Supporting Information
Least-squares fitting of FTMS transients
Tagir Aushev, Anton N. Kozhinov, and Yury O. Tsybin
Figure S1. Least-squares fitting (LSF) of an experimental transient signal
acquired for isolated monoisotopic ions of singly charged peptide MRFA (524
m/z) analyzed on the 10 T FT-ICR MS. Top panel shows a 24 ms long singlescan transient signal. Bottom panel shows an expanded view of the transient
with sampled points and a curve corresponding to the fitting function. The
sampled points are connected with a stair-step line for visual convenience
only.
1
Figure S2. Correlation between the measurement error, Δf, of FT signal
processing and the true frequency, fn , in numerical simulations of frequency
measurements performed for modeled sinusoidal signals. Conventional FT
signal processing workflow was used, including Hann apodization window
and single zero-filing. Out of N =10 points on the plot, the nth point,
n = 0, … , N-1, shows the analysis of the transient signal with frequency
fn = f0 + n Δdf / (N-1), where Δdf = 1/ (2T) is the frequency spacing in the
discrete Fourier spectra of these signals. The
following parameters
corresponding to LSF analysis of the ICR transient signals, Figure 2 and
Table 1, were used: length T = 24 ms, frequency f0 = 292,941.44 Hz (the
leftmost point on the plot), amplitude A = 0.405, and phase φ = – 86.70.
Additional results obtained for the other phase φ = – 80.50 did not differ
noticeably compared w.r.t. the effect under consideration (data not shown).
2
Figure S3. Phase jittering of the monoisotopic ion in the LSF analysis of the
set of 1,000 ICR transient signals acquired for the isolated isotopic
distribution of a doubly charged peptide substance P. No correlation between
the phase and the scan number was found.
3
Figure S4. Frequency (top) and amplitude (middle) distributions obtained
with LSF (solid lines) and FT (dashed lines) processing of 1,000 modeled
transient signals with 5 spectral components corresponding to isotopic
distribution of a doubly charged peptide substance P. Phase distributions
(bottom) were obtained with LSF. The modeled transient signals were
generated using experimental parameters (shown with red lines) derived
from the LSF results for the ICR transients, Figure 3. Note, only a single
initial phase value was used for the modeling.
4
Figure S5. Frequency distributions obtained with LSF processing of
5-component ICR transient signals at different lengths: (top) 48 ms; (middle)
24 ms; and (bottom) 12 ms. The set of 1,000 transients was acquired for the
isolated isotopic distribution of a doubly charged peptide substance P
analyzed on the 10 T FT-ICR MS.
5
Table S1. Validation of the LSF method for a transient signal whose Fourier
spectrum contains unresolved fine-structure clusters of isotopologues. The
transient signal, with length T = 24 ms and sampling frequency fs =
2.7306(6) MHz, was generated as a sum of sinusoidal components with zero
initial phases and values of amplitudes and frequencies corresponding to the
theoretical abundances and m/z of all isotopologues from the 5 clusters of
doubly charged peptide substance P. Ion frequencies were calculated for
10 T magnetic field, Figure 1 and Figure 3.
Cluster
0
1
2
3
Generated signal
Frequency, Amplitude,
Hz
a.u.
227737.1654
100.00
227568.9374
227568.5407
227567.8719
227567.7265
227567.3792
227400.9578
227400.6672
227400.5617
227399.8938
227399.7487
227399.4977
227399.4019
227399.3525
227399.2445
227399.0058
227398.8298
227398.6847
227398.5395
227398.3379
227398.1928
227397.8460
227233.2260
227232.9358
227232.8304
227232.1636
227232.0186
227231.8734
227231.7680
227231.7284
227231.6724
227231.6231
227231.5152
227231.3822
227231.2768
6.58
7.90E-01
68.14
4.95E-01
1.15
2.04E-01
4.47
5.19E-02
4.48
3.26E-02
5.38E-01
7.56E-02
3.91E-03
2.67
9.08E-03
22.85
3.37E-01
1.13E-03
7.84E-01
5.70E-03
6.55E-03
3.98E-03
2.94E-01
1.61E-03
1.39E-01
1.01E-03
3.05
3.54E-02
2.22E-02
2.35E-03
2.57E-04
1.76E-01
5.15E-02
5.97E-04
Expected values
LSF results
Frequency, Amplitude, Frequency, Amplitude,
Hz
a.u.
