On the Diffusion of Anti-Tuberculosis Drugs in Cyclodextrin-Containing Aqueous Solutions

Abstract

In this work, we propose a comprehensive experimental study of the diffusion of isoniazid, one of the first-line anti-tuberculosis drugs, in combination with another drug (ethambutol dihydrochloride) and with different cyclodextrins as carrier molecules, for facilitated transport and enhanced solubility. For that, ternary mutual diffusion coefficients measured by the Taylor dispersion method (D₁₁, D₂₂, D₁₂, and D₂₁) are determined for aqueous solutions containing isoniazid and different cyclodextrins (that is, α–CD, β–CD, and γ–CD) at 298.15 K. From the significant effect of the presence of these carbohydrates on the diffusion of this drug, interactions between these components are suggested. Support for this arose from models, which shows that these effects may be due to the formation of 1:1 (CDs:isoniazid) complexes.

1. Introduction

Although there are many studies on the structure of free drugs or drugs complexed with different carrier vehicles, such as cyclodextrins (CDs), in different media involving techniques such as voltammetry, Raman, and NMR [1,2,3] there are still little data on the transport behavior of drugs in different aqueous media, such as those used in tuberculosis (TB).

Tuberculosis (TB) is one of the most life-threatening chronic bacterial infections that affects people around the world, which has led the World Health Organization (WHO) to declare this disease a global emergency; it causes around 3 million deaths annually [4,5]. Currently, to treat TB, medications are used, including first-line drugs with a high specificity for Mycobacterium tuberculosis, also known as Koch’s bacillus, as currently recommended by international guidelines. Some examples of these drugs include isoniazid, ethambutol dihydrochloride, rifampicin, and pyrazinamide. To get rid of any persistent tuberculosis bacillus, TB patients will receive an initial extensive treatment with isoniazid, pyrazinamide, and rifampicin for the first two months, followed by another one with isoniazid and rifampicin for the next four months [6]. Since all these drugs are administered and absorbed orally, the extent of their absorption and their clinical effects depend on several factors, including the stomach and intestine’s pH values. Several studies have showed that despite their therapeutic effectiveness, many variables are still difficult to control, which has been heightened by the increasing incidence of multidrug-resistant TB, caused by resistant strains of bacteria [4,5,7].

The mitigation of these effects can be achieved by increasing bioavailability, with a consequent reduction in the dose of the drug needed, as well as its stabilization [8,9]. Thus, other approaches might be developed to reach these objectives. A few decades ago, the use of cyclodextrins (Figure 1) in pharmaceutical formulations became quite common due to the possibility of them forming supramolecular compounds with drugs, contributing to an increase in their solubility and stability [9,10]. In brief, cyclodextrins are cyclic oligosaccharides with a hollow truncated cone shape and amphiphilic characteristics, i.e., while their cavity has hydrophobicity, their hydrophilic exterior gives cyclodextrins water solubility [11].

The measurement of the intra- and intermolecular diffusion of multicomponent systems is, among the several techniques used, highly effective at evaluating the formation of supramolecular complexes. In the present work, the mass transport of isoniazid in different multicomponent systems (i.e., isoniazid + ethambutol dydrochloride and isoniazid + cyclodextrins (α–, β–, and γ–)) has been studied. For that, intermolecular diffusion coefficients were obtained using the well-known Taylor dispersion technique [9]. This technique uses a small pulse of a solution in another flowing solution and its evaluation results in the obtainment of the binary and ternary coefficients of isoniazid with different compounds in the solution.

As mentioned before, isoniazid, the hydrazide of isonicotinic acid, is an antibiotic used for standard anti-tuberculosis therapy.

The effect of molar fractions of different components of aqueous solutions on the intermolecular diffusion coefficients of ternary systems were measured and quantified. The obtained values were discussed in terms of the contributions of their molecular components to the formation of a supramolecular structure and how the main and cross-diffusion coefficients are affected by those interactions.

2. Materials and Methods

2.1. Materials

Table 1. Sample description.

