Association rate constant, kon

All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

The association rate (or on-rate ) can be likewise defined as the product of the association rate constant kon, in units of s the concentration of free pro-... 

As mentioned above in a qualitative sense, it can be seen from this equation that, for a given association rate constant kon, lower value of dissociation rate constant koff yields a smaller value of Ka and hence a higher equilibrium concentration of the desired protein-ligand complex. 

Reactions of NO were also studied with the synthetic heme protein discussed earlier, namely the recombinant human serum albumin (rHSA) with eight incorporated TPPFe derivatives bearing a covalently linked axial base, were also investigated. The UV-vis absorption spectrum of the phosphate buffer solution at physiological pH showed absorption band maxima at 425 and 546 nm upon the addition of NO to form the nitrosyl species, which was also formed when the six-coordinate CO-adducts were reacted with NO gas. EPR spectroscopy revealed that the albumin-incorporated iron(II) porphyrin formed six-coordinate nitrosyl complexes. It was observed that the proximal imidazole moiety does not dissociate from the central iron when NO binds to the trans position. The NO-binding affinity P1 /2no was 1.7 X 10 torr at pH 7.3 and 298 K, significantly lower than that of the porphyrin complex itself, and was interpreted as arising from the decreased association rate constant (kon(NO), 8.9 x 10 M s" -1.5 x 10 M s ). Since NO-association is diffusion controlled, incorporation of the synthetic heme into the albumin matrix appears to restrict NO access to the central iron(II). ... 

Nevertheless, one should note that it is not straightforward to compare the stability of structures with different molecularities. For example, the comparison of equilibrium association constants for unimolecular, bi- or tetramolecular quadruplexes is meaningless, as these constants are not expressed in the same units (unit-less, M and respectively). Similarly, a comparison of the AG° might be deceptive. For example, if one compares an intramolecular structure with a bimolecular one (self-complementary) which have the same Tm = 60°C at 1 pM strand concentration, one will determine a hG°(Tm) of 0 and —9.2 kcal moN respectively. Does this mean that the intermolecular complex is more stable Clearly not One faces a similar problem when comparing association rate constants (kon), which are expressed in s ... 

The rate of binding of two molecules A and B and formation of their complex AB can be quantified by the bimolecular association rate constant (on-rate constant), kon, whereas their unbinding is characterized by the dissociation rate constant (off-rate constant), kog. 

When the concentrations of injected ligase were increased in the range of 0.47-11.3 nM, binding amount showed a typical saturation curve. Binding and dissociation rate constants (kon and koff) and the association constant (fCa) could be obtained from time courses of Fig. 7. Results are summarized in Table 1. When the length of the terminal end increases or the terminal phos-... 

Because the interaction of isolated receptors and ligands in solution is typically close to a reaction-limited situation (as seen in the previous section), kon is essentially the association rate constant that would be experimentally measured for an isolated receptor in free solution if there... 

Fig. 10. Variation of the per receptor association and dissociation rate constants, fcf and kr, with the number of free receptors. Although the assumption is typically made that kt and kT are constants, this is not strictly true when diffusion effects are significant [see Eqs. (41) and (43)]. (fcf)maxrec and ( r)maxrcc> the maximum values of kt and kt, are given by kon and k0fl. The per cell association rate constant (kt )tdl also varies with the number of free receptors [see Eq. (40)] the maximum value (fcf)masCeii is given by (k + )ccll. 0 is the fractional surface coverage of cell area by receptors. For calculation of , s - 10 nm, a = 10 /nm, kon = 107 M 1 s , and D — 10-6 cm2/s.

Figure 7.28 Schematic illustration of sensograms. Real time observations of change in resonant angle Yt with receptor-ligand association (a, b, c etc) are used to determine values of unimolecular rate constant kon as a function of total ligand concentration [L]o. A wash step is then introduced to promote realtime dissociation of ligand from receptor. Subsequent real time changes in Yt with dissociation are used to determine values of unimolecular rate constant k tss-...

The binding of a small molecule ligand to a protein receptor follows a bimolecu-lar association reaction with second-order kinetics. For the reversible reaction of a ligand L and a protein P to form a non-covalendy bound complex C at equilibrium, Eq. (1) applies where kon and kgS represent the forward and reverse mass transfer rate constants. 

It should also be noted that when the rate of change in the protein-ligand complex concentration is zero (by definition, when the system is at equilibrium), this equation reduces to the equilibrium expression below, with the binding affinity constant defined as the ratio of the dissociation rate koff to tho association rate kon-... 

If [SJ > [E], the reaction is effectively first-order since the concentration of S is hardly affected by the reaction. If the second-order rate constant for the association is kon and that for dissociation is koff, then the system reduces to... 

Another alternative to occupancy theory is rate theory. Rate theory was developed by Paton through examination of receptors that bind stimulants.30 Paton proposed that a response is caused by the act of binding, not the state of being bound or free (Scheme 5.8). This seemingly subtle difference shifts the theory away from KD and toward kon and fcoff, the rate constants of association and dissociation. Interestingly, at equilibrium, KD is equal to koa/kon (Equations 5.19-5.21). For this reason, occupancy and rate theory are closely related. 

When pc 1, there is no limitation of association or dissociation by ligand diffusion, so ks = kon and k = koU are constants, as had been assumed in our analyses in previous sections. However, as p becomes comparable to 1, diffusion begins to have an influence on the rates of these processes. For the case of ligand binding to cell surface receptors when p is comparable to 1, the rate constants kf and kr are functions of R and, through (Ar + )cdl, the diffusion coefficient. 

Figure 4.24 Model for ligand binding to cell surface receptors. A single cell with R receptors is held in medium containing ligand at bulk concentrations Cl o- The system is characterized by rate constants for the intrinsic rate of association and dissociation (kon and kon), diffusion of ligand to the cell surface (D), and rate constants for the overall association and dissociation reactions (k[ and k ).

A series of symmetrically substituted fluorine derivatives of BAPTA (see Figure 3.3A) has been synthesized.One of these chelators is 5F-BAPTA (Figure 3.5A), which has a binding constant for Ca, of 1.4 x 10 M and a F NMR chemical shift, 8, that in the free ligand is different from that in the complex with Ca + (ASca2+ 6 ppm). The rate of Ca + dissociation, koft, is 5.7 X 10 s , which gives the rate of association, kon, as 8 x 10 M " s according to... 

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