From Page and Jencks 1971 by permission

interactions. We consider first the effect of solvation on translational and rotational entropies.

There will be some loss in translational and rotational entropy on solution. For a non-polar molecule, the magnitude of this loss is ~10 e.u. or a TAS contribution of ~ 3 kcal/mol at blood temperature when the same reference concentration is taken in the gas and liquid phases. The translational and rotational entropy loss on binding to a receptor site is thus expected to be not very different between binding in solution and in the gas phase.

3.3.3 Electrostatic interactions in solution

The dramatic efffect of hydration on electrostatic interactions has been mentioned in Section 3.2.1. Thus net ion-ion interactions are greatly reduced on hydration or may become unfavourable and only the consequent liberation of solvent molecules may create a significant entropy effect and favourable interaction. Except in close comparison of related molecules, therefore, gas phase comparisons are of limited utility. Weaker interactions such as ion-dipole interactions may similarly be largely suppressed by competitive solvent dipoles and contribute little to the overall free energy of interaction in a polar phase. While electrostatic effects will be largely suppressed by hydration, the final binding site of the ligand molecule will usually be within a macromolecule surrounded by mobile regions of polar and non-polar phases. Ligand concentration is usually referenced to aqueous solution. To estimate the energetics of hydration that must be lost for ligands to interact with a membrane or related protein, it can, therefore, be informative to reference the concentration to a non-aqueous hydrocarbon environment, when van der Waals interactions are automatically taken into account. The best reference model is obviously some hydrocarbon phase, but the partitioning model which has received the most attention has been the solvent octanol with its attendant problem of interaction with strong hydrogen bond acceptor solutes. This latter model is discussed in Chapter 5. An example of the insight gained on applying partitioning data to the thermodynamics of ligand-receptor protein binding is given in the next section.

3.3.4 van der Waals interactions in solution and the hydrophobic effect

There is a driving force for non-polar molecules to interact in aqueous solution which is termed the hydrophobic effect. This force at the macroscopic level causes aggregation of lipids in solution and the folding of proteins in self assembly. The source of this important effect has been of dispute. Earlier theories had interpreted this effect as being entropically driven due to the ordering of water molecules around nonpolar solutes with their resultant liberation on non-polar interatomic contact. More recent evidence has shown that this effect is predominantly or equally enthalpic in character.

Table 3.3 shows the incremental thermodynamics of partitioning of a methylene group in a homologous series between an aqueous and a hydrocarbon phase. There are relatively weak favourable enthalpic and large unfavourable entropic components in aqueous solution while in the hydrocarbon environment there is marked favourable enthalpy and weaker unfavourable incremental entropy. The thermodynamic contributions for transfer from the aqueous to the hydrocarbon phase then show the entropic and enthalpic components to produce similar difference contributions to the free energy transfer.

Table 3.3 Incremental thermodynamics of partitioning of the -CH2 group.

310°K

kcal mol 1

Partitioning phases

AG0

AH0

-TAS0

1. Cyclohexane/gas

-0.76

-1.12

+0.36

2. H2O/gas

+0.18

-0.67

+0.85

Cyclohexane/H2O

-0.94

-0.45

-0.49

(From Abraham (1982), by permission).

(From Abraham (1982), by permission).

Further insight into the cause of the hydrophobia effect comes from cavity models of solution. The unfavourable entropic effect on aqueous solvation appears to arise from the high number of states available to water and the resultant loss in entropy on forming a cavity to adapt the solvent. The free energy of solvation may be written as a sum of the free energies of formation of the cavity formation and of the solute-solvent interaction. Although the free energies of formation of the cavity are relatively similar in the aqueous and non-aqueous phases, the enthalpic and entropic components are quite different. In the non-aqueous phase, most of the work of cavity formation goes to the enthalpic maintenance of the excluded volume and only a small contribution to the entropy or configurational exclusion of volume; for water, the reverse is the case.

As molecules become progressively larger and structures more ordered, it is not possible to be categoric in the relation of forces to their resultant effects in solution, particularly when structural reorganisation becomes critical. Thus as more states become available, there is usually a weakening of enthalpy changes but a compensation in entropy effects. These compensatory effects can be shown to be large. The concept of molar concentration applied to thermodynamic changes in ordered structures such as liposomes is also less certain.

