β‐Cyclodextrin and folic acid host–guest interaction binding parameters determined by Taylor dispersion analysis and affinity capillary electrophoresis

The thermodynamic properties of molecular recognition in host–guest inclusion complexes can be studied by Taylor dispersion analysis (TDA). Host–guest inclusion complexes have modest size, and it is possible to get convergent results fast, achieving greater certainty for the obtained thermodynamic properties. Cyclodextrins (CDs) and their derivatives can be used as drug carriers that can boost stability, solubility, and bioavailability of physiologically active substances. A simple and effective approach for assessing the binding properties of CD complexes that are critical in the early stages of drug and formulation development is needed to fully understand the process of CD and guest molecules’ complex formation. In this work, TDA was successfully used to rapidly determine interaction parameters, including binding constant and stoichiometry, between β‐CD and folic acid (FA) along with the diffusivities of the free FA and its complex with β‐CD. Additionally, the FA diffusion coefficient obtained by TDA was compared to the results previously obtained by nuclear magnetic resonance. Affinity capillary electrophoresis (ACE) was also used to compare the binding constants obtained by different methods. The results showed that the binding constants obtained by ACE were somewhat lower than those obtained by the two TDA procedures.


INTRODUCTION
Noncovalent molecular interactions play an important role in physiological processes. Quantitative assessment of affinity constants with nanoliter samples can be a useful tool in assessing protein-protein and protein-ligand interactions, as well as a selection tool for drug delivery. Cyclodextrins (CDs) are often used in pharmaceutical formulations to improve solubility, stability, and bioavailability of the active pharmaceutical ingredients by forming host-guest complexes [1][2][3]. CDs are a class of cone-shaped molecules with a hydrophobic cavity due to α-1,4-linked glucopyranose units. There are three common types of CDs, including α, β, and γ-CD with 6, 7, and 8 glucopyranose units, respectively, to form different sized hydrophobic cavities. With the formation of CD complexes, the apparent activities of some molecules can be enhanced [4][5][6][7]. Molecules with hydrophobicity and appropriate size can form inclusion complexes with CDs by interacting with their hydrophobic cavities [8]. However, for many therapeutic compounds, the pH of the solution affects that their charges and the binding constants with the CDs are difficult to predict [9]. Folic acid (FA), or folate, aka vitamin B9, is a naturally occurring water-soluble molecule that aids in the synthesis and methylation of nucleic acids (DNA and RNA) and proteins (see structure in Figure 1A) [10,11]. FA used as a food supplement for pregnant women can reduce the risk of fetal congenital malformations and congenital heart defects. However, excessive intake of FA can cause allergy and even breast tumor [12,13]. FA is also used as a conjugate in prodrugs, such as taxol, camptothecin, and doxorubicin [14][15][16].
To improve the solubility, stability, and bioavailability of FA, β-CD complex in water has been investigated using electrospray ionization mass spectrometry, isothermal titration calorimetry (ITC), and nuclear magnetic resonance spectrometry [17]. Circular dichroism spectroscopy [18], fluorescence spectroscopy [19][20][21], ITC [22,23], and molecular docking simulation [24][25][26] have been used to study interactions between CDs and other drug molecules. It is noted that the in-depth characterization of CD-drug complexes for drug development is improved by developing new analytical tools. Recently, capillary electrophoresis (CE), a free solution-based approach, has shown significant potential as an alternative method for studying binding interactions [27][28][29][30]. With low sample consumption, fast analysis speed, and high separation efficiency, affinity capillary electrophoresis (ACE) [31,32] has been used to study noncovalent interactions involving biological molecules with no need for the immobilization of protein or ligand molecules [33][34][35].
Taylor dispersion analysis (TDA) is a flow-based approach used for assessing diffusion coefficient (D) and hydrodynamic radius (R h ) of the analyte with sizes ranging from small molecules, peptides, proteins to nanoparticles [36][37][38]. Dispersion of an analyte plug occurs in a laminar Poiseuille flow in accordance with the TDA theory, which states that convection (axial direction) and molecular (radial direction) diffusion work together to disperse an analyte plug [39,40]. With the use of an automated CE equipment, TDA can easily be performed, and the method gives direct information on the size of the molecules to be used in biology, medical, and material science. When there are two particles of different sizes in the system, a TDA signal with the sum of two populations can be deconvoluted to calculate the size of each particle [41,42]. CE-based TDA was first used to study the protein-ligand interaction at equilibrium and simultaneously characterize the size of the protein [43]. TDA was recently shown to be an effective and general method for finding equilibrium binding parameters for biomolecules [38,44].
Here, we developed a TDA method for determining the interaction between β-CD and FA in nanoliter samples. The procedure can be carried out using a CE instrument with a UV detector because only a pressure applied on a thin tube or capillary is needed. The aim of the work is to develop a fast and accurate TDA method for evaluating host-guest interactions, leading to the determination of the binding parameters, and diffusion coefficients, and analyte sizes, and to evaluate the potential of CDs for the effective inclusion of FA.

