Docking of Cisplatin on Fullerene Derivatives and Some Cube Rhombellane Functionalized Homeomorphs

Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals. This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus. That is why it seems to be important to connect CisPt with nanostructures and in this way prevent the drug from combining with the B vitamins. As a proposal for a new nanodrug, an attempt was made to implement Cispaltin (CisPt) ligand on functionalized C60 fullerenes and on a cube rhombellane homeomorphic surface. The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers. The behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C60, in terms of their (interacting) energy, geometry and topology was studied and a detailed analysis of structural properties after docking showed many interesting features.


Introduction
Cisplatinum (cisPt) (Figure 1) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors [1][2][3][4][5].As a chemotherapeutic drug it has been used for treatment of numerous human cancers including lung, bladder, testicular, head, and neck cancers [1] and ovarian carcinomas [4].It is effective against various types of cancers, including carcinomas, lymphomas, germ cell tumors and sarcomas [2].Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine, and to a lesser extent with adenine, found within double helical DNA.This in turn seriously interferes with DNA repair mechanisms, causing DNA damage and subsequently inducing apoptosis [6] in cancer cells.

Introduction
Cisplatinum (cisPt) (Figure 1) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors [1][2][3][4][5].As a chemotherapeutic drug it has been used for treatment of numerous human cancers including lung, bladder, testicular, head, and neck cancers [1] and ovarian carcinomas [4].It is effective against various types of cancers, including carcinomas, lymphomas, germ cell tumors and sarcomas [2].Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine, and to a lesser extent with adenine, found within double helical DNA.This in turn seriously interferes with DNA repair mechanisms, causing DNA damage and subsequently inducing apoptosis [6] in cancer cells.However, theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins containing aromatic rings with lone-pair orbitals [7].It is argued that such direct analogy to interactions with canonical purines can impair the therapeutic effect of Cisplatin.This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus [7].
That is why it seems to be important to connect CisPt with nanostructures and in this way make it prevent the drug from combining with the B vitamins.After passing through the cellular barrier, a rupture of the complex would occur and the free cisPt could interact with bases in the interior of the cell (Figure 2).However, theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins containing aromatic rings with lone-pair orbitals [7].It is argued that such direct analogy to interactions with canonical purines can impair the therapeutic effect of Cisplatin.This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus [7].
That is why it seems to be important to connect CisPt with nanostructures and in this way make it prevent the drug from combining with the B vitamins.After passing through the cellular barrier, a rupture of the complex would occur and the free cisPt could interact with bases in the interior of the cell (Figure 2).Rhombellans are new structures defined by Diudea [8][9][10][11][12][13] with rings in the form of rhombs or squares, which could be an alternative to classical carrier nanostructures.This new class of compounds, having drug-like properties, and creating bio-nano devices, can be suitable for medical chemistry.
Rhombellanes have certain specific features: (i) all strong rings are squares/rhombs; (ii) vertex classes consist of only non-connected vertices; (iii) the Omega polynomial has a single term: 1X^|E|; (iv) a line graph of the parent graph has a Hamiltonian circuit; and (v) they contain at least one K2.3 complete bipartite subgraph or the smallest rhombellane rbl.5.
Rhombellanes may be synthesized as real molecules, which represent a new class of hypothetical structures.Quantum calculations (at the B3LYP/6-31G (d, p) level of theory) [14,15] support the hypothesis that these substructures (at every level of complexity) are energetically feasible in the hope of a real synthesis [16][17][18][19][20].
There are many types of these structures, among which only those have been used which have functional groups that allow attachment of CisPt (Figure 3).Rhombellans are new structures defined by Diudea [8][9][10][11][12][13] with rings in the form of rhombs or squares, which could be an alternative to classical carrier nanostructures.This new class of compounds, having drug-like properties, and creating bio-nano devices, can be suitable for medical chemistry.
Rhombellanes have certain specific features: (i) all strong rings are squares/rhombs; (ii) vertex classes consist of only non-connected vertices; (iii) the Omega polynomial has a single term: 1Xˆ|E|; (iv) a line graph of the parent graph has a Hamiltonian circuit; and (v) they contain at least one K 2.3 complete bipartite subgraph or the smallest rhombellane Rbl.5.
