VolSurf manual
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Chapter 5. Overview of the programme GRID

Programme GRID is a computational procedure for determining energetically favourable binding sites on molecules of known structure. It may be used to study individual molecules such as drugs; molecular arrays such as membranes or crystals; and macro-molecules such as proteins, nucleic acids, glycoproteins or polysaccharides. Several different molecules can be processed one after the other as a "Set" of Targets in a single GRID run.

The overall procedure and some early results obtained with Programme GRID have been published in the Journal of Medicinal Chemistry. (1985). Volume 28. Pages 849-857. However the Programme has been updated and extended many times since that publication. (for more info, please see http://www.moldiscovery.com/soft_grid.php)

5.1. Energy functions of programme GRID

Programme GRID is used to calculate the energies of interaction between a chemical group (the "Probe") and another molecule (the "Target"). The results are written to file for further analysis, and the energies may also be displayed as three-dimensional contour surfaces, together with the structure of the Target molecule. The molecular shape of the Target and the interaction energies of the chosen Probe can then be viewed simultaneously. Negative energy levels delineate regions at which ligand binding should be particularly favoured. Positive energy levels normally define the surface of the Target.

The energies for contouring are computed by studying the interaction of the Probe group with the Target molecule. This Target can be a macromolecule such as a complete protein, or a small molecule like histamine or a drug. However, in VolSurf the target is limited to be a drug-like molecule.

GRID probes include many groups, but only the most representative for DMPK problems have been included in VolSurf.

When the interaction energies are calculated, the influence of Lennard-Jones interactions, electrostatic effects and hydrogen bonds are all considered.

The interaction of the Probe group with the Target is computed at sample positions (the grid points) distributed throughout and around the molecule. With the Probe at each grid point in turn, the interaction is calculated from:

in which indicates pairwise energy summation between the Probe at its grid point and every appropriate atom of the Target, and "S" is the appropriate entropic term at the grid point. The overall energy E_XYZ is then assigned to that point and written to file.

5.1.1. The Lennard-Jones potential

In the Lennard-Jones potential:

the interacting atoms are a distance d apart, and the Energy Variables A and B are calculated from the Van der Waals radius, polarizability and effective number of electrons of the atoms. These values are tabulated in datafile GRUB which is also present in VolSurf, and are assembled correctly during the calculation.

5.1.2. The electrostatic potential

The electrostatic interaction is:

where p and q are the electrostatic charges on the Probe group and the pairwise Target atom, and K is a combination of geometrical factors and natural constants. The macromolecular Target and the surrounding water have dielectrics of M and W respectively, and the depth of the charges p and q in the Target phase is P and Q. For small molecules the Target phase is effectively absent, and P and Q are both zero.

5.1.3. The hydrogen bond potential

The standard hydrogen bond interaction is computed from:

where f and f' are functions; U,U',U'' etc are angles and distances defining the geometrical arrangement of the atoms engaged in hydrogen bonding and their neighbours; and Q depends on the charges of the interacting atoms. Energy Variables C and D are computed from the hydrogen bond radii and hydrogen bond energies of the atoms, which are tabulated in Datafile GRUB.

The hydrogen-bonding functions U,U',U'' etc were devised in order to compute the interaction between explicit hydrogen-bonding atoms, and these functions have been described in the GRID User Manual. The functions ensure that only the appropriate number of hydrogen bonds with the correct hybridization are selected for inclusion in the E_HB term.

5.1.4. The entropy term

An entropic term is included in the GRID energy fuction for some special cases, such as for detecting selectivity unfavourable sites for water molecules over the target.

This is done by the DRY probe, which is a specific probe to compute hydrophobic energy. The general approach is to estimate the entropic component for an ideal flat hydrophobic surface, and then modify the result in order to take account of the detailed properties of the actual molecule. Programme Grid does this by calculating three separate energy components at each grid point, and combining these together in order to find the overall Grid energy at that point. The components are:

WENT. This is the ideal entropic contribution towards the hydrophobic effect. It favours the mutual association of hydrophobic molecules with each other in an aqueous environment. Ordered water in the hydration shell surrounding the Target is thought to be responsible for this entropic enhancement of binding, and the name WENT means Water ENTropy. The size of this component is determined in the Grid Force Field by making the simplifying assumption that WENT has the same magnitude at all "undisturbed" places on the surface of the Target molecule. However, as described below, much of the surface may actually be "disturbed" and this modulates the influence of WENT.
EHB. This measures the hydrogen-bonding interactions between water molecules and polar groups on the surface of the Target. Their strength (EHB) is determined for the hydrophobic Probe, by using the regular hydrogen-bonding functions for water in the Grid Force Field.
ELJ. This term measures the induction and dispersion interactions which occur between any pair of molecules. They tend to attract the molecules towards each other, and this energy component (ELJ) is assessed at each grid point by computing the regular Lennard-Jones function for water in the Grid Force Field.

