fundamentals of travelling wave ion mobility …€¦ · note that singly-and doubly-charged...
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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