Equilibrium constant effective dissociation

RGS proteins (see Abramow-Newerly et al. 2006 De Vries et al. 2000 Druey 2001 Neitzel and Hepler 2006 Tinker 2006 Willars 2006 for reviews) comprise a wide and rather diverse family, with 30+ members, but with a common 120-residue RGS domain that enables binding to the G-protein a-subunit. The effect of this is to lower the energy requirement for GTP hydrolysis and hence to accelerate the GTPase activity of the a-subunit. This is reflected in the faster offset of Ga or Gpy-mediated effector responses noted above. Because the effective dissociation equilibrium constant for G-protein-effector interaction (Kdlss) is determined by l+ff/kon x G (where G is the concentration of activated G-protein), RGS-accelerated GTPase activity reduces effector response to agonist, effectively... 

The dissociation equilibrium constants that determine the formation of ABR and ABR are so large (i.e., the corresponding affinities are so small) that the quantities of these doubly liganded forms are negligible. In effect, the binding of A and B is mutually exclusive. If, in addition, the affinity of B for the active form of the receptor is very low,... 

When studying competitive antagonism, it is sometimes necessary to include an uptake inhibitor or a ganglion blocker in all the bathing solutions used. If this compound has in addition some competitive blocking action at the receptor being studied, what effect will this have on estimation of the dissociation equilibrium constant for a competitive antagonist ... 

Measurement of dissociation equilibrium constants, which is of particular value in receptor classification and in the study of structure/activity relationships, where the effects of changes in chemical structure on affinity (and efficacy) are explored. 

Temperature has effects on both the rates of reaction and dissociation equilibrium constants. A rise in temperature will increase the rates of both association and dissociation, as shown in Table 5.1... 

Studying the ESPT of hydroxy aromatic sulfonates, Huppert and co-workers [40-44] suggested an alternative model based on the geminate proton-anion recombination, governed by diffusive motion. The analysis was carried out by using Debye-Smoluchowskii-type diffusion equations. Their ESPT studies in water-methanol mixtures showed that solvent effects in the dissociation rate coefficient are equal to the effects in the dissociation equilibrium constant [45], 4-Hydroxy-1-naphthalenesulphonate in a water-propanol mixture as the solvent system has been found to behave somewhat differently than water-methanol or water-ethanol media, with a possible role of a water dimer [46,47],... 

The substituent has to interact with the reaction centre through a longer distance in the case of the dissociation of the 2-phenylpropionic acids compared with that of benzoic acids and hence its effect on the dissociation equilibrium constant is less. 

Photoprotolytic reactions in micellar solutions were systematically studied by the authors of the present review with coworkers [15, 16, 66, 120-122]. Effective dissociation rate constants ki for a set of hydroxyaromatic compounds in anionic, cationic and uncharged micelles were determined from the dependence of fluorescence quantum yields on the concentration of micelles [Eq. (22)] or on the concentration of acid [Eq. (49)]. The latter method was also used for determining the effective equilibrium constants and effective rate constants of the reverse protonation reaction [Eq. (49)]. The data obtained are presented in Table 3. 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

When a Br nsted plot includes acids or bases with different numbers of acidic or basic sites, statistical corrections are sometimes applied in effect, the rate and equilibrium constants are corrected to a per functional group basis. If an acid has p equivalent dissociable protons and its conjugate base has q equivalent sites for proton addition, the statistically corrected forms of the Br insted relationships are... 

The above observation is significant, Theoretical considerations 102,103,104), as well as some experimental studies 105,106), revealed an effect of excluded volume on the rates and equilibria of polymeric reagents. For example, the equilibrium constant of dissociation of high molecular weight aggregates (MW > 1(f) such as... 

This expression for the equilibrium constant is found to contain the term V in the denominator. Since K must remain constant, an increase in V would cause % also to increase. Stated in an another form, the dissociation of AB is favoured by a reduction in the pressure. A pressure increase would bring down V, and to maintain the constant value of K, x must decrease. Thus, a pressure increase would tend to inhibit the dissociation of AB. As in the previous case, it will be of interest in this case also to examine the effects of some other factors on the equilibrium. It is left to the readers as an exercise to establish for this case the following results (i) the effect of the addition of either A or B is to suppress the degree of dissociation of AB (ii) the addition of an inert gas at constant volume does not alter the degree of dissociation of AB and (iii) the addition of an inert gas at constant pressure increases the degree of dissociation of AB. 

In order to illustrate this principle, let the effect of temperature on the equilibrium constant of an exothermic reaction, involving the oxidation of a metal to its oxides, be considered. Upon increasing the temperature of this reaction some of the metal oxides will dissociate into the metal and oxygen and thereby reduce the amount of heat released. This qualitative conclusion based on Le Chatelier s principle can be substantiated quantitatively from the Varft Hoff isochore. 

In contrast to the reactions of the cycloamyloses with esters of carboxylic acids and organophosphorus compounds, the rate of an organic reaction may, in some cases, be modified simply by inclusion of the reactant within the cycloamylose cavity. Noncovalent catalysis may be attributed to either (1) a microsolvent effect derived from the relatively apolar properties of the microscopic cycloamylose cavity or (2) a conformational effect derived from the geometrical requirements of the inclusion process. Kinetically, noncovalent catalysis may be characterized in the same way as covalent catalysis that is, /c2 once again represents the rate of all productive processes that occur within the inclusion complex, and Kd represents the equilibrium constant for dissociation of the complex. 

The ratio k 1/k1 is effectively the dissociation equilibrium constant3 for ES in step (1), and is usually designated by Km (Michaelis constant, with units of concentration). The rate of formation of the product, P, is determined from step (2) 4... 

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