Ion Mobility-Mass Spectrometry (IM-MS)

Literature Seminar #3 (2014.9.27)
Kiyomichi SHINODA

1

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

2

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

3

What is Ion Mobility?

§1 Introduction● Ion mobility achieves separation of compounds by their size and shape.

○ E = uniform electric field [均一電場]○ Ffriction = force of friction (caused by collisions of ions with the buffer gas)
○ Fel = force of elimination○ Pbuffer gas = pressure of buffer gas
This figure is cited from Bowers group web page.
(http://bowers.chem.ucsb.edu/theory_analysis/ion-mobility/index.shtml)
4What is Ion Mobility-Mass Spectrometry (IM-MS)?
● conceptual diagram of IM-MS
Ion
Mobility

Mass
Spectrometry

separation bysize and shapedetectioncf.) How about LC-MS or GC-MS??
HPLC
or
GC

Mass
Spectrometry

separation
by polarity

detection

5§1 Introduction

Recent Explosion in Research Using IM-MS§1 Introduction● number of peer-reviewed papers published annually combining IM and MS

F. Lanucara et al., Nat. Chem. 2014, 6, 281.

○ Especially, the application toward biomolecules is the current hot topic.
6

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

7§2 Basic Information of IM-MS

Three Types of Ion Mobility Spectrometry
a: Drift-Time Ion Mobility Spectrometry (DTIMS)
b: Traveling-Wave Ion Mobility Spectrometry (TWIMS)
c: Field-Asymmetric Ion Mobility Spectrometry (FAIMS)
a

b

DTIMS

c

TWIMS

FAIMS
F. Lanucara et al., Nat. Chem. 2014, 6, 281.

8

DTIMS (1): System Outline§2 Basic Information of IM-MS● Pulse of ions is introduced into a drift cell.

○ Static uniform electric field is applied.
○ filled with drift gas (typically helium)○ Ions travels in the direction of the applied fieldin uniform motion.

C. Uetrecht et al., Chem. Soc. Rev. 2010, 39, 1633.

Ions collide with gas and are separated based on its size and shape.
(Small ions travels faster than big ions.)● The time taken for an ion to drift through the cell (= drift time) is related to
its rotationally averaged cross-sectional area (= collision cross-section (CCS)).

index of ion size and shape9§2 Basic Information of IM-MSDTIMS (2): How to Calculate CCS?

● Mason-Schamp equation: provide the relationship between ion mobility and CCS(イオン移動度)(ドリフト速度)(電場)(分析対象イオンの価数)(ドリフトガスの密度)(分析対象イオンの質量)(ドリフトガス分子の質量)(ボルツマン定数)(ガスの温度)(衝突(散乱)断面積)

F. Lanucara et al., Nat. Chem. 2014, 6, 281.
C. S. Creaser et al., Analyst 2004, 129, 984.
T. Sugai, J. Mass Spectrom. Soc. Jpn. 2010, 58, 47.

As the recorded drift time of an ion can be easily converted to vd,
we can calculate CCS using this apparatus!!
10§2 Basic Information of IM-MSDTIMS (3): Advantages and Disadvantages● advantages○ ability to determine CCS: direct determination of CCS from Mason-Schamp eq.
○ high resolving power: An ion with CCS of 100 Å2 can theoretically be separated
from an ion with ±1 Å2 difference (= 1% uncertainty).

● disadvantages○ low detection efficiency: Ions are lost on several devices where entry or exit of ions
into the drift cell occurs.
○ hugeness of apparatus: Apparatus tend to become huge to provide high resolving power.

F. Lanucara et al., Nat. Chem. 2014, 6, 281.

11

TWIMS (1): System Outline§2 Basic Information of IM-MS● developed by Waters Corporation (S. Pringle et al., Int. J. Mass Spectrom. 2007, 261, 1.)

C. Uetrecht et al.,Chem. Soc. Rev. 2010, 39, 1633.

○ used for CCS determination: the condition

is met.

○ Radio-frequency voltages (高周波電圧) of opposite phases are applied to adjacent electrodes
and this voltages consist a sine curve potential barrier which confine the ions.
○ Direct current voltage (直流電圧) is applied to each electrode sequentially providing“traveling waves” and this “wave” propels ions from cell entrance to the exit.
● Higher mobility ions are carried by the wave, whereas lower mobility ions are trapped by
the wave, thus taking longer to move through the drift cell.
12§2 Basic Information of IM-MS

TWIMS (2): Advantages and Disadvantages● advantages○ high detection efficiency: RF voltages confine ions and prevent their diffusion.
○ ability to determine CCS: Although drift time calibration with analytes of similar
physical and chemical features with known CCS is needed, it is possible.

