Differentiation of isomeric metabolites of carbamazepine based on acid-base properties; Experimental vs theoretical approach

Journal of Chromatography A 1651 (2021) 462275

Contents lists available at ScienceDirect

Journal of Chromatography A
journal homepage: www.elsevier.com/locate/chroma

Differentiation of isomeric metabolites of carbamazepine based on
acid-base properties; Experimental vs theoretical approach
Paweł Mateusz Nowak a,∗, Mariusz Mitoraj b, Filip Sagan b, Renata Wietecha-Posłuszny a
a
b

Jagiellonian University in Kraków, Faculty of Chemistry, Department of Analytical Chemistry, Gronostajowa St. 2, 30-387 Kraków, Poland
Jagiellonian University in Kraków, Faculty of Chemistry, Department of Theoretical Chemistry, Gronostajowa St. 2, 30-387 Kraków, Poland

a r t i c l e

i n f o

Article history:
Received 3 February 2021
Revised 14 May 2021
Accepted 18 May 2021
Available online 24 May 2021
Keywords:
Acid-base properties
Capillary electrophoresis
Carbamazepine
Density functional theory
Metabolites

a b s t r a c t
Metabolism of carbamazepine is complex and leads to the three isomeric derivatives whose occurrence is
dependent on the type of sample material. Their unambiguous differentiation is overall important. In this
work, the qualitative analysis of 2-hydroxycarbamazepine, 3-hydroxycrbamazepine and carbamazepine10,11-epoxide was attempted for the first time using capillary zone electrophoresis, based on the models linking electrophoretic mobility with pKa value determining the acidity of the hydroxyl groups. For
this purpose, pKa values
were determined using electrophoretic and theoretical methods, and then the
compliance of the obtained mobility models with the measured values was analyzed. Despite the slight
difference in acidity
(0.3-0.4 pH unit), the obtained results prove that the correct identification of the
metabolites under consideration, and reliable prediction of the selectivity of their separation, are possible
on the basis of experimentally determined pKa values, even with highly simplified methods assuming the
lack of certain data. However, it is important to choose the optimal pH value, which should be close to
pKa . On the other hand, worse results were obtained for the theoretically determined mobilities, which
differed significantly from the experimental values. An attempt was also made to explain the acidity
of hydroxycarbamazepines and the associated thermodynamic parameters - deprotonation enthalpy and
entropy, with respect to their structure. The lack of intramolecular hydrogen bonds and the significant
contribution of entropic effects stabilizing the protonated form seems to be significant. The higher pKa
value for CBZ-2-OH probably results from the stronger effect of the energetically unfavorable organization
of solvent dipoles due to ionization.
© 2021 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY license ( />
1. Introduction
Carbamazepine (CBZ) is a commonly used psychotropic and anticonvulsant drug in patients suffering from epilepsy, bipolar disorder, schizophrenia and other diseases [1]. An overdose of CBZ
can lead to severe poisoning and death, especially in children, as
exemplified by the known cases of poisoning and even suicide attempts using CBZ [1,2]. It is metabolized in the liver by cytochrome
P450 mainly to the carbamazepine-10,11-epoxide (CBZ-EPO), but
there are also other isomeric derivatives with a hydroxyl group:
2-hydroxycarbamazepine (CBZ-2-OH) and 3-hydroxycarbamazepine
(CBZ-3-OH), the presence of which may depend on the type of biological material under analysis [3,4], see Fig. 1. For example, CBZEPO may not be the primary derivative found in postmortem material, such as bone marrow, which is an increasingly used alterna∗

Corresponding author at: Gronostajowa St. 2, 30-387 Kraków, Poland.
E-mail address: (P.M. Nowak).

tive material [4,5]. Given that CBZ-EPO, CBZ-2-OH and CBZ-3-OH
are isomers, the analytical methods used in the identification of
CBZ and its derivatives should be sufficiently selective to enable
their discrimination. This is also important for research into hitherto unknown pathways of CBZ biotransformation, for example involving the metabolism of corpse-decomposing microorganisms.
There are examples of the use of chromatographic and electrophoretic methods for the separation of CBZ metabolites [6-10].
The selectivity of these methods resulted mainly from the differences in hydrophobicity determining the different strength of interaction with the non-polar stationary phase (HPLC) or the micellar pseudostationary phase (MEKC). All known methods were
based on the classical calibration approach, required the possession
of appropriate standards to enable the identification of individual
metabolites in the tested material, based on the compliance of the
retention or migration times of analytes and standards.
In capillary electrophoresis (CE), migration time is determined
by electrophoretic mobility, which in turn depends on the charge

