Gj NkT log iiin

where N is Avogadro's number. Using the log10 scale, NkT=1.418 kcal mol-1 at blood temperature (37°C). Thus for two conformers differing in energy by l kcal mol-1, log10 n2 /n1~0.7 (where conformer 2 is the more favourable) giving a conformer population ratio n2/n1 of 5:1 at this temperature. (From Davies (1987), by permission)

The utility of Equation [3.10] is shown by a simple example in Figure 3.9 where the bioactive conformer with the basic side chain perpendicular to the aromatic ring (calculated on the intrinsic conformer preference in Table 3.5) of the CNS agent viloxazine (3.6, R=2-OCH3), an inhibitor of biogenic amine release, is plotted as a function of the potency component which has been referenced to a non-polar phase environment. The relation is of unit slope. (In this early example, octanol has been used as the reference non-polar solvent. As the relatively weak hydrogen bond proton acceptor properties of the solute phenoxy oxygen atom are weaker than those of the polar reference solvent octanol, little error is introduced in this set of data by the use of this solvent compared with that of a hydrocarbon).

While most data of this type are very much related to details of ligand conformation and of localised energetics in the target site, an advantage of such information is an understanding of the detailed thermodynamics of binding of closely related molecules as exemplified in Section 3.3.5. Plate 3.5 shows the development of a potential guanine nucleotide receptor a-helical model based on geometric constraints of the bound ligand hormone and the resultant constraints on the receptor a-helices. The comparative

Figure 3.8 Schematic representation of the free energy relations for the conformer i of the drug (A) interacting with the relevant receptor conformer jx of the receptor protein complex and possible pathways for relating the bound conformer free energy *Wto the reference free energy GA. The standard free energy of the conformer i of the drug is related to the average free energy GA by the conformer fraction or population /. A change of reference phase from aqueous to hydrocarbon is shown by the subscript L. The partition coefficient P defines the average free energy difference of A between the two phases and individual conformers in the different phase environments may be related similarly by conformer partition coefficients P (From Davies (1987), by permission).

Figure 3.9 (a) Potency 'in vivo'of viloxazine analogues plotted against a partitioning effect using the octanol/water model on

Figure 3.9 (a) Potency 'in vivo'of viloxazine analogues plotted against a partitioning effect using the octanol/water model on the log10 scale, (b) Residual variation in potency of viloxazine analogues after allowance for a partitioning effect plotted on the log10 scale against the fraction of the conformers having the side chain perpendicular to the aromatic ring. (From Davies (1987), by permission).

Table 3.5 Intrinsic conformer preference of substituted anisoles and related molecules at 37°C. Ab initio estimates and NMR data.

Table 3.5 Intrinsic conformer preference of substituted anisoles and related molecules at 37°C. Ab initio estimates and NMR data.

energetics between agonist and antagonist and the thermodynamics of binding and response of a partial agonist have led to ideas on proton shuttle mechanisms between Tyr-Arg-Tyr residue triads which show promise in identifying general proton transfer signalling mechanisms (Nederkoorn, Timmerman, Timms et al. (1997)).

3.5.3 Ligand design—macromolecular structure known

There are a number of simple ligand modelling strategies that have evolved to take advantage of the structural information on target proteins derived from X-ray crystallography or NMR spectroscopy. Given that the structure of the site is known, the strategies resolve to devising efficient schemes for the logical exploration of the space of the target site and the housing of the ligand's appropriate interacting groups. Whether to build upon interacting groups to probe obvious target sites and link these probes back to some representative molecule or whether to fill the volume of the site with nominal atoms and then to choose viable sub-sets for efficient interaction, the choice is perhaps dependent on the degree of understanding of the mechanism involved. Binding it should be remembered is a free energy process and those methods which incorporate the statistics of the binding both in macromolecule and in ligand should prove the most powerful. The limiting problem is likely to be computational effort but there is no substitute for knowledge of molecular structure.

3.5.3.1 Multiple fragment probes—locate and link methods

In the probe approaches, the so-called locate and link methods, a site specific small probe can be geometrically constructed or better its interaction calculated and the orientation for the best localised orientation of the small probe molecule determined. Variants on optimising the location of the probe can be generalised. One may place a set of small groups randomly on a coarse grid (0.5 A) and optimise the translational and orientational variables using search methods based on the rate of change in energy as a function of the variables or by stochastic methods such as Monte Carlo. Similar approaches using the protein-fragment interaction forces and employing molecular dynamics for locating probes on a large number of polar fragments (e.g. 1000) randomly distributed within the binding site are used to calculate, via Newton's laws, the independent motion of each fragment. By slowly cooling the system to absolute zero, optimal binding positions for the probe groups can be determined.

Steric features of a site can be exploited by constructing spheres in contact with the protein surface such that the centroids represent positions for locating interacting atoms. In place of calculation, optimal positions for groups to partner hydrogen bonding moieties in the protein can be derived from data surveys of small-molecule X-ray structures and via microwave spectroscopy and quantum mechanical calculations. The resulting positions for donor hydrogen or acceptor atoms and their connected atoms form a set of vectors on which candidate probe hydrogen bond groups can be overlayed.

A special case in refined X-ray structures is given by bound solvent water molecules which represent experimentally located probe fragments. Such water molecules can indicate opportunities for the location of hydrogen bond groups, although, dependent on their degree of interaction, not all can be replaced in an energetically favourable manner. Water is potentially tetracoordinate in hydrogen bonding through its two hydrogen bond proton donors and its two electron lone pairs as proton acceptors. Whether to treat a located water molecule as a candidate for replacement or as strongly held by the protein depends on the number of potential interactions made with the macromolecule. The following simple table on the categories of bound water and their implications for substitution may be constructed. H1 LP1 H2 LP2 Category of Implication

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