Equilibrium-binding constants

The equilibrium binding constant for this 1 1 association is Xu = ki/lLi. The Xu values were measured spectrophotometrically, and the rate constants were determined by the T-jump method (independently of the X,j values), except for substrate No. 6, which could be studied by a conventional mixing technique. Perhaps the most striking feature of these data is the great variability of the rate constants with structure compared with the relative insensitivity of the equilibrium constants. This can be accounted for if the substrate must undergo desolvation before it enters the ligand cavity and then is largely resolvated in the final inclusion complex. ... 

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... 

Ballistrieri, L. S., and J. W. Murray (1983), "Metal-Solid Interactions in the Marine Environment Estimating Apparent Equilibrium Binding Constants", Geochim. Cosmochim. ActaAl, 1091-1098. 

A second use of this type of analysis has been presented by Stewart and Benkovic (1995). They showed that the observed rate accelerations for some 60 antibody-catalysed processes can be predicted from the ratio of equilibrium binding constants to the catalytic antibodies for the reaction substrate, Km, and for the TSA used to raise the antibody, Kt. In particular, this approach supports a rationalization of product selectivity shown by many antibody catalysts for disfavoured reactions (Section 6) and predictions of the extent of rate accelerations that may be ultimately achieved by abzymes. They also used the analysis to highlight some differences between mechanism of catalysis by enzymes and abzymes (Stewart and Benkovic, 1995). It is interesting to note that the data plotted (Fig. 17) show a high degree of scatter with a correlation coefficient for the linear fit of only 0.6 and with a slope of 0.46, very different from the theoretical slope of unity. Perhaps of greatest significance are the... 

In some instances, flow cytometry assays are a superior alternative to conventional procedures for the determination of equilibrium binding constants (Stein et al., 2001). In contrast to assays that employ radiolabelled ligands, which measure population mean values for binding constants, flow cytometry methods can measure those values in individual cells, revealing heterogeneity in receptor expression within a population of cells or membrane vesicles. Furthermore, small samples can be characterized in a short period of time (hours). This approach to receptor-binding analysis may be limited only by the availability of a properly characterized fluorescent ligand. 

Stein RA, Wilkinson JC, Guyer CA, Staros JV. 2001. An analytical approach to the measurement of equilibrium binding constants application to EGF binding to EGF receptors in intact cells measured by flow cytometry. Biochemistry 40 6142-6154. 

In particular, the 1/2-met T3 site In T2 has EPR spectra and equilibrium binding constants =10 M for exogenous ligands... 

Many of the 60 known reactions catalyzed by monoclonal antibodies involve kinetically favored reactions e.g., ester hydrolysis), but abzymes can also speed up kinetically disfavored reactions. Stewart and Benkovic apphed transition-state theory to analyze the scope and limitations of antibody catalysis quantitatively. They found the observed rate accelerations can be predicted from the ratio of equilibrium binding constants of the reaction substrate and the transition-state analogue used to raise the antibody. This approach permitted them to rationalize product selectivity displayed in antibody catalysis of disfavored reactions, to predict the degree of rate acceleration that catalytic antibodies may ultimately afford, and to highlight some differences between the way that they and enzymes catalyze reactions. 

Fig. 8.13 (A) Dependence of C2HC13 consumed and concentration of products on initial concentration of C2HC13 reaction time was 19 s, light intensity was 0.046 min 1. (B) Plot of CqX/ln(l-.A ) vs tHr (l-X) The straight line showed the relationship —1 IkK + CoXJk x - X) — mtlIn(l-X), where C0 is initial concentration of C2HC13, X is the conversion ratio at time = t, which is calculated as C0 - C, (the concentration at time = t) /Cc m is the mass of Ti02 (1.3 g), k is the rate constant of the surface reaction and K is the equilibrium binding constant. (From S. Kutsuna et al., Atmos. Environ., 27A, 599 (1993))...

The secondary bonds, which may be formed much more slowly than the primary bonds, actually contribute more to the overall affinity. For example, the primary (Coulombic) bond between bovine serum albumin (BSA) and anti-BSA IgG is 3.3kcalM 1 whereas the secondary bond (van der Waals) is 28kJ, for a total AH = 42 kJ. Because the formation of the secondary bond is much slower, it is easier to prevent formation of the strong complex rather than to try to dissociate it. This is one reason why the competitive immunoassays yield results that correlate with the equilibrium-binding constants, but any such direct-binding assays have to rely on the measurement of the initial rate of binding. 

In contrast to [E]free, [E]total is observable. Eq. (2.3) is written with fCM, the Michaelis constant, instead of the equilibrium binding constant Ks unless the enzyme reaction is very fast (Section 2.3.3.) i.e., in almost all cases, fCM = Ks. In Eq. (2.3), the reaction rate is traditionally denoted by v [concentration/time] and fccat is the reaction rate constant [time4]. The equation describes a two-parameter kinetics, with a monotonically rising reaction rate with respect to substrate concentration and saturation at high substrate concentration. The maximum reaction rate at saturation is denoted by vmax, with vmax = fccat[E], The fCM value corresponds to the substrate... 

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