Variable Rate Coefficients

Variable rate binding coefficients were introduced in Chapter 2 [see for example, Eqs. (2.8a-2.8c)] and are not repeated here. Figures 3.3a and 3.3b show the influence of a variable adsorption (forward) reaction (or binding) rate coefficient, klt for a second-order reaction on the concentration of the antigen near the surface. The adsorption (or binding) rate coefficient, is of the form k1 = k't~b. This figure shows that, as time (t) and coefficient b increase, the concentration of the antigen near the surface increases both when lateral interactions are absent (Figure 3.3a) and when they are present (Figure 3.3b). This is to be expected since with an increase in either time (t) or b, ki decreases. This results in an increase in the antigen near the surface. Once again, the concentration of the antigen near the surface is higher when lateral interactions are present than when they are absent, everything else being the same (Figure 3.4).

It is worthwhile to compare the influence of an increasing and a decreasing adsorption reaction rate coefficient [of the form k, =k] 0exp( + fit)} for a second-order reaction on the concentration of antigen near the surface when lateral interactions are present and when they are absent. Figure 3.5a shows

Time (sec)

FIGURE 3.3 Concentration of antigen near the surface versus time for a variable adsorption rate coefficient (k1 = k't~b) (a) without and (b) with lateral interactions.

Sadana, A. and Madugula, A., Biotechnology Progress, 9, 259-266 (1993). Reprinted with permission from Academic Press.

Time (sec)

FIGURE 3.3 Concentration of antigen near the surface versus time for a variable adsorption rate coefficient (k1 = k't~b) (a) without and (b) with lateral interactions.

Sadana, A. and Madugula, A., Biotechnology Progress, 9, 259-266 (1993). Reprinted with permission from Academic Press.

that for an increasing adsorption rate coefficient, after a brief time interval as time increases the concentration of the antigen near the surface decreases, as expected for the cases when lateral interactions are absent or present. Note that this relatively low value of the variable rate coefficient (/? = 0.01) introduces nonlinearity in the attachment of the antigen to the antibody immobilized to the surface. Also, with the influence of lateral interactions, the concentration of the antigen near the surface increases faster and reaches a higher value than when lateral interactions are absent. No explanation is offered at present for the maximum exhibited in Figure 3.5a for ¡3 = 0.01. Figure 3.5b shows that, for a decreasing adsorption rate coefficient as time increases, the concentration of the antigen near the surface increases continuously for the cases when lateral interactions are present or absent. Note that this relatively low value of the variable rate coefficient (/? = — 0.01) also introduces nonlinearity in the attachment of the antigen to the antibody immobilized to the surface (see Figure 3.5a). Also, with the influence of c

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