● disadvantages○ relatively low resolving power: An ion with CCS of 900 Å2 is theoretically separated
from an ion with ±20 Å2 difference at most.
○ limitation of CCS determination: When system is complex and calibration is difficult, CCS determination is no longer carried out.

F. Lanucara et al., Nat. Chem. 2014, 6, 281.

13

FAIMS (1): System Outline§2 Basic Information of IM-MS● constructed of two electrodes, across which an electric field is established

C. Uetrecht et al.,Chem. Soc. Rev. 2010, 39, 1633.

○ As

is greater than 2☓10-17, determination of CCS is no longer possible.

○ Alternating asymmetric waveform makes ions oscillating and moving toward one electrode.
○ To protect ions of interest from contact with electrode and following neutralization, thecompensation voltage (補償電圧) is applied.
○ Thus, this apparatus operate as a mobility filter to achieve increased selectivity and peakcapacity before MS analysis.
14§2 Basic Information of IM-MS

FAIMS (2): Advantages and Disadvantages● advantages○ orthogonality toward MS: As there’s no correlation with CCS, FAIMS can be agreat filter of undesired ions.
○ High resolving power can be achieved by appropriate selection of buffer gas.

● disadvantages○ CCS can’t be determined.
○ limitation of application: limited only to post-ionization separation so far

F. Lanucara et al., Nat. Chem. 2014, 6, 281.

15

§2 Basic Information of IM-MS

Short Summary
a

b

DTIMS

c

TWIMS
Structural
Analysis

FAIMS
Post-Ionization
Separation

F. Lanucara et al., Nat. Chem. 2014, 6, 281.
16

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is Meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

17§3.1 Why Application toward Aβ is Meaningful?

Current Problem in Aβ Study

I. Ghosh et al., ChemMedChem 2007, 2, 1674.

major toxic species

However,...

oligomer structure hasn’t been studied sufficiently.
∵ Aβ changes its structure dynamically, so that well-establishedstructural study (e.g. NMR or X-ray crystal analysis) which needs
pure oligomer can’t be conducted smoothly.
18

§3.1 Why Application toward Aβ is Meaningful?

Advantages and Disadvantages of IM-MS Application● advantages○ quite small sample requirement: In contrast to NMR or X-ray analysis which
require milligrams of sample, IM-MS requires micrograms sample at most.
○ ability to detect intermediates:Very short analysis time (millisecond time scale)enables the detection of short-living species (e.g. oligomers).
○ no purification requirement: In contrast to NMR or X-ray, crude sample can be used.
○ ability to determine stoichiometry of complex: Stoichiometry of complex suchas Aβ oligomer and Aβ-inhibitor complex can be determined.

● disadvantages○ requirement of MD simulation for precise structural information: To obtain
detailed structural information such as secondary structure or atomic level
information, time-consuming and often challenging MD simulation is necessary.
○ low resolution power: Compared to NMR or X-ray which give structural information at
atomic level, 1% uncertainty in CCS is too big.

19

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is Meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

20§3.2 Obtainable Data and Their Explanation

Bowers’ Home-Made IM-MS● Prof. Michael T. Bowers

1962: obtained his B. S. from the Gonzaga University
1966: obtained his Ph. D. from the University of Illinois
1968: joined the University of California Santa Barbara faculty● classified to DTIMS → Direct estimation of CCS is possible!

This figure is cited from Bowers group
web page and is modified.
(http://bowers.chem.ucsb.edu/theory_
analysis/ion-mobility/index.shtml)
21

§3.2 Obtainable Data and Their Explanation

Mass Spectrum of [Pro19]Aβ42● [Pro19]Aβ42 (blue: negative charged side chain, orange: positive charged side chain)
DAEFR HDSGY EVHHQ KLVPF AEDVG SNKGA IIGLM VGGVV IA● 13C isotope distributions is also shown:show the dominant species of the peak of interest.
○ “z/n=-3”: Peaks are separated by 0.33 (1÷3) amu.
monomer-dominatedIn the dimer-dominated case,peak will be separated by1÷6 = 0.17 amu.
○ “z/n=-2”: Peak separation is ambiguous...

= z/n (z = charge, n = oligomer order)
Ex.) z/n = -2 = -2/1, -4/2, -6/3, …
several species in one peak
22

S. Bernstein, M. Bowers et al., J. Am. Chem. Soc. 2005, 127, 2075.

§3.2 Obtainable Data and Their Explanation

Collision-Induced Dissociation (CID)● The “z/n=-2” charge state peak was selected by the quadrupole and subjected to CID.

