Using APBS to compute binding desolvation energies

This tutorial shows how to use the APBS program to compute the electrostatic component of protein-protein binding free energy and the desolvation energy changes of the binding partners. The procedure has been described in the paper T. Wang, S. Tomic, R. R. Gabdoulline and R. C. Wade in Biophys. J. (2004), 87, 1618-1630. and applied to investigate the binding energetics of barnase and barstar and their mutants. In the procedure, the protein binding free energy (

) is defined to consist of three terms as in equation 1.

(1)

is the electrostatic interaction energy between barnase and barstar when they are bound in solution. and are the electrostatic desolvation free energies of barnase and barstar, respectively, which are defined as the loss of the electrostatic interaction energy between the solvent and the proteins upon binding.

We use a two-step procedure to calculate , and , as shown in Figure 1.

Figure 1. Schematic presentation of the steps of the binding free energy calculation for two solute proteins. The surrounding solvent is light blue. the solutes are green or white to represent the absence or presence of the charges, respectively.

Step 1) calculate the electrostatic energy of barnase (or barstar) and the surrounding solvent in the absence of barstar (or barnase). Step 2) calculate the electrostatic energy of barnase (or barstar) and the surrounding solvent with the second protein bound but without parial charges.

The electrostatic desolvation energy ( ,) is the difference between the electrostatic energies computted from these two steps. The electrostatic interaction

was calculated by equation 2.

(2)

phi is the electrostatic potential generated by barnase (or barstar) at the position of each atom of barstar (or barnase) at the second step; qi is the atomic charges of barstar (or barnase).

We start from a energy-minimized structure of the barnase-barstar complex. The pdb file is complex.pdb and the pqr file is complex.pqr. We will split complex.pqr and generate the following 4 pqr files for input to APBS.

1. bn.pqr, residues 1-110 in complex.pqr, which is barnase.

2. bs.pqr, residues 111-199 in complex.pqr, which is barstar.

3. complex_nobncharge.pqr, all residues in complex.pqr but the charges on barnase are zeroed out, which can be done manually or by using program zero_charge

4. complex_nobscharge.pqr, all residues in complex.pqr but the charges on barstar are zeroed out, which can be done manually or by using program zero_charge

The APBS input file is desol.apbsin. The parameters were set to be as consistent as possible with T. Wang, S. Tomic, R. R. Gabdoulline and R. C. Wade in Biophys. J. (2004), 12, 1563-74.. The interior dielectric constant was set to 2 and the solvent dielectric constant was 78 with an ionic strength of 50 mM and ionic radius of 1.5 A. The grid spacing was set to 0.35A. The dielectric boundary was defined as the van der Waals surface.

To set the dimensions of the grids, we first measured the X Y Z radii/diameters of the complex structure with the center on the postion (xyz=1.498 -2.077 -2.490) of the CG atom of D39/barstar as this residue is at the center of the binding interface. We use the pdb2radiusMycenter program.

>./pdb2radiusMycenter complex.pdb 1.498 -2.077 -2.49

Radius X Y Z = 29.881 19.313 27.993

Diameter X Y Z = 59.762 38.626 55.986

We leave ca. 20 A distance between the protein boundary and the grid boundary and thus set the grid dimension as 289 225 289.

Run APBS with the input file:

>$APBS/bin/apbs desol.apbsin > desol.apbsout

Check the output file desol.apbsout, you should get :

= energy 2 (complex_nobscharge) - 1 (bn_alone) = 110.399 kJ/mol (26.285 kcal/mol)

= energy 4 (complex_nobncharge) - 3 (bs_alone) = 97.817 kJ/mol (23.290 kcal/mol)

Another output file is complex_nobncharge_potential.dx (zip file), which is the potential of barstar, we now use this file to calculate the electrostatic interaction energy between the two proteins when they are bound to each other. First, we run a small program pqr2csv to convert the pqr file of barnase (bn.pqr) to the csv format (bn.csv).

>./pqr2csv bn.pqr bn.csv

Then, we use a auxiliary program provided in APBS to assign the potential at each atom postion of barnase (at_bn.phi) based on complex_nobncharge_potential.dx

>$APBS/share/tools/mesh/multivalue bn.csv complex_nobncharge_potential.dx at_bn.phi

Finaly, we compute the sum of the product of qi and phi as in equation 2 by using the program (pqr_phi2elect).

>./pqr_phi2elect at_bn.phi bn.pqr

Output: energy is -291.396 kJ/mol (-69.38 kcal/mol)

So, the electrostatic component of the binding free energy

= -69.38+26.285+23.290= -19.805 kcal/mol

Note: there is a difference of 2.415 kcal/mol when compared with the result in T. Wang, S. Tomic, R. R. Gabdoulline and R. C. Wade in Biophys. J. (2004), 12, 1563-74. where the UHBD program was used with dimension 110 110 110, focusing and an internal potential assignment procedure, which generated a binding free energy of -22.22 kcal/mol.

You may send your comments/questions to twang at ucdavis dot edu

Note: file complex_nobncharge_potential.dx is too big for attachment. If you need it, email me.