Graphical Ranking of Divisors to Get the Most out of a Resolution

Subscriber access provided by YORK UNIV

Article

Graphical Ranking of Divisors to Get the Most out of a Resolution-Enhanced Kendrick Mass Defect Plot Sayaka Nakamura, Robert Bernard Cody, Hiroaki Sato, and Thierry Nicolas Jean Fouquet Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b04371 • Publication Date (Web): 24 Dec 2018 Downloaded from http://pubs.acs.org on December 24, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Analytical Chemistry

1

Graphical Ranking of Divisors to Get the Most out of a Resolution-Enhanced

2

Kendrick Mass Defect Plot

3

Sayaka Nakamura,1 Robert B. Cody,2* Hiroaki Sato,1 Thierry Fouquet1*

4

1

5

Technology (AIST), Tsukuba, Ibaraki, Japan. 2 JEOL USA Inc., Peabody, MA, USA.

Research Institute for Sustainable Chemistry, National Institute of Advanced Industrial Science and

6 7 8

Abstract: Resolution-enhanced Kendrick mass defect (KMD) analysis using the new concept of

9

fractional base units (repeating unit R divided by an integer X, R/X as a mathematical moiety) is now

10

a powerful data processing tool to unravel complex mass spectra of polymers. It enhances a regular

11

KMD analysis using the chemical moiety R to compute mass defects with unprecedented separation of

12

ion series differing by their isotopic or co-monomeric content, end-groups or charge states in highly

13

visual KMD plots. The value of the divisor X dictates the gain of separating power from the regular to

14

the resolution-enhanced KMD plot and its choice strongly affects the ease and speed of data

15

interpretation. A simple tool to help selecting the best values of X depending on the users’ needs is

16

mandatory to rationalize the analysis and avoid a time-consuming trial-and-error methodology. We

17

propose two graphical representations intuitively ranking the well-suited divisors for the appropriate

18

separation of isotopes and/or co-oligomers for copolymeric mass spectral data. Rankings are extended

19

to any type of dataset from homopolymeric blends to terpolymers by generalizing the formulas with

20

three variables beyond the specific separation of isotopes. The “RANK” functions are now available in

21

commercial or home-made spreadsheet (available upon request) to interactively select divisors and

22

compute the associated KMD plots.

23 24 25

Table of Contents

26 27

ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

28

Page 2 of 18

Introduction

29

It has been a long journey from the change of basis proposed by Kendrick fifty years ago1 to the

30

compositional mapping of complex mass spectra from hydrocarbons2-4 and polymers5-10 using Kendrick

31

mass defect (KMD) plots. A “regular” KMD analysis first consists in peak-picking a high-resolution /

32

high-accuracy mass spectrum displaying peaks spaced by one or several repetitive moieties. Mass-to-

33

charge ratios (m/z) are then turned into Kendrick masses by an affine transformation

34

KM(R) = 𝑚/𝑧 ∙

round(R) R

(1)

35

with R the exact mass of a repeating unit used as “base unit”. The associated “defects” are evaluated

36

using

37

(2)

KMD = round(KM) ―KM

38

Plotting KMDs as a function of m/z produces visual and informative “maps”. Horizontally aligned

39

points correspond to ions of identical elemental composition modulo R while oblique alignments reveal

40

variations of elemental compositions in any moiety but R.3-8 All these steps may be done using

41

commercial programs dedicated to the KMD analysis or spreadsheets. It makes KMD analysis a very

42

simple data processing tool available to everyone equipped with a computer.

43

Analysts have taken a renewed interest in KMD analysis11 thanks to the recent introduction of

44

“resolution-enhanced” KMDs computed by replacing the “chemical” moiety R with a “mathematical”

45

moiety R/X, a fractional base unit with X being a positive integer.12 R

46

KM(R,X) = m/z ∙

round(X) R X

(3)

47

The associated KMD plots variably separate ion series differing by their end-groups,13 co-

48

monomeric content14 or charge states15 depending on the value of X, taking full advantage of the spectral

49

width of a KMD plot. Resolution-enhanced KMDs are also compatible with low-accuracy data as the

50

decrease of accuracy is counterbalanced by the improved separating power of the plot.12 In spite of its

51

undeniable capabilities for polymer and carbonaceous ions,16 the question remains: how to choose the

52

optimal divisor X of the fractional base unit R/X?