S. Bernstein, M. Bowers et al.,J. Am. Chem. Soc. 2005, 127, 2075.

CID○ Peaks are separated by 0.5 (= 1/2) amu → indicating the monomer generation○ Small peaks are observed at 0.25 (1÷4) amu, indicating some undissociated dimer remains.
● In summary, components larger than dimer construct the “z/n=-2” charge state.
23§3.2 Obtainable Data and Their Explanation

Arrival Time Distributions (ATD)● In ATD, different compounds which have the same charge state (z/n) can be distinguished.
○ Ion mobility can separate ions by their size and shape.
○ In “z/n=-q” peak of mass spectrum, the following species can be present:
Monomer-q, Dimer-2q, Trimer-3q, ...
○ These species are different in size, so they can be separated using IM.

ATD shows how species with different size and shape are separated.

24§3.2 Obtainable Data and Their Explanation

Assignment of Peaks in ATD (1)● ATD of “z/n=-3” charge state (injection energy = 40 mV)○ From 13C isotope distributions, this is a monomer-dominant peak.

These two peaks should be predominantly monomer!
<caution>
Strictly speaking, to confirm these two peaks are monomer,
we need to calculate the CCS from drift times
and compare them with the theoretical CCS
obtained from modeling (data not shown).
● ATD of “z/n=-2” charge state (injection energy = 40 mV)○ From 13C isotope distributions, this is a mixture of oligomers
and in fact, ATDs shows several peaks.

25

S. Bernstein, M. Bowers et al., J. Am. Chem. Soc. 2005, 127, 2075.

§3.2 Obtainable Data and Their Explanation

Assignment of Peaks in ATD (2)● injection energy dependence of the “z/n=-2” charge state○ As the injection energy increases, the peak at 740 μs
becomes dominant and no additional peaks wereobserved at longer drift times.
○ Injection with high energy gives the ion higher energy,
thus dissociation or conformation change occurs.
740 μs peak would be the monomer.
○ Other peaks are assigned as dimer, trimer and tetramer.
This assignment is reasonable because CID-conducted
13C isotope distributions shows the existence of dimer.
Also, native 13C isotope distribution clearly shows theexistence of larger oligomer than dimer.

S. Bernstein, M. Bowers et al.,J. Am. Chem. Soc. 2005, 127, 2075.
26

§3.2 Obtainable Data and Their Explanation

Assignment of Peaks in ATD (3)● ATD of “z/n=-5/2” charge state(injection energy = 40 mV)● injection energy dependence○ Trimers can’t be involved.
○ bigger than dimer
tetramer○ Monomers can’t be involved.
○ No peak with longer drift time
was observed.
dimer

S. Bernstein, M. Bowers et al.,J. Am. Chem. Soc. 2005, 127, 2075.
27

Short Summary§3.2 Obtainable Data and Their Explanation● flow chart of IM-MS analysis
1) analyze the MS chart2) analyze the ATD of z/nwhich you are interested in

Structural
Information○ 13C isotope distributions○ injection energy dependence○ Collision-Induced Dissociation○ CCS calculation and comparison of itwith theoretical CCS obtained from modeling.

28

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is Meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

29§3.3 Oligomerization Analysis

Subject of this Section

Nat. Chem. 2009, 1, 326.

30§3.3 Oligomerization Analysis

IM-MS Analysis of Aβ40
● mass spectrum and ATDs (z/n = -5/2)

S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.

○ As shown here, in “z/n=-5/2” charge state, tetramer and dimer was observed.
31

§3.3 Oligomerization Analysis

IM-MS Analysis of Aβ42
● mass spectrum and ATDs (z/n = -5/2)○ As shown here, in “z/n=-5/2” charge state,
dimer, tetramer, hexamer, and dodecamer (12-mer)was observed.

32

S. Bernstein, M. Bowers et al., J. Am. Chem. Soc. 2005, 127, 2075.

§3.3 Oligomerization Analysis

CCS Estimation of Aβ42 Oligomer (1)● Theoretical CCS for Aβ dimers were obtained as follows.
<assumption> Aβ monomer has a spherical shape (especially hard sphere)

Based on this, theoretical CCS for the dimers were calculatedwith the center-center distance of the two monomers as a variable parameter.

<calibration> Center-center distance was adjusted to give the experimental dimer CCS.

CCS of tetramer, hexamer, and dodecamer were calculated based on
the theoretical dimer (double hard sphere approximated dimer).

S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.
33§3.3 Oligomerization Analysis

CCS Estimation of Aβ42 Oligomer (2)● theoretical CCS and experimentally observed CCS for Aβ42 oligomers← Theoretical CCS was adjusted to observed CCS.

