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Tutorial: Energy Minimization

Swiss-PdbViewer includes a version of the GROMOS 43B1 force field [W.F. van Gunsteren et al. (1996) in Biomolecular simulation: the GROMOS96 manual and user guide. Vdf Hochschulverlag ETHZ].
This force field allows to evaluate the energy of a structure as well as repair distorded geometries through energy minimization. In this implementation, all computations are done in vacuo, without reaction field.

When to use energy minimization?

After having used the mutate or torsion tool, or more generally whenever you have manually distorted the protein, or reconstructed a loop.

What can energy minimization do?

It can repair distorted geometries by moving atoms to release internal constraints, as shown below:

In this example, the CZ of a phenylanalnine ring was artificially stretched out, which lead to bonds much too long.

 

phe1

 

By first invoking an energy computation, the C-terminal Oxygen (OXT) is added to the residue. Note that the residue must also be protonated, and in this case an N-terminal blocking group (HHT) is added. Then the energy computation can be done:

 

phe2

 

The direction in which atoms should be displaced in order to reach a lowe energy state are shown by dotted lines (this facility can be enabled from the Display menu), a minimal deplacement appears in dark blue, while a big deplacement appear in red (blue-green-red gradient).

--------------------------------------------------------------------------------------------- residue bonds angles torsion improper nonBonded electrostatic TOTAL --------------------------------------------------------------------------------------------- HHT 13 0.000 6.183 7.540 0.000 0.00 12.51 26.231 PHE 13 7829.213 393.991 0.984 137.742 -8.84 266.64 8619.726 OXT 13 0.000 0.000 0.000 0.000 -1.31 4.04 2.727 --------------------------------------------------------------------------------------------- KJ/mol 7829.213 400.174 8.524 137.742 -10.16 283.19 8648.685

After an energy minimization (200 cycles of Steepest Descent), the geometry is repaired, and all the force vectors are dark blue, which menas a minimum has been reached.

 

phe2

 

--------------------------------------------------------------------------------------------- residue bonds angles torsion improper nonBonded electrostatic TOTAL --------------------------------------------------------------------------------------------- HHT 13 0.007 0.071 7.538 0.000 0.00 10.78 18.393 PHE 13 1.945 4.276 1.479 1.478 -9.84 254.02 253.363 OXT 13 0.000 0.000 0.000 0.000 -1.78 5.13 3.350 --------------------------------------------------------------------------------------------- KJ/mol 1.952 4.347 9.017 1.478 -11.62 269.93 275.106

What energy minimization cannot do?

Energy minimization is good to release local constraints, "make room" for a residue, but it will not pass through high energy barriers and stops in a local minima. An example of the limitation is presented below:

As you can see, Asn43 is making a nice H-bond network with its environment (left image). What happens if we use the "Mutate" tool of Swiss-PdbViewer to find which rotamer would best fit in this place? Rotamer 13/16 is selected, as it makes a similar H-bonding network (right image).

rotamer1
rotamer2

Now select the next rotamer (14/16). It is a simple flip of the N and O atoms, which prevents the sidechain to make any H bonds (left image). Let's apply 400 cycles of Steepest descent (allowing only the Asn43 to move). As you can see (right image) the energy minimization was not able to flip the N and O atoms in order to restore a proper H-bonding network. The same is true if we start from another sub-optimal rotamer.

rotamer3
rotamer4

If the initial point is rotamer 11/16, some clashes with Phe 4 can be seen (left image). An energy minimization will simply displace the sidechain by gently pushing away atoms that clash, hence removing steric hindrances (right image). But as you can see the Hydrogen bonding network is not restored.

rotamer5
rotamer6

Does it allow to compare different conformations?

As long as there is the same number of degrees of freedom (same number of bonds, angles, torsions, non-bonded interactions...) yes. However, it cannot be used directly to compare two proteins with one mutated residue in order to tell which conformation is more stable.

Frequent problems.

For the force field to work, each residue needs a topology, which contains partial charge for each atom, all the bonds, angles, torsions, and so on. As thousands of compounds do exist, it is not possible to provide topologies for each compound, which means that currently Swiss-PdbViewer can only treat proteins and some frequent modified amino-acids. An extension to support all gromos topologies as well as other topologies is under way.

Note: for more information consult the GROMOS book, or other specialized litterature.