53

In a previous letter to the editor, we demonstrated that a “recommended range” of divisors X falls

54

between round(2/3R) and round(2R).17 For the basic methylene moiety R = CH2, the range of

55

recommended divisors is X = {9, …, 28} (= 20 divisors) which means twenty resolution-enhanced

56

KMD plots should be drawn to find the most favorable map. The range becomes larger with 60 divisors

57

and plots for a poly(ethylene glycol) backbone (R = 44.0262, X = {29, ..., 88}) up to 534 divisors and

58

plots for a poly(phenylsulfone) sample (R = 400.0768, X = {267, …, 800}) or more. A systematic

59

computation of all the plots would cancel the benefit of KMD analysis as a high-speed data processing

60

tool.

61

To reduce the trial-and-error to its minimum, a user would advantageously select a divisor from a

62

short list to instantly compute the KMD plots depending on his/her expectations. A resolution-enhanced


Page 3 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


63

KMD analysis of homo-, co- or terpolymers (one, two or three repeating units within the same

64

backbone) may indeed separate ion series depending on their isotopic composition and/or end-groups

65

and/or co-monomeric content. A first tool to choose the well-fitted divisors X has been proposed

66

elsewhere17 based on the separation of isotopes but valid for homopolymers only. A more convenient

67

and visual approach should be developed that can extend beyond homopolymers. This article describes

68

the concepts of two “ranking function” named RANK1 and RANK2 intuitively positioning the optimal

69

divisors in graphs for a resolution-enhanced KMD analysis of copolymers separating the ion series by

70

one co-monomer and/or the isotopic content. These functions are generalized for the selection of the

71

best divisors for a resolution-enhanced KMD analysis separating ions by any moiety such as end-groups

72

for homopolymers or three repeating units for the notoriously complex case of terpolymers.

73 74

Experimental

75

Polymer samples

76

(H, OH)-ended poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) triblock

77

copolymer8,18 (P(EO-b-PO-b-EO), repeating units: EO = 44.0262 and PO = 58.0419, ~10 wt% EO,

78

Mn~1100 g mol-1) was from Sigma Aldrich (St Louis, US). PEO “monostearate” was purchased from

79

Wako Pure Chemicals Industries (Osaka, Japan).13 A terpolyester formed upon the polymerization of

80

adipic acid condensed on 1,4-butanediol, 2,2-dimethyl-1,3-propanediol and 3-methyl-1,5-pentanediol

81

(repeating units: C10H16O4, C11H18O4 and C12H20O4, W-2300) was kindly supplied by a Japanese

82

company (name upon request).

83 84

Mass spectrometry

85

High-resolution mass spectra were recorded using a JMS-S3000 MALDI SpiralTOFTM mass

86

spectrometer (JEOL ,Tokyo, Japan)19 with a solvent-free sample preparation20 using {(2E)-2-methyl-3-

87

[4-(2-methyl-2-propanyl)phenyl]-2-propen-1-ylidene}malononitrile aka DCTB as matrix (Tokyo

88

Chemical Industry, Japan) and sodium trifluoroacetate NaTFA as cationizing agent (Sigma Aldrich).

89

MSTornado control (JEOL) was used for data recording, mMass 5.521 for data treatment and Illustrator

90

CC (Adobe Inc., San Jose, CA, USA) for artworks.