Chemical Name	Source	CAS Number	Mass Fraction Purity a
Isoniazid	Sigma-Aldrich(Sigma-Aldrich Quimica S.L., Lisboa, Portugal)	54–85–3	>0.99
Ethambutol dihydrochloride	Sigma-Aldrich (Sigma-Aldrich Quimica S.L., Lisboa, Portugal)	1070–11–7	>0.99
α–Cyclodextrin b	Sigma-Aldrich (Sigma-Aldrich Quimica S.L., Lisboa, Portugal)	10016–20–3	≥0.98
β–Cyclodextrin c	Sigma-Aldrich (Sigma-Aldrich Quimica S.L., Lisboa, Portugal)	7585–39–9	> 0.97
γ–Cyclodextrin d	Sigma-Aldrich (Sigma-Aldrich Quimica S.L., Lisboa, Portugal)	17465–86–0	≥0.98
H2O	Millipore-Q water (ρ = 1.82 × 105 Ω m at 298.15 K)	7732–18–5

^a The mass fraction purity is on a water-free basis; these data are provided by the suppliers. ^b α–cyclodextrin with a water mass fraction of 0.14. ^c β–cyclodextrin with a water mass fraction of 0.13. ^d γ–cyclodextrin with a water mass fraction of 0.10.

indicates all reagents, which were used as received, in the present work: α–cyclodextrin, β–cyclodextrin, γ–cyclodextrin, ethambutol dihydrochloride, and isoniazid. All of these compounds were used without further purification. The solutions were prepared in calibrated volumetric glass flasks, using ultrapure water as solvent (Millipore, Darmstadt, Germany, Milli-Q Advantage A10, specific resistance = 1.82 × 10⁵ Ω m, at 298.15 K). The weighing was carried out using a Radwag AS 220C2 balance with an accuracy of ±0.0001 g.

2.2. pH Measurements

The pH measurements of the solutions were carried out with a radiometer pH meter PHM 240 with an Ingold U457-K7 pH conjugated electrode; pH was measured in fresh solutions, and the electrode was calibrated immediately before measuring each set of solutions using the IUPAC-recommended pH 4.0, 7.0, and 10.0 buffers. From the pH meter calibration, a zero pH of 6.10 ± 0.07 and sensitivity higher than 98.5% were obtained.

2.3. Taylor Dispersion Method

The fundamentals and general technical details of the Taylor dispersion technique for measuring mutual diffusion coefficients are well described in the literature [12,13]. However, the specific details of the apparatus used in this study are described below.

Dispersion profiles were generated by injecting, at the start of each run, via a 6-port Teflon injection valve (Rheodyne, model 5020), 0.063 mL of solution into a laminar carrier stream of a slightly different composition at the entrance to a Teflon capillary dispersion tube of length 3048.0 (±0.1) cm and an internal radius 0.03220 ± (0.00003) cm. This tube and the injection valve were kept at 298.15 (±0.01) K in an air thermostat. The broadened distribution of the disperse samples was monitored at the tube outlet by a differential refractometer (Waters model 2410). The refractometer output voltages, V(t), were measured at 5 s intervals by a digital voltmeter (Agilent 34401 A; Agilent Technologies, Santa Clara, CA, USA).

$$V\left(t\right)=V_0+V_1+V_{max}{(t_R/t)}^{1/2}\left[W_{1}exp\left(-{\displaystyle \frac{12D_1{\left(t-t_R\right)}^2}{r^{2}t}}\right)+(1-W_1)exp\left(-{\displaystyle \frac{12D_2{(t-t_R)}^2}{r^2}}\right)\right]$$

(1)

Equation (1) was fitted to the experimental dispersion profiles of these ternary solutions {isoniazid plus cyclodextrins (α, β or γ–CDs) or isoniazid plus ethambutol dydrochloride}, to attain the values of the different D_ik coefficients.

In Equation (1), D₁ and D₂ represent the eigenvalues of the matrix of the ternary D_ik coefficients; V₀, V₁, and V_max are the baseline voltage, the baseline slope, and the peak high, respectively; and W₁ and (1 − W₁) are normalized pre-exponential factors.

