Titanocene / cyclodextrin supramolecular systems: a theoretical approach

Quantitative structure-activity relationships (QSARs)

Molecular modelling and conformational analysis of titanocenes were performed by using the default parameters of MM+ functionality from the HyperChem 5.11 package [35]. This method is appropriate especially for organic molecules, but in our organometallic series the “inner” metal did not have a major influence on the overall geometry of compounds. Titanocenes with cytotoxic activity indicate a reduced number of stable conformations, especially for structures with a lower flexible bonds (codes 01TC, 02TC, 08TC to 10TC); structures having dimethyl-vinyl-silyl-ethyl or trivinyl-silyl-ethyl moieties at the Si, or pyridinium-methyl moieties at the cyclopentadienyl rings have a higher number of stable conformers; the most stable conformations are partially superimposed, especially at the titanocene skeleton. The most stable conformations have all flexible substituents (Y, R, and R’ from the general structure, Table 1 and Scheme 1) oriented close to a pseudoplan formed by Ti and the gravity centres of the two cyclopentadiene rings (Figure 1) [see Additional file 1.

No	Code	Structure	pA 1	pA 2	pA 3
1	01TC	M: Si; X: CH3; Y: CH=CH2; R: all H; R’: all CH3	4.10	4.20	3.87
2	02TC	M: Si; X: CH3; Y: H; R: all CH3; R’: all CH3	3.96	4.23	3.93
3	03TC	M: Si; X: CH3; Y: (CH2)2Si(CH3)2(CH=CH2); R: all H; R’: all CH3	3.72	3.81	3.70
4	08TC	M: Si; X: CH3; Y: CH3; R: all H; R’: all CH3	3.87	4.18	4.02
5	09TC	M: Ge; X: CH3; Y: CH3; R: all H; R’: all CH3	3.81	4.14	3.97
6	10TC	M: Si; X: CH3; Y: H; R: all CH3; R’: all CH3	3.96	4.23	3.94
7	11TC	M: Si; X: CH3; Y: CH3; R: 3-CH3, 2,4,5-H; R’: all CH3	3.93	4.06	4.00
8	18TC	M: Si; X: CH3; Y: (CH2)2Si(CH=CH2)3; R: all H; R’: all CH3	3.70	3.70
9	23TC	M,X,Y: none; R: 3-CH2(3-pyridinium); R’: all H	3.94
10	24TC	M,X,Y: none; R: 3-CH2(3-pyridinium); R’: 3-CH2(3-pyridinium)	4.25
11	26TC	M,X,Y: none; R: 3-CH2(4-pyridinium); R: 3-CH2(4-pyridinium);	4.97

^(a) cytotoxic activity was expressed as the logarithm of the inverse inhibitory concentration 50%, pIC ₅₀ = log(1/IC ₅₀ ); pA ₁ , pA ₂ , pA ₃ were used for in vitro cytotoxic activity against HeLa, K562, and Fem-x cell lines, respectively.

n = 11; r = 0.80; F = 10.5; q ² _cv = 0.75

Geometry optimization of titanocene / cyclodextrin supramolecular systems

It is known that the cytotoxic activity of titanocene dichloride is different from cisplatin action (the last being more toxic, but with higher cytotoxic activity): titanocenes conduct to adduct with DNA and prevent the replication and/or transcription, resulting in cell death [22]. Thus, the transport of titanocene to the DNA is very important, but the lower water solubility and instability (hydrolysis of chloride ligands) reduces the access to the target - biomacromolecules; on the other hand, if the hydrophobicity is increased (the QSAR study indicates a higher in vitro biological activity for more hydrophobic titanocenes), the titanocene transfer in aqueous layer is decreased (especially in the case of the in vivo experiments). Thus, the increase of the hydrophobicity in order to enhance the in vitro cytotoxic activity conducts to a less water solubility and a harder transport of the titanocenes to the target. The water solubility of hydrophobic molecules could be realized by molecular encapsulation in matrices such as cyclodextrins. Among the increasing of water solubility, the advantage of this procedure is to protect of easier hydrolysable titanocenes against degradation and controlled release to the target (i.e. DNA); further, the higher hydrophobicity of modified titanocenes conduct to a better interaction with the hydrophobic inner cavity of cyclodextrins.