91 92

Kendrick mass defect analysis

93

Points were peak-picked from the mass spectra with or without deisotoping using mMass (maximum

94

charge state: 1, isotope mass tolerance: 0.01 m/z) and a relative intensity threshold set at 0.5%. KMD

95

plots were independently computed using either msRepeatFinder v.2 (JEOL), Mass Mountaineer™

96

(massmountaineer.com) and a home-made “Kendo” Excel sheet (available upon request). A KMD plot

97

is a bubble chart displaying KMDs (y-axis) as a function of m/z (x-axis) and intensities (via the size of

98

disks). DP plots and ranking functions RANK1 and RANK2 were generated using either Mass

99

Mountaineer or “Kendo”. A DP plot (DP: degree of polymerization) is a bubble chart displaying the



Page 4 of 18

100

referenced KMDs strictly identical to the discrete content in one or the other repeating unit using the

101

sum of the masses of the end-groups and adducted ion as reference.22

102 103

Results and discussion

104

Invalidity of the default divisors for copolymers: RANK1

105

The variation of KMD replacing one

12C

carbon atom by its first

13C

isotope in the elemental

106

composition of any ion (∆m = ―12 + 13.003355 = +1.003355) using R/X as the base unit is noted

107

KMD ― 12C + 13C(R,X). Within the “recommended range” of divisors, KMD ― 12C + 13C(R,X) varies linearly

108

with the minimal step per iteration of X.17 The minimum of its absolute value is reached for X =

109

round(R) so the separating power for the 13C isotopes of the associated KMD plot is minimal. It strictly

110

corresponds to the regular KMD plot computed with R as the base unit (Equations S1-S4) and accounts

111

for the condensed appearance of all the plots in the literature using a chemical moiety as the base unit.

112

Decreasing or increasing X iteratively from X = round(R), the separating power for the 13C isotopes of

113

the associated resolution-enhanced KMD plots is increasing stepwise. From these results compiled with

114

a PEO homopolymer standard,17 a default divisor X = round(R)-1 was proposed for the resolution-

115

enhanced KMD analysis with the fractional base unit R/(round(R)-1) extensively used in practice.11-14

116

The regular KMD plot from a deisotoped mass spectrum of a P(EO-b-PO-b-EO) triblock copolymer

117

(EO or EO/44 as the base unit) is depicted in Figure 1A. It displays a typical condensed and unresolved

118

cloud of points covering a narrow 0.1 range offering the worst possible visualization of data. The

119

resolution-enhanced KMD plot using X = 43 as the default divisor (round(EO) = 44, X = round(EO)-1

120

= 43) is depicted in Figure 1B. If EO/PO co-oligomers are greatly separated depending on their content

121

in PO (one line per fixed composition in PO and a varying content in EO, e.g. EOxPO14-16 highlighted

122

with grey rectangles), the gain of separation is too great. EOxPO16 co-oligomers indeed appear between

123

EOxPO14 and EOxPO15 series due to a severe aliasing22 (blue, red, green and yellow points being aliased

124

once, twice, three and four times) making the plot poorly intuitive. A manual anti-aliasing can be done

125

once all the ion series have been assigned by adding an integer N = {0,1,2…} to aliased KMDs. The

126

anti-aliased resolution-enhanced KMD plot using X = 43 as the default divisor is depicted is Figure 1C

127

with a spectral width of 4 instead of 122 (i.e. N = 0-4,) but displaying EO/PO co-oligomers in the correct

128

order. The whole procedure remains impractical and requires a complete assignment which ruins the

129

benefit of a KMD analysis. In other words, the default divisor mildly expanding the 13C isotopes of a

130

homopolymer is no longer valid when considering the separating power of a resolution-enhanced KMD

131

plot for a generic R2 repeating unit from a P(R1-co-R2) copolymer.


Page 5 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


132 133

Figure 1. (A) Regular KMD plot (deisotoped sodiated (H,OH)-ended P(EO-b-PO-b-EO), base unit:

134

EO or EO/44). (B) Aliased resolution-enhanced KMD plot using EO/43 as base unit. (C) Anti-

135

aliased plot with a spectral width at ~4. (D) Variation of KMDs with PO using EO/X as base unit.

136

(E) RANK1(EO,PO). Resolution-enhanced KMD plot using (F) EO/47 and (G) EO/50 as the base

137

units with no aliasing.

