## 2 Methods
### Conceptual View of Our Procedure for Predicting the Binding Poses and Energies
#### 2.1.1 Predicting the Complex of DNA Binding Protein and Each DNA Sequence  
To predict the binding conformation of any sequence of DNA to the p53 protein, as shown in Figure 1, we first collected the complex structures of the p53 protein and DNA (including partial binding conformations) from the Protein Data Bank (PDB). There are many crystal structures (including substructures) registered in PDB, and we selected 15 crystal structures (PDB ID: 5 MG7 [16], 4 MZR [17], etc., as shown in Table 1) that accurately predict the complex structure. It has already been reported in many previous studies that the binding motif sequence of p53 protein is (5\({}^{\prime}\)-C(A/T)(T/A)G-3\({}^{\prime}\)) [18]. Therefore, the DNA structural parts were superposed to minimize the Root Mean Square Deviation (RMSD) of the backbone structure of the binding motif (ribose and phosphate sites) in each crystal structure data. The same procedure was used for the p53 protein portion, where the atomic coordinates forming the protein backbone were superimposed to minimize the RMSD. After superposition of each substructure, the average coordinates of each atom were calculated to create a representative binding conformation that serves as the initial structure for the estimation. Based on this representative binding conformation, a binding conformation with an arbitrary DNA sequence is created by substituting only DNA bases such that the binding interaction between the two binding motifs is not changed. If the number of bases between two binding motifs in the DNA sequence for which binding is to be inferred is different from the representative binding conformation, the initial structure is created by overlapping the two motifs such that the RMSD of the atomic coordinates of the two motifs is minimized. As the estimated binding conformation to be created here will be followed by structural relaxation, using the energy minimization method, and conformational sampling, using molecular dynamics with the relaxed structure as the initial structure, even a roughly estimated structure will not cause major problems. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**PDB ID** & **Year** & **X-mer** & **Title 3** \\ \hline
5 MCT & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
5 MCU & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
5 MCV & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
5 MCW & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
5 MF7 & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
5 MG7 & 2018 & Tetramer & Structure 26: 1237–1250.e6, 2018 \\
6 FJ5 & 2018 & Dimer & Structure 26: 1237–1250.e6, 2018 \\
4 MZR & 2014 & Tetramer & J. Mol. Biol. 426: 936–944, 2014 \\
4 HJE & 2013 & Dimer & Nucleic Acids Res. 41: 8368–8376, 2013 \\
3 KMD & 2010 & Dimer & Structure 18: 246–256, 2010 \\
3 KZ8 & 2010 & Dimer & Nat. Struct. Mol. Biol. 17: 423–429, 2010 \\
2 AC0 & 2006 & Tetramer & Mol. Cell 22: 741–753, 2006 \\
2 ADY & 2006 & Tetramer & Mol. Cell 22: 741–753, 2006 \\
2 AHI & 2006 & Tetramer & Mol. Cell 22: 741–753, 2006 \\
2 ATA & 2006 & Dimer & Mol. Cell 22: 741–753, 2006 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Crystal structures used to create representative bonding structures. Figure 1: Schematic diagram of the proposed theoretical prediction strategy, BC-BEP, of complex conformation and binding affinity. (**A**) After determining the average conformation of the reported Protein Data Bank crystal structures to binding motif sites, the binding structures were predicted based on the sequence similarity of the target DNA. (**B**) Thermodynamic sampling was performed in a mimicked biological environment for the predicted complex structure. Subsequently, the binding energies were estimated to account for the difference in the energy between the dissociated and complex states.