is normally a CHARACTER*4 variable, although it is actually read by the Format Statement as A5 (See the warning above). ATOMIN defines the atom name. It is analogous to ATM above and ensures that the correct Energy Variables are appended to the correct atom. In any one "Recognised Molecule" type, every atom has a unique name ATOMIN. However the same name may occur again in another "Recognised Molecule" type. Thus the alpha carbon atom occurs as ' CA ' in every amino-acid, and may have different Energy Variables in each.

is a real variable which measures the Van der Waals radius of the atom in Angstrom.

(integer) is a factor which has been described as the number of effective electrons surrounding the atom. It determines the strength of the Van der Waals attraction. In early Version of the Programmes (before Version 15) a real variable EFFNIN was used, but the number of electrons must be an integer and NEFFIN is the name for an integer under the Fortran-77 convention.

(real) is the polarizability of the atom in Angstrom ³.

(real) is the electrostatic charge on the atom. Units are the charge of the electron (with changed sign).

(real) is the strongest hydrogen-bond attraction energy (i.e. the most negative value of EHB) at the optimum position of the hydrogen bond function:

EHB = C/(d⁸) - D/(d⁶)

in which d is the straight-line distance between two identical heavy atoms which are interacting by hydrogen bond formation, such as two hydroxyl groups. The Units of EHB are Kcal/Mole.

(real) is HALF of the straight line distance d which corresponds to the strongest hydrogen-bond attraction energy between the same two heavy atoms. It may therefore be regarded as a hydrogen bonding radius, and will normally be somewhat less than the corresponding Van der Waals radius. Units are Angstrom.

The optimum hydrogen-bonding distance is 2*RMININ Angstrom, and one may calculate C and D in the above equation for EHB from the transposed formula:

C = -3.0 * EMININ * ( (2*RMININ)⁸ )

D = -4.0 * EMININ * ( (2*RMININ)⁶ )

An example will make this clear. If the strongest oxygen- oxygen H-bond between two hydroxyl groups has a length 2.8 Angstrom and strength -4.0 Kcal/mole, then:

C = -3.0 * (-4.0) * (2.8⁸) = 45336. and

D = -4.0 * (-4.0) * (2.8⁶) = 7710.

which are the values used in the next Programme GRID.

For completeness, it is necessary to mention three further points:

1. The Concept of a hydrogen-bonding radius RMININ between two identical atoms is still used, even if the atoms would not actually hydrogen bond to each other. Thus a value RMININ is assigned to carbonyl oxygen, although one carbonyl oxygen could not hydrogen bond to another because they are both obligate donors.

2. In fact it is most common to find two different atoms hydrogen-bonding together, such as amide NH to carbonyl. In this case the value of D is taken as the geometric mean of the D values of the individual groups, which are each calculated as described above. The hydrogen-bond strength EHB is then calculated from this geometric mean, and from the arithmetic mean of the individual hydrogen-bonding radii RMININ.

3. The strength of a hydrogen bond is modified by the electrostatic charges of the hydrogen-bonding atoms. For instance a carbonyl oxygen will accept stronger hydrogen bonds if it has a high negative charge, and weaker hydrogen bonds if it is more positive. Hence two atoms both having nominal values of EMININ=4.0 Kcal/mole, might actually make a hydrogen bond of strength 5.0 Kcal/mole if they had appropriate electrostatic charges.

   This may be an important effect, for example, in determining partition coefficients between water and a hydrophobic phase. The neutral sp³ methylamine molecule CH3.NH2 and the sp³ cation CH3.NH3+ can both make three hydrogen bond interactions with water. However the three bonds donated from the cation are charge reinforced, and so favour its partition into the hydrogen-bonding water phase.

(integer) is the maximum number of hydrogen bonds which the atom can donate (-1 < IDIN < 9). In practice, values of IDIN greater than 4 may reduce the operating speed of the next Programme GRID significantly. Nevertheless it is practical to use values upto 9. The standard version of datafile GRUB does not contain any values for IDIN. It is set to zero, and the appropriate values are then decided by Programme GRIN according to the hydrogen bonding type (N1IN) as described below. However the user may edit GRUB to set specific values for IDIN for any particular atom or group, and the value assigned in GRUB will then override the default value determined by N1IN.

(integer) is the maximum number of hydrogen bonds which the atom can accept (-1 < IAIN < 9). In practice, values of IAIN greater than 4 may reduce the operating speed of the next Programme GRID significantly. Never-the-less it is practical to use values upto 9.

The standard version of datafile GRUB does not contain any values for IAIN. It is set to zero, and the appropriate values are then decided by Programme GRIN according to the hydrogen bonding type (N1IN) as described below. However the User may edit GRUB to set specific values for IAIN for any particular atom or group, and the value assigned in GRUB will then override the default value determined by N1IN.

(Integer) Is the Type of the atom, which defines its hybridization and hydrogen bonding geometry. See Type of Hydrogen Bond and HYDROGEN BOND GEOMETRY.

(real) is the charge of the hydrogen ATOMS which are covalently bonded to the ATOM whose symbol comes at the start of the record in GRUB. This charge is not used if the ATOM is being treated as an Extended Atom. Thus the CB record of Alanine refers to a methyl group, and the HQIN variable would only be used if the PDB file actually had one ATOM record for the carbon and three separate ATOM records for the three ATOM hydrogens of the methyl.

(integer) is the number of hydrogen ATOMS which are covalently bonded as part of the Extended ATOM whose symbol comes at the start of the record in GRUB. Thus the CB record of Alanine refers to a methyl group, and NUMHIN has the value 3 because there are three hydrogens in this methyl group.