THEORY
In a capillary, an analyte plug disperses while migrating through a capillary under Poiseuille laminar flow conditions, and the analyte temporal variance ( 2 ) is linked to its diffusion coefficient (D) as shown in the following equation [45,46]: where R c is the capillary radius, t d is the average elution time, and σ t is the standard deviation of the Gaussian peak in time domain, respectively. The Stokes-Einstein equation is used to calculate the solute's hydrodynamic radius, R h [37]: where k B is the Boltzmann constant, η is the viscosity, and T is the temperature (Kelvin) of the carrier liquid in the capillary.
The linear velocity (u) of the analyte is determined by the following equation [47]: where L d is the capillary length from the injection end to the detector, P is the mobilization pressure applied to push the liquid through the capillary, and L c is the total length of the capillary. Importantly, the CE instrument can be used to determine the viscosity of the carrier liquid within the capillary as shown in the following equation: The viscosity and analyte elution time of pure water as a reference is denoted as η 0 and t 0 , respectively. Therefore, analytical elution time is proportional to carrier viscosity when mobilization pressure and size of the capillary are fixed.
If the capillary has two detector windows (double detection TDA), the difference in the variance can be used to calculate the diffusion coefficient directly. However, if double detection is not possible, a single detection window can be used as well as long as the length of the injection plug is less than 1% of the effective capillary length. Analyte elution time, t d,obs , should be adjusted by the pressure ramp time (t ramp ) while performing TDA in a single detection window according to the following equation: The pressure ramp and the injection volume should also be taken into consideration in the corrected elution time and corrected peak variance using the following equations [48]: where t d,corr is the corrected elution time, V i is the injection volume, V d is the capillary volume from the inlet to the detection window, and σ corr is the corrected peak variance. Two conditions must be met to obtain reliable D values (less than 3% error) [38,49,50]. First, the elution time must be significantly greater than the time required to diffuse through the capillary radius as shown in the following equation: where τ is an unitless parameter proportional to the elution time, and is the maximum relative error of D determination that may be accepted (3%). The longitudinal dispersion should be minimal, relative to the radial dispersion, which is the second condition described in the following equation: where the Peclet number (Pe) is the ratio of convection and diffusion contributions to mass transfer. To meet the second condition, the value of Pe should be greater than what is defined in Equation (9), depending on the expected relative error of the diffusivity. Because τ > 1. 25 and Pe > 40 were satisfied for all TDA measurement in this study, Taylor's requirements are fulfilled.

Sample preparation
HCl solutions with the same concentration were used to adjust the Tris-HCl buffers (10-35 mM Tris) to a pH of 10.0. FA stock solution was diluted with the Tris-HCl buffer and a certain amount of β-CD (0-2.5 mM) dissolved in the Tris-HCl buffer as described in Section 4.

Optimization of TDA for the study of FA interaction with β-CD
Free FA was used to determine optimum parameters such as mobilization pressure, capillary length, and buffer concentration to establish a balance between the accuracy of the predicted diffusion coefficient and the elution peak shape.
Different mobilization pressures ranged from 6.89 × 10 3 to 3.45 × 10 4 Pa were tested. Figure 1B shows the Taylorgrams obtained from using a sample of 50 µM FA in 20 mM Tris-HCl (pH 10.0). The Taylorgrams are Gaussian shaped when the TDA analysis is performed in plug mode. According to Equation (3), the linear velocity, u, of the analyte in a laminar flow is proportional to the mobilization pressure, and the elution time inversely proportional to the mobilization pressure. As shown in Table S1, the R 2 values from the Gaussian fit were close to 1, indicating that desired Gaussian peaks were obtained. It was found that the lowest standard deviation in the diffusion coefficient calculated from the FA peaks was when the mobilization pressure of 2.07 × 10 4 Pa for the four duplicate runs. Therefore, 2.07 × 10 4 Pa was selected for the rest of the work.
Appropriate capillary length should be used in developing TDA methods. To ensure that the elution time is longer than what is needed for the capillary radius used, as determined by Equation (8), different lengths of the capillaries were tested. When a longer capillary is used instead of a shorter one, the Pe value was reduced when the same pressure was used. When the Pe value is higher than the limit described in Equation (9), the longitudinal diffusion becomes insignificant, and Taylor dispersion becomes dominant. FA solutions were injected into the capillaries (50 µm id) with different lengths of 50-70 cm. The elution time of FA was longer for longer capillaries, as shown in Table S2. When the total length of the capillary was 60 cm, the R 2 value was near 1. Therefore, 60 cm capillary length (50 cm to the detector) was used for the rest of the TDA measurement.
Buffer concentration may affect the repeatability of the analyte peak shape and the diffusion coefficient obtained. Tris-HCl (pH 10.0) was used as the run buffer. A range of buffer concentrations (10-35 mM) was examined to study the peak shape changes over time and predicted diffusion coefficient. Table S3 shows that for this buffer, the R 2 value was close to 1 regardless of the concentration. Because the standard deviation of the measured diffusion coefficient reached its minimum when the buffer concentration was 20 mM, this concentration was used for all subsequent experiments. In addition, Tris-HCl buffers of different pH values (7.0-10.0) were used for TDA experiments, and the results showed that the change of pH has little effect on the results of the predicted diffusion coefficient and the elution peak shape (Table S4). In the following ACE experiment, the use of Tris-HCl buffer with a pH of 10.0 could reduce the adsorption of FA on the capillary internal face, so Tris-HCl solution (pH = 10.0) was chosen as the buffer for TDA and ACE experiments.