Hz
a.u.
227737.165
99.996
227737.1654
100.00
±0.001
±0.005
Phase, °
-0.003
±0.005
227567.9613
77.15
227567.960
±0.001
77.119
±0.005
-0.001
±0.007
227399.2299
36.52
227399.228
±0.003
36.460
±0.005
0.002
±0.014
227230.7855
12.84
227230.790
±0.008
12.800
±0.005
0.009
±0.041
6
4
227231.1197
227231.1011
227230.9562
227230.8113
227230.7056
227230.6100
227230.5607
227230.4650
227230.4528
227230.4157
227230.3079
227230.2144
227230.1188
227230.0695
227230.0387
227229.9617
227229.8938
227229.7489
227229.7233
227229.6039
227229.5476
227229.4026
227229.2577
227229.0564
227228.9115
227228.5652
227065.7414
227065.4517
227065.3464
227064.6805
227064.5882
227064.5358
227064.3908
227064.2856
227064.2461
227064.1901
227064.1409
227064.0332
227063.9003
227063.7951
227063.7434
227063.6382
227063.6197
227063.4750
227063.3302
227063.3300
227063.2248
227063.1852
227063.1292
227063.0800
227063.0405
227062.9845
227062.9723
227062.9353
227062.8395
227062.8276
227062.7343
227062.6948
227062.6388
227062.5896
227062.5774
2.11E-02
1.50
2.22E-02
7.44E-05
1.80E-01
5.15E-02
2.66E-03
3.75E-04
1.82
8.94E-06
1.22E-02
6.19E-03
4.31E-04
4.50E-05
5.02
3.07E-02
1.13E-01
7.71E-04
5.17E-05
1.58E-06
2.63E-01
3.88E-03
1.30E-05
4.46E-03
3.24E-05
2.46E-05
5.45E-05
9.14E-03
3.14E-05
2.71E-03
1.05E-02
1.97E-05
2.00E-01
1.10E-03
1.46E-03
4.58E-05
7.98E-06
5.46E-03
3.38E-03
1.85E-05
1.20E-01
1.39E-03
4.67E-02
6.89E-04
2.31E-06
1.02
1.19E-02
1.51E-02
1.60E-03
1.75E-04
5.06E-05
1.16E-05
1.20E-01
5.88E-07
3.51E-02
8.03E-04
4.07E-04
2.55E-04
1.34E-05
2.96E-06
1.44E-02
227062.5716
3.60
227062.59
±0.03
3.584
±0.005
0.05
±0.15
7
227062.5589
227062.4819
227062.4327
227062.4141
227062.3491
227062.3250
227062.2694
227062.2438
227062.1639
227062.1247
227062.0869
227062.0684
227062.0192
227061.9237
227061.9115
227061.8745
227061.7790
227061.7668
227061.7297
227061.6735
227061.6221
227061.5780
227061.5287
227061.4980
227061.4332
227061.4211
227061.3840
227061.3533
227061.2763
227061.2086
227061.1830
227061.0875
227061.0639
227061.0383
227061.0076
227060.9306
227060.9191
227060.8629
227060.7181
227060.6926
227060.5734
227060.5171
227060.3724
227060.2277
227060.0267
227059.8820
227059.5363
3.30E-01
2.02E-03
9.64E-05
7.44E-03
2.93E-04
3.29E-02
5.07E-05
3.40E-06
3.97E-02
1.04E-07
2.43E-04
1.73E-02
8.93E-04
2.55E-04
6.10E-01
6.09E-06
8.56E-07
8.32E-03
1.25E-08
2.07E-03
2.56E-05
2.93E-04
3.06E-05
8.15E-01
2.13E-06
2.09E-02
1.03E-07
2.49E-02
1.40E-04
2.59E-04
3.52E-05
1.62E-06
1.08E-06
2.56E-07
5.78E-02
1.75E-04
1.51E-09
1.30E-03
8.87E-06
1.94E-07
1.82E-08
1.50E-03
2.21E-05
7.41E-08
1.68E-05
1.22E-07
6.86E-08
8
Table S2. Mean values and standard deviations of frequencies, amplitudes,
and initial phases obtained with LSF and FT methods for the modeled
transients with 5 spectral components corresponding to isotopic distribution
of a doubly charged peptide substance P. The modeled transient signals were
generated using experimental parameters derived from the ICR transients.
