19.1.1. Nucleic acid counter-ions

DNA and RNA Targets should normally be represented by ATOM records in the PDB file. They have many charged phosphate groups, and would have a very large net anionic charge in the absence of counter-ions. Programme Grin will therefore add a potassium counter-ion for each phosphate in the middle of the nucleic acid sequence, and a magnesium ion for the 5* terminus. This is only done when the DNA is represented by ATOM records, and when the name of each DNA (or RNA) atom is specified by the PDB input file to agree with the Brookhaven convention and the atom name in the first part of Datafile GRUB.

This use of DNA counter-ions normally results in an uncharged Target for Programme Grid. Of course the procedure can not be rigourously justified, and it must be used with caution. However, more serious errors would occur with charged Probes, if there were no counter-ions on the nucleic acid Target.

19.1.2. The position of DNA counter-ions

The counter-ions are placed by Programme GRIN at 10.0 Angstrom distance from each phosphorus atom of the DNA. They are normally located in the water phase, well "off-shore" from the regular Target atoms. However, with some conformations of DNA it may not be easy to find an appropriate position. This could also happen for example, if the DNA was liganded to another molecule such as a repressor protein.

This Version of GRIN therefore checks for the prior presence of such ligands, and alternative counter-ion positions are tried if the first is unacceptable. A counter-ion record is always inserted by GRIN in order to maintain the correct connectivity in the GRINKOUT file, but some of these counter-ions may be marked with a cross to show that they have been rejected because they would make an unacceptably close contact with another Target atom (See Cross X). The Cross ensures that Programme GRID will not take them into consideration as a part of the Target.

Of course the User can include his own counter-ions in any PDB file. However, particular care is required with DNA and RNA Targets, because Programme GRIN will add counter-ions as described above. (Further information about the treatment of counter-ions is given under the heading Metal cations of the target).

If you want to add a DNA counter-ion with a different name or different properties, we recommend that you let GRIN add its own counter-ions and then edit the GRINKOUT file in order to change the name or properties or position of the counter-ion. Remember that lines may never be added to a GRINKOUT file, nor may they be deleted, nor may their sequence be changed as this would corrupt the connectivity matrix. However, if you do not want some of the counter-ions in the GRINKOUT file, you can always eliminate them with a cross (see Cross X).

19.1.3. The properties of counter-ions

Counter-ions on the Target may be represented by ATOM or HETATM records. The HETATMs are normally assigned the default Type 0 (ITYPE=0), and their position in the Target is then fixed at the place specified by their coordinates in the PDB file.

ATOM records may alternatively be used for sodium, potassium and chloride counter-ions, and these ions are then assigned to the special Type 120. DNA counter-ions are also assigned as Type 120, and the User may reassign Type 0 counter-ions to Type 120 in the GRINKOUT file as described above.

A Type 120 counter-ion of the Target is fixed so long as Directive MOVE=0 in the main Programme Grid. However, Type 120 counter-ions can move in response to the Probe when MOVE>0 or MOVE<0 in Grid.

Grid works like this:

• The regular Grid energy is computed with the Probe at its grid point. If MOVE>0 in Grid the flexible side-chains of the Target will move in response to the Probe because this is the main effect controlled by Directive MOVE. If MOVE≤0 in Grid the flexible side-chains will not move.

• A search is then made by Grid for any Type 120 counter-ions which are very near the Probe, and are therefore predicted to make particularly powerful interactions. For example the Probe at its grid point might coincidentally be at exactly the same position as a counter-ion of the Target, so that a large energy of repulsion would be computed. If the position of that counter-ion had been fixed, as would be the case when ITYPE=0, this repulsion would appear in the Grid map as a Van der Waals surface round the counter-ion.

• Such Van der Waals surfaces displayed round each counter-ion would probably be misleading, because counter-ions are not normally fixed in solution. Furthermore any statistical analysis of the Grid maps could be distorted by the artificially high positive energies around each of these ions.

• Such local distortions around each ion are smoothed out, while the overall effect of the ion cloud is maintained, when TYPE 120 counter-ions are used and when MOVE≠0 in Programme Grid. Note that the smoothing algorithm in this Version of Programme Grid cannot deal with a close cluster of Type 120 ions. We therefore recommend a separation of at least 6 Angstrom between each Type 120 ion and its nearest Type 120 neighbour in the Target.

• When a multi-atom Probe is being used, a wider spacing of at least 8 Angstrom between Type 120 counter-ions is recommended.

• The first Programme Grin normally adds counter-ions to DNA or RNA Targets, and Grin normally ensures the necessary 6 Angstrom separation. However, if the User adds his or her own counter-ions to the PDB file, he or she should make quite sure that sufficient separation is maintained.

• This separation requirement sometimes prevents Programme Grin from finding an acceptable place for a DNA counter-ion. When this happens it behaves like this:

  • A counter-ion is added by Grin to the GRINKOUT file, in order to maintain the connectivity matrix. This will normally be a potassium ion, but it will then be crossed off the list (see Cross X) because it is not in an acceptable place. This Cross means that it will not be considered as part of the Target when Programme Grid does the main calculation.