Determining the complex size and the free FA concentration
The TDA experiments were performed as follows: The mixture of FA and β-CD was injected into the capillary filled with β-CD solution. The concentration of the β-CD in the injection was the same as its concentration in the carrier phase. They flow together and bind to form a complex. A Gaussian peak was obtained at 210 nm to get an elution profile obtained from 50 µM FA along with 0.75 mM β-CD. As shown in Figure 2, with 0.75 mM β-CD, the Taylorgram of FA showed a normal Gaussian shape that includes different molecular populations, which was a convolution of individual Gaussian peaks with a different diffusion coefficient represented by each. Two distinct peaks obtained by deconvolution correspond to the coexistence of the β-CD- FA complex and free FA because β-CD does not absorb at 210 nm. The determination of the hydrodynamic radius, R h , was carried out by making use of the Stokes−Einstein relationship (see Equation 2). Curve fitting of the two Gaussian peaks gives one of the diffusion coefficients of (1.49 ± 0.08) × 10 -10 m 2 /s with a hydrodynamic radius (R h ) of 1.64 ± 0.08 nm, which corresponds to the size of the free FA. The results obtained for the FA molecules in a free solution corroborate quite well with the values found in the literature [51]. The second Gaussian peak resulted in a size equivalent to 2.43 ± 0.14 nm for the β-CD-FA complex with the diffusion coefficient of (1.01 ± 0.06) × 10 -10 m 2 /s ( Table S5).
As a function of the pressure-driven flow and its properties, the diffusion coefficient is not a constant. According to the Taylor-Aris dispersion model (Equation 2), at the low Peclet number where the diffusion and convection effect coexist, an increase in temperature leads to an increase in the diffusion coefficient of the solute. Automated CE instrumentation allows for easy temperature regulation with the capillary cartridge.
Taylorgrams were acquired in the presence of β-CD concentration ranging from 0 to 2.5 mM. The results demonstrated that, with the increased β-CD concentration from 0 to 1.0 mM, only a gradual decrease in the peak height of the free FA was observed, whereas that of the complex species increased ( Figure 3A). It is worth mentioning that the peak height and the corresponding FA concentration were linearly related. The results showed that more FA-β-CD complex was formed when β-CD concentration was increased. At higher β-CD concentrations (1.0-2.5 mM), the amounts of FA and FA-β-CD no longer change. Figure 3B gives the distribution of the radii of the measured objects and shows that there were no obvious changes in R h values of free FA and the complex (about 1.6 and 2.4 nm, respectively) within the range of β-CD concentration used.

Determining binding parameters of the β-CD and FA interaction
In Taylor's theory, the final distribution of the FA concentration has the Gaussian distribution when the peak passes through the detector. The width of the concentration distribution is inversely proportional to the diffusion coefficient (Equation 1). In the presence of β-CD, the Taylorgram of FA showed a normal Gaussian shape, which was a convolution of individual Gaussian peaks with different diffusion coefficients represented by each component (free FA and the CD-FA complex). Based on their unique peak widths, two distinct peaks can be obtained by deconvolution corresponding to the coexistence of the free FA and the CD-FA complex. The individual peak heights are proportional to the corresponding concentrations of FA and CD-FA complex, respectively. Figure 4A shows the peak height (H) of the complexes as a function of the β-CD concentrations. The tangent to the curve at the origin is represented by the redline. At a given value of H, the distance from the ordinate to the tangent is equal to the concentration of the bound β-CD (A b ), whereas the concentration of the free β-CD (A) is given by the distance from the tangent to the curve [52]. The obtained values of free and bound FA were plotted using the following corrected Scatchard equation [36]: where r denotes the number of β-CD bound per mole of FA, K is the apparent binding constant, and n represents the total number of binding sites. The r/A values were plotted against r according to Equation (10). In Figure 4B, the experimental data were fitted to the binding isotherm (n and K denote the fitting parameters). The model fitted the experimental points quite well. Using nonlinear curve fit, the estimated binding constant K was found to be (9.44 ± 0.79) × 10 2 M -1 , and n is 1.43 ± 0.03 (R 2 = 0.965). In an attempt to confirm the accuracy of TDA results, we also fitted the experimental data to the binding isotherm with a 1:1 stoichiometry using Østergaard's method [53].
In Equation (11), [L] is the concentration of β-CD. The FA-β-CD complex variance is represented by 2 , whereas 2 represents the observed variance derived from a Gaussian fit without β-CD. K = (5.30 ± 1.66) × 10 2 M -1 (R 2 = 0.979) is the binding constant of the interaction between β-CD and FA, as seen in Figure 5. These results are consistent with those obtained from Equation (10). However, using Østergaard's method could not obtain the binding stoichiometry for higher ordered complexes.