3.3.5 Some experimental observations—Thermodynamics of ligand binding to receptor proteins

The thermodynamics of binding of small ligand molecules within known protein sites should be computable to a good degree of accuracy. The difficulty lies not with the flexibility of the small ligand but with the uncertainty in accommodating the potential flexibility of the macromolecular structure when based on a crystal structure. The position may be exemplified by data on ligand binding to guanine nucleotide-coupled receptor proteins (GCPRs, refer to Plate 3.5) where the structures are not yet experimentally determined. The GCPRs are a dominant class of hepta-helical membrane-spanning proteins linking cytoplasmic events through a heterotrimeric GaPy-protein on the cytoplasmic side of the cell to a signalling hormone binding to the receptor. Typical data for binding of related phenoxypropanolamine ligands to a turkey erythrocyte P-adrenergic receptor are given in Table 3.4, a receptor closely related to the mammalian p1-adrenergic receptor. The prediction for the binding of the antagonist, propranolol from the weak partial agonist, practolol may be made with good accuracy. Practolol possesses a p-NHCOCH3 group, and data at the free energy level on the mammalian receptor are concordant with an -NH hydrogen bond proton donor interaction with the

Table 3.4 Flexibility of the protein and ligand hydration effects in the thermodynamics of binding of phenoxypropanolamine (a) and phenethanolamine (b) ligands to the turkey erythrocyte p-adrenoceptor. (a) Prediction of the binding of propanolol from practolol(t) and (b) adrenaline from isoprenaline(t).

Table 3.4 Flexibility of the protein and ligand hydration effects in the thermodynamics of binding of phenoxypropanolamine (a) and phenethanolamine (b) ligands to the turkey erythrocyte p-adrenoceptor. (a) Prediction of the binding of propanolol from practolol(t) and (b) adrenaline from isoprenaline(t).

receptor, not of particular strength and which can be modelled empirically using data from a long chain ester solvent. The main enthalpic difference between the binding of the two compounds is due to loss of hydration on the amidic C=O moiety of practolol. The structure-activity relations have indicated high flexibility in the hydrophobic residues surrounding given regions of the ligand and those residues surrounding the bound 2-substituents in phenoxy ring compounds show a receptor environment akin to a hydrophobic liquid accommodating even large substituents. Agonists on the other hand such as isoprenaline show a strong enthalpic binding with a marked negative entropy. Despite ~12 kcal/mol enthalpic difference in the binding, the free energies of binding of the agonist and antagonists are quite similar. Without some indication of the regions of flexibility of the protein residues and an understanding of the energetics controlling activation of the signal, small empiric perturbations about the structure of the known ligand might still offer the best way of achieving partial agonism even if a detailed crystal adrenoceptor structure were available. Given the crystal structure on the other hand, a theoretical mobilisation of the structure using molecular dynamics or molecular mechanics with developed potentials for the interactions of interest should provide a good thermodynamic prediction.

3.4 INTRAMOLECULAR FORCES AND CONFORMATION

3.4.1 Conformation in the gas phase. Intrinsic conformation

Intrinsic conformational preference in small molecules is a guide to interpretation in larger systems. Conformational preference in the gas phase is very largely dictated by the net outcome of electrostatic and bond orbital interactions. We have already commented on the repulsive or destabilising ('4 electron') interaction, the 'exchange repulsion', of occupied bond orbitals in the overlap of closed shells of electrons and the stabilising ('2 electron') interaction of an occupied bond orbital with an unoccupied antibonding orbital giving rise to some charge transfer. All chemists are familiar with the concept of delocalised (molecular orbitals arising from overlap of the atomic n orbitals allowing reactivity at a site remote from the site of substitution. A set of molecular orbitals can be given an equivalent representation in terms of local bond or group orbitals of the molecule. In the case of n orbitals, the resultant interaction may extend over several atomic centres. For singly bonded flexible systems, there are more localised bond orbital interactions from vicinal orbitals about the bond which can dictate or contribute to structural preference. A knowledge of bond or group orbital interactions can thus give insight into the resultant preferred conformation of flexible systems. The term hyperconjugation has been used to define the favourable interaction of these orbitals and in view of their importance in conformational studies, a wider simple introduction to bond orbitals and their interaction is given, following Jorgensen and Salem (1973).

