Equilibrium binding constant surface concentration

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))...

In this equation, is the association equilibrium constant for the binding of A with L, is the association rate constant for this reaction, and is the corresponding dissociation rate constant. The terms [A], L and A-L represent the concentration of the analyte in solution at equilibrium and the surface concentrations of the ligand and analyte-ligand complex under these same conditions. 

Thermodynamic control (Figure 1, right) is based on adsorption of substances until quasi-equilibrium stage. In this case, the surface ratio of the adsorbed species is defined by the ratio of products of their concentration and binding constant. This deposition is much less influenced by poorly controllable fluctuations of external conditions and provides much better reproducibility. The total coverage can be almost 100%. Because of these reasons, the thermodynamic control is advantageous for preparation of mixed nanostructured monolayers for electrochemical applications including a formation of spreader-bar structures for their application as molecular templates for synthesis of nanoparticles. 

By using a resonant mirror biosensor, the binding between YTX and PDEs from bovine brain was studied. The enzymes were immobilized over an aminosilae surface and the association curves after the addition of several YTX concentrations were checked. These curves follow a typical association profile that fit a pseudo-first-order kinetic equation. From these results the kinetic equilibrium dissociation constant (K ) for the PDE-YTX association was calculated. This value is 3.74 p,M YTX (Pazos et al. 2004). is dependent on YTX structure since it increases when 44 or 45 carbons (at C9 chain) group. A higher value, 7 p,M OH-YTX or 23 p,M carboxy-YTX, indicates a lower affinity of YTXs analogues by PDEs. 

Fig. 4. Transient and equilibrium binding of ligand to cell surface receptors for the case of ligand concentration L approximately constant and equal to L . The fraction of total surface receptors bound, u, is shown, (a) The equilibrium value, eq, is plotted as a function of the logarithm of the ratio L0/KD. (b), (c) u is plotted as function of scaled time r for several values of the ratio Ln/Ku. The initial value and time course of u in (b) correspond to an association experiment. The initial value and time course of u in (c) correspond to a dissociation experiment.

A simple one-site, two-sided transporter is diagrammed in Fig. 6. The transporter, T, can reversibly bind with the substrate, C, on either side of the membrane. The equilibrium dissociation constants, D, and Dg, are the ratio of the reaction rate for the dissociation reaction to that for the association reaction (off-rate to on-rate) on the inside and outside surfaces of the membrane, respectively. The units of D are millimolar (mM, or whatever units are being used for concentration). 

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 dependences of pH and C-potential on the adsorbed amount of M(H20)2+ at the total metal ion concentrations of 3 x10-3 mol dm-3 are shown in Figures 7 and 8, respectively. The amount adsorbed for each M2+ increases with the pH, and the inflection points are shifted toward the lower pH region in the order of Co2+, Zn2+, Pb2+, Cu2+, which corresponds to the order of the hydrolysis constant of metal ions. To explain the M2+-adsorption/desorption, Hachiya et al. (16,17) modified the treatment of the computer simulation developed by Davis et al. (4). In this model, M2+ binds coordina-tively to amphoteric surface hydroxyl groups. The equilibrium constants are expressed as... 

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