The mutual diffusion of isoniazid-containing multicomponent solutions can be described by the following ternary diffusion equations (Equations (2) and (3)):

J₁ = −D₁₁∇c₁ − D₁₂∇c₂

(2)

J₂ = −D₂₁∇c₁ − D₂₂∇c₂

(3)

where J₁ and J₂ are the molar fluxes of isoniazid (1) and cyclodextrins or ethambutol dydrochloride (2), driven by the concentration gradients ∇c₁ and ∇c₂ of solute 1 and 2, respectively. The cross-diffusion coefficients D₁₂ and D₂₁ represent the coupled flux of each solute, driven by the concentration gradient in the other solute. The main diffusion coefficients D₁₁ and D₂₂ give the flux of each solute, driven by its own concentration gradient. A positive D_ik cross-coefficient (i ≠ k) indicates the co-current coupled transport of solute i from regions of higher to lower concentrations of solute k. On the other hand, a negative D_ik coefficient indicates the counter-current coupled transport of solute i from regions of lower to higher concentrations of solute k.

3. Results and Discussion

3.1. Aqueous Isoniazid (1) + Cyclodextrin (2) Solutions

Table 2. Ternary diffusion coefficients, D₁₁, D₁₂, D₂₁, and D₂₂ of the aqueous isoniazid (component 1) + CDs (component 2) + solutions and their respective standard deviations of the means, S_D, at 25.00 °C.

C1 a	C2 a	X b	D11 ± SD c	D12 ± SD c	D21 ± SD c	D22 ± SD c	D12/D22 d	D21/D11 e
Isoniazid (C1) + α − CD (C2)
0.000	0.010	0.000	0.787 ± 0.007	0.018 ± 0.011	0.001 ± 0.001	0.379 ± 0.001	0.047	0.001
0.005	0.005	0.500	0.785 ± 0.009	−0.033 ± 0.012	0.009 ± 0.022	0.380 ± 0.006	−0.087	0.011
0.010	0.000	1.000	0.786 ± 0.010	−0.046 ± 0.017	0.003 ± 0.014	0.382 ± 0.008	−0.120	0.004
Isoniazid (C1) + β − CD (C2)
0.000	0.010	0.000	0.714 ± 0.011	0.020 ± 0.003	0.008 ± 0.001	0.349 ± 0.001	0.057	0.011
0.005	0.005	0.500	0.740 ± 0.011	−0.029 ± 0.006	0.005 ± 0.013	0.350 ± 0.004	−0.083	0.007
0.010	0.000	1.000	0.787 ± 0.010	−0.040 ± 0.015	0.002 ± 0.014	0.352 ± 0.003	−0.114	0.002
Isoniazid (C1) + γ − CD (C2)
0.000	0.010	0.000	0.789 ± 0.010	0.011 ± 0.008	0.010 ± 0.006	0.329 ± 0.003	0.033	0.013
0.005	0.005	0.500	0.787 ± 0.009	0.010 ± 0.005	0.014 ± 0.006	0.310 ± 0.008	0.032	0.018
0.010	0.000	1.000	0.791 ± 0.008	0.005 ± 0.009	0.002 ± 0.003	0.332 ± 0.005	0.015	0.002

^a C₁ and C₂ in mol dm⁻³. ^b X = C₁/C₂ for ternary systems. ^c D ± S_D/(10⁹ m² s⁻¹) represents the mean diffusion coefficients of 4 to 6 replicate measurements. ^d D₁₂/D₂₂ gives the number of moles of isoniazid counter-transported per mole of cyclodextrin. ^e D₂₁/D₁₁ gives the number of moles of cyclodextrins co-transported per mole of isoniazid.

shows the average experimental diffusion coefficients for aqueous isoniazid (component 1) + CDs (component 2). These data were obtained from at least four independent measurements. The main diffusion coefficients D₁₁ and D₂₂ were generally reproducible within ±(0.010 × 10⁻⁹ m² s⁻¹), and their cross-coefficients were, in general, reproducible within about ±(0.020 × 10⁻⁹ m² s⁻¹). The pH of the aqueous isoniazid solutions measured was approximately 6.50, very close to the pH value of the water (6.52) used in the preparation of these solutions.