/>0021-9673/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( />

P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275

The main idea of
this work is to investigate the possibility
of differentiating isomeric CBZ metabolites using the CE technique
on the basis of physicochemical parameters, allowing to perform
right identification without standards. We focused on CBZ-2-OH
and CBZ-3-OH because they are ionizable due to the presence of
phenolic groups, therefore they can be easily distinguished electrophoretically from CBZ-EPO which remains neutral at physiological pH. In particular, the aim of this study was to: (i) determine

for the first time the pKa values
of CBZ-2-OH and CBZ-3-OH using an experimental method, and related thermodynamic parameters ( H° and -T S°); (ii) relate the obtained values
to the
structural effects, and explain a potential acidity difference; (iii)
test the possibility of using pKa values
to identify these compounds without using a standard, based on the compatibility of
electrophoretic mobility measured experimentally for the sample
and obtained from physicochemical models; (iv) test the possibility
of modeling the separation selectivity in terms of predicting optimal conditions for separation and identification; (v) compare various experimental and theoretical pKa determination methods in
terms of achieving the above objectives.

Fig. 1. The structures of CBZ and its isomeric metabolites produced during the
phase I metabolic reactions catalyzed by CYP enzymes.

and size of the analyzed species. The charge depends on the degree
of ionization, which is determined by the relationship between the
value of acid dissociation constant (pKa ) and the pH of environment. Knowing the pKa value makes it possible to predict electrophoretic mobility under given conditions, and thus model the
position of the peaks corresponding to the analytes on the electropherogram. It also gives rise to an attractive possibility of identifying analytes without having standards, based on physicochemical models prepared on the basis of previously known pKa values. For a huge number of organic drugs and their metabolites,
approximate pKa values
have been estimated using theoretical
algorithms such as ChemAxon, and are freely available in online
molecular databases. Unfortunately, the determined values
are
often inaccurate, and it is particularly difficult to correctly predict
the pKa difference for isomers. A potential solution is to use more
advanced theoretical methods for pKa determination based on density functional theory (DFT), but these also often fail if there is a
need to predict slight differences in pKa values. Therefore, the best
solution seems to determine them experimentally with high accuracy. Among the available methods for this purpose, it is worth
highlighting CE, which ensures high accuracy, very low consumption of reagents and samples, and the possibility of simultaneous analysis of several compounds, as it is a separation technique
[11,12].

The classical method of CE-based pKa determination requires
the analysis of the relationship between electrophoretic mobility
and pH, while maintaining a constant ionic strength of the running
buffers [11,13]. The pKa value is determined by the position of inflection point on fitted sigmoid Boltzmann’s curve with respect to
the pH axis. This method is quite time-consuming as it requires the
determination of mobility in at least 5-6 buffers with different pH.
Noticeably, other simpler methods are known which require the
measurement of the mobility in only two buffers, when the analyte
is fully ionized and partially ionized, respectively. The examples are
the internal standard capillary electrophoresis (IS-CE) method developed by the Rosés’ research group [14-19], and the two-values
method (TVM) proposed by our team [13,20,21]. The TVM method
does not require the use of internal standards, but only the knowledge of the pH of the buffer corresponding to the partial ionization. It is worth emphasizing that the accuracy of this method has
turned out to be comparable to the classical method several times
[13,20,21], within 0.1-0.2 pH unit. In the TVM method, pKa value
of monoprotic acid can be calculated using Eq. 1

pKa = pH + log

μA− − μep
μep

2. Material and methods
2.1. Materials
The analytical standards of CBZ-EPO, CBZ-2-OH and CBZ-3-OH
were supplied by (Sigma-Aldrich (St. Louis, MO, USA). All standard
solutions were prepared in the deionized water (MilliQ, MerckMillipore Billerica, MA, USA) and filtered through the 0.45 μm
regenerated cellulose membrane, then degassed by centrifugation.
The analytes concentration in the sample was 50 μg•mL−1 for CBZEPO and CBZ-2-OH, and 100 μg•mL−1 for CBZ-3-OH. The salts used
for preparing buffers and dimethyl sulfoxide (DMSO) were supplied
by Sigma-Aldrich. Other chemicals (organic solvents and washing