138 139

Instead of KMD ― 12C + 13C(R,X), KMD +R2(R1,X) is a more relevant function dictating the variation

140

of KMDs while adding R2 to any generic elemental composition using R1/X as the base unit (Figure

141

1D with R1 = EO and R2 = PO). As for KMD ― 12C + 13C(EO,X), KMD+PO(EO,X) is either erratic or null

142

for X below round(2/3EO) or above round(2EO) while it varies linearly with the smallest step at each

143

iteration of X comprised between round(2/3EO) and round(2EO). It validates the generic recommended

144

range of divisors regardless of R and the variation of elemental composition. With the exact mass of

145

one repeating unit as the only input required for the data processing, a list of all the possible divisors



Page 6 of 18

146

and their associated variation of KMD is predetermined as a very first step towards the selection of a

147

few well-suited divisors.

148

Identifying the optimal divisors to avoid aliasing for the resolution-enhanced KMD plot is not

149

obvious from the graph of KMD+PO(EO,X). Instead, a first ranking function RANK1 is proposed being

150

simply the absolute values of KMD+PO(EO,X):

151

RANK1(R1,R2) = |KMD +R2(R1,X)|

(4)

152

RANK1 is a function of the exact mass of the repeating units R1 and R2 only while X falls in the

153

recommended range itself a function of R1 (X ∈ round 3R1 ,…,round(2R1) ). RANK1 tends towards

154

0.5 for the highest value of KMD+R2(R1,X) and tends to 0 for the lowest value of KMD+R2(R1,X).

155

Minima are thus associated with the divisors X that result in minimal separation for R2 in the resolution-

156

enhanced KMD plot computed with R1/X as the base unit. A user can then easily infer how a KMD

157

plot would change depending on the value of the divisor X simply by looking at the position of the

158

points in the RANK1 graph.

{

(2 )

}

159

RANK1(EO,PO) is depicted in Figure 1E with a logarithmic scale for the y-axis to emphasize the

160

global and local minima (Figure S1 for the regular scale). The global minimum is reached for X = 44

161

corresponding to the regular KMD analysis. Choosing a value of X associated with a local minimum of

162

RANK1 improves the separating power of the plot as reflected by the position of the points, the higher

163

the minimum the higher the separation until aliasing occurs. The resolution-enhanced KMD plots

164

computed with EO/47 (Figure 1F) and EO/50 (Figure 1G) separate the EO/PO co-oligomers to a higher

165

and higher extent with the clusters of points covering a ~0.5 and ~1 range on the verge of aliasing but

166

maximizing the advantage of the resolution-enhanced analysis. For X = 50, it resembles the anti-aliased

167

KMD plot computed with EO/43 (Figure 1C) with EO/PO co-oligomers separated in an intuitive order

168

PO14 < PO15 < PO16 but no anti-aliasing is needed. Of note, aliasing may occur with local minima but it

169

is not possible to foresee to what extent as it depends on the number of ion series (e.g. end-groups) and

170

the number of lines per ion series (e.g. isotopes) which are initially unknown. The graphical ranking of

171

the divisors using RANK1 and their subsequent selection represents nevertheless a great savings in time

172

as compared to the systematic computation of all the 60 resolution-enhanced KMD plots (Figure S2)

173

for a selection of the best map a posteriori.

174 175

Application 1: resolution-enhanced DP plot

176

A direct application consists in the easy computation of “DP plots” (DP: degree of polymerization)

177

using the “referenced KMD” concept.22 Knowing the nature of the end-groups and the adduct ion of a

178

given copolymeric distribution, a DP plot displays the discrete composition in the co-monomers as y-

179

and x-axes in lieu of the abstruse KMD and m/z. The regular DP plot computed from the mass spectrum

180

of the sodiated (H,OH)-ended P(EO-b-PO-b-EO) copolymer after automatic deisotoping using EO (or

181

EO/44) and PO (or PO/58) as base units and (H2O, Na) as reference is depicted in Figure 2A. The


Page 7 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


182

content in EO (from 0 to ~14) and PO (from ~10 to 24) is barely evaluated but the plot remains fuzzy

183

with poor point alignment due to the low separation power of the regular KMD plots and the limited

184

accuracy of the mass measurements.

185 186

Figure 2. (A) Regular DP plot (deisotoped sodiated (H,OH)-ended P(EO-b-PO-b-EO), base units:

187

EO/44 and PO/58). (B) RANK1(PO,EO). (C) Resolution-enhanced DP plot using EO/47 and PO/54

188

as the base units.