Model structure which had themost close CCS value
to experiment CCS
was successfully obtained.

S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.
34§3.3 Oligomerization Analysis

Comparison between Aβ42 and Aβ40 (1)● ATDs of Aβ42 and Aβ40 for “z/n = -5/2” charge state○ In the case of Aβ42, oligomers bigger than tetramer
were observed.
○ In contrast, in the case of Aβ40, oligomers bigger thantetramer were not observed at all.

Tetramers can represent the difference
between Aβ40 and Aβ42?

S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.
35§3.3 Oligomerization Analysis

Comparison between Aβ42 and Aβ40 (2)● comparison of tetramer conformation between Aβ42 and Aβ40

This difference can lead to the differencein aggregation mechanism.

S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.
36§3.3 Oligomerization Analysis

Comparison between Aβ42 and Aβ40 (2)● comparison of aggregation mechanism between Aβ42 and Aβ40

○ Aβ42 tetramer has a room of addition of another dimer to form hexamer or dodecamer.
In contrast, Aβ40 tetramer doesn’t have a room of addition and doesn’t form hexamer.
IM-MS could show the difference of
aggregation mechanism between Aβ42 and Aβ40!
S. Bernstein, M. Bowers et al., Nat. Chem. 2009, 1, 326.
37

Short Summary§3.3 Oligomerization Analysis● Application of IM-MS achieves the mechanistic study of Aβ42 and Aβ40 aggregation
based on the difference of tetramer conformation.

S. Bernstein, M. Bowers et al.,Nat. Chem. 2009, 1, 326.
38

Table of Contents§1 Introduction§2 Basic Information of IM-MS§3 Application toward Amyloid β Protein (Aβ)§3.1 Why Application toward Aβ is Meaningful?
§3.2 Obtainable Data and Their Explanation§3.3 Oligomerization Analysis§3.4 Mechanism Analysis of Aggregation Inhibitor

39§3.4 Mechanism Analysis of Aggregation Inhibitor

Subject of this Section

J. Am. Chem. Soc. 2013, 135, 16926.

40§3.4 Mechanism Analysis of Aggregation Inhibitor

IM-MS Analysis of Aβ(25-35)● mass spectrum and ATD for m/z = 707 (n/z = 2/3)

○ Dimers and tetramers were observed.

C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.
41§3.4 Mechanism Analysis of Aggregation Inhibitor

IM-MS Analysis of Aβ(25-35) with EGCG
● mass spectrum and ATD for m/z = 707 (n/z = 2/3)

○ Most peaks observed were hetero-oligomers of Aβ(25-35) and EGCG.
○ Tetramers were not observed.
C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.
42§3.4 Mechanism Analysis of Aggregation Inhibitor

Oligomer Growth Model (1)● Correlation with linear line means that observed oligomer had a β-sheet structure.
○ triclinic: ideal out-of-register β-sheet (each monomer chain is shifted by one amino acid residue)○ isotropic: ideal homolytic growth (oligomer grows equally in all spatial dimensions)

EGCG inhibited the β-sheet conformation appearance.
43

C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.

§3.4 Mechanism Analysis of Aggregation Inhibitor

Oligomer Growth Model (2)● As Aβ(25-35) oligomer grows, β-sheet tendency becomes dominant.
○ monomer and dimer: isotropic
no β-sheet
structure○ trimer and tetramer: increasing β-sheet tendency

extended β-sheet trimers A: extended β-sheet tetramer
B: β-barrel tetramer○ bigger than pentamer: β-sheet

C. Bleiholder, M. Bowers et al.,J. Am. Chem. Soc. 2013, 135, 16926.

Trimer or tetramer supposed to be essential
for the structural conversion to β-sheet.
44§3.4 Mechanism Analysis of Aggregation Inhibitor

ATDs Comparison● ATDs for m/z = 707 (n/z = 2/3)

EGCG seemed to inhibit the formation of β-barrel liketetramer or similar species.

45§3.4 Mechanism Analysis of Aggregation Inhibitor

Circular Dichroism (CD)● 0.5 mg/mL of Aβ(25-35) was incubated at r.t. with or without 10 mM EGCG (Aβ:EGCG=5:1).

○ Aβ(25-35) spectrum indicatedthe presence of β-sheet structure.
○ Aβ(25-35) + EGCG spectrum indicatedthe presence of random-coil structure.

This result strongly support the previous IM-MS analysis.

46

C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.

§3.4 Mechanism Analysis of Aggregation Inhibitor

Atomic Force Microscopy (AFM)● 200 μM of Aβ(25-35) was incubated at r.t. with or without EGCG (Aβ:EGCG=1:1).
○ without EGCG

○ with EGCG

● Fibril formation was prevented using EGCG.