Rhombellanes may be synthesized as real molecules, which represent a new class of hypothetical structures.Quantum calculations (at the B3LYP/6-31G (d, p) level of theory) [14,15] support the hypothesis that these substructures (at every level of complexity) are energetically feasible in the hope of a real synthesis [16][17][18][19][20].
There are many types of these structures, among which only those have been used which have functional groups that allow attachment of CisPt (Figure 3).However, theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins containing aromatic rings with lone-pair orbitals [7].It is argued that such direct analogy to interactions with canonical purines can impair the therapeutic effect of Cisplatin.This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus [7].
That is why it seems to be important to connect CisPt with nanostructures and in this way make it prevent the drug from combining with the B vitamins.After passing through the cellular barrier, a rupture of the complex would occur and the free cisPt could interact with bases in the interior of the cell (Figure 2).Rhombellans are new structures defined by Diudea [8][9][10][11][12][13] with rings in the form of rhombs or squares, which could be an alternative to classical carrier nanostructures.This new class of compounds, having drug-like properties, and creating bio-nano devices, can be suitable for medical chemistry.
Rhombellanes have certain specific features: (i) all strong rings are squares/rhombs; (ii) vertex classes consist of only non-connected vertices; (iii) the Omega polynomial has a single term: 1X^|E|; (iv) a line graph of the parent graph has a Hamiltonian circuit; and (v) they contain at least one K2.3 complete bipartite subgraph or the smallest rhombellane rbl.5.
Rhombellanes may be synthesized as real molecules, which represent a new class of hypothetical structures.Quantum calculations (at the B3LYP/6-31G (d, p) level of theory) [14,15] support the hypothesis that these substructures (at every level of complexity) are energetically feasible in the hope of a real synthesis [16][17][18][19][20].
There are many types of these structures, among which only those have been used which have functional groups that allow attachment of CisPt (Figure 3).Despite the initially expected chemical inactivity of C60 and its derivatives, it was found that fullerenes can be functionalized [21].Due to the mode of functionalization, there were distinguished exo-and endohedral forms of fullerenes and heterofullerenes.The essence of Despite the initially expected chemical inactivity of C 60 and its derivatives, it was found that fullerenes can be functionalized [21].Due to the mode of functionalization, there were distinguished exo-and endohedral forms of fullerenes and heterofullerenes.The essence of exohedral chemistry is the chemical reactions of attachment "outside" of fullerene molecules, in which the structure of the carbon cage remains unchanged.Unlike other organic, aliphatic and aromatic compounds, fullerenes do not contain hydrogen atoms or other functional groups, so they cannot undergo substitution reactions (except for Heterofullerens).Substitution reactions occur only with "functionalized" fullerenes, i.e. when they have been attached to specific groups of atoms.C 60 and its homologues have interesting and often unique properties, and after functionalization the C 60 molecule can bind any functional group (Figure 4) [21].At the same time, it is indifferent, non-toxic and so small that it easily comes into contact with cells, proteins and viruses.In the docking procedure with Cisplatin several exohedral forms of C 60 fullerenes were used, such as 1-(Diethoxyphosphorylmethyl)-7-(2,2,2-trifluoroethoxy)(C 60 -Ih) [5,6]fullerene;9-(diethoxyphosphorylmethyl)-1H-(C 60 -Ih) [5,6]fullerene; Methyl 9-(2-trimethylsilylethyl)(C 60 -Ih) [5,6]fullerene-1-carboxylate and others (Figure 4).For the transposition of cisPt at the cellular level through numerous barriers and to avoid their connection with the B group vitamins [7], an attempt was made to deposit Cisplatin on rhombellanes and functionalized fullerenes C60, as possible nanodrug complexes.The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested For the transposition of cisPt at the cellular level through numerous barriers and to avoid their connection with the B group vitamins [7], an attempt was made to deposit Cisplatin on rhombellanes and functionalized fullerenes C 60 , as possible nanodrug complexes.The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers.
Detailed analysis of structural properties after docking showed interesting features.Behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C 60 , in terms of their (interacting) energy, geometry and topology, was studied.After the docking procedure, the optimal values of ligand-rhombellane and ligand-C 60 fullerene affinities were found, which is an important result for homeomorphs.

