-9699 (2008)

5. Y. Zhong, S. Hyung, B. Ruotolo, Analyst 136, 3534-3541 (2011)

6. SIMION 3D v8.1, Scientific Instrument Services, Inc., www.simion.com

7. B.T. Ruotolo, K. Giles, I. Campuzano, A.M. Sandercock, R.H. Bateman, C.V. Robinson, Science 310

1658 (2005) .

8. Haynes, S. E., Polasky, D. A., Dixit, S. M., Majmudar, J. D., Neeson, K., Ruotolo, B. T., and Martin, B.

R. Anal Chem, 89 (11), 5669-5672 (2017)

but systematic deviations towards low CCS. This is why the 1+ and 2

+

ions were omitted from the calibration dataset. These deviations are a

result of the slightly different radial distributions adopted by different ion

populations, and will be reported on more fully in future work.

As in the work of Zhong et al.5, pure mobility CCS calibrations of

experimental data (Figure 5A-C) show large residuals at high wave

velocities, where relaxation effects are largest. This dependence is

largely removed by the new mass-to-charge dependent calibration form

used in Figure 5D. However, as with the simulated data, there is

remaining structure in the residuals that requires further investigation.

As well as suggesting improved calibration methods, this work should

lead to improved guidance for TWIM experimental design.

CONCLUSION

Improved understanding of behaviour of ions in TWIM devices

New approach to TWIM calibration, motivated by theoretical

results, tested with simulated and experimental data

Significantly improved calibrations obtained for a diverse protein

and peptide mixture (spanning 151Å2 to 13,400Å

2, 1

+ to 40

+)

Remaining structure in residuals needs further investigation

Figure 2. A roll-over event for a single wave of arbitrary shape and

wavelength λ moving rightwards with a velocity v. A) At time t=0 the

wave has just reached an ion at x=0 (depicted by the red dot). B) At

time t=T the wave has passed under the ion which now sits at the left

hand extreme of the wave. During this time, it can be seen that the ion

has moved to the right by a distance vT-λ. C) The same roll-over event

depicted in the travelling wave frame with gas flowing from the right.

Figure 2 depicts a single roll-over event A), B) in the laboratory refer-

ence frame. From these figures it can be seen that the ion moves a dis-

tance vT-λ during the rollover period T, so that the average ion velocity

must satisfy the fundamental TWIM equation

Since v and λ are known experimental parameters, the problem reduces

to finding the period T.

Pure Mobility Result: Smoothly Moving Waves

We consider first the scenario in which the waves move smoothly and

an ion always moves at its terminal “drift” velocity K E(X) where K is the

ion mobility and E(X) is the instantaneous electric field corresponding to

the potential V(X) i.e. E(X) = -dV(X)/dX.

By considering the roll-over event C) in the reference frame which

moves along with the travelling wave it is possible to show3 that in the

absence of velocity relaxation effects the period T satisfies

This result generalises that of Shvartsburg and Smith4 to arbitrary asym-

metric waveforms.

Pure Sinusoidal Waves

Owing to field relaxation, the potential along the central axis of the de-

vice is approximately sinusoidal (see Figure 1). We therefore consider

where V0 is the T-wave amplitude and the wavenumber k=2π/λ. Using

(2) we find that the average ion velocity is

where we have introduced the important dimensionless quantity

Note that as γ →1 the average ion velocity v̅ion→v. This corresponds to

the undesirable “surfing” condition in which the ion is pushed along at

the same speed as the travelling wave. The opposite limit γ →0 corre-

sponds to an ion which is not influenced at all by the travelling wave

(low mobility, low wave height or high wave velocity).

Velocity Relaxation

An important difference between drift tubes and ion mobility in time-

dependent fields is the presence of velocity relaxation effects. An ion in

a mobility device at a velocity other than its drift velocity K E(X) takes a

finite time to reach the steady state condition. In a TWIM device the

field experienced by most ions is perpetually changing, so it is important

to consider the magnitude of these effects and the extent to which they

can be avoided or controlled. Our starting point is the equation of mo-

tion:

which includes the electrostatic force and a linear restoring drag force

with coefficient q/K which reproduces the relaxation-free behaviour (2) in

the limit m/q → 0. For the sinusoidal electric field (3) we can transform

this3 into an equivalent dimensionless equation in the travelling wave

frame:

where we have introduced another important dimensionless quantity:

Equation (6) can be solved perturbatively when α is small, and to order α

4 we find

3 that the average ion velocity is:

Calibration

In the absence of velocity relaxation effects, the average ion velocity for

a symmetric wave predicted by (1) and (2) can be expanded in powers

of K2:

where the coefficients c2, c4, c6, c8 … depend on travelling wave param-

eters and K is inversely proportional to CCS. This is therefore a natural

starting point for CCS calibration of a TWIM device.

(1)

(4)

and

(3)

(9) has to be modified when velocity relaxation effects are introduced.