  • A count is maintained of the potassium counter-ions which have been crossed off.

  • Grin continues to process the PDB file for the DNA Target. When it finds an acceptable counter-ion position it adds a magnesium ion instead of the normal potassium. This divalent magnesium provides the extra counter-ion charge which was lost when the previous potassium was crossed off the list.

  • As a result of this procedure the final GRINKOUT file for the DNA (or RNA) may therefore have several different sorts of counter-ion:

    • Regular potassium counter-ions.

    • Potassium counter-ions which have been crossed off the list.

    • Magnesium counter-ions which were used instead of potassium in order to restore the charge balance.

  • Of course the final Target may not be electrically neutral in the GRINKOUT file, because other molecules may also be present in the PDB input file. For instance, a cationic repressor protein or ligand might be bound to the DNA, and that protein or ligand would bring its charges with it. The User will want to consider how those charges should be dealt with, and may want to add more counter-ions.

19.1.4. Protein counter-ions

Programme GRIN treats the carboxy terminal of a protein, and the carboxy groups of ASP, GLU and similar amino-acid side-chains, as anionic by default. Similarly, the N-terminal nitrogen and ARG and LYS side-chains are treated as cationic, and the overall net charge of the protein is then calculated by subtraction. This is an arbitrary calculation, because the true net charge depends upon many factors including the local pH and ionic strength; the local dielectric environment; and the pK_a values of the ionizable groups. Brown et al showed many years ago (Proc.Roy.Soc.B, (1976) 193.387) that pK_a values in a protein depend upon the local environment. They can alter when ligands bind, or when the protein conformation changes.

It sometimes happens, however, that the overall net charge calculated by GRIN is very large, and this charge will then dominate the predicted interactions of charged Probes. For instance the most favourable grid point for a sodium cation Probe might be in one of the corners of the grid (so that it got away as far as possible from the Target) if that Target was itself a polyvalent cation!

Programmes GRID, MINIM and FILMAP can be used to find suitable places at which to add counter-ions, and thus diminish the calculated net charge of a Target. This is usually the most appropriate way in which to deal with cationically charged proteins, because deprotonisation of Arginine side-chain nitrogens is virtually impossible, and deprotonisation of Lysine is rare.

The situation is a little more complicated when the protein has excess negative charge. Countercations can be introduced near ionised carboxy side chains, but in some cases it may be more appropriate to protonate some of the carboxy groups. In order to protonate the side-chain of aspartic acid, for example, it is necessary to alter the name of the residue in the PDB file and rerun GRIN. Appropriate residue names (eg: ASZ and ASZ1 for aspartic acid) are provided in datafile GRUB.DAT, and should be chosen with care.

This Programme GRIN will print a list to the lineprinter output file (GRINLOUT.DAT), suggesting whether protonation or counter-ions should be used in order to neutralise the charge of a Target. However, these suggestions must be regarded as very tentative, and should not be relied on. For serious research the ionization state of the individual ionizable groups of the Target should be determined experimentally, by NMR for example.

From the version 21, the work of the routines Minim and Filmap has been incorporated and fully automatised in GREATER. To perform the neutralisation task, the User must only select the counter-ions to be added to the macromolecular Target. GREATER automatically computes the appropriate map for the selected counter-ion, finds the energy minima, uses a simulating annealing procedure to postprocess the minima in order to select the minima location subset that gives the most favorable overall interaction energy, and fills in the target with the counter-ions in those minima. The counter-ions are also automatically added to the PDB file, so that the User may inspect their position using Gview.

19.2.1. HETATM Charges according to the Principle of Electronegativity Equalization

Saunderson's revised electronegativity values (J. Amer. Chem. Soc. (1983). Volume 105. p2259.) are used. by Programme GRIN, which selects the appropriate value for each HETATM record in the Target. This is done on the basis of the chemical symbol, which is why the Protein Data Bank conventions for the atom name must be strictly followed (See above).

19.2.2. Charge distribution according to a semiempirical method.

From the version 22 of GRID a new way to calculate atomic charges for HETATMs is available in Programme GRIN. Setting the Directive IHAC to 1 the atomic charges will be computed using a pseudoempirical Hamiltonian. The method is implemented for working on drug-like molecules: it can be applied only to HETATMs, with the limit of 100 HETATMs for molecule. In case the semiempirical method does not assign the charges to the whole molecule GRIN reverts to the Saunderson algorithm and a warning message is printed to the Lineprinter OUTput file. It could happen for a few reasons, such as: an atomic number not supported is found, or an open shell molecule is found, or the Self-Consistent-Field is not achieved.

The QINH values assigned from GRUB to HETATMs are not used, because the charge distribution of the entire molecule is calculated starting from its wave-function.