reagents) were supplied by Avantor Performance Materials Poland.
S.A. (Gliwice, Poland).
2.2. CE method
The PA 800 plus Capillary Electrophoresis instrument was used
(Beckman-Coulter, Brea, CA, USA), equipped with the diode array detector (DAD). The unmodified bare fused-silica capillary was
used. It was of 60.0 cm total length, 50.0 cm effective length, and
of 50 μm internal diameter (Beckman-Coulter). Between runs the
capillary was rinsed with 0.1 M NaOH for 1 min, and running
buffer for 2 min. Before the first use of the capillary at a working day: methanol for 10 min, 0.1 M HCl for 3 min, deionized water for 5 min, 0.1 M NaOH for 10 min, and running buffer for 10
min were applied. For the fresh capillary conditioning, the latter
sequence was used but the duration of each individual step was
doubled. The pressure applied equaled to 137.9 kPa (20 psi). Sample injection was conducted using the forward pressure of 3.45 kPa
(0.5 psi) for 5 s. During separations the separation voltage of 20.0
kV (normal polarity) was applied, without the external pressure.
The voltage ramp time was 0.2 min. The measured current values
were between 20-40 μA. Based on our previous experience [22],
we could assume that the influence of Joule heat on the pKa values
at such low current values
is small and negligible in the context of the objectives of this work. The temperature of cooling liquid was set at 25, 35, 45 and 55°C, as specified in the further text.
The detection was carried out at the wavelength of 200 and 230
nm in parallel, for measuring mobility and monitoring separation
of three isomers, respectively. DMSO was used as the electroosmotic flow marker, at the concentration of 0.1% (v/v). The buffer
solutions were prepared based on the same receipts as in our previous works [21,22]. In short, 200 mM NaH2 PO4 was mixed with

(1)

where μep is electrophoretic mobility – it needs to be measured in
the partially ionized state of a molecule at known pH, and μA- is
mobility of the ionic form.
2

P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275

100 mM Na2 HPO4 and further diluted with deionized water to 50
mM ionic strength (phosphate buffer), or 50 mM Na2 B4 O7 •10H2 O
was mixed with 10 0 0 mM NaOH or HCl and further analogously
diluted (borate buffers). The pH values were measured by a highclass laboratory pH-meter. Each sample was analyzed in triplicate.
The ionic strength of all running buffers was kept constant on the
level of 50 mM. The pKa values determined in this work are valid
for this ionic strength. The thermodynamic values valid for the
zero ionic strength can be obtained using the Debye-Hückel model
[23].

2.4. Modelling electrophoretic mobility based on pKa
In order to model the dependence of electrophoretic mobility
on pH, Eq. (4) was used:

μep =

Electrophoretic mobility was calculated as:

Ltot Le f f
·
Unom

1
1

−
ttot
teo f

(2)

where μep is the electrophoretic mobility, Ltot and Leff are the total and effective capillary lengths (m), Unom is the nominal (programmed) separation voltage (V); ttot is the total (observed) migration time of analyte (s); while teof is the time measured for the
neutral marker of electroosmotic flow – DMSO (s).
The pKa values were determined by two known experimental
methods based on the CE technique, the classic one, consisting in
fitting the Boltzmann curve to the dependence of electrophoretic
mobility on pH, and the TVM, requiring only two measurements of
mobility, see Eq. (1). Moreover, the classical method was applied at
four different temperatures (25-55°C), hence the Van’t Hoff model
was used to determine the values
of thermodynamic parameters: enthalpy and entropy of the deprotonation process. For this
purpose, the dependencies of the obtained pKa values
on the
inverse absolute temperature were used [22,24], described by Eq.
(3):

pKa =

H◦
S◦
−
2.303RT
2.303R

10−pKa + 10−pH

(4)

where μep is electrophoretic mobility at a given pH, and μA- is mobility of the ionic form.
The mobility values
obtained experimentally in the buffer
with the highest pH, corresponding to full ionization, were used as
the mobilities
of the ionic form. However, it is worth remembering that in the absence of a standard for a given substance,
these values
may not be directly measurable. In this case, literature data should be used, if available, or estimations can be
done based on models linking mobility under given conditions and
molecular weight or others [25-27]. A comprehensive review of advanced theories and models enabling such predictions was done
by Jouyban and Kenndler [28]. Otherwise, a potential approximate
approach is to use known ionic mobility of a structurally similar
compound instead analyte, especially if the predicted difference in
size is small. In order to check how important for the correct identification of CBZ metabolites based on pKa is the correct determination of the mobility of the ionic species, an additional simulation was carried out. This model differed from the classical model
in that the ionic mobilities
of CBZ-2-OH and CBZ-3-OH were
intentionally changed with each other, introducing a model error,
leaving the correctly determined pKa values
unchanged. This approach, called mistaken ionic mobilities (MIM), was also included
in the comparison of the above-described models.

2.3. Determination of pKa values

μep =

μA− · 10−pKa

2.5. Theoretical model
Structures of the compounds were optimized in the ADF2019
suite [29] at the DFT/BLYP-D3/TZP level of theory [30,31]. COSMORS [32] solvation model was used for pKa calculations as implemented in the ADF2016 suite.

