## 2 Results
### The Characteristics of Platinum Agents Combining with a Monomeric Atax1 Protein
#### 2.1.2 Free Energy and Interaction Analysis of Platinum + Atox1 Complexes  
To address the affinity of three platinum agents to the Atox1 protein, the binding free energy calculations for the CisPt + Atox1, TransPt + Atox1 and OxaliPt + Atox1 models have been carried out by using MM-PBSA methodology based on the standard molecular dynamics simulations. Because each platinum center in the three agents forms two equivalent covalent bonds with two same residues Cys12 and Cys15, such covalent interactions were ignored in the binding free energy calculations. All energy terms and the total binding free energies for the non-covalent interactions in these models have been given in Table 1. It can be seen that the ligand of the oxaliplatin agent binding to the Atox1 protein with the binding free energy of \(-4.13\) kcal\(\cdot\)mol\({}^{-1}\) in the OxaliPt + Atox1 model is energetically favorable, which proposes that this extra interaction coming from the oxaliplatin ligand with the Atox1 protein will be helpful to efficiently weaken the DNA-targeted activity of the platinum agent in the nucleus. However, the calculated binding free energies of 5.28 and 12.41 kcal\(\cdot\)mol\({}^{-1}\) in the CisPt + Atox1 and TransPt + Atox1 models predict the insignificant interaction contribution by the cisplatin/transplatin ligand-Atox1 protein interface. To explore the affinity property between the oxaliplatin ligand and the protein, the occupancies of occurrences of dominant hydrogen bonds at the oxaliplatin ligand-Atox1 protein interface were analyzed by calculating the percentages of simulation times, and are shown in Table 2 and Figure 6. The criteria for an intermolecular/intramolecular hydrogen bond was a donor-acceptor distance of \(<\)3.5 A and a donor-proton-acceptor angle of \(>\)120\({}^{\circ}\)[33, 34]. The formations of extra hydrogen bonds between the N-H groups/N atom of the oxaliplatin ligand and the C atoms/C-H group of the residue Cys15 of the \(\beta\)1-\(\alpha\)1 loop in the Atox1 protein respectively with the occupancies of the 176.6% and 30.6% have been found, which supports the calculated affinity for the oxaliplatin ligand-Atox1 protein interface in the OxaliPt + Atox1 model. To further examine the differences of interactions between the platinum ligand  
\begin{table}
\begin{tabular}{c c c c} \hline
**Component** & **CisPt + Atox1** & **TransPt + Atox1** & **OxaliPt + Atox1** \\ \hline Receptor & Atox1 & Atox1 & Atox1 \\  & Cisplatin & Transplatin & Oxaliplatin \\ Ligand & ligand & ligand & ligand \\ \(\Delta E_{\rm ele}\) & \(-46.47\) & \(11.24\) & \(-35.54\) \\ \(\Delta E_{\rm vdw}\) & \(-0.64\) & \(-2.47\) & \(-9.09\) \\ \(\Delta E_{\rm int}\) & \(0.00\) & \(0.00\) & \(0.00\) \\ \(\Delta  
and the protein, hydrophobic interactions, which are defined as a distance shorter than 4.5 A between carbon atoms with sp\({}^{3}\) hybridization, were also analyzed by calculating the percentages of simulation times for the OxaliPt + Atox1 model and are shown in Table 2 and Figure 6 if they occurred in more than 50% of the snapshots, making percentage numbers \(>\) 100 possible [35]. It can be seen that the OxaliPt + Atox1 model spends the total occupancies of 742.5% in the formations of hydrophobic interactions between the oxaliplatin ligand and the Atox1 protein. For example, the formations of hydrophobic interactions between the diaminocyclohexane of the oxaliplatin agent and the residues Cys15 of the \(\beta\)1-\(\alpha\)1 loop, Ala18 of the \(\alpha\)1 helix, Thr58 of the \(\alpha\)2-\(\beta\)4 loop in the Atox1 protein are maintained respectively with the occupancies of 197.2%, 76.3% and 50.9% for the OxaliPt + Atox1 model. As expected, the existence of such extra hydrogen bonds and hydrophobic interactions leads to the ligand plane of the oxaliplatin agent inlaying into the binding pocket, consequently causes the considerable deformation of the Atox1 protein.