189 190

A resolution-enhanced DP plot using the default divisors X = 43 for EO (round(EO) = 44, X =

191

round(R)-1 = 43) and X = 57 for PO (round(PO) = 58, X = round(R)-1 = 57) exhibits a strong aliasing

192

due to an over-expansion of the KMD dimension highlighted by non-integer DPs (Figure S3).

193

Automatic anti-aliasing is possible, but it complicates the data treatment with additional parameters

194

(minimal and maximal DPs, tolerance).22 Instead, well-suited divisors are readily selected from RANK1

195

computed with EO (Figure 1C) and PO as base units (Figure 2B). Local minima associated with X =

196

47 for EO and X = 54 for PO lead to a limited expansion of the KMD dimension. The resulting DP plot

197

using EO/47 and PO/54 is depicted in Figure 2C with no aliasing but a striking re-alignment of points

198

along integer values as the discrete content in EO and PO.

199 200

RANK1 with three variables: R1, R2 and 13C



Page 8 of 18

201

In the first section, only one variation of KMDs has been considered – either KMD ― 12C + 13C(R,X) or

202

KMD+R2(R1,X) – but their combination would be of interest for a controlled gain of separating power

203

depending on the content in 13C and R2. Figure 3A displays KMD ― 12C + 13C(EO,X) (red dots) together with

204

KMD+PO(EO,X) (black dots) with the range of divisors X = {round(2/3EO),…,round(2EO)} being

205

common to both functions. It becomes less and less obvious to spot the well-suited divisors for the

206

resolution-enhanced KMD analysis.

207

Based on Equation 4, a generalized definition of RANK1 using three variables becomes: RANK1(R1,R2,13C) = |KMD +R2(R1,X)| + |KMD ― 12C + 13C(R,X)|

208

(5)

209

with R1 the repeating unit used as base unit for the regular KMD plot, R2 the other repeating unit and

210

X the divisor for the resolution-enhanced KMD plot using R1/X as base unit. From its definition, it is

211

obvious that if KMD +R2(R1,X) and KMD ― 12C + 13C(R,X) are small (low separating power in the KMD

212

plot for a change of elemental composition in R2 and 13C), then RANK1 is small. If KMD +R2(R1,X)

213

and/or KMD ― 12C + 13C(R,X) tends to 0.5 then RANK1 tends to 1. It thus ranks the divisors in terms of

214

variation of KMD for both R2 and 13C, with the lowest separating power for the global minimum and

215

higher separating powers for local minima (the higher the minimum the higher the separation by both

216

R2 and 13C until aliasing occurs). The associated plot using EO as R1, PO as R2 and 13C is depicted in

217

Figure 3B and displays a series of global (X=44, regular KMD analysis) and local minima (e.g. X = 88,

218

X = 41, X = 47…).

219

The regular KMD plot computed from the raw mass spectrum of the P(EO-b-PO-b-EO) triblock

220

copolymer (no deisotoping; generic composition EOxPOy and 12C / 13Cz isotopes forming the isotopic

221

distribution, 12C being the first peak of the pattern) using X = 44 (global minimum of RANK1) displays

222

a condensed and unresolved cluster of points (Figure S4). Zooming in is mandatory but errors of mass

223

measurement lead to misaligned points departing from the horizontal alignment.

224

From the third lowest minimum of RANK1 in Figure 3B associated with X = 41, the resolution-

225

enhanced KMD plot computed with EO/41 as the base unit now displays an expanded cluster spreading

226

over ~0.7 (Figure 3C). Clear horizontal alignments of points are assigned to a fixed composition in

227

12C/13C

228

rectangles, EOxPO15 and EOxPO16). It is an indisputable enhancement of data visualization, while the

229

speed of processing is considerably increased as compared to a systematic analysis of the 60 plots in

230

the hope of coming across a favourable situation (Figure S4).

isotopes (red rectangles in inset in Figure 3C, EOxPO16, 13C1, 13C2) or a fixed PO content (grey


Page 9 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


231 232

Figure 3. (A) Variation of KMDs adding a PO repeating unit (black dots) or replacing 12C by 13C

233

(red dots) with EO/X as the base unit. (B) RANK1(EO,PO,13C). (C) Resolution-enhanced KMD plot

234

(raw sodiated (H,OH)-ended P(EO-b-PO-b-EO), base unit: EO/41).

