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.