(3)

3. Results and discussion

where R is the gas constant (8.3145 J•mol−1 •K−1 ). Accordingly,
the pKa values determined at various temperatures were plotted
against the inverse absolute temperature (1/T) and fitted by the
linear function. Subsequently, the enthalpic ( H°) and entropic (T S°) terms were calculated from the slope and intercept, respectively. The temperature of 25°C (298K) was used to calculate the
-T S° term.
To check how much the potential inaccuracy of pKa values
affects the correctness of models predicting electrophoretic mobility and selectivity of CBZ-2-OH and CBZ-3-OH separation at
25°C, an additional approach was applied. It consisted in the deliberate use of erroneous pKa values, determined for a much higher
temperature (55°C). It was done to check whether, in the absence
of adequate data, it is possible to use pKa values that are adequate
to completely different thermal conditions. It is known in the literature that the resolution in the CE technique can change drastically
with temperature, as we demonstrated in the past for cathinones
[22]. Often, optimal separation temperature is the one which lacks
precisely determined pKa values. On that account, testing the usability of pKa from other temperature seems an interesting scientific goal.
Apart from the pKa values
determined experimentally, two
theoretical models were used: pKa values
available in the online
database of molecules (DrugBank) obtained with the ChemAxon algorithm, and obtained with the COSMO-RS model based on DFT
computational methods, see Section 2.5.

3.1. Acidity and thermodynamics of deprotonation

On the basis of the obtained electropherograms at the temperature of 25°C and various pH values, the electrophoretic mobilities
were calculated and then used to determine the pKa using the classical and other methods considered in this work. As regards TVM
method, the mobility data obtained only at pH close to 9.5 and
11.5 were used for that purpose, as they correspond to the partial
ionization close to 50% and complete ionization, respectively. These
conditions are most preferred for the TVM method [13,20,21].
The respective data are shown in Table 1 and Fig. 2 (electropherograms). The plots of mobility data versus pH, and the fitted curves related to all models (discussed in the next section) are
shown in Fig. 3.
As can be seen from Table 1, the TVM method gives very similar
values to the classical method, for the Temp 55 approach the differences are already noticeable, about 0.2-0.3 pH units, while the
theoretical approaches give pKa values
that differ significantly.
Although ChemAxon allowed to obtain the pKa value of CBZ-3OH almost identical to the classical method, this result should be
considered rather coincidental. This is evidenced by a significantly
larger error for CBZ-2-OH, and the fact that this algorithm did not
predict a higher pKa value for CBZ-2-OH, which somehow suggests
that it does not see any structural differences in these compounds.
The DFT method turned out to be even more inaccurate, but it is
worth emphasizing that it correctly predicted that CBZ-3-OH has a
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P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275

Fig. 2. Electropherograms obtained at various pH values and wavelength of 230 nm for the mixture of isomeric CBZ metabolites (CBZ-EPO, CBZ-2-OH and CBZ-3-OH).

Fig. 3. Electrophoretic mobility values (μel ) of CBZ-2-OH (red) and CBZ-3-OH (blue) measured experimentally (triangles) versus predicted by the respective pKa -based models
(dotted lines), described in the text. The light gray rectangles indicate the conditions in which right identification of isomer is unfeasible due to overlapping of models. The

dark gray rectangles indicate the conditions in which identification would be false, assuming that the analyte is the isomer whose model is closer to the experimental data.

4


P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275
Table 1
The pKa values and ionic mobilities of CBZ-2-OH and CBZ-3-OH obtained using the respective approaches.
Method

Parameter

CBZ-2-OH

CBZ-3-OH

Classical

pKa
ionic mobility (10−7 m2 s−1 V−1 )
pKa
pKa
pKa
pKa

9.55 (0.02)∗
-0.274 (0.002)∗
9.51 (0.01)∗∗

9.38 (0.04)∗
9.15
9.90

9.17 (0.05)∗
-0.285 (0.004)∗
9.18 (0.02)∗∗
8.95 (0.16)∗
9.19
9.70

TVM
Temp 55
ChemAxon
DFT

∗
The parameter errors determined with the OriginPro 2020 software during function
fitting;
∗∗
errors expressed as the standard deviations from the three replicates. The data apply
to the ionic strength of 50 mM and temperature of 25°C, except Temp 55 (55°C).