Fully geometry optimization of titanocene / cyclodextrin supramolecular systems or docking of organometallic compounds in cyclodextrins [38, 39] could provide information on the stability of complexes and suggest chemical modifications for new titanocenes with higher cytotoxic activity. In our theoretical experiments of fully geometry optimization of titanocene / cyclodextrin supramolecular systems in vacuum (the default HyperChem molecular mechanics MM+ force field was used), only the interaction of the hydrophobic moiety of titanocene with the inner cavity of cyclodextrins from the secondary face was efficient (higher stability of the complex). The main interactions which stabilize the titanocene / cyclodextrin complex in vacuum were bond stretching energy, the angle bending energy, the torsional energy, and the energy arising from van der Waals interactions of non-bonded pairs of atoms. Due to the fact that all titanocene compounds from the studied series are chemically similar molecules, we have an internal consistency from the force field point of view [15, 40–49].

In the case of α-cyclodextrin, the interaction of titanocenes with the secondary face is poor, even with structures having thin hydrophobic chains (e.g. 03TC, 18TC, 23TC, 24TC, and 26TC; Figure 2) [see Additional file 1]; the worst interaction was observed for the case of titanocene oriented to the primary face of α-cyclodextrin or with the titanocene moiety in the front of both cyclodextrin rings. Theoretical interaction energy between titanocenes and α-cyclodextrin was in the range of 11.9 kcal/mole to 19.7 kcal/mole (Table 5). The best interactions of titanocenes with α-cyclodextrin were obtained in the case of structures having compounds monosubstituted at the Si (02TC and 10TC, E _int. 19.7 kcal/mole and 17.0 kcal/mole, respectively) or having flexible chain connected to this atom (03TC and 18TC, E _int. 18.0 kcal/mole and 17.0 kcal/mole, respectively). Lower interaction energies between titanocenes and α-cyclodextrin were obtained for compounds di-substituted at the Si atom with short chain moieties (methyl or vinyl) and for those substituted at the cyclopentadienyl rings with pyridinium-methyl moieties (Table 5). These low interaction energies are especially due to the geometric compatibilities, which are close to the limits and the interactions with the hydrophobic inner cavity of α-cyclodextrin are reduced. This is the reason that the hydrophobicity (expressed as logP) is not important (r < 0.5) in relation with the titanocene / α-cyclodextrin interaction energy, while the hydration energy (E _hydr. ) weak correlates with this interaction energy (Eq. 5).

$\begin{array}{ccc}{E}_{int.,aCD,i}\hfill & =\hfill & 15.54\left(\pm 0.57\right)\hfill \\ +0.356\left(\pm 0.137\right)\cdot E_{hydr.,aCD,i}\hfill \end{array}$

(5)

n = 11; r = 0.656; F = 6.8

The superior homologues, β- and γ-cyclodextrins, are more proper for molecular encapsulation of the studied titanocenes (Figures 3 and 4). In all β- and γ-cyclodextrin complexes the mono- or disubstituted silyl moiety, the bulky moiety (dimethyl-vinyl-silyl or trivinyl-silyl substituents) from the edge of the corresponding substituent, or the pyridinium-methyl substituent from the cyclopentadienyl ring are almost completely encapsulated in the cyclodextrin cavities [see Additional file 1]. In these cases the hydrophobicity of titanocenes (quantified by the logarithm of the 1-octanol/water partition coefficient) was important for the molecular encapsulation process and the interaction energy correlates with logP in a statistically significant way (Eq. 6 and Eq. 7). Thus, better interactions were obtained with the titanocenes having pyridinium-methyl substituents on the cyclopentadienyl rings (codes 24TC and 26TC), the interaction energy being 23.7-24.3 kcal/mole and 27.3-28.1 kcal/mole for β- and γ-cyclodextrin, respectively (Table 5). Higher interaction energies were obtained also for titanocenes having monosubstituted silyl moieties, 02TC and 10TC, especially in the case of γ-cyclodextrin complexes (28.4 kcal/mole and 28.6 kcal/mole, respectively; Table 5). Furthermore, a statistically significant correlation between titanocene / β- and γ-cyclodextrin interaction energies was observed (r = 0.82) [see Additional file 1].

$\begin{array}{ccc}{E}_{int.,bCD,i}\hfill & =\hfill & 16.24\left(\pm 1.64\right)\hfill \\ +4.459\left(\pm 1.687\right)\cdot log{P}_{bCD,i}\hfill \end{array}$

(6)

n = 11; r = 0.578; F = 4.1

The stability of the titanocene / cyclodextrin supramolecular system is observed from Figure 5 for β- and γ-cyclodextrin cases: the better stability is obtained in the case of γ-cyclodextrin, followed by β-cyclodextrin case, and finally for α-cyclodextrin complex after more than double number of iterations. This variation of the energy interaction reveals the possibility of forming the titanocene/cyclodextrin complexes and the stability of these supramolecular systems [see Additional files 1 and 2].

