Conformational entropy is a crucial factor for molecular recognition, in terms of both multiple states and structural changes of the ligand and protein upon binding. The conformational entropy can be estimated from the statistical thermodynamics relationship between the number of states and entropy. With three-model signaling systems based on ligand and receptor recognition, this chapter clearly presents the dependence of binding free energy and ligand conformational entropy change. The first and foremost representative set of molecules includes antagonists of muscarinic receptors with both flexible and rigid scaffolds of carbon chains containing aromatic and aliphatic rings. The second set of molecules is constructed from tricyclic antidepressants, which are ligands of dopamine receptors, containing both rigid and flexible side chains. The third set of molecules compares only morphine and met-enkephalin as a pair of small rigid and large flexible ligand of opiate receptors. This chapter discusses the possible effect of the structural changes of the protein to conformational entropy.

The interest to conformational entropy is grounded in developing new drugs, as the term “conformational entropy” can be changed straightforwardly through structure modification. Considerable loss in conformational entropy might essentially restrict the overall binding affinity between a ligand and a receptor. Designing conformationally restricted ligands can have some advantages in avoiding such restrictions. However, there are known problems in the computation of conformational entropy. First, conformational entropy contribution is often implicit, as the varied structure of compounds occurs with alterations in many enthalpic and entropic factors as well as changes in conformational entropy. Second, only the total change in the ligand–receptor binding entropy can be determined through experiments.

The components of entropy change shown in Equation (4.11) can be estimated using computational, semi-quantitative, and empirical methods. For example, the method for the estimation of a ligand’s configurational entropy was proposed in a previous study [1], where conformational entropy (number of occupied energy wells) is only a part of the configurational entropy change (another part is vibrational entropy considering the width of the occupied energy wells).

Yet, we are interested in designing a model that can extract “pure” conformational contribution to entropy change. That is, the change in the structure of substances should presumably minimize the change in the enthalpy and components of the entropy not related to its conformational part. For such substances, it is convenient to choose mAChR antagonists with a common chemical structure—amino esters of substituted glycolic and acetic acids (Figure 5.1) previously discussed in Chapter 4.

The selected substances have a similar molecular weight and size, charge distribution, and basicity of the amino group and the same pharmacophore. In addition, anchoring cyclic substituents in the acidic part of the molecule have similar contributions (ΔΔG) to the mAChR binding free energy: for example, the contribution of phenyl, thienyl, and cyclohexyl groups to free energy change is −2.80, −2.95, and −2.40 kcal/mol, respectively (see Table 4.3). The chosen substances possess no selectivity to the subtypes of muscarinic acetylcholine receptors.