Table 2
The pKa values and their errors, obtained
at various temperatures using the classical
method.
CBZ-2-OH

CBZ-3-OH

Temp.

pKa

Error

pKa

Error

25°C
35°C
45°C
55°C

9.55
9.47
9.41
9.38

0.02
0.05
0.07
0.10

9.17
9.13
9.07
8.95

0.05
0.09
0.06
0.12

(obtained with OriginPro software). In the case of enthalpy, CBZ-2OH and CBZ-3-OH are within the error range, while of entropy, the
values could be considered statistically different.
CBZ-2-OH turned out to have a slightly higher pKa value, i.e.
lower acidity, compared to CBZ-3-OH. This difference is not large,
around 0.3-0.4 pH units, especially when compared to the differences we observed in the past for other regio-isomers of the phenolic group – coumarin derivatives [33-35]. For hydroxycoumarins,
the greatest differences were almost 5 pH units [35]. This shows
that the structural factors and related thermodynamic picture determining the dissociation of CBZ-2-OH and CBZ-3-OH are quite
similar.
The relatively small ratio of enthalpic to entropic factors observed for both compounds is noteworthy. Assuming the correctness of the determined parameters, it can be concluded that the
higher pKa value of CBZ-2-OH results from the entropy-related effects, as the deprotonation enthalpy for this compound is lower
and thus more favorable, see Fig. 3. To explain these results, it will
be helpful to analyze the theoretically optimized structures of CBZ2-OH and CBZ-3-OH, presented in Fig. 5, as well as the results obtained by us in the past for other classes of compounds: coumarins
and cathinones [22,24,33-35].
It is seen from Fig. 5, that the theoretically calculated pKa is 9.9
and 9.7 for CBZ-2-OH and CBZ-3-OH, respectively. It is in a qualitative accord with the experimental trend. According to the COSMORS model, a slightly lower pKa of CBZ-3-OH can be explained by
the more pronounced stabilization of its anion upon solvation in
water as the estimated solvation energy in by around 1 kcal/mol
lower for CBZ-3-OH than CBZ-2-OH. It entails shifting the equilibrium towards the deprotonated form. Furthermore, more favorable
solvation energy of an anion may be tied with more compact hydration sphere, thus lowering the hydrodynamic radius.
In our previous work, high deprotonation enthalpy and low entropy values were attributed to the spontaneous formation of intramolecular hydrogen bonds stabilizing the protonated form, detected during the theoretical description of the optimized conformations of warfarin and 10-hydroxywarfarin [24,33-35]. Such
OH•••O bonds were found between the phenolic and carbonyl
groups. On the other hand, the lower enthalpy values were char-

Fig. 4. The Van’t Hoff plots and resulting thermodynamic functions obtained for

CBZ-2-OH and CBZ-3-OH using the classical CE methodology of pKa determination.
The errors of thermodynamic parameters are show in the brackets.

pKa value lower than CBZ-2-OH. This may indicate that the model
used in this approach correctly predicts the structural effects that
differ these isomers, but it is associated with some systematic
error. Similar relationships were observed for the DFT/COSMO-RS
model in the previous studies, where, despite large absolute differences, the qualitative trends turned out to be consistent with the
experiment [33-35].
The separation of CBZ isomeric metabolites observed at various
pH values is illustrated in the corresponding electropherograms Fig. 2. As can be seen, complete separation of the peaks derived
from the isomeric CBZ derivatives was possible starting from pH
8.5 up to the most basic. The best resolution is observed at pH
9.6 and 10.4, where the difference in the degree of ionization of
CBZ-2-OH and CBZ-3-OH has a significant impact. At pH 11.7, both
CBZ-2-OH and CBZ-3-OH are completely ionized, hence the differences in migration times are related only to the hydrodynamic
size. As can be seen from Fig. 2, the resolution is still sufficient, although its difference in mobility is less than 5%. The high pH value
can therefore also be used for the electrophoretic separation of the
compounds under consideration, although the selectivity increases
drastically when taking into account the effect of different pKa values.
The measurements were then repeated for higher temperatures
(35, 45 and 55°C), thanks to which the Van’t Hoff model was used
to estimate the thermodynamic parameters describing the contribution of enthalpy and entropy factors to the deprotonation processes of CBZ-2-OH and CBZ-3-OH, see Fig. 4. The pKa values obtained at various temperatures are shown in Table 2. The thermodynamic parameters were chartered on account of standard errors
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Journal of Chromatography A 1651 (2021) 462275

Fig. 5. The optimized structures of CBZ-2-OH and CBZ-3-OH in a gas-phase, together with the pKa values calculated based on DFT/BLYP-D3/COSMO-RS approximation. The
structures of the deprotonated forms are very similar (not shown).