235 236

Inverted separation by R2 and 13C: RANK2

237

Ranking the divisors associated with a high separating power for both R2 and 13C is not favored as

238

it will lead to extreme expansion of the KMD dimension for both changes of composition and severe

239

aliasing. The last possibility is a high separating power for a change of composition in R2 and a low

240

separating power of KMDs for the isotopic composition in

241

resolution-enhanced KMD plot would display a set of condensed groups of points, every group differing

242

from the other in its content in R2 while isotope patterns would be clustered within one group. An

243

intuitive function to rank the divisors X associated with a high value of KMD +R2(R1,X) and a low value

244

of KMD ― 12C + 13C(R1,X) or vice-versa may be |KMD +R2(R1,X)| ― |KMD ― 12C + 13C(R1,X)|. It remains

245

too simple as it is not sensitive to the relative gain of separation between R2 and

246

|KMD +R2(R1,X)|/|KMD ― 12C + 13C(R1,X)| should indeed be either maximal or minimal to ensure the

247

best separation of R2 relatively to 13C.

248

A refined function RANK2 is thus:

13C


– or vice versa. For example, a

13C.

The ratio


Page 10 of 18

|KMD +R2(R1,X)| ― |KMD ― 12C + 13C(R1,X)|

RANK2(R1,R2,13C ) = |KMD

249

+R2(R1,X)|

(6)

+ |KMD ― 12C + 13C(R1,X)|

250

If |KMD +R2(R1,X)| and |KMD ― 12C + 13C(R1,X)| are low or high, then RANK2 tends towards 0. If

251

|KMD +R2(R1,X)| or |KMD ― 12C + 13C(R1,X)| is high then RANK2 tends towards +1 for

252

|KMD +R2(R1,X)|

253

|KMD ― 12C + 13C(R1,X)|. RANK2 thus reveals the best divisors for a high separating power by R2 and a

254

low separating power by 13C isotopes as global and local maxima, and vice versa as global and local

255

minima.

>

|KMD ― 12C + 13C(R1,X)|)

or

towards

-1

for

|KMD +R2(R1,X)|
250 > 164 > 193 > 136 > 236 > 178, the broader the ellipses).

379 380

Conclusion

381

Two functions have been developed to graphically rank the divisors depending on the user’s need

382

for a rationalized resolution-enhanced KMD analysis of polymer ions. Based on very simple formulas

383

and requiring no inputs other than the mass of the repeating units (i.e. the same input as for any KMD

384

analysis), they are now available in a commercial program and in our home-made “Kendo” Excel sheet

385

available upon request (Figure S10 for screenshots). For an ultimate user-friendly analysis, divisors X

386

are directly selected from RANK1 / RANK2 and the associated resolution-enhanced KMD plots

387

instantly computed. Other user-friendly selection tools are conceivable such as a scroll bar to adjust the

388

enhancement of separation in the KMD plot (i.e. choosing an expected KMD +R2(R1) for the program

389

to find the divisor X associated with the closest actual KMD +R2(R1,X)). It is nevertheless a matter of

390

programming and comfort of use only as any selection of the well-suited divisors will be based on either

391

KMD +R2(R1,X) or the RANKs functions.

392

The application to terpolymeric mass spectral data replacing the variation of KMDs for 13C isotopes

393

by a generic variation for a third repeating unit R3 will be invaluable for analysts facing complex



394

industrial formulations, turning the uninformative regular KMD plot of a terpolymer into a set of

395

copolymeric or homopolymeric clusters in the resolution-enhanced plots via a sequential analysis.

