Dissociation constant, estimation

Black, J. W., Feff, P, Shankley, N. P., and Wood, J. (1985). An operational model of pharmacological agonism The effect of E/[A] curve shape on agonist dissociation constant estimation. Br. J. Pharmacol. 84 561-571. 

The dissociation constants of trityl and benzhydryl salts are KD 10 4 mol/L in CH2C12 at 20° C, which corresponds to 50% dissociation at 2-10-4 mol/L total concentration of carbocationic species (cf. Table 7) [34]. The dissociation constants are several orders of magnitude higher than those in analogous anionic systems, which are typically KD 10-7 mol/L [12]. As discussed in Section IV.C.l, this may be ascribed to the large size of counterions in cationic systems (e.g., ionic radius of SbCL- = 3.0 A) compared with those in anionic systems (e.g., ionic radius of Li+ 0.68 A), and to the stronger solvation of cations versus anions. However, the dissociation constants estimated by the common ion effect in cationic polymerizations of styrene with perchlorate and triflate anions are similar to those in anionic systems (Kd 10-7 mol/L) [16,17]. This may be because styryl cations are secondary rather than tertiary ions. For example, the dissociation constants of secondary ammonium ions are 100 times smaller than those of quaternary ammonium ions [39]. 

The C—H bonds of hydrocarbons show little tendency to ionize and alkanes alkenes and alkynes are all very weak acids The acid dissociation constant for methane for exam pie IS too small to be measured directly but is estimated to be about 10 ° (pK 60)... 

The observed rate constant is plotted on the vertical axis against pH on the horizontal axis. This plot is particularly suited for the estimation of dissociation constants. 

The initial goal of the kinetic analysis is to express k as a function of [H ], pH-independent rate constants, and appropriate acid-base dissociation constants. Then numerical estimates of these constants are obtained. The theoretical pH-rate profile can now be calculated and compared with the experimental curve. A quantitative agreement indicates that the proposed rate equation is consistent with experiment. It is advisable to use other information (such as independently measured dissociation constants) to support the kinetic analysis. 

This property of the sigmoid curve permits to be easily estimated. This is an advantage of the k-pH plot. If the inflection point cannot be accurately located, the dissociation constant may still be estimated. Let [H j = Ka in Eq. (6-64) then Eq. (6-66) results. 

This dependence of pHi n on the rate constants as well as the dissociation constant has sometimes been overlooked by authors evaluating log A -pH curves, and the literature contains examples of such plots that have been erroneously used to estimate p/c . 

The dissociation constant is most accurately estimated from kinetic data when all of the data points are used in the evaluation. There are several ways to do this. The Henderson-Hasselbalch equation... 

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. 

Equation 6.19 predicts an increasing IC50 with either increases in L or 1. In systems with low-efficacy inverse agonists or in systems with low levels of constitutive activity, the observed location parameter is still a close estimate of the KB (equilibrium dissociation constant of the ligand-receptor complex, a molecular quantity that transcends test system type). In general, the observed potency of inverse agonists only defines the lower limit of affinity. 

Aim To measin e the binding of a radioligand (or ligand that is traceable by other means) to a receptor. The object is to obtain an estimate of the equilibrium dissociation constant of the radioligand-receptor complex (denoted Kd) and the maximal number of binding sites (denoted Umax)-... 

In order to estimate the value of the dissociation constant of the TaF72 complex according to the aforementioned scheme (61), TaF72 = F + TaF6, analysis of the available volume values was performed using a modified method developed by Frank and Foster [329]. This method is based on two main initial assumptions. The first is that the dissociation constant remains... 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

Mass spectrometric studies yield principally three types of information useful to the radiation chemist the major primary ions one should be concerned with, their reactions with neutral molecules, and thermodynamic information which allows one to eliminate certain reactions on the basis of endothermicity. In addition, attempts at theoretical interpretations of mass spectral fragmentation patterns permit estimates of unimolecular dissociation constants for excited parent ions. 

Using these equations, Lowe and Walmsley [48] have calculated the dissociation constants for sugar binding at the extracellular surface of the membrane (K s = b a in Fig. 2) and at the cytoplasmic surface (K. = elf = bid) x [dgich]) from the estimated rate constants for carrier re-orientation and the measured Michaelis constants. The dissociation constant for binding at the extracellular surface of the membrane, calculated in this way, is approximately lOmM and is largely unaffec-... 

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