Association and dissociation rates

Note The apparent association and dissociation rates quoted here reflect the overall rates of complex formation and dissociation (i.e., they reflect the rate-limiting steps in the overall process of complex formation and dissociation). 

To distinguish between simple, reversible slow binding (scheme B) and an enzyme isomerization mechanism (scheme C), one can examine the dependence of kobs on inhibitor concentration. If the slow onset of inhibition merely reflects inherently slow binding and/or dissociation, then the term kobs in Equations (6.1) and (6.2) will depend only on the association and dissociation rate constants k3 and k4 as follows ... 

The interaction between the receptor and the G-protein is transient and rapidly reversible. This is indicated, for example, by the fact that a single light-activated rhodopsin molecule may activate 500 to 1000 transducin molecules during its 1 to 3 sec lifetime. Hence, the interaction should, in the endpoint, be governed by the normal laws of chemical interaction and expressible in terms of association and dissociation rate constants and binding affinity. The question then arises as to whether the affinity of different receptors for different G-proteins varies. That is, is there specificity in receptor-G-protein coupling, and, if so, what determines this ... 

Cramer and co-workers (1967) have recently measured rate constants as well as equilibrium constants for the association of p-nitrophenol and a series of azo dyes with cydohexaamylose. The general structure of the dyes employed in this study is illustrated in Fig. 4. p-Nitrophenol and p-nitro-phenolate bind to cydohexaamylose with rate constants of about 108 M l sec-1, near the diffusion-controlled limit. Within the series of dyes, however, binding rates decrease by more than seven orders of magnitude as the steric bulk of the dye is increased. Equilibrium constants, on the other hand, are roughly independent of the steric nature of the substrate, indicating that association and dissociation rates are affected by similar... 

The dynamics of a supramolecular system are defined by the association and dissociation rate constants of the various components of the system. The time-scale for the dynamic events is influenced by the size (length-scale) and by the complexity of the system. The fastest time for an event to occur in solution is limited by the diffusion of the various components to form encounter complexes. This diffusion limit provides an estimate for the shortest time scale required for kinetic measurements. The diffusion of a small molecule in water over a distance of 1 nm, which is the length-scale for the size of small host systems such as CDs or calixarenes, is 3 ns at room temperature. In general terms, one can define that mobility within host systems can occur on time scales shorter than nanoseconds, while the association/dissociation processes are expected to occur in nanoseconds or on longer time scales. The complexity of a system also influences its dynamics, since various kinetic events can occur over different time scales. An increase in complexity can be related to an increase in the number of building blocks within the system, or complexity can be related to the presence of more than one binding site. 

In a typical SPR experiment real-time kinetic study, solution flows over the surface, so desorption of the guest immobilized on the surface due to this flow must be avoided.72 In the first stage of a typical experiment the mobile reactant is introduced at a constant concentration ([H]0) into the buffer flowing above the surface-bound reactant. This favors complex association, and the progress of complex formation at the surface is monitored. The initial phase is then followed by a dissociation phase where the reactant is removed from the solution flowing above the surface, and only buffer is passed over the surface to favor dissociation of the complex.72 74 The obtained binding curves (sensograms) contain information on the equilibrium constant of the interaction and the association and dissociation rate constants for complex formation (Fig. 9). 

The values for k+ and k were compared for temperature jump and stopped-flow conditions for DNA concentrations where the decay followed a mono-exponential function and no migration between DNA molecules occurred (see below).94 This report shows the importance of detecting fluorescence signals at the magic angle, which eliminated the fast components in the kinetics due to artifacts. The values for the association and dissociation rate constants obtained by both techniques are similar. 

The apparent rate constant increased with the concentration of DNA and values for the association (ka) and dissociation (kd) rate constants were determined from the linear relationship of k° s with the sum of the association process (fJDNA]) and dissociation process (ka), equivalent to Equation (3) (Table 5). Note that the parameters k and kd will be employed when these values were determined from overall apparent rate constants to differentiate them from rate constants (k+ and k ) determined for an elementary process. The most important conclusion from this work is that despite similar equilibrium constants the association and dissociation rate... 

Table 5 Association and dissociation rate constants for anthraquinone derivatives with ct-DNA and polydeoxynucleotides from ref. 101...

Surface plasmon resonance studies were employed to measure the equilibrium constants and association and dissociation rate constants of bisnaphthalimide derivatives (20, 21) with hairpin DNA immobilized on the metal surface.123 The equilibrium constants were higher and the dynamics slower for compounds 20 and 21 when compared to the equilibrium constants and dynamics of the model monomer (19). The values for ka and kd were determined from the change in the surface plasmon resonance signal when, respectively, the ligand solution was flowed over the... 

