Agconf Conformational Changes of Ligand and Receptor

The restriction of motions that are accounted for in AGtransl+rot described above refer to the "overall" motion of the molecule. However, there is an additional type of motion, which is more or less frozen upon ligand binding. Most ligand molecules are flexible, which means that in the aqueous phase outside the binding cavity in the protein, the ligand undergoes conformational changes by rotation about single bonds. For example, the dihedral angles in hydrocarbon chains changes between gauche and anti conformations resulting in a mixture of ligand conformations, i.e. different ligand shapes. A ligand generally binds to a protein in a single well-defined conformation that positions functional groups used for binding in appropriate locations in space for interactions with their binding partners in the protein. This implies that the motions corresponding to the conformational freedom in aqueous solution are to a large extent frozen in the binding site. As discussed above for AGtransl+rot, this leads to a decrease in the entropy (conformational entropy) giving a more negative AS and TAS and thus a free energy cost for binding. The magnitude of AGconf due to TASconf has been estimated to be 1-6 kJ/mol per restricted internal rotation and depends on the "tightness" of the ligand-protein complex as in the case of AGtransl+rot (Section 1.3.1).

A second energy contribution to AGconf comes from changes in ligand conformation between aqueous solution and ligand-protein complex. Comparisons of ligand conformations observed in x-ray structures of ligand-protein complexes and ligand conformations in aqueous phase (as calculated by state-of-the-art computational methods) show that a ligand in general does not bind to the protein in its preferred conformation (lowest energy conformation) in aqueous solution. An example of this is shown in Figure 1.4. Palmitic acid prefers the well-known all-anti (zigzag) conformation of the hydrocarbon chain in aqueous solution, but binds to the adipocyte lipid-binding protein with an affinity (Ki) of 77 nM in a significantly folded conformation. The energy required for palmitic acid to adopt the binding conformation has been calculated to be 10.5 kJ/mol. This conformational energy penalty is detrimental to binding and has the effect of increasing the Ki value in comparison to a case in which the ligand binds in its preferred conformation in aqueous solution.

As shown in Section 1.2, a conformational energy penalty of 5.9 kJ/mol corresponds to a decrease in affinity (increase of Ki) by a factor of 10. For each additional 5.9 kJ/mol of conformational energy penalty, the affinity decreases further by a factor of 10. It is consequently of high importance in the design of new ligands using x-ray determined protein structures (see Chapter 2) or pharmacoph-ore models (see Chapter 3) to avoid introducing significant conformational energy penalties in the designed ligands. Calculations of the conformational energy penalties for ligands in a series of x-ray structures of ligand-protein complexes indicate that these energy penalties in general are below 13 kJ/mol. This may be used as a rule of thumb in ligand design. In this context, it is important to

Lowest energy conformation in aqueous solution

Bioactive conformation + 10.5 kJ/mol

FIGURE 1.4 (a) Palmitic acid bound to the adipocyte lipid-binding protein (pdb-code 1LIE) and (b) the preferred conformation of palmitic acid in aqueous solution and the conformation bound to the protein.

FIGURE 1.5 (a) Epibatidine (orange) bound to the AChBP. The orange C-loop belongs to the epibatidine-AChBP complex (pdb-code 2BYQ), the green C-loop belongs to the uncomplexed AChBP (apo-form, pdb-code 2BYN). (b) a-conotoxin Iml (yellow carbons) bound to AChBP (pdb-code 2BYP). The yellow C-loop belongs to the a-conotoxin Iml-AChBP complex, the green C-loop belongs to the uncomplexed AChBP.

FIGURE 1.5 (a) Epibatidine (orange) bound to the AChBP. The orange C-loop belongs to the epibatidine-AChBP complex (pdb-code 2BYQ), the green C-loop belongs to the uncomplexed AChBP (apo-form, pdb-code 2BYN). (b) a-conotoxin Iml (yellow carbons) bound to AChBP (pdb-code 2BYP). The yellow C-loop belongs to the a-conotoxin Iml-AChBP complex, the green C-loop belongs to the uncomplexed AChBP.

note that in calculations of conformational energy penalties, the conformational properties of the unbound ligand "in aqueous phase" must be used as the reference state (see Further Readings).

In terms of AGconf, rigid molecules have an advantage relative to more flexible ligands. The binding of a rigid ligand does not result in a loss of conformational entropy and if the ligand has only one possible conformation (or has one strongly preferred conformation corresponding to the binding conformation), the conformational energy penalty is zero. Although highly rigid molecules are ideal as ligands, it is a great challenge to design such ligands. For instance, functional groups taking part in interactions in the binding cavity have to be designed to occupy precisely correct positions in space, as no (or very small) adjustments of their positions are possible in a rigid ligand.

So far only conformational changes in the ligand have been discussed, but conformational changes most often also occur in the protein. Not only may the amino acid side chains adjust their conformations to optimize their interactions with the ligand, but the protein backbone conformation may also change. In some cases, this may result in major movements of, for example, loops or even entire protein domains. Examples of such movements are shown in Figure 1.5. The C-loop in the acetylcholine binding protein (AChBP) and most probably also the corresponding loop in, for example, nicotinic acetylcholine and GABAa receptors adjusts its position in response to the size of the ligand (Figure 1.5). This has implications for the pharmacological profile of the ligand (see also Chapter 16).

Protein flexibility is a major challenge in structure-based drug design (see Chapter 2) and is currently the focus of much research.

1.3.3 Agpo|ar—Electrostatic Interactions and Hydrogen Bonding

AGpolar is the free energy change due to interactions between polar functional groups in the ligand and polar amino acid residues and/or C=O and NH backbone groups in the binding cavity of the protein. In addition, indirect ligand-protein interactions via water molecules in the binding cavity are frequently observed. These interactions include ion-ion, ion-dipole, and dipole-dipole interactions, which are well described in books on physical chemistry to which the reader is referred to for details. The attraction between opposite charges or antiparallel dipoles plays an important role in ligand-protein recognition.

The strength of any electrostatic interaction (Epolar) is given by Coulomb's Law (Equation 1.6):

where q and qj are integer values for ion-ion interactions and partial atomic charges (summed over the participating atoms) for other polar interactions e is the dielectric constant Tj is the distance between the charges

In Equation 1.6, it is important to note that the electrostatic energy Epolar depends on the dielectric constant (e), which measures the shielding of the electrostatic interactions by the environment. The dielectric constant of water is 78.4 (25°C). Epolar is difficult to quantify in proteins as e is not uniform throughout the protein but depends on the microenvironment in the protein. A value of about 4 is often used for a lipophilic environment in the interior of a protein.

The relative strength of the different types of electrostatic interactions is ion-ion > ion-dipole > dipole-dipole. Ion-ion interactions do not depend on the relative orientation of the interacting partners, whereas ion-dipole and dipole-dipole interactions are strongly dependent on the relative orientation of the interacting moieties. For instance, the interaction between antiparallel dipoles is attractive, whereas that between parallel dipoles is repulsive.

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