Docking Procedure
The structures of rhombellane homeomorphs were prepared by Topo Cluj Group [8][9][10][11][12][13], while the functionalized C 60 structures were downloaded from the PubChem Database [22].The docking procedure was realized with the use of non-commercial docking program AutoDock 4.2 [23,24].This employs a stochastic Lamarckian genetic algorithm for computing ligand conformations and simultaneously minimizing its scoring function, which approximates the thermodynamic stability of the ligand bound to the target fullerene.For all considered nanocarriers there were established grid box dimensions equal to 26 × 26 × 26 Å.The center of the grid box was placed in the center of the considered nanomolecules.In most cases, the center of the grid box had xyz coordinates equal to 000.During the docking procedure, the molecules were loaded and stored as pdb-files, after assigning hydrogen bonds.The investigated ligands were loaded, and their torsions along the rotatable bonds were assigned and then saved as "ligand.pdbqt".The grid menu after loading "pdbqt" was toggled [25].For the search of the ligand-Rbl nanostructure and ligand-C 60 interactions, the map files were selected directly, setting up the grid points separately for each structure.The Lamarckian genetic algorithm completed the docking parameter files [26].The structural analysis of the obtained complexes related with the identification of hydrogen bonds was realized with use of the Visual Molecular Dynamics (VMD) package [27].

Results and Discussion
The results are presented in the following tables and figures.Rhombellane structures are given by their atom number.
Table 1 and Figure 5 represent binding affinity in kcal/mol of the ligand cisPt molecule relative to spherical nanosystems, such as rhombellane structures (first eleven structures in tables) and functionalized fullerene C 60 (structures 12 to 21 in tables) obtained during docking stage.Among Rbl homeomorphs, Cisplatin has the highest affinity for Rbl 444 with an affinity value of −2.72 kcal/mol and for Rbl 360b with an affinity value of −2.66 kcal / mol (Table 1, Figure 5).The lowest binding energy is observed in the case of Staffanes (stf) 114 (Table 1, Figure 5).Among functionalized structures of C 60 fullerene, the best affinity is shown by CID_16156307, followed by CID_10121832 and finally the CID_10121831 structure with values of affinity equal to −3.44, −3.13 and −2.83 kcal/mol, respectively (Table 1, Figure 5).Among Rbl homeomorphs, Cisplatin has the highest affinity for Rbl 444 with an affinity value of −2.72 kcal/mol and for Rbl 360b with an affinity value of −2.66 kcal / mol (Table 1, Figure 5).The lowest binding energy is observed in the case of stf 114 (Table 1, Figure 5).Among functionalized In general, the examined structures show a significantly larger affinity in the case of C 60 functionalized fullerene than in the case of Rbl homeomorphs.The obtained affinity values are collected in Tables 2 and 3.The values of binding energy are correlated with values of the K max constant and the highest values are obtained in the case of 444 fullerene and 360b nanostructure (Table 2).
The two last columns show the equilibrium K value of the bonds, calculated using the equation: where K b is the binding constant, R is the gas constant (J/mol*K), T is the temperature of 298 K and ∆G b is the binding affinity (J/mol).
The higher the K value, the more the reaction proceeds towards the formation of the complex.Table 3 presents K max values of the binding constant estimated with use of the binding free energy obtained for the best complex of the ligand with functionalized fullerene C 60 .The highest values of the binding energy are also here correlated with values of the constant K max .This value is higher in the case of derivatives CID_16156307 of C 60 fullerene, followed by CID_101218236 and CID_101218232 (Table 3).
Cisplatin (cisPt) and functionalized fullerene C 60 easily create two or three hydrogen bonds between them with strong and medium strength (Figure 6).Table 3 presents Kmax values of the binding constant estimated with use of the binding free energy obtained for the best complex of the ligand with functionalized fullerene C60.The highest values of the binding energy are also here correlated with values of the constant Kmax.This value is higher in the case of derivatives CID_16156307 of C60 fullerene, followed by CID_101218236 and CID_101218232 (Table 3).
Cisplatin (CisPt) and functionalized fullerene C60 easily create two or three hydrogen bonds between them with strong and medium strength (Figure 6).