396 397

ASSOCIATED CONTENT

398

Supporting Information

399

Identity of KM(R) and KM(R, X = round(R)); RANK1 using a regular and a logarithmic scale;

400

Resolution-enhanced KMD plots from the deisotoped mass spectrum of P(EO-b-PO-b-EO) using EO/X

401

(X = 29,…,88); Regular and resolution-enhanced DP plots for P(EO-b-PO-b-EO) using EO and PO or

402

EO/43 and PO/57. Resolution-enhanced KMD plots from the raw mass spectrum of P(EO-b-PO-b-EO)

403

using EO/X (X = 29,…,88); Variation of KMDs and RANKs functions for R1 = EO, R2 = C18H34O, R3

404

= C2H4. Resolution-enhanced KMD plots from the deisotoped mass spectrum of PEO monostearate

405

using EO/X (X = 29,…,88); Resolution-enhanced KMD plots from the mass spectrum of a terpolyester

406

using C10H16O4/X (X = 133,…,257); Variation of KMDs and RANKs functions for R1= C10H16O4, R2

407

= C11H18O4, R3 = C12H20O4.; Resolution-enhanced KMD plots of the selected ion series using

408

C10H16O4/X (X = 136, 150, 164, 178, 193, 207, 221, 236 and 250, local maxima of RANK2);

409

Screenshots from our Excel sheet with RANK functions.

410 411

AUTHOR INFORMATION

412

Corresponding Authors

413

* Email: [email protected]

414

ORCID: Thierry Fouquet: 0000-0002-9473-9425

415

* Email: [email protected]

416

ORCID: Robert Cody: 0000-0002-6624-8530

417 418

REFERENCES

419

(1) Kendrick, E. A Mass Scale Based on CH2 = 14.0000 for High Resolution Mass Spectrometry of

420

Organic Compounds. Anal. Chem. 1963, 35, 2146-2154.

421

(2) Hsu, C. S.; Qian, K.; Chen, Y. C. An innovative approach to data analysis in hydrocarbon

422

characterization by on-line liquid chromatography-mass spectrometry. Anal. Chim. Acta 1992, 264, 79-

423

89.

424

(3) Krajewski, L. C.; Rodgers, R. P.; Marshall, A. G. 126 264 Assigned Chemical Formulas from an

425

Atmospheric Pressure Photoionization 9.4 T Fourier Transform Positive Ion Cyclotron Resonance

426

Mass Spectrum. Anal. Chem. 2017, 89, 11318–11324.

427

(4) Hughey, C. A.; Hendrickson, C. L.; Rodgers, R. P.; Marshall, A. G. Kendrick Mass Defect

428

Spectrum: A Compact Visual Analysis for Ultrahigh-Resolution Broadband Mass Spectra. Anal. Chem.

429

2001, 73, 4676–4681.


Page 16 of 18

Page 17 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


430

(5) Sato, S.; Nakamura, S.; Teramoto, K.; Sato, T. Structural Characterization of Polymers by MALDI

431

Spiral-TOF Mass Spectrometry Combined with Kendrick Mass Defect Analysis. J. Am. Soc. Mass

432

Spectrom. 2014, 25, 1346-1355.

433

(6) Fouquet, T.; Aizawa, H.; Sato, H. Taking MALDI SpiralTOF high-resolution mass spectrometry

434

and mass defect analysis to the next level with ethylene vinyl acetate vinyl alcohol terpolymers. Rapid

435

Commun. Mass Spectrom. 2016, 30, 1818-1822.

436

(7) Fouquet, T.; Mertz, G.; Delmee, M.; Becker, C.; Bardon, J.; Sato, H. The Definitive Evidence of a

437

Plasma Copolymerization of Alkyl and Perfluorinated Acrylates Using High Resolution Mass

438

Spectrometry and Mass Defect Analysis. Plasma Process. Polym. 2016, 13, 862-868.

439

(8) Cody, R. B; Fouquet, T. Paper spray and Kendrick mass defect analysis of block and random

440

ethylene oxide/propylene oxide copolymers. Anal. Chim. Acta 2017, 989, 38-44.

441

(9) Qi, Y.; Hempelmann, R.; Volmer, D. A. Two-dimensional mass defect matrix plots for mapping

442

genealogical links in mixtures of lignin depolymerisation products. Anal. Bioanal. Chem. 2016, 408,

443

4835-4843.