acteristic for structures showing no intramolecular contacts [35].
High pKa values
observed despite the lack of such bonds (e.g.
for 6-hydroxycoumarin pKa is about 9 - similar to CBZ derivatives),
were explained by the unfavorable entropic effects caused most
probably by the organization of water molecules due to ionization, significantly increasing the polarity of a given area of
the
molecule [35]. This effect was also visible in electrophoretic mobility of the ionic form, as the increase in the hydrodynamic radius due to the growth of solvation shell. It is also worth mentioning that the formation of intramolecular hydrogen bonds by protonated forms should be considered as entropically favorable in the
context of deprotonation (the effect of molecular disorganization
as a result of their breaking), which lowers the pKa value despite
strong enthalpic stabilization of the protonated form. Accordingly,
for 10-hydroxywarfarin, with pKa close to 6.0, H° is 34.3 kJ/mol
while -T S° is close to 0 [24]. Therefore, in each case the entropic
effects occurred to be extremely important.
The above considerations, combined with the analysis of the
optimized structures (Fig. 4), suggest the lack of strong intramolecular hydrogen bonds for CBZ-2-OH and CBZ-3-OH, and a significant
influence of entropic factors related to the organization of solvent
molecules around the ionized phenolic group. This effect is probably slightly stronger for CBZ-2-OH, hence the higher pKa value,
which is also confirmed by the comparison of the mobility of the
ionic species. As shown by electrophoretic data, the hydrodynamic
radius of CBZ-2-OH is 4.1% larger than that of CBZ-3-OH (the electrophoretic mobilities of the ionic species are -0.285 and -0.273
10−7 m2 s−1 V−1 for CBZ-3-OH and CBZ-2-OH, respectively) This can
be explained by the fact that the phenol group of CBZ-2-OH is
more distant from the polar amide group than CBZ-3-OH (Fig. 5),
hence after its ionization the molecule gains a new polar region
attracting and organizing additional water dipoles.

overlapping or erroneous, are marked in Fig. 3 with light gray and
dark gray rectangles, respectively. It was assumed that the identity
of the analyte is determined by the model closest to the experimental value (marked by triangle in Fig. 3), without knowing the
value of the experimental mobility for the second isomer.
As regards the experimental approaches, the identification
based on the pKa value is correct in most cases. Errors are observed for CBZ-2-OH at the two lowest pH values
where the absolute mobility is low, and thus the model is sensitive to potential
errors, e.g. due to weak interactions of the analytes with buffer
components or capillary walls. It is worth noting that all experimental models, even MIM and Temp 55 based on the intentionally
entered incorrect data, correctly identify isomers at pH around 9.5
and 10.5, where the degree of ionization of compounds is high, but
still incomplete. In the case of MIM, the error appears at the highest pH, above 11.5, which is due to the obvious assumptions of this
approach. The most important thing is that at pH close to the pKa
values
(about 9.5), the experimental points are very close to the
theoretical ones, making the identification unambiguous.
The agreement of the experimental values
of electrophoretic
mobility with those calculated with the use of models was also
tested by means of the t-student statistical test, assuming the
significance level of α =0.05. The obtained results are presented
in Table 3, which shows whether in a given case these values
coincide in the assumed significance range. It turns out that,
apart from the lowest pH, the values
are in most cases in agreement. Deviations are observed for the lowest pH, where the ionization degree is minute and the mobility values
are very low
and thus subjected to high uncertainty, and pH 9.6. However, it
should be borne in mind that in the latter case, a very small dispersion of experimental mobility was noted (high precision), which
could have influenced the statistical test result. Fig. 3 shows that
at this pH the differences are very small, therefore the correct and

easy identification of the isomers is possible with any model except ChemAxon and DFT. From the above observations it follows
that the distinction between CBZ-2-OH, CBZ-3-OH and CBZ-EPO
is fully possible with the CE technique without additional buffer
modifiers like surfactants, and without having the standards of the
substances, based only on physicochemical models. It is important
that the application of the fast pKa determination method – TVM,
as well as the pKa values determined for the temperature differing
by as much as 30 degrees, does not affect the correctness of the
analysis.
Moreover, the use of erroneous (intentionally interchanged) values
of the mobility of ionic species also does not cause erroneous identification, provided that pH of running buffer is close to
pKa . This proves that the pKa difference of about 0.3-0.4 pH unit is
sufficient for that purpose, despite the noticeable mobility differences of the ionic species above 4%. It also suggests that in the absence of any data on ionic mobilities, when considered compounds

