Conformational equilibrium constant

Thermodynamically it would be expected that a ligand may not have identical affinity for both receptor conformations. This was an assumption in early formulations of conformational selection. For example, differential affinity for protein conformations was proposed for oxygen binding to hemoglobin [17] and for choline derivatives and nicotinic receptors [18]. Furthermore, assume that these conformations exist in an equilibrium defined by an allosteric constant L (defined as [Ra]/[R-i]) and that a ligand [A] has affinity for both conformations defined by equilibrium association constants Ka and aKa, respectively, for the inactive and active states ... 

Thus, as described by Equation (2.1), the equilibrium dissociation constant depends on the rate of encounter between the enzyme and substrate and on the rate of dissociation of the binary ES complex. Table 2.1 illustrates how the combination of these two rate constants can influence the overall value of Kd (in general) for any equilibrium binding process. One may think that association between the enzyme and substrate (or other ligands) is exclusively rate-limited by diffusion. However, as described further in Chapter 6, this is not always the case. Sometimes conformational adjustments of the enzyme s active site must occur prior to productive ligand binding, and these conformational adjustments may occur on a time scale slower that diffusion. Likewise the rate of dissociation of the ES complex back to the free... 

The study of receptor-ligand binding is one of the most important applications of free energy simulations [1]. To approach this problem theoretically, one must first partition the conformational space into bound and unbound states. There is no unique way to do this, but in practical situations there is often a natural choice. The equilibrium binding constant is... 

The conductivity of salts in solvents of low dielectric constant, and of metals in liquid ammonia, exhibit minima which may be explained in terms of an equilibrium between ions and a coulombic compound of two ions, or "ion pairs." This equilibrium conforms to the law of mass action. At limiting conductance in solutions of sodium in liquid ammonia, part of the current is carried by metal ions, but seven-eighths is carried by electrions. Following the BLA model, it is assumed that when two ion pairs, consisting of a sodium ion and an electron, come together, the spins of the two electrons couple to form disodium spinide. Increase in conductivity past the minimum is assumed to be caused by dissociation of disodium spinide into sodium ions and spinions. 

When sodium chloride is dissolved in water at ordinary temperatures, it is practically completely dissociated into sodium and chloride ions which, under the action of an external field, move in opposite directions and independently of each other subject to coulombic interactions. If, however, sodium chloride is dissolved in a solvent of lower dielectric constant, and if the solution is sufficiently dilute, there is an equilibrium between ions and a coulombic compound of the two ions which are commonly termed 4 ion pairs. This equilibrium conforms to the law of mass action when the interaction of the ions with the surrounding ion atmosphere is taken into account. In solvents of very low dielectric constant, such as the hydrocarbons, sodium chloride is not soluble however, many quaternary ammonium salts are quite soluble, and their conductance has been measured. Here at very low concentrations, there also is an equilibrium between ions and ion pairs which conforms to the law of mass action but at higher concentration, in the neighborhood of 1 X 10 W, or below, a minimum occurs in the conductance. Thereafter, it may be shown that the conductance increases continuously up to the molten electrolyte, provided that a suitable electrolyte and solvent are employed which are miscible above the melting point of the electrolyte. 

Finally, the rate of copolymerization should be slow enough. This guarantees that, during the chemical reaction, the equilibrium concentration fields remain approximately constant, and the growing chain has an equilibrium conformation between successive attachments of the monomers. Therefore, the CDSD regime is realized when... 

Fig. 6. A multistate model of receptor function with three states. The receptor population consists of an inactive receptor conformation (R) in equilibrium with two (or more) active receptor conformations (R and R ). Each active conformation can differentially activate effector mechanisms, leading to response 1 or response2 in the absence of an agonist. Two isomerization constants (L and M) define the propensity of the receptor to adopt an active conformation in the absence of a ligand. Agonists can differentially stabilize R vs R depending on the value of the equilibrium dissociation constants KA and KA relative to KA. Inverse agonists can also have differential effects on response 1 vs. response2 depending upon the relative values of L and M and of the affinity constants. Additional active states with additional isomerization and affinity constants can be added. Adapted from Leff et al. (86) and Berg et al. (22).

The photocyclization of o-alkoxy phenyl ketones to yield benzofuranols (57 and 58) represents one of the earliest example of 8-H-abstraction from the lowest n, n triplet Wagner et al. [18] have provided detailed photokinetic data studying the photocyclization of a variety of o-alkoxyphenyl ketones 56, and have revealed that quantum efficiency for cyclization for 56d was the lowest (0.023) and that for 56f the highest (1.00). The diastereoselectivity for cyclization of 56 was found to be higher in benzene and lower in polar solvents. From the estimated kH values (0.6-25 x 106 s 1), it was inferred that the low rate constant for 56e (8 x 106 s ) compared to that for 56g (25 x 106s 1) i s due to the alkyl chain in the alkoxy groups that points away from the o-carbonyl moiety in the most populated equilibrium conformations (Table 8.1). 

Figure 2.6. Schematic representation of the dependence of the ET constants logarithm on the equilibrium Gibbs energy AG0 1, non-equilibrium conformational and solvational processes 2, partial non-equilibrium processes, J.n and AGoneq are slightly dependent on AG0 3, equilibrium processes. Arrows a and b are conditions for the maximum X = AGo and A.1 1 = AGonK respectively. (Likhtenshtein, 1996). Reproduced in permission.

The orientational mechanism of EB in solutions of r id-chain polymers and the possibility of determining rotatory diffusion constants of their molecules from dispersion curves may be utilized for the characterization of equilibrium conformational properties of their drains. The theory of rotational friction of kinetically rigid molecules developed by Hearst makii% use of the statistics of worm-like chains can be employed for this purposes. The results of this theory for the two limiting cases of molecular conformation refering to the slightly bent rod and the worm-like coil are expressed by Eqs. (27) and (28) (Sect. 2.3). 

Van der Waals complexes ean be observed speetroseopieally by a variety of different techniques, including microwave, infrared and ultraviolet/visible speetroseopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forees between stable moleeules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sourees of information available on intermolecular forces, especially in the region aroimd the potential minimum. The measured rotational constants of Van der Waals complexes provide information on intermoleeular distances and orientations, and the frequencies of bending and stretching vibrations provide information on how easily the complex can be distorted from its equilibrium conformation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

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