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

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.

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 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 (http://creativecommons.org/licenses/by/4.0/) 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 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: pm.nowak@uj.edu.pl (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 https://doi.org/10.1016/j.chroma.2021.462275 0021-9673/© 2021 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 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 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 pKa = pH + log μA− − μep μep 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 min, and running buffer for Before the first use of the capillary at a working day: methanol for 10 min, 0.1 M HCl for min, deionized water for min, 0.1 M NaOH for 10 min, and running buffer for 10 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 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 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 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 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 − 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) 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 and Fig (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 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 P.M Nowak, M Mitoraj, F Sagan et al Journal of Chromatography A 1651 (2021) 462275 Fig 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 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 P.M Nowak, M Mitoraj, F Sagan et al Journal of Chromatography A 1651 (2021) 462275 Table 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 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 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 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 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 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 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 The pKa values obtained at various temperatures are shown in Table The thermodynamic parameters were chartered on account of standard errors P.M Nowak, M Mitoraj, F Sagan et al Journal of Chromatography A 1651 (2021) 462275 Fig 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 - 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 [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 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 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 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 P.M Nowak, M Mitoraj, F Sagan et al Journal of Chromatography A 1651 (2021) 462275 Table 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 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) 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 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] References [1] A.C Moffat, M.D Osselton, B Widdop, Clarke’s Analysis of Drugs and Poisons, 2, 3rd ed., Pharmaceutical Press, London, 2004 [2] J Soderstrom, L Murray, M Little, F.F.S Daly, Toxicology case of the month: carbamazepine overdose, Emerg Med J 23 (2006) 869–887 [3] C.G Smollin, M.S Petrie, T Kearney, Carbamazepine and carbamazepine-10,11-epoxide clearance measurements during continuous venovenous hemofiltration in a massive overdose, Clin Toxicol 54 (2016) 424–427 [4] R Wietecha-Posłuszny, S Lendor, M Garnysz, M Zawadzki, P Kos´ cielniak, Human bone marrow as a tissue in post-mortem identification and determination of psychoactive substances - screening methodology, J Chromatogr B 1061–1062 (2017) 459–467 [5] A Majda, K Mrochem, R Wietecha-Posłuszny, Sz Zapotoczny, M Zawadzki, Fast and efficient analyses of the post-mortem human blood and bone marrow using DI-SPME/LC-TOFMS method for forensic medicine purposes, Talanta 209 (2020) 120533 [6] M.A Raggi, V Pucci, A Maurizio, J Muzikar, E Kenndler, Separation of carbamazepine and five metabolites, and analysis in human plasma by micellar electrokinetic capillary chromatography, J Chromatogr B 770 (2002) 217–225 [7] X.-S Miao, Ch.D Metcalfe, Determination of carbamazepine and its metabolites in aqueous samples using liquid chromatography-electrospray tandem mass spectrometry, Anal Chem 75 (2003) 3731–3738 [8] Y.-Y Lin, C.-C Wang, Y.-H Ho, C.-S Chen, S.-M Wu, Analysis of carbamazepine and its five metabolites in serum by large-volume sample stacking–sweeping capillary electrophoresis, Anal Bioanal Chem 405 (2013) 259–266 [9] E Shokry, F Villanelli, S Malvagia, A Rosati, G Forni, S Funghini, D Ombrone, M.D Bona, R Guerrini, G la Marca, Therapeutic drug monitoring of carbamazepine and its metabolite in children from dried blood spots using liquid chromatography and tandem mass spectrometry, J Pharm Biomed Anal 109 (2015) 164–170 [10] W Jiang, T Xia, Y Yun, M Li, F Zhang, S Gao, W Chen, UHPLC-MS/MS method for simultaneous determination of carbamazepine and its seven major metabolites in serum of epileptic patients, J Chromatogr B 1108 (2019) 17–24 ´ [11] P Nowak, M Wozniakiewicz , P Kos´ cielniak, Application of capillary electrophoresis in determination of acid dissociation constant values, J Chromatogr A 1377 (2015) 1–12 [12] S.K Poole, S Patel, K Dehring, H Workman, C.F Poole, Determination of acid dissociation constants by capillary electrophoresis, J Chromatogr A 1037 (2004) 445–454 ´ [13] P.M Nowak, M Wozniakiewicz , M Piwowarska, P Kos´ cielniak, Determination of acid dissociation constant of 20 coumarin derivatives by capillary electrophoresis using the amine capillary and two different methodologies, J Chromatogr A 1446 (2016) 149–157 [14] E Fuguet, C Ràfols, E Bosch, M Rosés, Fast high-throughput method for the determination of acidity constants by capillary electrophoresis I Monoprotic weak acids and bases, J Chromatogr A 1216 (2009) 3646–3651 [15] J.M Cabot, E Fuguet, C Ràfols, M Rosés, Fast high-throughput method for the determination of acidity constants by capillary electrophoresis II Acidic internal standards, J Chromatogr A 1217 (2010) 8340–8345 [16] E Fuguet, C Ràfols, M Rosés, A fast high throughput method for the determination of acidity constants by capillary electrophoresis Basic internal standards, J Chromatogr A 1218 (2011) 3928–3934 [17] J.M Cabot, E Fuguet, C Ràfols, M Rosés, Determination of acidity constants by the capillary electrophoresis internal standard method IV Polyprotic compounds, J Chromatogr A 1279 (2013) 108–116 [18] J.M Cabot, E Fuguet, M Rosés, Determination of acidity constants of sparingly soluble drugs in aqueous solution by the internal standard capillary electrophoresis method, Electrophoresis 35 (2014) 3564–3569 [19] J.M Cabot, E Fuguet, M Rosés, P Smejkal, M.C Breadmore, Novel instrument for automated pKa determination by internal standard capillary electrophoresis, Anal Chem 87 (2015) 6165–6172 ´ , P.M Nowak, M Gołab ˛ , P Adamowicz, M Kała, [20] M Wozniakiewicz P Kos´ cielniak, Acidity of substituted cathinones studied by capillary electrophoresis using the standard and fast alternative approaches, Talanta 180 (2018) 193–198 ´ [21] P.M Nowak, P Leszczenko, J Zarusinska , P Kos´ cielniak, Acidity constant of pH indicators in the supramolecular systems studied by two CE-based methods compared using the RGB additive color model, Anal Bioanal Chem 412 (2020) 577–588 ´ [22] P.M Nowak, M Wozniakiewicz , M Mitoraj, F Sagan, P Kos´ cielniak, Thermodynamics of acid-base dissociation of several cathinones and1-phenylethylamine, studied by an accurate capillary electrophoresis method free from the Joule heating impact, J Chromatogr A 1539 (2018) 78–86 [23] P Debye, P Huckel, On the theory of electrolytes, Phyz Z 24 (1923) 305–325 ´ [24] P.M Nowak, M Wozniakiewicz , M.P Mitoraj, F Sagan, P Kos´ cielniak, Enthalpy–entropy relations in the acid–base equilibrium of warfarin and 10-hydroxywarfarin; joint experimental and theoretical studies, RSC Adv (2015) 74562–74569 [25] J.M Miller, A.C Blackburn, Y Shi, A.J Melzak, H.Y Ando, Semi-empirical relationships between effective mobility, charge, and molecular weight of pharmaceuticals by pressure-assisted capillary electrophoresis: applications in drug discovery, Electrophoresis 23 (2002) 2833–2841 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/ST4/0 054) Compliance with ethical standards from the grant no P.M Nowak, M Mitoraj, F Sagan et al Journal of Chromatography A 1651 (2021) 462275 [26] C-E Lin, Y-T Chen, Migration behavior and separation of benzenediamines, aminophenols and benzenediols by capillary zone electrophoresis, J Chromatogr A 871 (20 0) 357–366 [27] Y Cheng, H Yuan, A simple approach to the prediction of electrophoretic mobilities of diverse organic acids, Anal Chim Acta 565 (2006) 112–120 [28] A Jouyban, E Kenndler, Theoretical and empirical approaches to express the mobility of small ions in capillary electrophoresis, Electrophoresis 27 (2006) 992–1005 [29] ADFSCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, 2019 http://www.scm.com [30] S Grimme, J Antony, S Ehrlich, H Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J Chem Phys 132 (2010) 154104 [31] E Van Lenthe, E.J Baerends, Optimized Slater-type basis sets for the elements 1–118, J Comput Chem 24 (2003) 1142–1156 [32] F Eckert, M Diedenhofen, A Klamt, Towards a first principles prediction of pKa: COSMO-RS and the cluster-continuum approach, Mol Phys 108 (2010) 229–241 ´ [33] P Nowak, M Garnysz, M.P Mitoraj, F Sagan, M Wozniakiewicz , P Kos´ cielniak, Analytical aspects of achiral and cyclodextrin-mediated capillary electrophoresis of warfarin and its two main derivatives assisted by theoretical modeling, J Chromatogr A 1377 (2015) 106–113 ´ [34] P Nowak, P Olechowska, M Mitoraj, M Wozniakiewicz , P Kos´ cielniak, Determination of acid dissociation constants of warfarin and hydroxywarfarins by capillary electrophoresis, J Pharm Biomed Anal 112 (2015) 89–97 [35] P.M Nowak, F Sagan, M.P Mitoraj, Origin of remarkably different acidity of hydroxycoumarins–joint experimental and theoretical studies, J Phys Chem B 121 (2017) 4554–4561 ´ [36] P.M Nowak, M Wozniakiewicz , P Kos´ cielniak, Seven approaches to elimination of the inherent systematic errors in determination of electrophoretic mobility by capillary electrophoresis, Anal Chem 89 (2017) 3630–3638 ... 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. .. 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... 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