Table 7 Association and dissociation rate constants for the binding of 22 to d(GCG-Y-GCG) complementary base paired oligonucleotides at 25 °C...

In the case where the arylsulfonate group is a benzene instead of a naphthalene the relaxation kinetics for guest complexation with a-CD measured by stopped-flow showed either one or two relaxation processes.185,190 When one relaxation process was observed the dependence of the observed rate constant on the concentration of CD was linear and the values for the association and dissociation rate constants were determined using Equation (3). When two relaxation processes were observed the observed rate constant for the fast process showed a linear dependence on the... 

Table 8 Equilibrium constants and association and dissociation rate constants for derivatives 27 and 28 with a-CD determined by temperature jump (27, T — 14 °C, I — 0.5 M), stopped-flow (28, T = 25 °C, /= 0.1 M) and with pressure jump experiments (29, T = 25 °C, /= 0.15 M)...

Compounds 30-32 formed 2 1 complexes with CDs (Scheme 13). The formation of the 1 1 complex was fast and for this reason only one relaxation process was observed. In the cases where the 2 2 complex was present its formation was also fast and only one relaxation process for the 2 1 complex was observed in the temperature jump experiments. Since the equilibria are coupled the expression for the observed rate constant includes Kt, (and K22 when the 2 2 complex is present), k21, k2, and the concentrations of guest, 1 1 complex and CD.180 182 The values for the association and dissociation rate constants and equilibrium constants were obtained from the non-linear fit of the dependence of kobs on the total concentration of CD (Table 9). 

Table 9 Equilibrium constants and association and dissociation rate constants for guests that form complexes with CDs with multiple stoichiometries...

Table 10 Association and dissociation rate constants of inorganic anions with /i-CD at 25 °C using a frequency range from 15 to 205 MHz166...

Global compartmental analysis can be used to recover association and dissociation rate constants in some specific cases when the lifetimes are much shorter than the lifetimes for the association and dissociation processes. An example is the study for the binding dynamics of 2-naphthol (34, Scheme 14) with / -CD.207 Such an analysis is possible only if the observed lifetimes change with CD concentration and at least one of the decay parameters is known independently, in this case the lifetime of the singlet excited state of 33 (5.3 ns). From the analysis the association and dissociation rate constants, as well as intrinsic decay rate constants and iodide quenching rate constants, were recovered. The association and dissociation rate constants were found to be 2.5 x 109M-1 s 1 and 520 s 1, respectively.207... 

Table 15 Equilibrium constants in the ground (K) and excited state (AV) and association and dissociation rate constants for guest molecules with fi—CD200...

Sigmundsson K., Masson G., Rice R., Beauchemin N., and Obrink B. (2002), Determination of active concentrations and association and dissociation rate constants of interacting biomolecules an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification, Biochemistry 41, 8263-8276. 

Using a glassy carbon electrode modified with a mercury film, Weber et al. [66] measured the association and dissociation rate constants for the complex formed between Pb + and the 18-crown-6 ether. It was found that Pb + forms a complex with 18-crown-6 with a stoichiometiy of 1 1 in both nitrate and perchlorate media. The formation constant, for the nitrate and perchlorate systems are (3.82 0.89) X 10 and (5.92 1.97) x lO mol Ls , respectively. The dissociation rate constants, are (2.83 0.66) x 10 with nitrate and (2.64 0.88) x 10 s with perchlorate as counter ion. In addition, the binding of Pb + with benzo-18-crown-6 embedded in a polymerized ciystalline colloidal array hydrogel has been also analyzed [67]. 

Figure 3.14 shows the results of mathematical modeling experiments that simulate the ALIS response for a protein-ligand complex versus time when subjected to changes in inhibitor concentration and variation in other parameters. Figure 3.14A models a system consisting of 5 xM protein and 1 pM ligand with typical association and dissociation rates (ks.on=0-l s, ks-off = 0.01 s ... 

Kao and Tsien studied the Ca +-binding kinetics of fura-2 and azo-1 by temperature-jump relaxation methods. In 140 mM KCl at 20°C, the respective association and dissociation rate constants for fura-2 were 6x10 M s and 97 s these kinetic properties were insensitive to hydrogen ion concentration over the pH range from 7.4 to 8.4. Azo-1 was studied in 140 mM KCl At 10°C, azo-... 

Surface plasmon resonance (SPR) M Mass-induced refractive index change in real time for direct measurement of association and dissociation rate constants... 

The association and dissociation rates are especially slow for the AEC complexes of the relatively rigid ligand 30, which is thus efficiently poisoned by Ba2+ and Sr2+ cations. 

Fast association and dissociation rates require that the ligand be flexible (fast association) and that the complexes be not too stable (fast dissociation). 

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