This result also support the previous IM-MS analysis.

47

C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.

§3.4 Mechanism Analysis of Aggregation Inhibitor

Binding Simulation of EGCG (1)● three binding sites of EGCG and binding simulation of each site

C. Bleiholder, M. Bowers et al.,J. Am. Chem. Soc. 2013, 135, 16926.

OH
OH
HO

O

OH
O

OH

OH

O

≡

OH
OH

48

§3.4 Mechanism Analysis of Aggregation Inhibitor

Binding Simulation of EGCG (2)● Aβ(25-35) can bind to EGCG using all three binding sites.

○ This tridentate binding mode can only be accomplishedwhen the bound Aβ chain takes on a unordered structure.
(data was not shown in the paper...)Formation of β-sheet which is observed in
the aggregation of Aβ(25-35) is prevented.

This binding property might inhibit the generation of
β-barrel like tetramer strongly and thus inhibit the formation of fibrils.

49

C. Bleiholder, M. Bowers et al., J. Am. Chem. Soc. 2013, 135, 16926.

§3.4 Mechanism Analysis of Aggregation Inhibitor

Short Summary: Aggregation Pathway of Aβ(25-35)

β-barrel like tetramers

C. Bleiholder, M. Bowers et al.,J. Am. Chem. Soc. 2013, 135, 16926.
50

§3.4 Mechanism Analysis of Aggregation Inhibitor

Short Summary: Aggregate-Inhibiting Pathway of EGCG

β-barrel like tetramers

C. Bleiholder, M. Bowers et al.,J. Am. Chem. Soc. 2013, 135, 16926.
51

Summary● application to Aβ42 and Aβ40 oligomerization analysis○ Using appropriate approximation, structure difference between
Aβ42 tetramer and Aβ40 tetramer was distinguished.

Aβ42

Aβ40

● application to mechanism analysis of aggregation inhibitor○ Combining MD simulation and IM-MS analysis, advanced
information of Aβ(25-35) aggregation and its inhibition
by EGCG was obtained.

The most important ability of IM-MS to detect intermediates is successfully utilized!

52

Appendix

53

Derivation of Mason-Schamp Equation (1)気相移動度測定においては，イオンの速度はAppendix of §2に依存した一定の値をとる。

特に，低電場極限(電場効果が熱運動に対し無視できるほど小さい)，すなわち(1)が満たされているとき，イオンは等速運動するようになり，その速度は(2)と書けることが知られている。
一方，イオンとガス分子との衝突時の運動量変化を解析すると，(3)が得られる。ここで τ は，「イオンがバッファーガスに衝突する間の時間」であり，(4)と書ける (分母＝｢単位時間でイオンが衝突するバッファーガス分子の数｣)。
T. Sugai, J. Mass Spectrom. Soc. Jpn. 2010, 58, 47.
54

Derivation of Mason-Schamp Equation (2)Appendix of §2(4) 式を (3) 式に代入すると，下式が得られる。
(5)
ただしは，｢全イオンと全バッファーガスの相対速度の絶対値の平均値｣である。

低電場極限においては，に対し熱運動近似を施すことができて，(5) 式は(6)と書き直すことができる。近似せずより厳密に取り扱うと，(7)となるので，(2) 式とあわせて(8)が得られる (Mason-Schamp equation)。
T. Sugai, J. Mass Spectrom. Soc. Jpn. 2010, 58, 47.
55

To Achieve High Resolving Power in DTIMS

Appendix of §2半値幅分解能 (近接したピークを高さの半分の高さ位置で分離できること) は(9)で表される。(9) 式は，定数項を考えなければとなり，分解能は「電位とバッファーガス温度の比に依存する」といえる。
ゆえに，高分解能を実現するためには，電位を高く設定すればよいが，高電位下では放電が起こる可能性がある。これを防ぐため，DTIMSではバッファーガス圧力が高く設定されている。なお，この圧力の高さは，結果的に (8) 式成立の前提である(1)を満たすことにつながっている。また，であるから，｢高電位かつ低電場｣
は，装置を大きくすることによっても実現できる。
T. Sugai, J. Mass Spectrom. Soc. Jpn. 2010, 58, 47.
56

σ/n (Å2)

Gap Study between Model CCS and Exp. CCSAppendix of §3.3

>
Model
v
Exp.
>

oligomer order (n)○ As n increases σ/n decreases.
∵ Oligomerization induces a certain amountof structural accommodation...?
○ As model is based on dimer size information,
it can overestimate CCS of larger oligomers.
Thus, the inequality shown left is reasonable.

57