Supplementary Information
Comparative Study of Three Methods for Affinity Measurements: Capillary
Electrophoresis Coupled with UV Detection and Mass Spectrometry, and Direct Infusion
Mass Spectrometry
Gleb G. Mironov, Jennifer Logie#, Victor Okhonin, Justin B. Renaud, Paul M. Mayer and
Maxim V. Berezovski*
Department of Chemistry, University of Ottawa, 10Marie Curie, Ottawa, Canada K1N 6N5;
#Present address: Department of Chemical Engineering and Applied Chemistry,
University of Toronto, Toronto, Canada M5S 3E1
*To whom correspondence may be addressed. E-mail: maxim.berezovski@uottawa.ca
A) S-Flurbiprofen, [M-1H]1-=243.0824
B) Ibuprofen, [M-1H]1-=205.1229
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C) Resveratrol, [M-1H]1-=227.0708
D) PDDA, [M-1H]1-=283.097
E) Folic acid, [M-1H]1-=440.1319
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F) Naproxen, [M-1H]1-=229.0865
G) Diclofenac, [M-1H]1-=315.9908
H) Phenylbutazone, [M-1H]1-=307.1447
Figure S1. MS spectra for eight SMs: (A) s-flurbiprofen, (B) ibuprofen, (C) resveratrol , (D)
PDDA, (E) folic acid, (F) naproxen, (G) diclofenac, (H) phenylbutazone.
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PDDA-1CD, [PDDA+CD-2H]2-=708.2296
PDDA-2CD, [PDDA+2CD-2H]2-=1275.414
PDDA-3CD, [PDDA+3CD-3H]3-=1228.064
Figure S2. Complex stoichiometry of PDDA-CD complexes. (A) one CD molecule with one
PDDA molecule, (B) two CD molecules with one PDDA molecule, (C) three CD molecules
with one PDDA molecule.
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Figure S3. Ion mobility drift times for modified CD ((2-Hydroxypropyl)-β-cyclodextrin) and
CD-SM complexes.
Complexes of CD with SM detected by MS can be inclusion complexes or adducts formed
during ionization. To distinguish them we used simple approach based on comparison of drift
times of complexes and chemically modified CD, (2-Hydroxypropyl)-β-cyclodextrin. Was
shown that modified CD posses the same mass as SM-CD complexes and a different drift time.
Collision cross section (CCS) of the inclusion complex shouldn't greatly differ from CCS of free
CD due to dwelling of SM partially inside CD. In opposite, chemically modified CD posses
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hydroxypropyl groups on its surface what greatly increases a drift time in an ion mobility
experiment. Differences in drift times of SM-CD complexes, free CD and modified CD can be
clearly seen in Figure S3. Due to these differences we can propose, that majority of SM-CD
complexes in the affinity experiments are inclusion complexes.
DATA STATISTICS IN A PRESENCE OF SYSTEMAT IC ERRORS
In the case, discussed below, we will have a deal with the significant systematic difference
between the model and the experimental data. In theory, in this case we should improve our
model. Unfortunately, it is not possible with good enough precision (at least, on current stage).
Here we will modify standard approximation data statistics, for decreasing automatically
influence of these systematic errors.
Standard quadratic error, used for approximation of data with the random Gaussian error, has the
form
N
H 
 f  p, x   d 
i
2
i
(0.1)
Sti2
i 1
Where di are the values from the N data set, Sti are the standard deviations for the data, f is a
function, modeled data as dependent from characterizing conditions of experiments values xi
and approximation parameters p . For gradients of the error by approximation parameters will
have
N
f  p, xi   f  p, xi   di 
H
 2
p
p
Sti2
i 1
(0.2)
If we have only random error, statistical average of quadratic deviation will be
 f  p, x   d 
i
2
i
 Sti2
(0.3)
With systematic error, instead (0.3) it will be inequality
 f  p, x   d 
i
i
2
 Sti2
(0.4)
If experimental data has higher systematic error, we should use this data with smaller weight in a
total error. Our empirical approach to taking into account the systematic errors we be based on
the using in (0.2) instead square of the standard deviation their sum with actual difference
between the data and the model:


EffSti2  Stei2   f  p, xi   di  / 2
2
(0.5)
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It means that (for gradients, divided by 2, in comparison with (0.2))
N
N
f  p, xi   f  p, xi   di 
f  p, xi 
 f  p, xi   di  (0.6)
H


2

2
p i 1
p
EffSti2
p
i 1
Sti2   f  p, xi   di 
Gradient (0.6) corresponds to error function
  f  p, x   d 2 
i
i

H   ln 1 
2


Sti
i 1


N
(0.7)
That will be used instead error function(0.1), in our data analysis. Accordingly, for the estimation
of data precision, in comparison with the model, we will use effective standard deviations(0.5).
PRECISION OF THE PARAMETERS EVALUATION
Variations of the parameters p can be defined from the (0.6) as
 N
1 f  p, xi  f  p, xi  
Mˆ   


2
p
p
 i 1 EffSti

N
f  p, xi  di
p  Mˆ 
p
EffSti2
i 1
1
(0.8)
Where d i is an error of the i-th data. Average square for the variation will be
 p 
 2
 M M


 ,
N,N

f  p, xi  f  p, x j 
p 
i 1, j 1
Assuming, that data errors are
 p 
 2
 M M


 ,
N

p
di d j
EffSti2 EffSt 2j
-correlated, we can simplify expression:
2
f  p, xi  f  p, xi  di
p 
i 1
(0.9)
p
EffSti4
(0.10)
Next assumption will be that
di2  EffSti2
(0.11)
And finally we can get
 p 
 2
N
  M  M  
 ,
i 1
f  p, xi  f  p, xi 
p

p

1
 M  (0.12)
2
EffSti
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