Characterization of the interaction of β-CD-FA by ACE
In ACE analysis, the apparent binding constant for small compounds may be determined using the following equa-TA B L E 1 Binding parameters of β-cyclodextrin (CD)-folic acid (FA) interactions measured by Taylor dispersion analysis (TDA) and affinity capillary electrophoresis (ACE) methods.

F I G U R E 6
Nonlinear regression of the binding isotherm of β-cyclodextrin (CD) and folic acid (FA) using affinity capillary electrophoresis (ACE) method.
tion based on electrophoretic mobility [27]: where ν is the viscosity correction factor. In Equation (12), the effective electrophoretic mobility of the sample plug ( ) is determined by the weighted average of the electrophoretic mobilities of the unbound FA molecules and their complexes ( , and , , respectively). Faster FA peak migration is associated with an increase of β-CD concentration in the run buffer. The absolute value of effective electrophoretic mobility decreases as more FA is bound to β-CD. Viscosities were not significantly affected by the presence of β-CD in the run buffer as the concentration was less than 10 mM [54]. Table 1 shows the binding constant determined from a nonlinear regression analysis after plotting the effective electrophoretic mobility of FA versus the β-CD concentration ( Figure 6).
It is difficult to compare our findings to those of prior research because of the differences in measurement conditions [42]. The binding constants of the β-CD-FA system can be determined using the TDA and ACE techniques described in previous studies. As shown in Table 1, the binding constant obtained from our TDA experiments is consistent with that from TDA data using Østergaard's method. Additionally, the binding stoichiometry obtained using our TDA method was 1.43 ± 0.03, suggesting that the β-CD-FA complexes with a 1:1 and 2:1 ratio are both formed in a solution. The form of the 2:1 β-CD-FA complex in aqueous solution coincides with the result obtained by the previous study of the inclusion of FA with β-CD [55]. MOPAC molecular simulation and UV spectroscopy showed that both ends of the FA molecule could enter the cavity of β-CD and that β-CD and FA formed an inclusion complex in a ratio of 2:1. The infrared absorption analysis and molecular simulation showed that the pteridine and glutamic acid group at each end of the FA molecule could insert into the cavity of β-CD to form an inclusion complex. According to the ACE findings, the binding strength of β-CD to FA is weaker than that determined using TDA techniques. The ACE experiment's Joule heat may be a reason for the discrepancy, and the 1:1 stoichiometry assumption may also affect the obtained binding constant. Consequently, it is important to interpret the binding data in the context of the interaction environment. In addition, several FA conjugated CD systems have been reported, and the effect of conjugation of CD has been demonstrated to improve the stability and interactions of FA with its targeted receptor (FRα) [56]. It is important to understand the binding mechanism of FA with β-CD in the development of drug delivery systems; thus, it can serve as a basis for future studies on the targeted drugs in the treatment of cancer.

CONCLUDING REMARKS
In the current study, TDA is used for assessing the host-guest binding parameters in the β-CD and FA interaction, and the diffusion coefficients of both free and bound FAs in a free solution. The binding constants (K = (9.44 ± 0.79) × 10 2 M -1 ) of β-CD with FA were determined with Scatchard method by fitting the binding isotherm nonlinearly. The result suggested that the β-CD-FA complexes with a 1:1 and 2:1 ratio are both formed in a solution. The reasonable radius of the free and complexed molecules added confidence in the results obtained. The binding constant was compared to those obtained using other TDA and ACE methods from previous studies, and they were in relatively good agreement in terms of order of magnitude. Low sample consumption, fast analysis time, and straightforward measurement were among the TDA method's advantages. A commercially available CE equipment with autosamplers was used in this study to perform fast noncovalent interaction evaluation using the TDA method. We believe that TDA will be more widely used to study binding interaction systems, including synthesized pharmaceuticals and biological targets.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors have declared no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding authors upon reasonable request.