A flow cell of adequate dimensions 4x11x1 cm (to be inserted in a detector of gamma radioactivity) consisted of two polymethylmethacrylate plates, between which were pressed two mica plates separated by a spacer. A top view of the cell is provided in Fig. 5. The data acquisition was performed using the same kind of procedure as for capillary geometry (Boumaza et al. 1992; Le and Déjardin 1998). For a detection window of width w and a channel height h, the radioactivity jump at the arrival of radiolabeled protein solution is Av ~ whCb, while the surface radioactivity on the two faces (mica plates) is As ~ 2wr. Therefore r(t) = (h/2)CbAs(t)/Av and k(t) = (h/2)(dAs/dt)/Av.
Recently we studied (Vasina and Déjardin 2004) the adsorption of a-chymotrypsin onto mica at different concentrations of Tris buffer at pH 8.6. Examples of the adsorption kinetics data are given in Fig. 6. The initial adsorption rate is linear with a protein solution concentration in the range considered (Fig. 7).
In Fig. 3 some of our results emphasizing the peculiarities of the representation given by Eq. 9 are plotted. The scanning of adsorption with
convection is viewed as straight lines passing through the origin with their slope increasing with wall shear rate y as 0.538 (y/x)1/3. The application of Eq. 9 to the adsorption of a-chymotrypsin onto mica in the rectangular channel provides two parameters: the diffusion coefficient D and the adsorption kinetic constant ka (for instance, in 10-2 M Tris buffer, pH 8.6: D = 8.8 ± 0.7x 10-7 cm2 s-1 and ka = 4.4 ± 0.5x 10-4 cm s-1). The two-parameter fit was performed using SigmaPlot®.
The depletion (Eq. 2) with its complement to unity, say k(x, y)/ka or C(x, 0, y)/ Cb, is directly visualized in Fig. 3. Moreover, given the curvature of the function k(u'), the thickness of the depletion layer is always smaller than that of the Leveque model, as k(x, y) = Dd(x, y)/6(x, y) with d(x, y) = 1 in the Leveque limit, therefore 6(x, y)/6Lev(x, y) = d(x, y)/[k(x, y)/ kLev(x, y )]. Both terms of the ratio are noted in Fig. 3.
In our experiments, the detection occurs between 2.5 and 5.5 cm from the channel entrance, therefore £ = 0.75. Taking into account this range of integration (Eqs. 9 and 14), we obtain for Tris buffer 10-2 M at pH 8.6, corrections of -1% for the protein diffusion coefficient D and +6% for its adsorption kinetic constant ka.
When comparing the present treatment to other works in the literature, we should mention that we do not assume any value for the protein diffusion coefficient. The calibration is providedby the increase in radioactivity when the radiolabeled protein solution arrives in a channel of known geometry or by its drop when the radiolabeled solution is replaced by buffer. We do not assume any Leveque regime with a known diffusion coefficient, as is sometimes assumed in fluorescence (TIRF) experiments (Wertz and Santore 1999, 2002).
Was this article helpful?