3.4.2 General rules for the interaction between orbitals of different energy

1. When two orbitals interact, they yield a lower energy bonding combination and a

Introduction to the principles of drug design and action 74 higher energy antibonding combination

Introduction to the principles of drug design and action 74 higher energy antibonding combination

2. The destabilisation of orbital (energy EA) is always slightly larger than the stabilisation of orbital (energy EB and EB<EA).

3. Only energy levels which are close together interact strongly, the closer the better.

4. Only orbitals which overlap significantly interact.

5. If a given energy level interacts with several others of significantly different energy, the interactions are pairwise additive.

3.4.3 Examples of orbital interaction e.g. C-C c bonds, C-C n bonds

Two carbon p atomic orbitals interacting 'end on' (in this interaction there is zero angular momentum about the bond which is defined as a c interaction) are shown diagrammatically (Figure 3.1) to produce a c C-C orbital of lower energy and a c* C-C antibonding orbital. The atomic contributions are out of phase in the antibonding orbital and characterised by a node (where there is zero charge density). The two electrons occupy the lower bonding orbital and there is a net energy stabilisation on interaction.

Figure 3.1 Two carbon p orbitals interacting to produce a bonding o C-C orbital of lower energy and a higher o* antibonding orbital. (From Jorgensen and Salem (1973), by permission).
Figure 3.2 Interaction of 2p carbon atomic orbitals to produce n-orbital overlap for a double bond. (From Jorgensen and Salem (1973), by permission).

Figure 3.2 shows the interaction of 2p orbitals to produce a n orbital overlap, in the case of forming the second bond in a double bond. Three carbon orbitals lie in the plane at right angles to the paper, and the 2p carbon orbitals are perpendicular to them. On interaction, the higher energy n* antibonding orbital has the atomic contributions out of phase and there is now a nodal plane perpendicular to the C-C bond. The two electrons occupy the the lower energy n bonding orbital and there is net energy stabilisation. The carbon double bond is thus seen to consist of a c C-C bond and a n C-C bond.

In the case of azoborane the relevant atomic orbitals are the 2p nitrogen orbital containing the electron lone pair, and the vacant 2p boron orbital. On interaction there is net stabilisation in energy, the two electrons of the nitrogen atom occupying the N-B bonding orbital and a planar structure is formed (Figure 3.3).

When electron lone pairs are present in both orbitals as in hydrazine (3.1), the additional electrons would have to enter the n* antibonding orbital and from rule 2 (Section 3.4.2) the net energy would be destabilising. The hydrazine structure is thus staggered, with the electron pairs lying in a gauche position.

For the same reason the azadipeptide (3.2) would be expected to show no tendency to delocalize across the N-N bond and calculation shows the amidic groups to lie preferentially at 90° to one another. In the N,N dialkyl hydrazino group in the ring system (3.3) the X-ray structure shows the amidic groups to lie in a similar orientation (Figure 3.4) although other forces in this cyclic system may be acting.

For single bonds involving a heteroatom, the possibility exists that a vicinal atom may have a vacant antibonding orbital to produce 2-electron stabilisation. The strength of this interaction will be dependent on the energy difference between these orbitals and the

3.4.4 Electron donor-acceptor interaction

3.4.5 Hyperconjugation

Figure 3.3 Overlap of 2p nitrogen orbital

containing the electron lone pair and the vacant 2p boron orbital in azaborane (From Radom (1982), by permission).

extent of their overlap. In principle, any bonding-antibonding interaction will produce some effect but the highest occupied molecular orbital is usually that occupied by a heteroatom lone pair and the high energy of the localised orbital will have a dominant effect on structural preference. In the case of the vacant antibonding orbital, the more electronegative the neighbouring atom or its substituent, the lower will be its energy. The typical shapes of bonding and antibonding hybrid C-X orbitals are shown in Figure 3.5.

Maximum overlap of the bonding and antibonding orbitals tends to occur when the bonds of the neighbouring groups are antiperiplanar (trans), or in the case of the lone pair when it is similarly antiperiplanar to the C-X bond. The strongest hyperconjugative interaction will thus tend to occur when a heteroatom lone pair is antiperiplanar to an electronegative substituent. The anomeric effect in sugars or in substituted pyranose or

Figure 3.4 Structure of a fraction of the phthalazino (2,3-b)phthalazine-5,12-dione molecule. (From Cariati, Cauletti, Ganadu, Piancastelli and Sgamelloti (1980), by permission).

