Interceptor potential of C₆₀ fullerene aqueous solution: a comparative analysis using the example of the antitumor antibiotic mitoxantrone

Abstract

We performed a qualitative and quantitative analysis of intermolecular interactions in aqueous solution between the antitumor antibiotic mitoxantrone and C₆₀ fullerene in comparison with interactions between the antibiotic and well-known aromatic molecules such as caffeine and flavin mononucleotide, commonly referred to as interceptor molecules. For these purposes, we obtained equilibrium hetero-association constants of these interactions using a UV/Vis titration experiment. Special attention was paid to the interaction of C₆₀ fullerene with mitoxantrone, which has been quantified for the first time. Based on the theory of interceptor-protector action and using a set of measured equilibrium constants we managed to estimate the relative biological effect of these mixtures in a model living system, taking human buccal epithelium cells as an example. We demonstrated that C₆₀ fullerene is able to restore the functional activity of the buccal epithelium cell nucleus after exposure to mitoxantrone, which makes it possible to use C₆₀ fullerene as regulator of medico-biological activity of the antibiotic.

Appendix: Calculation of the A D factor

The A_D factor is calculated according to Eq. (7):

$$A_{{\text{D}}} = \frac{{\theta_{X}^{\left( 0 \right)} - \theta_{X} }}{{\theta_{X}^{\left( 0 \right)} }},$$

(8)

where θ_X and $\theta_{X}^{\left( 0 \right)}$ are the mole fractions of NOV-DNA complexes in the presence and in the absence of interceptor molecules, respectively. Therefore, the calculation of the A_D factor is reduced to calculation of these mole fractions.

Consider a three-component system containing mitoxantrone molecules (X), interceptor molecules, i.e., caffeine, flavin mononucleotide or C₆₀ fullerene (Y), and DNA (N). Let us introduce the total concentrations of these species as x₀, y₀ and N₀, respectively. Note, the DNA concentration is measured in moles of base pairs per liter. To describe non-cooperative DNA binding we use standard approach taken from Ref. (Evstigneev et al. 2008).

For such a system, the mass balance equations are written in general form as follows (Evstigneev et al. 2019):

$$\left\{ \begin{gathered} x_{0} = x_{{{\text{het}}}} + K_{XN} x_{1} N_{1} \hfill \\ y_{0} = y_{{{\text{het}}}} + K_{YN} y_{1} N_{1} \hfill \\ N_{0} = N_{1} + K_{XN} x_{1} N_{1} + K_{YN} y_{1} N_{1} \hfill \\ \end{gathered} \right.,$$

(9)

where x_het, y_het are the overall concentrations of X- and Y-containing hetero-aggregates including monomers, respectively; x₁, y₁ are the monomer concentrations of X and Y compounds; N₁ is the concentration of free DNA; K_XN, K_YN are the equilibrium constants of X and Y monomers bound to DNA. Equation (9) can be easily rewritten to

$$\left\{ \begin{gathered} x_{0} = x_{{{\text{het}}}} + \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} + K_{YN} y_{1} }}N_{0} \hfill \\ y_{0} = y_{{{\text{het}}}} + \frac{{K_{YN} y_{1} }}{{1 + K_{XN} x_{1} + K_{YN} y_{1} }}N_{0} \hfill \\ \end{gathered} \right.,$$

(10)

The θ_X quantity is given as

$$\theta_{X} = \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} + K_{YN} y_{1} }}.$$

(11)

Now, we can easily reduce Eq. (10) to obtain the equation for calculation of the $\theta_{X}^{\left( 0 \right)}$ quantity by mental exclusion of interceptor molecules from the system. This is expressed in zeroing of all the terms in Eq. (10) related to Y molecules. Thus, one obtains the equation

$$x_{0} = \left. {x_{{{\text{het}}}} } \right|_{{y_{1} = 0}} + \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} }}N_{0} ,$$

(12)

to be solved for $\theta_{X}^{\left( 0 \right)}$ as $\frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} }}$.

The explicit form of the x_het and y_het quantities depends on particular model of hetero-association which, in turn, is selected upon the type of interacting molecules. We study the interceptor molecules of two different types, viz. aromatic ligands (caffeine and flavin mononucleotide) containing planar chromophore which makes molecules be able to form stacking complexes with similar compounds and DNA, and C₆₀ fullerene possessing specific affinity to aromatic ligands which mitoxantrone belongs to. Moreover, C₆₀ fullerene is assumed not to bind with DNA (see “Description of biological data within the framework of the IPA theory” of the paper). Therefore, we should consider two cases of competitive DNA binding.