Variable NUMHIN is used if the PDB file actually has one ATOM record for the carbon and separate ATOM records for the ATOM hydrogens of the methyl. The reported number of hydrogen ATOMS in the PDB file is then checked against NUMHIN to be sure they are all present.

In some cases the number of hydrogens can change. For example, NUMHIN has the value 1 for the backbone amide nitrogen of alanine, but an N-terminal alanine will have an NH3 cationic nitrogen. Appropriate adjustments for this will be made by Programme GRIN

Values for the Van der Waals radii of atoms go back to the early work of Pauling (The Nature of the Chemical Bond) and Bondi (J. Phys. Chem. (1964). Volume 68. 441.; J. Phys. Chem. (1966). Volume 70. 3006.). A more recent review was published by Charton (Topics in Current Chemistry. (1983). Volume 114. 57.).

Although the effective number of electrons is a concept which has appeared in the literature since the early twentieth century, it has not been adequately defined. The original parameterisation for GRID was based on the values published by Brooks et al (J. Comput. Chem. (1983). Volume 4. 187), and their published values are still followed. For many atoms, however, it has been necessary to derive new values for NEFFIN, and this has been done on the following basis. The editors of this User Manual would value comments on the interpretation and computation of NEFFIN values. They make no attempt to justify the following procedure.

It is assumed that the interactions of an atom will be determined by its NEFFIN value; by its polarizability ALPHIN; and by the field. NEFFIN is the effective number of electrons in the atom, but all the electrons may not be equally polarizable. Some allowance must be made for this.

NEFFIN values have therefore been computed as follows:

1. Consider systems with complete outer shells. e.g. the chloride ion; the sodium ion or sp³ carbon.

2. Let N be the "number of electrons in the outer shell". Thus for the extended atom CH3 (i.e. a methyl group consisting of one sp³ carbon bonded to three hydrogen atoms) N is 8 for the complete outer shell of carbon. Subtract 1 from N for each bond to a neighbouring atom, in order to calculate n which is the "modified number of electrons in the outer shell" (i.e. there is one bond from the methyl to the rest of the molecule, so subtract 1 from 8 to give n=7). On the other hand for a protein backbone amido NH group (treated as an extended atom), subtract 2 (one for the bond to the adjoining alpha carbon and one for the bond to the adjoining carbonyl carbon) giving n=8-2=6. For a carbon atom in an aldehyde group, treated as an individual atom and NOT as an extended CH group, subtract 4 (i.e. subtract one for the bond to the hydrogen; one for the bond to the rest of the molecule; and two for the double bond to the oxygen) giving n=8-4=4.

3. Let Z be the "effective atomic number" for the species with a complete outer shell of electrons, and adjust in the same way to give the "modified atomic number" z. Thus for CH3 (the extended methyl group with one bond to the rest of the molecule) Z=10 and z=10-1=9.

4. Calculate NEFFIN = (n + z)/2

   This gives an NEFFIN value somewhat larger than the modified number of outer shell electrons, so that some weight is given to the polarizability of the electrons in the inner shells. However, the value of NEFFIN is "a rather doubtful quantity" as first stated by Margenau (Rev. Modern Phys. (1939). Volume 11. 1.). It is fortunate that NEFFIN only appears as a square root term in the expression for the van der Waals energy, so that its precise value is not as critical as it might otherwise be.

values of polarizability may be estimated by the method of Miller et al (J. Amer. Chem. Soc. (1979). Volume 101. 7206).

values for ATOMS may be calculated by using Programme GRIN itself. Suppose, for example, you want to enter methyl chloride as a Recognised Molecule in the GRUB listing. The hetatm coordinates of a methyl chloride molecule would be prepared as a PDB file for input to GRIN, and the GRINKOUT output would show the appropriate charge for the chlorine and all the other atoms. It would only be necessary to add up the carbon and hydrogen charges for the extended methyl group.

If a charge was required for a Probe group, or a new entry in the HET section at the end of GRUB, the same approach would be used. For instance a chlorine Probe would have one charge if it represented the chlorine of methyl chloride; another charge if it represented the chlorine of chloro-benzene, and a third for the chlorine of chloroform. Whilst an average value would usually be acceptable for a chlorine Probe in preliminary studies, GRIN may be used as described above in order to find mutually compatible charges for the three different types of chlorine Probe.

is related to factors which were first considered by Pauling (the Nature of the Chemical Bond). The strongest hydrogen bonds are formed by small atoms of high electronegativity, so that oxygen forms stronger bonds than nitrogen. The hydrogen bonds formed by second row elements of the periodic table are much weaker, and one may neglect hydrogen bonding by the atoms of the third and later rows.

Alterations in the net electrostatic charge on an atom apparently changes the strength of its hydrogen bonds, but this is dealt with separately in the GRID force field.

is less than the Van der Waals radius of an atom by an amount which is usually related to the strength of its hydrogen bonds. Thus the EXTENDED hydroxyl group has a van der Waals radius of 1.65 Angstrom which is reduced by 0.25 Angstrom to a hydrogen bonding radius of 1.40 Angstrom. On the other hand the reduction is only 0.05-0.15 Angstrom for the EXTENDED nitrogen atom which tends to make weaker hydrogen bonds.

In some cases the Van der Waals radius and the hydrogen bond radius are almost identical. This happens, for example, with hetero-molecules in which the heavy atoms and hydrogens are each explicitly considered. In this case it is the radius of the hydrogen-bonding hydrogens which is reduced, rather than the radius of the central nitrogen itself.