444

(10) Dier, T. K. F.; Egele, K.; Fossog, V.; Hempelmann, R.; Volmer, D. A. Enhanced Mass Defect

445

Filtering To Simplify and Classify Complex Mixtures of Lignin Degradation Products. Anal. Chem.

446

2016, 88, 1328-1335.

447

(11) Morgan, T. E.; Ellacott, S. H.; Wootton, C. A.; Barrow, M. P.; Bristow, A W. T.; Perrier, S.;

448

O'Connor P. B. Coupling Electron Capture Dissociation and the Modified Kendrick Mass Defect for

449

Sequencing of a Poly(2-ethyl-2-oxazoline) Polymer. Anal. Chem. 2018, 90, 11710-11715.

450

(12) Fouquet, T.; Sato, H. Extension of the Kendrick Mass Defect Analysis of Homopolymers to Low

451

Resolution and High Mass Range Mass Spectra Using Fractional Base Units. Anal. Chem. 2017, 89,

452

2682-2686.

453

(13) Fouquet, T.; Shimada, H.; Maeno, K.; Ito, K.; Ozeki, Y.; Kitagawa, S.; Ohtani, H.; Sato, H. High-

454

resolution Kendrick Mass Defect Analysis of Poly(ethylene oxide)-based Non-ionic Surfactants and

455

Their Degradation Products. J. Oleo Sci. 2017, 9, 1061-1072.

456

(14) Fouquet, T.; Sato, H. Improving the Resolution of Kendrick Mass Defect Analysis for Polymer

457

Ions with Fractional Base Units. Mass Spectrom. (Tokyo) 2017, 6, A0055.

458

(15) Fouquet, T.; Cody, R. B.; Ozeki, Y.; Kitagawa, S.; Ohtani, H.; Sato, H. On the Kendrick Mass

459

Defect Plots of Multiply Charged Polymer Ions: Splits, Misalignments, and How to Correct Them. J.

460

Am. Soc. Mass Spectrom. 2018, 29, 1611-1626.

461

(16) Zheng, G.; Morimoto, M.; Sato, H.; Fouquet, T. Resolution-enhanced Kendrick mass defect plots

462

for the data processing of mass spectra from wood and coal hydrothermal extracts. Fuel, 2019, 235,

463

944-953.

464

(17) Fouquet, T.; Sato, H. How to choose the best fractional base unit for a high‐resolution Kendrick

465

mass defect analysis of polymer ions. Rapid. Commun. Mass Spectrom. 2017, 31, 1067-1072.



466

(18) Sato, T.; Teramoto, K.; Satoh, T.; Ueda, Y. Ethylene Oxide-Propylene Oxide block Copolymer

467

Analysis by MALDI Spiral-TOF/TOFKobunshi Ronbunshu 2012, 69, 406-415.

468

(19) Satoh, T.; Tsuno, H.; Iwanaga, M.; Kammei, Y. The design and characteristic features of a new

469

time-of-flight mass spectrometer with a spiral ion trajectory. J. Am. Soc. Mass Spectrom. 2005, 16,

470

1969-1975.

471

(20) Trimpin, S.; Keune, S.; Räder, H.J.; Müllen, K. Solvent-free MALDI-MS: Developmental

472

improvements in the reliability and the potential of MALDI in the analysis of synthetic polymers and

473

giant organic molecules. J. Am. Soc. Mass Spectrom. 2006, 17, 661-671.

474

(21) Strohalm, M.; Kavan, D.; Novák, P.; Volný, M.; Havlícek, V. mMass 3: A Cross-Platform

475

Software Environment for Precise Analysis of Mass Spectrometric Data. Anal. Chem. 2010, 82, 4648-

476

4651.

477

(22) Fouquet, T.; Cody, R.B.; Sato, H. Capabilities of the remainders of nominal Kendrick masses and

478

the referenced Kendrick mass defects for copolymer ions. J. Mass Spectrom. 2017, 52, 618-624.


Page 18 of 18

Graphical Ranking of Divisors to Get the Most out of a Resolution

Recommend Documents