Expanding (8) in powers of K2 and (m/q)

2, we find that we need to in-

clude extra terms of the form:

Ion Optical Simulations of a Realistic Device

The above treatment deals with a simplification of the real experimental

system. In order to obtain a more realistic test of the new calibration

scheme we created a SIMION6 model that included discrete stepping of

the travelling wave, an anharmonic and radially dependent TW field, off-

axis motion with RF confinement and diffusion using the SDS collision

model. We simulated drift times for a range of ion species and applied

both the conventional power-law calibration7 and a calibration given by

(9) and (10) including terms up to order K6 and (m/q)

4.

Experimental

All the samples were purchased from Sigma-Aldrich. For native protein

ions, glutamate dehydrogenase (GDH) (G7882), alcohol dehydrogenase

(ADH) (A7011), avidin (A9275), cytochrome c (C2506), and ubiquitin

(U6253) samples were prepared at a concentration of 5μM in 200mM

ammonium acetate. Denatured cytochrome c ions and polyalanine

(P9003) ions were generated from samples dissolved in 49.5/49.5/1

water/methanol/formic acid solution.

Experimental data was acquired using a Synapt G2 HDMS instrument

(Waters). Ions were generated using nano-electrospray ionization

(nESI). Ion transmission voltages were optimized for each native protein

ion to minimize activation and preserve native-like structure. Arrival time

distributions (ATDs) were recorded over a broad range of travelling

wave amplitudes and velocities at a pressure of ~3.5 mbar in TWIM cell.

ATDs were extracted using TWIMExtract8. Data processing and CCS

calibration were done using in-house python scripts.

RESULTS

Figure 3 shows the simulated effect of velocity relaxation on singly

charged polyalanine (green) and tetraalkylammonium salts (red) under

typical Synapt TWIM conditions. The largest change (-1.8%) occurs for

the most massive ion (Ala)14. The included species are typical of those

used in TWIM calibrations. Relaxation effects are largest for ions with

high α and low γ.

Figure 4 shows residual CCS errors following two calibrations created

using simulated data. Results are plotted for a wide range of species

ranging from singly charged polyalanine to GDH. 1+ and 2

+ polyalanine

ions were omitted from the calibration set for reasons discussed below.

The top plot A) shows the result for a standard two-parameter power-

law calibration, while a new six-parameter calibration of the form given

by (9) and (10) was used in the bottom plot B).

Figure 5 shows RMS residuals resulting from calibration of the experi-

mental data under a wide range of experimental conditions. The top

row shows two-parameter mobility-only calibrations while the bottom

row shows two six-parameter calibrations (mobility only and mass-to-

charge dependent).

(6)

(7)

(5)

(8)

(2)

(10)

A

(9)

B

C

Figure 5. RMS residuals for calibration of experimental TWIM data for

the same species as Figure 4 (all ions included). A) two-parameter

power law calibration B) K2,K

4 terms C) K

2,K

4,K

6,K

8,K

10,K

12 terms D)

K2,K

4,K

6,K

4(m/q)

2, K

6(m/q)

2, K

6(m/q)

4 terms.

2 parameter calibrations

6 parameter calibrations

A B

C D

Figure 4. Simulated CCS residuals for A) a standard power-law calibra-

tion and B) a calibration using terms from (9) and (10) up to order K6

and (m/q)4. Note that singly- and doubly-charged polyalanine species

(blue and orange series) were omitted from the calibration set. Simulat-

ed instrument settings were V0=16.7V, v=600ms-1

, 3 mbar N2 gas. Spe-

cies with CCS ranging from to 151 to 13,400Å2, mass 231Da to 336kDa

and charge states from 1+ to 40

+ are plotted. In the legend, the native

proteins are labelled with asterisks.

.

.

.

,

DISCUSSION

In calibrated experiments both calibrants and analytes are affected by

velocity relaxation, but only differential effects appear in the results.

Moreover, relative shifts in measurements of K or CCS are about half of

those of the corresponding velocity shift. This accounts for the success

of existing calibration strategies which do not explicitly incorporate relax-

ation effects.

However, it is known that care must be taken when including species of

widely differing mass and mobility in a calibration. Indeed, previous

work5 shows that calibration residuals are largest under conditions for

which velocity relaxation effects are expected to be important i.e. high

wave velocity and low pressure.

The successful calibration of the simulated data in Figure 4 demon-

strates that the improved calibration is flexible enough to accommodate

many features of a real device not explicitly included in the theoretical

development outlined above. However, close examination of Figure 4B

reveals that the lower charge state (polyalanine) ions still show small

Figure 3. Percentage change in average ion velocity when relaxation

effects are included, plotted as a function of α and γ. The green dots

represent (Ala)n, n=3..14 and the red dots represent methyl-octyl TAA

salts under typical Synapt conditions (V0=16.7V, v=1000ms-1

, 3 mbar N2

gas). In all cases, the average ion velocity is reduced by relaxation ef-

fects.

%

%

%

%

%

%

%

%

A

B