## Thermodynamic Analysis

One approach that has the potential of distinguishing between the effects of agonists and antagonist on the receptor is to evaluate the thermodynamic properties of their receptor interactions [73-75]. This approach is based on the premise that differences in the interaction of agonists and antagonists with receptors would be reflected in differences in enthalpy and/or entropy, the factors that determine free energy change (G). Enthalpy (H) is the heat content of a substance per unit mass and reflects the internal energy in the system. Entropy (S) is a measure of the randomness or disorder of the system. Changes in enthalpy and entropy associated with a chemical reaction are related to the change in free energy by the following equation, which holds for conditions of constant temperature, volume and pressure:

AH is the change in enthalpy; T is the absolute temperature; and AS refers to the change entropy. AG is the difference in free energy of the reactants and the products. A reaction will be favored if the free energy associated with the products is lower than that associated with the reactants. There is a net loss of free energy when the product is formed. AG can be related to the equilibrium constant (Kequil) which is the reciprocal of the dissociation constant, KD, by the following equation:

AG is the free energy change under standard conditions. When a chemical reaction reaches equilibrium, AG = 0 and the equation becomes:

-equil

equil

Substituting the dissociation constant (KD) for Kequji:

At standard conditions:

Combining equations [74] results in the Van't Hoff Equation:

When ln KD is plotted against l/T, a straight line is formed with a slope of AH°/R and a Y intercept of AS°/R. Since R is the gas constant which is known, AH° and AS° can be calculated.

One problem with interpreting changes in enthalpy and entropy is that changes in thermodynamic properties associated with the binding of a drug to a receptor may reflect a summation of chemical changes associated with the interaction process. These include such interactions as the binding of the drug to receptor recognition site, changes in the specific conformation of the receptor as a result of the binding of an agonist, changes in the nonspecific conformation of the receptor as a result of binding of an antagonist, the interaction of an agonist-receptor complex with a membrane component, hydrophobic bonding resulting from the interaction of lipophilic groups on the drug with the membrane, displacement of water molecules surrounding the drug and receptor, among others. Therefore, changes in enthalpy and entropy may reflect over all drug effects other than those mainly concerned with the drug-receptor interaction.

While a variety of receptors have been studied, it has been generally difficult to distinguish between the effects of agonists and antagonists on the basis of differences in their thermodynamic properties. The most interesting results are from studies of P-adrenoceptors [73,76,77]. Based on calculations from studies of the binding of ligands to membranes at different temperatures, it has been found that antagonist binding to the P-adrenoceptor produces a negative free energy that is due to large changes in entropy. The latter was postulated to be due to hydrophobic binding. Agonist binding was also associated with a decrease in free energy, but it was largely attributed to an increase in enthalpy, which was able to overcome a concomitant small decrease in entropy. Studies of the thermodynamic changes produced by agonists and antagonists were also done on solubilized P-adrenoceptors, and the changes in entropy and enthalpy for agonists and antagonists were similar to those reported for membrane bound receptors. This suggests that the enthalpy and entropy changes associated with agonist binding to receptors in the low affinity state is not related to interactions with the lipid membrane environment of the receptor or the interaction of the agonist-receptor complex with G protein.

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