Calculation of electrostatic binding energies for the PKA-balanol system requires higher-resolution electrostatics calculations than could be easily visualized in the previous section. We will use focusing to generate the finer data from the coarser calculations performed in the earlier calculations. This procedure is outlined in the following APBS input file which is available for download here.
Example 2. Balanol-PKA energy calculation APBS input
read mol pqr bx6_7_lig_apbs.pqr # Balanol mol pqr bx6_7_apo_apbs.pqr # Protein kinase A mol pqr bx6_7_bin_apbs.pqr # Complex end elec name bal # BALANOL ENERGY CALCULATION mg-auto dime 65 65 65 # Grid dimensions cglen 70 70 70 # Coarse grid lengths cgcent mol 3 # Coarse grid centered on the complex fglen 16 16 16 # Fine grid lengths fgcent mol 1 # Fine grid centered on the complex mol 1 lpbe # Linearized PB bcfl sdh # Monopole boundary condition ion 1 0.000 2.0 # Zero ionic strength ion -1 0.000 2.0 pdie 2.0 # Solute dielectric sdie 78.00 # Solvent dielectric chgm spl0 # Linear charge discretization srfm smol # Smoothed molecular surface srad 0.0 # Solvent probe radius swin 0.3 # Surface spline window (not used) sdens 10.0 # Sphere density temp 298.15 # Temperature gamma 0.105 # Surface tension (not used) calcenergy total calcforce no end elec name pka # PROTEIN KINASE A CALCULATION mg-auto dime 65 65 65 cglen 70 70 70 cgcent mol 3 fglen 16 16 16 fgcent mol 1 mol 2 lpbe bcfl sdh ion 1 0.000 2.0 ion -1 0.000 2.0 pdie 2.0 sdie 78.00 chgm spl0 srfm smol srad 0.0 swin 0.3 sdens 10.0 temp 298.15 gamma 0.105 calcenergy total calcforce no end elec name complex # COMPLEX CALCULATION mg-auto dime 65 65 65 cglen 70 70 70 cgcent mol 3 fglen 16 16 16 fgcent mol 1 mol 3 lpbe bcfl sdh ion 1 0.000 2.0 ion -1 0.000 2.0 pdie 2.0 sdie 78.00 chgm spl0 srfm smol srad 0.0 swin 0.3 sdens 10.0 temp 298.15 gamma 0.105 calcenergy total calcforce no end print energy complex - pka - bal end quit
This APBS input file represents a "non-canonical" method for computing energies. In any electrostatic energy calculation, care needs to be taken to remove self-interaction terms. This removal is usually accomplished via a solvation energy calculation (cf. the Born example). However, in this example, we remove the self-interaction energies via a series of calculations which use exactly the same grid spacings, lengths, and centers. Since all atoms in the complex are present in the apo protein and ligand, the self-interaction terms are effectively removed.
$ apbs apbs-energy.in
One question that should arise is: why is the binding unfavorable? The Coulombic contribution to the binding energy is favorable (you can use the APBS program coulomb to evaluate this); but there is a substantial polar desolvation penalty for binding of the substrate to the protein. However, our current calculation has neglected apolar contributions to the energy. These terms, which usally scale with the surface area, favor the binding. Using the APBS program acc, we can determine that over 1000 A2 of solvent-accessible surface area is lost when the complex is formed. Using even conservative values of the apolar energy surface tension (which usually ranges between 0.105 to 210 kJ/A2), we can see that this buried surface area provides stabilization to the complex.