In order to compute the overall energy for the hydrophobic Probe, it is assumed that the hydrogen bonds to polar atoms of the Target disturb the ordered arrangement of water molecules in the hydration shell. This disturbance tends to oppose WENT which depends upon the good ordering of the surface waters. Furthermore hydrogen bonds may be broken when the hydrophobic surfaces come together, and the overall energy of the hydrophobic Probe is therefore computed at each grid point as:

WENT + ELJ - EHB

5.1.4.1. The favourable components WENT and ELJ

Ordered water is commonly observed in the X-ray crystal structures of proteins, but that water is usually making obvious hydrogen bonds to polar groups on the macromolecular surface. One may sometimes find ordered water in a completely hydrophobic region, but this is by no means common and the ordering which is thought to be responsible for the hydrophobic effect cannot, in general, be observed on an X-ray time scale. Some other type of ordering on a faster time scale must be postulated, and the present model is constructed on the assumption that it is the hydrogen bonds of water which are ordered at the undisturbed hydrophobic surfaces of the Target.

Many of the hydrogens of bulk water are making hydrogen bonds, but the present model assumes that a still higher proportion of hydrogens in the hydration shell are engaged in hydrogen bonding. However, this hydration shell is not uniform, because some parts may overlay a polar surface of the Target, while other parts overlay a hydrophobic region. When the Target atoms are hydrophobic they cannot make hydrogen bonds with water molecules, and those waters in the shell must therefore make their hydrogen bonds from one water molecule to another water. These water-water hydrogen bonds generate an ordered "structure of water", and it is this ordering which is disturbed by the interference of polar Target atoms.

In order to estimate the size of WENT it may be noted that there are enough hydrogens in water to have four hydrogen bonds per oxygen atom, and the assumption is made that every hydrogen in the hydration shell does make its hydrogen bond. This is of course a limiting assumption, and in reality such perfect order is not to be expected. We also assume that only three hydrogen bonds are made by each oxygen in bulk water, instead of the four which are theoretically possible in an ideal tetrahedral arrangement. Once again this seems to be an extreme limit, and the actual proportion may well be greater than 3/4.

The four possible hydrogen bonds of a bulk water molecule may be numbered 1,2,3 and 4. Then the three assumed bonds could be selected as numbers 1,2,3 or 2,3,4 or 3,4,1 or 4,1,2. There would be four permutations, and the corresponding contribution to the Free Energy of the water would then be:

WENT = -(1.386*308*1.987)/1000 = -0.848 Kcal/Mole

where Ln(4)=1.386 and 308 Kelvin is taken as body temperature and 1.987 cal/mole.K is the gas constant.

On this model, the hydrogens of water are ordered in hydrophobic regions of the hydration shell, in the sense that all hydrogen bonds are actually made and they are all made from one water molecule to another. On the other hand the hydrogens are more disorganised in bulk water, and are also disorganised wherever the surface of the Target is polar.

When two hydrophobic surfaces come together there will be a favourable induction/dispersion interaction between the molecules, and ELJ is used in order to estimate this component. The displacement of ordered water molecules from the hydrophobic surfaces into bulk water also makes a favourable contribution WENT. Thus (ELJ+WENT) is used to estimate the favourable part of the hydrophobic interaction.

It is not claimed that WENT=-0.848 Kcal/Mole measures the "correct" entropic component, whatever "correct" may mean. One could argue that -0.848 Kcal/Mole may be a high estimate because it was calculated on the basis of limiting assumptions which may tend to overestimate the result. However, one must also bear in mind that water would be displaced from the surfaces of both interacting molecules, and this could be a counter argument for doubling the entropic contribution. These factors tend to oppose each other, and we have therefore retained the original estimate WENT=-0.848 Kcal/Mole for the present computations.

