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To evaluate free energy changes of bio-molecules in a water solution, ab initio molecular dynamics (MD) simulations such as Quantum Mechanical Molecular Mechanics (QM/MM) and MD are the most theoretically rigorous methods (Car and Parrinello 1985; Kuhne, Krack et al. 2007), although the calculation cost is far too large for large molecular systems that contain many electrons. Therefore, all-atom MD simulations based on classical mechanics (i.e., Newton’s equations) are used for the usual bio-molecular systems. As the conventional free energy perturbation (FEP) method based on all atom MD simulation is a strict method, to elucidate the molecular principles upon which the selectivity of a TCR is based, FEP simulations are used to analyse the binding free energy difference of a particular TCR (A6) for a wild-type peptide (Tax) and a mutant peptide (Tax P6A), both presented in HLA A2. The computed free energy difference is 2.9 kcal mol-1 and the agreement with the experimental value is good, although the calculation is very time-consuming and the simulation time is still insufficient for fully sampling the phase space. From this FEP calculation, better solvation of the mutant peptide when bound to the MHC molecule is important to the greater affinity of the TCR for the latter. This suggests that the exact and efficient evaluation of solvation is important for the affinity calculation (Michielin and Karplus 2002). Other FEP calculations of the wild-type and the variant human T cell lymphotropic virus type 1 Tax peptide presented by the MHC to the TCR have been performed using large scale massively parallel molecular dynamics simulations and the computed free energy difference using alchemical mutationbased thermodynamic integration, which agrees well with experimental data semiquantitatively (Wan, Coveney et al. 2005). However, the conventional FEP is still very timeconsuming when searching for so many unknown docking structures because all-atom MD for a large molecular system is a computationally hard task and MD simulations must be done not only in initial and final states but also in many intermediate states.

Practical Estimation of TCR-pMHC Binding Free-Energy Based on the Dielectric Model and the Coarse-Grained Model