The binary diffusion coefficients of α–, β–, and γ–cyclodextrins at 0.01 mol dm⁻³ are as follows: (0.368 ± 0.005) × 10⁻⁹ m² s⁻¹, (0.337 ± 0.004) × 10⁻⁹ m² s⁻¹, and (0.321 ± 0.003) × 10⁻⁹ m² s⁻¹, respectively [14]. Taking into account that the binary diffusion coefficients for isoniazid are 0.826 ± 0.003 and 0.823 ± 0.004 × 10⁻⁹ m² s⁻¹ (for initial concentrations equal to 0.001 and 0.010 mol dm⁻³, respectively), and from the analysis of Table 2, it can be concluded that the main diffusion coefficient D₁₁ is slightly lower than those obtained for the respective binary diffusion coefficients (within 4% deviations) [15], whilst the D₂₂ values are similar to their respective binary diffusion coefficients [14,16,17].

Regarding the experimental D₁₂ and D₂₁ values, the results also indicate a weak interaction between isoniazid and alpha– and beta–cyclodextrins (D₁₂ < 0). On the other hand, no interaction was detected with gamma–cyclodextrin. In fact, for the γ–CD-containing system, the D₁₂ values are approximately zero, given the uncertainty of this method (that is, 2–3%). The supramolecular interactions between γ–CD and small molecules are complicated by the size of CD’s cavity: 427 ų [18]; such a volume allows for the occurrence of stoichiometric interactions greater than 1:1, as well as the total inclusion of the guest molecule. Therefore, we can hypothesize that such behavior, in terms of the cross-diffusion coefficients, might be due to the whole encapsulation of the isoniazid; consequently, the guest molecule is hindered by the host. This is supported by the behavior of the host–guest association of surfactants with cyclodextrins seen in the self-diffusion coefficients [19].

In contrast, for all cyclodextrins, their D₂₁ values should be zero, within the experimental error. In other words, it can be inferred that cyclodextrin diffusion is not affected by the isoniazid gradient.

Considering that D₁₂/D₂₂ gives the number of moles of isoniazid counter-transported per mole of β–CD, we may predict that, at these concentrations, one mole of diffusing β–CD counter-transports at most 0.12 mol of isoniazid. Using D₂₁/D₁₁ values, at the same concentrations, we can expect that a mole of diffusing isoniazid co-transports, at most, 0.092 mol of β–CD.

Support for the possible coupled diffusion resulting from the formation of inclusion complexes can be obtained from a more detailed treatment of the diffusion on multicomponent systems, developed and described in the literature (e.g., [19,20]). Assuming that there is an inclusion equilibrium between isoniazid and β–CD (Equations (4) and (5)) (or α–CD) and using the limiting diffusion coefficients of the free and complexed species indicated in

Table 3. Limiting diffusion coefficients, D_s, of free and complexed species at T = 298.15 K.

Species	Ds/(10−9 m2 s−1)
Isoniazid	0.826 a
β–CD	0.326 b
α–CD	0.353 c
ISO–β–CD	0.320 d

^a [15]; ^b [16]; ^c [14]; ^d considering that the volume of the complexed species (Isoniazid–β–CD) is the sum of the volumes of the isoniazid molecules and β–cyclodextrin molecules isolated, the diffusion coefficient of these complexes was estimated from the known values of D_ISO and D_β–CD using (D_ISO⁻³ + D_β–CD⁻³)^−1/3.

, an estimation of the respective constants of equilibrium were computed and are equal to K = 20 M⁻¹ and K = 22 M⁻¹, respectively. It should also be stressed that the measurement of the interdiffusion coefficients does not allow us to conclude whether the interaction occurs through a preferential rim of cyclodextrins [21].

ISO (aq) + β–CD (aq) ⇆ ISO–β–CD (aq)

(4)

$$K={\displaystyle \frac{[\mathrm{I}\mathrm{S}\mathrm{O}-\beta –\mathrm{C}\mathrm{D}]}{\left[\mathrm{I}\mathrm{S}\mathrm{O}\right][\beta –\mathrm{C}\mathrm{D}]}}$$

(5)

3.2. Aqueous Isoniazid (1) + Ethambutol Dihydrochloride (2) Solutions

Table 4. Ternary diffusion coefficients, D₁₁, D₁₂, D₂₁, and D₂₂ of aqueous isoniazid (component 1) + ethambutol dihydrochloride (component 2) + solutions and the respective standard deviations of their means, S_D, at 25.00 °C.