3.2. Modeling of electrophoretic mobility
The simulation of electrophoretic mobility variation as a function of pH was carried out using the pKa values listed in Table 1,
they include: (i) the values determined using the classical method
– which should be deemed as the most accurate; (ii) TVM - a simpler and faster alternative to the classical approach; (iii) Temp 55 using intentionally erroneous pKa values, adequate for the temperature of 55 instead of 25°C; (iv) ChemAxon - a simple theoretical
algorithm available on-line; and (v) DFT - a theoretical approach
based on DFT and COSMO-RS model [30-32] that we have often
used in the past to study the acidity of other classes of compounds
[22,24,33-35]. The results are shown in Fig. 3.
The MIM approach was also used, in which the mobilities of the
CBZ-2-OH and CBZ-3-OH ionic forms were intentionally changed
with each other, which is visible as the intersection of the graph
lines at pH around 10.5. The particular cases in which identification based on the models would be impossible due to their mutual
6


P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275

Table 3
The results of the t-test showing whether the experimental values
statistically significant manner (‘+’ means yes, ‘-‘ means no).
classical

MIM

of electrophoretic mobility coincide with the theoretical values

TVM

Temp 55

obtained from a given model in a

ChemAxon

DFT

pH

CBZ-2-OH

CBZ-3-OH

CBZ-2-OH

CBZ-3-OH

CBZ-2-OH

CBZ-3-OH

CBZ-2-OH

CBZ-3-OH

CBZ-2-OH

CBZ-3-OH

CBZ-2-OH

CBZ-3-OH

7.5
8.5
9.6
10.4
11.7

+
+
+
+

+

+
+
+

+
+
-

+
+

+
+
+
+

+
+
+

+
+
+

+
+
+

+
+

+
+
+

+
+

+

All experimental approaches predict a maximum difference in
mobility in a similar pH range, approximately 9.2-9.4, which corresponds to the mean of the pKa values
of both compounds. The
errors measured against the reference experimental values
are
small, which is of particular importance in the case of the simplified methods: TVM and Temp 55. This confirms that in addition
to identifying unknown analytes for which there are no available
standards, pKa values
can be used in the optimization of separation conditions in order to increase resolution of individual peaks.
If there is a need to determine the pKa value using an experimental
method, the classical approach can be replaced by a much faster
TVM, and the use of pKa values
adequate for different thermal
conditions can also be considered. As far as theoretical approaches
are concerned, the ChemAxon model is completely useless, while
the DFT model as the optimal pKa value suggests 9.8. Noticeably, in
these conditions the real mobility difference is only half the maximum difference, which should be considered as a partially satisfactory result.

Fig. 6. The dependence of selectivity between CBZ-2-OH and CBZ-3-OH on pH, presented as a difference of electrophoretic mobility ( μ) obtained from experimental
data (reference, black triangles) versus estimated using various pKa -based models

(colored dotted lines).

4. Discussion and conclusions
The relatively high pKa values of CBZ-2-OH and CBZ-3-OH indicate strong structural effects stabilizing the non-ionized state of
the phenolic groups. Probably the most important are the energetically unfavorable entropic effects resulting from the influence of
deprotonation on the organization of solvent molecules. This is evidenced by the larger hydrodynamic radius observed for CBZ-2-OH,
which exhibits a slightly higher pKa value and possibly a larger
contribution of solvent-related effects. This is also confirmed by
the small contribution of enthalpic factors to the total change of
Gibbs free energy, indicating small changes in the heat capacity of
the system due to proton release. Such outcomes probably exclude
the formation of strong non-covalent bonds stabilizing the nonionized state. The abovementioned conclusions shed new light on
the understanding of the relationship between acidity and molecular structure, and therefore may be useful in the future in developing better theoretical models that allow the estimation of pKa values
with greater accuracy than the theoretical approaches studied in this work (ChemAxon and DFT).
Efficient differentiation and correct identification of the isomeric metabolites of CBZ: CBZ-2-OH, CBZ-3-OH and CBZ EPO are
possible on the basis of physicochemical models connecting electrophoretic mobility with the pKa value. Although the difference
in the acidity of CBZ-2-OH and CBZ-3-OH is not large, about 0.30.4 pH units, it translates into quite significant differences in mobility observed at pH values
close to pKa ,
and hence is sufficient. Potential errors resulting from the application of the rapid
pKa estimation method - TVM, from the assumption of pKa values
appropriate for temperature differing by 30 degrees - Temp 55,
as well as from the intentionally interchanged ionic mobilities of
CBZ-2-OH and CBZ-3-OH, did not significantly affect the accuracy
of the models. Despite some inaccuracies, the correct identification
of peaks is possible provided that pH of buffer is close to pKa .