The leftmost column lists the values used for transient signal modeling.
Note, only a single initial phase value was used for the modeling. FT bias
values are given relative to the FT standard deviations. N/A indicates that
ion phases were calculated using LSF only.
Parameters
Amplitude 1
Frequency 1,
Phase 1, 0
Amplitude 2
Frequency 2,
Phase 2, 0
Amplitude 3
Frequency 3,
Phase 3, 0
Amplitude 4
Frequency 4,
Phase 4, 0
Amplitude 5
Frequency 5,
Phase 5, 0
Hz
Hz
Hz
Hz
Hz
True
value
28.8
227737.4
-79
22.4
227568.35
-64
10.5
227399.67
-49
3.8
227231.32
-33
1.2
227064.1
-19
LSF mean
28.80
227737.40
-79.0
22.40
227568.35
-64.0
10.50
227399.66
-49.0
3.80
227231.34
-33.1
1.20
227064.1
-19
LSF
std
0.06
0.05
0.2
0.05
0.05
0.3
0.05
0.11
0.6
0.05
0.32
1.5
0.05
1.0
5
FT mean/bias
FT std
28.70/-1.4
227736.81/-8.4
N/A
22.32/-1.1
227568.48/1.4
N/A
10.46/-0.7
227400.39/3.8
N/A
3.78/-3.3
227232.63/2.4
N/A
1.20/0.0
227066.2/1.3
N/A
0.07
0.07
N/A
0.07
0.09
N/A
0.06
0.19
N/A
0.06
0.54
N/A
0.06
1.6
N/A
9
Table S3. Mean values and standard deviations of frequencies, amplitudes,
and initial phases obtained with LSF and FT methods for the modeled
transients with 5 spectral components corresponding to isotopic distribution
of a doubly charged peptide substance P. The modeled transient signals were
generated using experimental parameters derived from the Orbitrap
transients. The leftmost column lists the values used for transient signal
modeling. FT bias values are given relative to the FT standard deviations.
N/A indicates that ion phases were calculated using LSF only.
Parameters
Amplitude 1
Frequency 1,
Phase 1, 0
Amplitude 2
Frequency 2,
Phase 2, 0
Amplitude 3
Frequency 3,
Phase 3, 0
Amplitude 4
Frequency 4,
Phase 4, 0
Amplitude 5
Frequency 5,
Phase 5, 0
Hz
Hz
Hz
Hz
Hz
True
value
68
468962.89
168
54
468788.82
105
26
468614.89
44
9.1
468440.92
-16
1.6
468265.97
-67
LSF
mean
68.00
962.890
168.00
54.00
788.820
105.00
26.00
614.891
44.00
9.1
440.92
-16.00
1.6
265.97
-67.0
LSF
std
0.02
0.006
0.03
0.02
0.009
0.05
0.02
0.016
0.08
0.02
0.05
0.25
0.02
0.27
1.4
FT mean/bias
FT std
67.93/-2.9
468962.68/-21.4
N/A
53.992/-0.3
468788.97/11.7
N/A
25.899/-4.1
468614.84/-1.4
N/A
9.12/0.8
468440.58/-4.4
N/A
1.60/0.2
468265.95/-0.05
N/A
0.02
0.01
N/A
0.024
0.01
N/A
0.025
0.03
N/A
0.02
0.08
N/A
0.02
0.43
N/A
10