Figure 3.4 Structure of a fraction of the phthalazino (2,3-b)phthalazine-5,12-dione molecule. (From Cariati, Cauletti, Ganadu, Piancastelli and Sgamelloti (1980), by permission).

Figure 3.5 Bonding and anti-bonding C-H hybrid sp3 orbitals. The solid (dashed) lines represent orbital amplitude contours of positive (negative) phase. The position of the C-C bond in the fragments is indicated. The corresponding overlap of the orbitals (with the appropriate phase) may be judged by superposition of the two C-C bonds. Each contour corresponds to half the amplitude of the preceding one. (From Brunck and Weinhold (1979), by permission).

dioxan rings where an electronegative substituent lies preferentially axial is an example of an effect where bond orbital interaction dominates the conformer preference. The effect even so is not large being of the order 1-1.5 kcal mol-1 at blood temperature giving an axial to equatorial preference of 5-15:1.

Possible acetal conformations (3.4 a-f) are shown where R, R7 are alkyl substituents (Deslongchamps, (1983)). The antibonding orbitals of interest will lie on the bond with the electronegative oxygen heteroatom and be preferentially antiperiplanar to an oxygen atom electron lone pair. Conformers d, e and f have two anomeric effects, a and b have only one, while conformer c has no suitable bond orbital interaction. However, conformers e and f have steric repulsion from alkyl R7 substituents and the order of stability is found to be d, a, b, c with estimated energies of 0, +1.0, +1.9, +2.9 kcal mol-1 respectively.

An example involving the nitrogen lone pair is shown in the conformer preference of (3.5a) and (3.5b) where conformer (3.5b) has a 500-fold population preference.

3.4.6 General remarks

Conformer preference in flexible c bonded systems is more usually a balance between electrostatic, exchange repulsion and bond orbital effects. The favourable 'two electron' interaction has been emphasized here to give some insight into the structure of conformer preference. More detailed reading may be cited (Csizmadia (1982), Deslongchamps (1983)).

It is possible to estimate the relative components contributing to the conformer preference in saturated systems by the following considerations. Figure 3.6a shows eclipsed and staggered forms of an aliphatic system using Newman projections. On rotating about the bond there is an energy well or barrier every 60° due to the exchange repulsion and the rotation is three-fold symmetric. In the case of hyperconjugation, the rotation of the antibonding orbital through 90° minimises the interaction and there is a 2-fold interaction on rotation about the bond through 360° (Figure 3.6b). For an electrostatic interaction, on the other hand, there is a 1-fold interaction on bond rotation though 360° (Figure 3.6c). The components and their resultant interaction may thus be separated and are shown experimentally in Figure 3.7.

Ph OCH,

Figure 3.6 Relative components contributing to the conformer preference in a saturated aliphatic system (a) steric (b) bond orbital (c) electrostatic.

EfliiSr

Résultant

Êlectroitalin Q-rtilâl irtTiract nrt

Dihadrd inglt

Figure 3.7 Resultant interaction of components contributing to conformer preference illustrated in Figure 3.6 (from Radom (1982) by permission).

Dihadrd inglt

3.5 MOLECULAR MODELLING 3.5.1 Introduction

The term 'molecular modelling' embraces a wide definition and it is convenient to categorise approaches to modelling dependent on the degree of information known. Even where the target structure is totally unknown it should be possible to determine structural information from the target site ligand either by selective synthetic ligand constraints or by analysis of the available pharmacological data. Early development in the pharmaceutical industry relied on such methods utilising small perturbations about the structure of a target hormone and such methods continue to have strong utility. While the structural information obtained from such approaches is not independent of the mode of binding of the particular set of ligands, even here, there are indications of efficiency from the overall gross ligand potency. Synthetically-based identification of the bioactive conformers using constrained molecules aided by temperature studies on receptors using isolated membranes or intact cells 'in vitro' yield thermodynamic conformer binding data and quantitative information on the mode of binding which should allow determination of the geometry around localised bonds of the ligand in many instances and, importantly, allow for some decomposition of the energetics of the binding in closely related ligands. While considerable localised information on the target site can be obtained from such methods, selective binding to sites remote from the biological action remain elusive without wide-scale random screening.