CID_11468612_cispt CID_16156307_cispt
CID_101218232_cispt CID_101218236_cispt CID_101382121_cispt The criterion for classification of the strength of hydrogen bonds is the assessment of the distance between acceptor and hydrogen atoms: strong interactions are characterized by a distance <1.6 Å, medium by values in the range from 1.6 Å to 2.0 Å, and weak by distances <3 Å.
The complex nanostructure CID_16156307 (C72H9F2OP)-CisPt has been created by two hydrogen bonds with medium strengths, i.e., 1.94 Å and 2.16 Å; both are between the oxygen of the phosphoryl group of the nanocarrier and the hydrogen of the amino groups of CisPt (Figure 6).Again, two hydrogen bonds have been created in the case of CID_ 101218236 (C69H9Cl3O) and CID_101218232 (C63H4ClF3O) complexes.The first case involves the oxygen atom of the methoxy group while the second involves the oxygen atom of the ethoxy group, and both form a HB with the hydrogen atom of the amino groups of CisPt with values 2.18 Å, 2.19 Å and 2.01 Å (Figure 6).Three hydrogen bonds appeared only in the case of CID_10138212 (C62F6), all with medium strength, i.e., 2.13 Å, 2,13 Å and 2.51 Å (Figure 6), respectively.The structures of formed complexes are presented in Figure 6.
Despite the fact that affinity is higher in the case of functionalized fullerene C60-cisPt, compared to affinities of Rbl-CisPt complexes, the latter created a larger number of hydrogen bonds (Figure 7).The best binding energy has been observed for the 444 nanostructure with four hydrogen bonds of medium strength, i.e., 1.88 Å, 1.95 Å, 1.96 Å and 2.03 Å, respectively.Also, for The criterion for classification of the strength of hydrogen bonds is the assessment of the distance between acceptor and hydrogen atoms: strong interactions are characterized by a distance <1.6 Å, medium by values in the range from 1.6 Å to 2.0 Å, and weak by distances <3 Å.
The complex nanostructure CID_16156307 (C 72 H 9 F 2 OP)-CisPt has been created by two hydrogen bonds with medium strengths, i.e., 1.94 Å and 2.16 Å; both are between the oxygen of the phosphoryl group of the nanocarrier and the hydrogen of the amino groups of cisPt (Figure 6).Again, two hydrogen bonds have been created in the case of CID_ 101218236 (C 69 H 9 Cl 3 O) and CID_101218232 (C 63 H 4 ClF 3 O) complexes.The first case involves the oxygen atom of the methoxy group while the second involves the oxygen atom of the ethoxy group, and both form a Hydrogen Bond (HB) with the hydrogen atom of the amino groups of cisPt with values 2.18 Å, 2.19 Å and 2.01 Å (Figure 6).Three hydrogen bonds appeared Symmetry 2019, 11, 874 9 of 11 only in the case of CID_10138212 (C 62 F 6 ), all with medium strength, i.e., 2.13 Å, 2,13 Å and 2.51 Å (Figure 6), respectively.The structures of formed complexes are presented in Figure 6.
Despite the fact that affinity is higher in the case of functionalized fullerene C 60 -cisPt, compared to affinities of Rbl-CisPt complexes, the latter created a larger number of hydrogen bonds (Figure 7).The best binding energy has been observed for the 444 nanostructure with four hydrogen bonds of medium strength, i.e., 1.88 Å, 1.95 Å, 1.96 Å and 2.03 Å, respectively.Also, for the 360b nanostructure there were created four hydrogen bonds with medium strength, i.e., 2.08 Å, 2.09 Å, 2.26 Å and 2.56 Å, respectively (Figure 7).The worst affinity is represented by the stf114 fullerene.Even so, in this case there are also four hydrogen bonds formed between the nanostructure and Cisplatin.The structures of formed complexes are presented in Figure 7.
The complex nanostructure CID_16156307 (C72H9F2OP)-CisPt has been created by two hydrogen bonds with medium strengths, i.e., 1.94 Å and 2.16 Å; both are between the oxygen of the phosphoryl group of the nanocarrier and the hydrogen of the amino groups of CisPt (Figure 6).Again, two hydrogen bonds have been created in the case of CID_ 101218236 (C69H9Cl3O) and CID_101218232 (C63H4ClF3O) complexes.The first case involves the oxygen atom of the methoxy group while the second involves the oxygen atom of the ethoxy group, and both form a HB with the hydrogen atom of the amino groups of CisPt with values 2.18 Å, 2.19 Å and 2.01 Å (Figure 6).Three hydrogen bonds appeared only in the case of CID_10138212 (C62F6), all with medium strength, i.e., 2.13 Å, 2,13 Å and 2.51 Å (Figure 6), respectively.The structures of formed complexes are presented in Figure 6.
Despite the fact that affinity is higher in the case of functionalized fullerene C60-cisPt, compared to affinities of Rbl-CisPt complexes, the latter created a larger number of hydrogen bonds (Figure 7).The best binding energy has been observed for the 444 nanostructure with four hydrogen bonds of medium strength, i.e., 1.88 Å, 1.95 Å, 1.96 Å and 2.03 Å, respectively.Also, for the 360b nanostructure there were created four hydrogen bonds with medium strength, i.e., 2.08 Å, 2.09 Å, 2.26 Å and 2.56 Å, respectively (Figure 7).The worst affinity is represented by the stf114 fullerene.Even so, in this case there are also four hydrogen bonds formed between the nanostructure and Cisplatin.The structures of formed complexes are presented in Figure 7.