Case 1: caffeine and flavin mononucleotide are the interceptor molecules

To describe the aggregation of aromatic compounds, such as caffeine and flavin mononucleotide, with mitoxantrone we use 1:2 hetero-association model (Thordarson 2011). The corresponding mass balance equations are given in Eq. (2) in “Hetero-association model for the antibiotic and aromatic interceptors, CAF/FMN” of the paper. They exactly equal to the x_het and y_het quantities in Eq. (10). Thus, one obtains:

$$\left\{ \begin{gathered} x_{0} = x_{1} + K_{h} x_{1} y_{1} + \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} + K_{YN} y_{1} }}N_{0} \hfill \\ y_{0} = y_{1} + 2K_{Y} y_{1}^{2} + K_{h} x_{1} y_{1} + \frac{{K_{YN} y_{1} }}{{1 + K_{XN} x_{1} + K_{YN} y_{1} }}N_{0} \hfill \\ \end{gathered} \right..$$

(13)

Putting y₁ = 0 in Eq. (13) yields:

$$x_{0} = x_{1} + \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} }}N_{0} ,$$

(14)

which has exact solution in the following form:

$$x_{1} = \frac{{ - 1 - K_{XN} \left( {N_{0} - x_{0} } \right) + \sqrt {\left( {1 + K_{XN} \left( {N_{0} - x_{0} } \right)} \right)^{2} + 4K_{XN} x_{0} } }}{{2K_{XN} }}.$$

(15)

Hence, we readily obtain the expression for the $\theta_{X}^{\left( 0 \right)}$ quantity:

$$\theta_{X}^{\left( 0 \right)} = \frac{{ - 1 - K_{XN} \left( {N_{0} - x_{0} } \right) + \sqrt {\left( {1 + K_{XN} \left( {N_{0} - x_{0} } \right)} \right)^{2} + 4K_{XN} x_{0} } }}{{1 - K_{XN} \left( {N_{0} - x_{0} } \right) + \sqrt {\left( {1 + K_{XN} \left( {N_{0} - x_{0} } \right)} \right)^{2} + 4K_{XN} x_{0} } }}.$$

(16)

Numerical solution of Eq. (13) allows one to obtain the θ_X quantity to be further substituted into Eq. (8) along with Eq. (16) to calculate A_D factor for NOV-CAF-DNA and NOV-FMN-DNA systems.

Case 2: C₆₀ fullerene is the interceptor molecule

To describe the aggregation in NOV-C₆₀ system we use up-scaled model (Mosunov et al. 2019). Similarly to the above, the x_het and y_het quantities are given as the first and the second equation, respectively, in Eq. (4) in “Complexation model for the antibiotic and C₆₀ fullerene” of the paper.

The exclusion of protector mechanism of action, i.e. DNA binding of C₆₀ fullerene, results in K_YN = 0. Hence, the set of equations to calculate θ_X in the form of $\frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} }}$ is written as:

$$\left\{ \begin{gathered} x_{0} = x_{1} + BK_{{{\text{h1}}}} x_{1} C_{{{\text{R1}}}} + C_{{\text{M}}} \frac{{HK_{{{\text{h2}}}} x_{1} }}{{1 - K_{{{\text{h2}}}} x_{1} }} + \frac{{K_{XN} x_{1} }}{{1 + K_{XN} x_{1} }}N_{0} \hfill \\ C_{0} = BC_{{{\text{R1}}}} + BK_{{{\text{h1}}}} x_{1} C_{{{\text{R1}}}} + C_{{\text{M}}} \frac{{1 - \left( {1 - B} \right)BK_{{\text{F}}} C_{{{\text{R1}}}} }}{{1 - BK_{{\text{F}}} C_{{{\text{R1}}}} }} \hfill \\ \end{gathered} \right.,$$

(17)

where C_D0, C_D1 were substituted for x₀, x₁, respectively.

Setting C_R1 and C_M to zero in Eq. (17) yields the equation similar to Eq. (14). Thus, one can numerically solve Eqs. (17), (16) to obtain the θ_X and $\theta_{X}^{\left( 0 \right)}$ quantities, respectively, and further substitute them into Eq. (8) to calculate A_D factor for NOV-C₆₀-DNA system.

Table

Table 3 The values of the equilibrium parameters of complexation needed to calculate the A_D factor

3 summarizes all the parameters needed to calculate the A_D factor for both cases.