There is an increasing data base on target macromolecules. The three dimensional structures of 4,000 now exist in the Brookhaven Protein Data bank and amino acid sequences of a further 150,000 are available. Structure-based ligand design is, therefore, a reality in a number of therapeutic areas. Plate 3.1 shows the localised

102 57

structure of a typical serine protease containing the characteristic Asp —His — Ser195 catalytic triad involved in the peptide bond rupture. The catalytic site of trypsin in the presence of the bovine pancreatic trypsin inhibitor shows the presence of an anionic site for preferential binding to basic residues involved in the peptide bond rupture. Plate 3.2 shows the inhibition of this site in the enzyme a-thrombin by the natural ligand inhibitor Hirudin where selective binding to remote 'exo-sites' is exemplified. A variety of simple logical approaches can be deployed to examine the possibilities of occupying the binding site efficiently. Their disadvantage in accurate prediction, as mentioned earlier, is the inability of the crystal structure to convey the varying degrees of flexibility within the site. The selective binding to remote sites, however, should be efficient and of great therapeutic advantage.

It will be convenient to classify possible predictions in terms of ligand, protein and DNA targets based on the scale and predictability of the problem. As we are concerned, here with ligand design, the main emphasis in this chapter will be to concentrate on the strategies available to rational ligand design both when the macromolecular structure is known and unknown. Examples of the scale of some interactions involving protein-protein, protein-single strand DNA and protein-double stranded DNA are given in Plates 3.4, 3.8 and 3.9. Plate 3.8 shows the binding of a zinc finger domain to a single strand of DNA while protein ocupancy of the major and minor grooves of a piece of double stranded DNA is shown in Plate 3.9.

3.5.2 Thermodynamics of ligand binding and conformer identification

When a ligand binds to a receptor or its target enzyme, often the energy of hydration is lost from most regions of the molecule and the interaction becomes essentially nonaqueous in character. It can, therefore, be useful to change the reference phase for binding to that of a model hydrocarbon liquid when simple correlations of potency and change in reference phase indicate the inherent flexibility of the target macromolecule in given regions of the molecule. Some consequences are exemplified in Section 3.3.5. Such correlations at the free energy level automatically introduce a good approximation to the van der Waals forces operating in the binding in closely related molecules. Often a 2-3 kcal/mol variation in observed binding is reduced to little more than 0.15 kcal/mol when introducing this reference change providing a useful base line for exploring other effects within a given mode of binding. As a major target is to maximize efficient binding it is important to identify whether the binding conformation is dominant or whether only a small fraction of the ligand productively binds to the macromolecule. It is useful, therefore, to represent the gross ligand binding constant in a conformer representation and to examine possible relations between the phase environment and the conformer representation (Davies (1987)).

In terms of standard partial free energies, the gross binding constant may be written as

where the subscripts AR, A and R refer to the complex, drug and receptor respectively, and k is the Boltzmann constant, T the absolute temperature.

Using second indices to identify the conformer i of the drug A engaged in binding, with j* its receptor counterpart, then, for the ij* conformer interaction, Equation [3.3] may be written

Using conformer populations f of A, and f* of R, and the relations

and summing over the bound states

where Kij*, the conformer binding constant is given by

The binding constant is a sum of the conformer binding constants weighted by their appropriate conformer fractions.

It is more convenient to define the conformer binding constant referenced to the average states of A and R.

It is often helpful to consider comparative drug binding with a change of reference to a hydrocarbon lipid phase L. The standard free energy change of A can then be written

and since jiV n*

where fL is the conformer fraction of i in a nonaqueous medium and Pi is the conformer-or micro- partition coefficient of the species i which, often, is easily estimated (Davies, Sheard and Taylor (1981)). It follows that

These relations may be observed from the free energy diagram in Figure 3.8. The appropriate thermodynamic relations may be similarly expressed. The two equations show the relations between conformer populations in aqueous and nonaqueous phases.

For a set of close analogues which bind to the receptor in the same way, Kij* f* is often invariant and the binding constant will vary directly with the relevant conformer fraction of the ligand. For a rotation about a single bond, the conformer population can be readily calculated from the rotamer energetics by use of the Boltzmann distribution. The reason that classical statistics can be applied to rotamer energetics is that, unless the barrier to rotation is very high, conformer interchange is very fast. The number of molecules with energy Ei is given by

The relative population between two states 1 and 2 is given by

More strictly, writing AG2-1 for the free energy difference between the two rotamers and taking logarithms

0 0

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