Titanocene structure selection and cytotoxic activity

Titanocenes with potential anticarcinogenic properties were recently synthesized by Gómez-Ruiz et al.[16, 17] and Potter et al.[22] and have structural variability at the cyclopentadienyl moieties. All these new titanocene structures (eleven organometallic compounds) with cytotoxic activity against cervical carcinoma cell line HeLa, human myelogenous leukemia cell line K562, and human malignant carcinoma cell line Fem-x were considered in this theoretical study. Cytotoxic activity was expressed as the logarithm of the inverse inhibitory concentration 50%, pIC ₅₀ = log(1/IC ₅₀ ); pA ₁ , pA ₂ , pA ₃ were used for cytotoxic activity against HeLa, K562, and Fem-x, respectively (Table 1).

Molecular modelling

Molecular modelling of titanocene molecules as well as α-, β-, and γ-cyclodextrins was performed by using the molecular mechanics MM+ functionality from the HyperChem 5.11. The MM+ molecular mechanics force field with a RMS of 0.005 kcal/mole, a number of maximum cycles to limit the search directions of fifteen times the number of atoms, and a Polak-Ribiere algorithm (a gradient method using one-dimensional searches) were used in the molecular modelling process. Bond dipole was used to calculate all nonbonded electrostatic interactions. In the MM+ calculations potential energy depends on bond lengths, bond angles, torsion angles, and nonbonded interactions (van der Waals forces, electrostatic interactions, and hydrogen bonds) [50, 51].

Conformational analysis

In order to find the most stable conformation even for titanocenes or cyclodextrins, a conformational analysis by using Conformational Search functionality (HyperChem 5.11) was performed. In titanocene structures only some side chains have flexible bonds. On the other hand, the flexible bonds in cyclodextrins were only those corresponding to the hydroxymethyl from C⁵ position of glucopyranose unit; the flexible rings were all glucopyranose rings and the corresponding macrocyclic ring. The following conditions were set up for conformational search: variation of the flexible torsion angles ±60º ÷ ±180º, energy criterion for acceptance of the conformation 4 kcal/mole above minimum, all conformations with atomic distances lower than 0.5 Å, and differences between torsion angles lower than 15º were not considered as well as conformations with energy differences lower than 0.05 kcal/mole (duplicates); the maximum number of optimization and iterative calculations was 1000 and maximum 20 conformations were retained. The hydrogen atoms were neglected.

Geometry optimization of titanocene / cyclodextrin supramolecular systems

The geometry optimization of titanocene (the most stable conformations) / cyclodextrin (α-, β-, and γ-cyclodextrin) complexes was realized by using the molecular mechanics interactions of the host-guest molecules in vacuum. The titanocene and cyclodextrin structures in minimal energy conformations were set up at distances of ~8Å between the gravity centres of the host-guest molecules, and the titanocene structure was oriented with the hydrophobic side chain in front of the primary (A) or secondary (B) face of cyclodextrin (the principal axis corresponding to the biocompound or side chain moiety was perpendicular to the A or B plan of cyclodextrin). The complex was modeled in absence of water molecules by using the same MM+ functionality and the interaction was stopped when the RMS gradient was lower than 0.005 kcal/mole. The titanocene-cyclodextrin interaction energy was evaluated as the difference between the overall energies of these two molecules and the energy of the complex.

Structural parameters, correlations, and QSARs

The main molecular descriptors of titanocenes were evaluated by using QSAR Properties functionality from the HyperChem 5.11 package. The following descriptors were calculated and were used as structural parameters for obtaining correlations with titanocene-cyclodextrin interaction energy or quantitative structure-activity relationships (QSARs): van der Waals molecular surface (S ^vdW , Ų; van der Waals surface area was carried out by an approximate developed by Still and co-workers [52, 53]), van der Waals molecular volume (V ^vdW , ų; the grid method described by Bodor et al. [54] was used for van der Waals volume calculation. The QSAR Properties functionality uses the atomic radii of Gavezotti [55] for this method), hydration energy (E _hydr , kcal/mole; the method of calculation is developed by Ooi et al. [56]. The calculation is based on exposed surface area, and employs the surface area as computed by the approximate method, weighted by atom type), logarithm of the octanol/water partition coefficient (logP; it was calculated by means of atomic contributions [57, 58]. Metal atoms were excepted from calculation; this approximation did not significantly affect the final results due to the “hidden” positions of these metal atoms), refractivity (Rf, ų; the refractivity is estimated by the same method as logP, presented by Ghose and Crippen [59]), and polarizability (Pol, ų; this parameter was estimated according to an additive method of Miller [60], where the different increments are associated with different atom types).