Conclusions
As a proposal for a new nanodrug, an attempt was made to implement the Cisplatin (CisPt) ligand on the functionalized C60 fullerenes and on a cube rhombellane homeomorphic surface.Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors.Theoretical studies suggest that nonspecific interactions of Cisplatin can also take place with many competitive

Conclusions
As a proposal for a new nanodrug, an attempt was made to implement the Cisplatin (cisPt) ligand on the functionalized C 60 fullerenes and on a cube rhombellane homeomorphic surface.Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors.Theoretical studies suggest that nonspecific interactions of Cisplatin can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals.It is argued that such a direct analogy to the interaction of canonical purines can impair the therapeutic effect of Cisplatin, which might be an indicator of the reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus.This is why it seems to be important to connect cisPt Should be "cisPt" with nanostructures and, in this way, make it impossible to combine the drug with the B vitamins.Behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C 60 , in terms of their (interacting) energy, geometry and topology was studied.The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers.The docking procedure was realized with use of AutoDock 4.2.Detailed analysis of structural properties after docking showed many interesting features.Among Rbl homeomorphs, Cisplatin has the highest affinity for Rbl 444 with an affinity value of −2.72 kcal/mol and Rbl 360b with an affinity value of −2.66 kcal/mol.Among functionalized structures of C 60 fullerene the best affinity is shown by CID_16156307, followed by CID_10121832 and finally CID_10121831, with values of affinity equal to −3.44, −3.13 and −2.83 kcal/mol, respectively.In general, the examined structures show a significantly larger affinity in the case of C 60 functionalized fullerene than in the case of Rbl homeomorphs.Cisplatin (cisPt) and functionalized fullerene C 60 easily create two or three hydrogen bonds between them with strong and medium strength.High ligand-nanostructure affinity is reflected by the number and most of all the quality of formed hydrogen bonds.However, despite the fact that affinity is better in the case of functionalized fullerene C 60 -cisPt compared with affinities of complexes Rbl-CisPt Should be "cisPt", the latter created a larger number of hydrogen bonds but of lesser quality.The performed investigations enabled the identification of the most promising rhombellane and functionalized C 60 fullerene structures that could be used as nanocarriers for cisPt molecules.

Figure 2 .
Figure 2. rupture of the complex after passing through the cellular barrier.

Figure 2 .
Figure 2. Rupture of the complex after passing through the cellular barrier.

Figure 2 .
Figure 2. rupture of the complex after passing through the cellular barrier.

Figure 5 .
Figure 5. Graphical presentation of the values of binding affinity [kcal/mol] of the ligand CisPt molecule relative to spherical nanosystems (rhombellane structures and functionalized fullerene C 60 ) obtained during docking stage, generated by software Autodock 4.2.

Figure 6 .
Figure 6.The structure of functionalized fullerene C60 and Cisplatin complexes.

Figure 6 .
Figure 6.The structure of functionalized fullerene C 60 and Cisplatin complexes.

Figure 7 .
Figure 7.The structure of cube rhombellane and Cisplatin complexes.

Figure 7 .
Figure 7.The structure of cube rhombellane and Cisplatin complexes.

Table 1 .
Values of binding affinity [kcal/mol] of the ligand CisPt molecule relative to spherical nanosystems (rhombellane structures and functionalized fullerene C 60 ) obtained during the docking stage, generated by software Autodock 4.2.

Table 2 .
The best binding affinity of ligand CisPt, maximum and minimum bind energy, and Kmax values of the binding constant estimated with use of the binding free energy obtained for the best complex of ligand with nanostructure Rbl after the docking procedure, generated by software Autodock 4.2.

Table 3 .
The best binding affinity of the ligand CisPt, maximum and minimum binding energy and Kmax values of the binding constant estimated with use of the binding free energy obtained for the best complex of the ligand with functionalized fullerene C 60 after the docking procedure, generated by software Autodock 4.2.