Chapter 34. Competition between probe and water

Hydrogen-bond energies in the Grid Force Field are traditionally computed assuming a straightforward interaction between Target and Probe such as:

  O: + H--N   -->   O:- - - H--N

in which the symbol - - - indicates the hydrogen bond. More generally one may write:

  T: + H--P   -->   T:- - - H--P

in which P and T are the Grid Probe and the interacting heavy atom of the Target. However, these traditional equations ignore the presence of water which normally saturates biological systems and can interact with both Target and Probe.

A more comprehensive set of equations is required in order to deal with the water such as:

 (1)      T:- - - H--O--H   -->   T: + HOH          E1                
 (2)      P--H- - -:OH2   -->   P--H + OH2          E2                
 (3)      T: + H--P   -->   T:- - - H--P            E3                
 (4)      H--O--H + :OH2   -->   H--O--H- - -:OH2   E4

in which E1, E2, E3 and E4 are the energies at each stage of the process. Equation 1 represents release of the Target group from hydrogen-bonding in the aqueous phase; Equation 2 is the corresponding release of the Probe; Equation 3 is formation of the Target- - -Probe hydrogen bond; and Equation 4 represents reformation of hydrogen-bonds by the waters released in reactions (1) and (2). Care is required in the assignment of a positive or negative sign to each E term.

With these equations the total energy (ET) would be computed as:

ET = E1 + E2 + E3 + E4 + N*WENT

where WENT = -0.848 Kcal/Mole and represents the entropic benefit of releasing one bound water into the bulk water phase. WENT is calculated as shown in Chapter 16, and in the present example N=2 because two bound waters are released.

The equation for ET can immediately be recast as:

  ET    = EPOINT + EBAL          where:
  EPOINT= E1 + E3                and:
  EBAL  = E2 + E4 + N*WENT

in which EPOINT must be determined at each individual Grid Point, because it depends on the interaction of the Target with the Probe, and on the competing interaction of the Target with water at the same grid point. On the other hand EBAL only depends on the properties of water and the properties of the Probe. It is called the Balancing Energy, and is a constant term for any particular Probe.

Grid calculates ET=EPOINT+EBAL when directive LEAU is set to LEAU=3. This energy should be zero when the chosen Probe is itself water, but the regular energy parameters in the current Version of Datafile GRUB actually give a value of 0.3 Kcal/mole for a water Probe. This is regarded as a calibration error, and all the energies computed with this Version of the Programme when LEAU=3 are appropriately adjusted. The adjustment is included in EBAL, and is clearly shown as a CORRECTION TERM FOR ACCUMULATED ERRORS in the lineprinter output when LEAU=3.

The resulting energies when LEAU=3 are written to the GRIDKONT file, and analysed into their individual components when they are positive and therefore indicate that a water molecule at the grid point would interact more favourably with the Target than the chosen Probe. Negative energies are truncated to zero, and are not analysed because the regular results from Grid are more appropriate indicators of favourable binding sites. Thus the energies and Grid Contour Maps obtained when LEAU=3 show positions on the Target at which the Probe interactions would actually be disfavoured relative to water.

It is important to know if these specifically unfavourable places exist on a Target, because they can influence the affinity and selectivity of drug-receptor interactions, and the orientation of a ligand at its receptor site. A well-known example occurs with the enzyme dihydrofolate reductase, which binds the purine ring of its substrate in one orientation, and the corresponding ring of its inhibitor methotrexate (MTX) after an 180 degree ring rotation. The significant structural difference between these two ligands is the replacement of an oxygen atom in the substrate by a nitrogen in MTX, and the inhibitor was originally designed on the assumption that it would bind exactly like the substrate itself.

The bound orientation of MTX was observed many year's ago by X-ray crystallography. This Version of Grid shows (when directive LEAU=3) that an oxygen of the substrate would be precisely located at a place in the enzyme cleft which is maximally unfavourable to oxygen, if the substrate were to bind in the same way as MTX. Indeed it appears as if two backbone carbonyl oxygens of the enzyme are an important structural feature which ensures that the substrate does not bind like MTX, because dihydrofolate reductase can only give a stereo-chemically correct product if the substrate ring is rotated 180 degrees away from the MTX orientation.

Results such as these suggest that ligand selectivity may be critically influenced by pre-bound water molecules, because water is not easily displaced by polar but inappropriate ligand atoms. One misplaced polar atom such as carbonyl may give such a big positive energy that it forces the ligand into a completely different orientation, and causes several otherwise apparently acceptable hydrogen bonds to be misaligned or broken altogether.