Rate constants for binding and

Affinity is expressed as the affinity constant ATa, which is the ratio between the rate constants for binding and dissociation of antibody and antigen. 

There are two important results from this analysis. First, the rate constants for binding and dissociation can be obtained from the slope and intercept, resp>ec-tively, of a plot of the observed rate versus concentration. In practice this is possible when the rate of dissociation is comparable to ki [S] under conditions that allow measurement of the reaction. At the lower end, resolution of i is limited by the concentration of substrate required to maintain pseudo-first-order kinetics with substrate in excess of enzyme and by the sensitivity of the method, which dictates the concentration of enzyme necessary to observe a signal. Under most circumstances, it may be difficult to resolve a dissociation rate less than 1 sec by extrapolation of the measured rate to zero concentration. Of course, the actual error must be determined by proper regression analysis in fitting the data, and these estimates serve only to illustrate the magnitude of the problem. In the upper extreme, dissociation rates in excess of 200 sec make it difficult to observe any reaction. At a substrate concentration required to observe half of the full amplitude, where [S] = it., the reaction would proceed toward equilibrium at a rate of 400 sec. Thus, depending upon the dead time of the apparatus, much of the reaction may be over before it can be observed at the concentrations required to saturate the enzyme with substrate. 

Unzai S et al Rate constants for O2 and CO binding to the alpha and beta subunits within the R and T states of human hemoglobin. J Biol Chem 1998 273 23150. 

Non-statistical successive binding of O2 and CO to the four heme centers of hemoglobin ( cooperativity ) has been thoroughly documented. It is difficult to test for a similar effect for NO since the equilibrium constants are very large ( 10 M ) and therefore difficult to measure accurately. It is found that the four successive formation rate constants for binding NO to hemoglobin are identical. In contrast, the rate constant for dissociation of the first NO from Hb(NO)4 is at least 80 times less than that for removal of NO from the singly bound entity Hb(NO). This demonstrates cooperativity for the system, and shows that it resides in the dissociation process. The thermodynamic implications of any kinetic data should therefore always be assessed. 

Alberty analyzed the anion effect on pH-rate data. He first considered a one-substrate, one-product enzyme-catalyzed reaction in which all binding interactions were rapid equilibrium phenomena. He obtained rate expressions for effects on F ax and thereby demonstrating how an anion might alter a pH-rate profile. He also considered how anions may act as competitive inhibitors. The effect of anions on alcohol dehydrogenase has also been investigated. Chloride ions appear to affect the on- and off-rate constants for NAD and NADH binding. See also pH Studies Activation Optimum pH... 

For reduced catalysts in solution, protonation competes with the reaction with CO2 (step 2 of Sch. 2). Protonation of the reduced metal results in the formation of a transition metal hydride, which may ultimately lead to the formation of hydrogen or formate. Protonation can be quite fast and favorable. For example, [Co (r c-Me6[14]4,ll-diene)]+ has binding constants of 2.5 x 10 and 2.5 x 10 pKa = 11.4) for the reaction with CO2 and protons, respectively [53]. Similarly, the rate constants for binding protons... 

Hassett, J. P., and E. Milicic, Determination of equilibrium and rate constants for binding of a polychlorinated biphenyl congener by dissolved humic substances , Envion. Sci. Technol, 19, 638-643 (1985). 

Just as in enzyme kinetics (see chapter 7), Km here is an algebraic function of the microscopic rate constants for binding, dissociation, and translocation of the substrate in either direction. 

The oxidation of homoserine by Cr(VI) has been compared with that of simple alcohols and 4-hydroxybutyric acid (HBA). The formation of CrOj during the oxidation was taken as evidence for the intermediacy of Cr(II). Whilst the rate law for homoserine has a first- and a second-order term, the rate laws for alcohols and HBA display only the second-order term. The second-order rate constants for HBA and homoserine are similar (suggesting that the ammo group of homoserine does not participate in binding to the chromium in this pathway), and about 10 times lower than for the alcohols, accounted for in terms of carboxylate binding to Cr(VI) in the intermediate ester (2), lowering the rate. The additional first-order term seen only for homoserine must arise from involvement of the amino group and this additional pathway is proposed to proceed via a tricyclic intermediate (l).13... 

The kinetics of binding of N02 to the four subunit methemoprotein, methemo-globin (metHb) were investigated. The rate constants for fast and slow reactions were comparable with literature values.325 The thermally derived activation parameters indicated that the reactions all proceed by a dissociative mechanism. It was predicted that hydrostatic pressure could affect the compressibility of the four subunits and quaternary structure of metHb, and therefore volume parameters of reliable value for the reactions of metMb would not be obtained. 

Waters CM, Oberg KC, Carpenter G, Overholser KA. Rate constants for binding, dissociation, and internalization of EGF effect of receptor occupancy and ligand concentration. Biochemistry 1990 29 3563-3569. 

The self-assembled diad Zn P-PH2P consisting of a zinc porphyrin donor and a free base porphyrin acceptor (Scheme 7.4) was studied by time-resolved fluorescence [21]. The driving force of the assembly is the site selective binding of an imidazole connected to a free base porphyrin. Evidence for Forster back transfer was obtained from the analysis of the fluorescence decay (Fig. 7.8) and the relevant rate was quantitatively evaluated for the first time. The transfer efficiency [13] is 0.98, and the rate constants for direct and back transfer were found to be 24.4 x 10 s and 0.6 X 10 s respectively. These values are consistent with the Forster energy transfer mechanism. 

The equilibrium dissociation constant, Ay, is a measure of binding affinity, defined as the free ligand concentration when 50% of the binding sites are occupied. It is equivalent to the ratio of the rate constants for dissociation and association, Ay = Arott/A on. Accordingly, the magnitude of Ay can be measured either at equilibrium, or as k0(flk0n. Several approaches have been used to measure these parameters in kinase drug discovery.34 Below, I outline some of the widely used methods. 

Erickson, J., Goldstein, B., Holowka, D., and Baird, B The effect of receptor density on the forward rate constant for binding of ligands to cell surface receptors. Biophys. J. 52, 657 (1987). 

Mathews. A.J. Olson. J.S. Assignment of rate constants for O2 and CO binding to alpha and beta subunits within R-and T-state human hemoglobin. Methods Enzymol. 1994, 232. 363-386. 

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