2.8 Calculation of free energy of Protein-DNA complex
The molecular mechanics generalized Born surface area (MM-GBSA) method has been applied to compute the relative binding free energies for the protein-DNA complexes57,58.
ΔGbind = ΔEbonded + ΔEvdW + ΔEele -TΔS + ΔGegb + ΔGesurf (Equation 1)
in which the first three terms represent binding free energy components in gas phase and the last two terms denote solvation free energies. ΔEbonded includes energetics for bond, angle, and dihedral terms. ΔEvdW and ΔEele are van der Waals, and electrostatic interactions between protein and DNA and these two components were calculated using molecular mechanics force fields. ΔGegb is polar solvation energy and can be calculated with the GB model developed by Onufriev et al. (igb=5)59. The last term ΔGesurf is non-polar solvation free energy, which is determined using the following equation.
ΔGesurf = γ × ΔSASA + β (Equation 2)
where the parameters γ and ΔSASA respectively denote the surface tension and the difference in the solvent accessible surface areas caused by ligand associations. For our current work, γ and β were assigned as 0.0072 kcal·mol·Å−2 and 0 kcal·mol−1, respectively59. Due to the high cost in the calculation of TΔS term, we did not perform entropy calculations. Further, it is usually approximated that in comparing the relative stabilities of different complexes, the entropic contributions are not significant, and they were not included in this study. The other free energy components were calculated based on the snapshots extracted from the last 150ns of the production MD trajectories. An ionic strength of 0.15M was also used during the GB calculations.
The relative free energies calculated by MM-GBSA were further decomposed into residue contributions. It is important to note that the interaction energies calculated in this manner are not directly comparable to experimental results, nor will they sum to the total binding energy but can be compared relatively to the mutants. This type of decomposition analysis is useful for identifying residues that have the most considerable effects on the binding energy.