C1 a	C2 a	X b	D11 ± SD c	D12 ± SD c	D21 ± SD c	D22 ± SD c	D12/D22 d	D21/D11 e
Isoniazid (C1) + Ethambutol dihydrochloride (C2)
0.000	0.010	0.000	0.775 ± 0.012	0.011 ± 0.003	0.008 ± 0.037	0.903 ± 0.001	0.012	0.010
0.005	0.005	0.500	0.780 ± 0.009	0.109 ± 0.012	0.009 ± 0.022	0.890 ± 0.005	0.122	0.011
0.010	0.000	1.000	0.785 ± 0.003	0.478 ± 0.099	0.014 ± 0.008	0.815 ± 0.021	0.590	0.018

^a C₁ and C₂ in mol dm⁻³. ^b X = C₁/C₂ for ternary systems. ^c D ± S_D/(10⁹ m² s⁻¹) represents the mean diffusion coefficients of 4 to 6 replicate measurements. ^d D₁₂/D₂₂ gives the number of moles of isoniazid co-transported per mole of cyclodextrin. ^e D₂₁/D₁₁ gives the number of moles of cyclodextrins co-transported per mole of isoniazid.

shows the ternary mutual diffusion coefficients for dilute aqueous isoniazid (1) + ethambutol dihydrochloride (2) solutions containing (C₁ + C₂) = 0.010 mol dm⁻³. The reported mutual diffusion coefficients are the average of four to six replicate D_ik measurements of each composition. The main diffusion coefficients, D₁₁ and D₂₂, were generally reproducible within ±0.02 × 10^–9 m² s⁻¹. The cross-coefficients were reproducible within ±0.10 × 10^–9 m² s⁻¹. For the sake of comparison, the binary diffusion coefficients of ethambutol dihydrochloride (0.001 and 0.010 mol dm⁻³), in aqueous solutions, are (1.055 ± 0.003) × 10⁻⁹ m² s⁻¹ and (0.907 ± 0.002) × 10⁻⁹ m² s⁻¹, respectively [15].

From the analysis of Table 4, it can be seen that the ratio D₁₂/D₂₂, at tracer concentrations of isoniazid and 0.010 mol dm⁻³ ethambutol dihydrochloride, is almost zero (i.e., 0.012). Additionally, all D₂₁/D₂₂ values are almost zero. However, we can highlight the higher positive value obtained for D₁₂/D₂₂ at tracer concentrations of ethambutol dihydrochloride and isoniazid at 0.010 mol dm⁻³. We can say that in these circumstances, the coupled diffusion that occurs is not negligible. One mole of diffused ethambutol dihydrochloride co-transports up to 0.6 mol of isoniazid. These interactions can be harmful to living organisms, since both drugs are used together to treat tuberculosis and their effectiveness may be shortened, with a consequent need for the use of an overdosage. Since there is this unforeseen transport, the concentration gradient of isoniazid may be smaller in the target areas of the compound in the human body, which may render it ineffective in fulfilling the purpose of the treatment.

4. Conclusions

Based on the measured ternary diffusion coefficients of the aqueous ternary systems studied (that is, isoniazid/cyclodextrins and isoniazid/ethambutol dihydrochloride), it can be concluded that coupled diffusion does take place, affecting the diffusion behavior of this anti-tuberculosis drug in those media. The data obtained for the systems isoniazid/β–CD and isoniazid/α–CD were interpreted on the basis of the formation of complexes between isoniazid and β–cyclodextrin molecules, whose K values, obtained for these equilibria, were 20 mol dm⁻³ and 22 mol dm⁻³.

In relation to isoniazid and ethambutol, through the analysis of secondary diffusion coefficients, a favorable transport of isoniazid in the direction of the ethambutol concentration gradient (“co-transport”) was found. This interaction can be harmful, as the two medicines in question are used together to treat tuberculosis and their effectiveness can be altered. Once this unforeseen transport occurs, the concentration gradient of isoniazid may be lower in the target areas of this compound in the human body, which may make it ineffective in achieving its treatment purpose.