It is interesting to compare the relative magnitudes of ELJ, WENT and EHB in the Grid Force Field. The entropic term (-0.848 Kcal/Mole) is bigger than a typical Lennard-Jones energy between two atoms which is about -0.2 Kcal/Mole for carbons, oxygens and nitrogens. On the other hand it is less than many hydrogen bond energies which are characteristically -2 -3 or even -4 Kcal/Mole. Thus WENT tends to dominate the hydrophobic effect, but is itself overwhelmed by polar interactions (See below).

Of course the actual size of the entropic contribution (-0.848 Kcal/Mole) would be altered if different assumptions were made, and a more realistic partition function were used. However, altered assumptions about the partition function would not change the difference between the computed hydrophobic energy at one grid point, and the computed energy at another. On the present model this difference depends upon the particular properties of the Target surface. The entropic contribution is assumed to be constant at an undisturbed hydrophobic surface.

5.1.4.2. Unfavourable hydrophobic components

Even in a predominantly hydrophobic region, there may still be a few polar atoms on the surface of the Target, and those polar atoms will often make hydrogen bonds to water in the hydration shell. They can influence the hydrophobic effect in two distinct ways:

They disrupt the local ordering of water in the hydration shell. This diminishes the favourable entropic component.
Any hydrogen bonds by polar atoms of the Target to water may be broken when the hydrophobic surfaces come together, because the water will be displaced and the polar atoms will then, in general, face the opposing hydrophobic surface. This breaking of hydrogen bonds is enthalpically unfavourable.

The energy EHB of these hydrogen bonds is therefore set against the favourable components (ELJ+WENT), and the overall hydrophobic interaction energy of the Grid Probe is finally computed as:

ELJ + WENT - EHB

If the final result is a positive energy, the surface is said to be hydrophilic and the energy of the hydrophobic Probe is set to zero.

5.2. VolSurf Probes

The following GRID probes are available to the VolSurf Users:

  OH2     Water
  DRY     The Hydrophobic Probe
  BOTH    The Amphipatic Probe
  O::     sp² carboxy oxygen atom
  N1      Neutral flat NH (eg. amide)
  N:=     sp² N with lone pair
  N3+     sp³ amine NH3 cation
  O-      sp² phenolate oxygen

OH2

The water probe: it is treated as an extended oxygen ATOM or HETATM, and is allowed to donate two hydrogen bonds and to accept two. It will have sp³ tetrahedral geometry, or sp² flat trigonal geometry, or something in between as appropriate.

DRY

The hydrophobic probe finds places at which hydrophobic atoms on the surface of a Target molecule will make favourable interactions with hydrophobic atoms on another molecule. It is a distinguishing characteristic of these hydrophobic interactions that they only occur when both the molecules are immersed in water.

This hydrophobic Probe may be regarded as a modified water Probe. Like water, it must be able donate and accept hydrogen bonds, and must be electrically neutral.

BOTH

The amphipatic probe identifies regions of the target at which a significant polar interaction can still occur, although the local environment is predominantly hydrophobic.

O::

This probe is an anionic sp² carboxy oxygen atom bonded to one other atom, which accepts two hydrogen bonds in the direction of its lone pairs. This probe can also be used for other atoms with similar geometry. These include aldehyde, amide, nitro, nitroso, phenolate and sulphonamide, sulphoxide oxygens. In addition it is used for the oxygens of unionised sulphate esters, unionised sulphonate esters, unionised alkyl sulphonates and unionised alkyl sulphinates, as well as sp² nitrogen with two lone pairs and one double bond.

N1

This probe represents a nitrogen amide NH group (e.g a protein backbone NH) and and neither donates nor accepts a hydrogen bond.

N:=

This probe is a sp² nitrogen with one lone pair (e.g. uncharged pyridine) and can accept one hydrogen bond, but cannot donate.

N3+

This probe mimics a charged sp³ NH3 group (e.g. methylamine cation) bearing three hydrogen atoms each of which can in principle donate one hydrogen bond.

O-

This is the oxygen of a phenol which is ionised. It therefore is not bonded to hydrogen, but bears a partial negative charge and two lone pairs. The bond from the oxygen to the aromatic ring has some double bond character, and the lone pairs are therefore constrained to stay in the plane of the ring. No hydrogen bonds are donated, but one or two may be accepted by this probe.

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