are isomers, it can be safely assumed that they are the same, with
the difference only in pKa values.
The theoretical models (ChemAxon and DFT) turned out to be
much less effective. In the case of ChemAxon, the problem is

the very high similarity of the CBZ-2-OH and CBZ-3-OH models,
which basically excludes their use. The DFT approach, in turn, significantly elevates the pKa values, thus leading to the erroneous
identification of CBZ-2-OH as CBZ-3-OH in practically the entire
pH range. However, assuming that experimental signals from both
CBZ-2-OH and CBZ-3-OH are observed, but their identity is unknown, the DFT model allows to correctly identify them based on
the relative mobility relationship. In practice, however, such a situation may be quite rare, and the overall usefulness of both theoretical models in this regard should be considered low.
As mentioned earlier, for the correct identification of analyte on
the basis of its electrophoretic mobility resulting from pKa , it is important to select pH of buffer, the value of which should be close
to pKa . When the unknown analyte can be one of two, such as
in this case CBZ-2-OH or CBZ-3-OH, the optimal pH value should
coincide with the maximum difference in electrophoretic mobility
of these compounds. Moreover, the pH value selected in this way
will most often also be optimal in the case of the traditional approach to qualitative analysis, based on the use of standards of a
given substance and comparison of migration times, as high resolution of peaks is generally desirable for many reasons. Therefore, it seems interesting to also compare the considered models
in terms of predicting the separation selectivity of CBZ-2-OH and
CBZ-3-OH measured by the difference of respective electrophoretic
mobilities. This is shown in Fig. 6, where all models were compared to the experimental values
obtained in the three buffers
with different pH, close to the pKa values.
7


P.M. Nowak, M. Mitoraj, F. Sagan et al.

Journal of Chromatography A 1651 (2021) 462275

The pKa and ionic mobility values, needed to apply Eq. (4) and
simulate the mobility of analyte at given pH, can be obtained from
literature, molecular databases or estimated theoretically (simulation of effective ionic mobility is well described in [28]). In such a
scenario, physicochemical models may replace the classic calibration approach requiring the availability of analytical standards for

the given substances. This may be particularly useful for the analysis of compounds for which standards are not readily available,
for example for hitherto unknown metabolites of known drugs,
or for newly developed chemical structures and their derivatives.
For CBZ, the usefulness of such an approach is also high. Although
CBZ-EPO is the major metabolite of CBZ found in blood and urine
[1-3], CBZ 2-OH and CBZ-3-OH may be the dominant metabolites
found in the alternative biological material, e.g. bone marrow collected post-mortem [4,5]. Taking into account that the availability
of CBZ-2-OH and CBZ-3-OH standards is limited compared to CBZEPO in many laboratories, electrophoretic analysis conducted at pH
between 9-10 allows to easily identify given metabolite. Especially
useful may be the integration of the method with MS detector, to
unequivocally exclude the presence of other metabolites with different mass. Such an approach is simple due to the fact that no
buffer additives are needed which may be incompatible with MS
detector, like surfactants.
Therefore, it seems extremely important for the community of
analytical chemists to experimentally determine pKa for the largest
possible pool of chemical compounds, including metabolites of
known drugs, and to publish them in sources available to other analysts. It is also important to strive to improve the accuracy of the
theoretical pKa estimation methods, which could replace the need
to use experimental methods that require the physical possession
of analytical standards. Although the approaches to identification
based on physicochemical properties presented here are never as
reliable as the classical calibration, they can be an interesting complement to it, especially in cases when standards are not readily
available. We believe that this non-standard approach to identification is an interesting perspective for the future that should be
further developed. In our opinion the attention should be payed
to testing and improving the known models enabling quick estimation of ionic mobilities based on molecular weight in particular
electrophoretic conditions [27,28], and to studying the impact of
potential effects such as undesirable interactions with buffer constituents, capillary walls, or excessive Joule heating [22,36].

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Declaration of Competing Interest
The authors declare no competing interests.
CRediT authorship contribution statement
Paweł Mateusz Nowak: Conceptualization, Data curtion, Formal analysis, Investigation, Methodology, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing.
Mariusz Mitoraj: Conceptualization, Data curtion, Formal analysis,
Investigation, Software, Writing – original draft, Writing – review
& editing. Filip Sagan: Data curtion, Formal analysis, Investigation.
Renata Wietecha-Posłuszny: Conceptualization, Data curtion, Formal analysis, Investigation, Methodology, Writing – original draft,
Writing – review & editing.
Acknowledgments
R. W-P acknowledges the financial support
National Science Centre, Poland (Sonata Bis 6,
2016/22/E/ST4/0 0 054).
Compliance with ethical standards

from the
grant no.

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9