Quantitative analysis of the protein adsorption kinetics requires that the amount of adsorbed protein is known as a function of time. The example shown in the following section relies on the use of Total Internal Reflection Fluorescence (TIRF) and fluorescein labeled lipoprotein (FITC-LDL) for measurements of protein adsorption kinetics. In this case the fluorescence signal has to be independently calibrated into the adsorbed amount. Two independent quantitation schemes were used to quantify protein adsorption and the respective results were compared: one was based on the transport-limited adsorption and the other was based on adsorption of protein measured by autoradiography. The fluorescence intensity measured for FITC-protein adsorption on the hydrophilic silica surface, is shown as a function of time in Figure 1. Since the initial FITC-LDL adsorption on the hydrophilic silica increased linearly with time, it was assumed that this adsorption might be limited by transport of protein through an unstirred layer close to the surface. In the case of transport-limited adsorption and for very slow or no desorption, the experimental dsorption rate is only limited by the availability of protein molecules at the adsorbing surface, resulting in a situation in which, every protein molecule that collides with the surface sticks to it.
Figure 1. Fluorescence intensity of adsorbing FITC-LDL shown as a function of time for the adsorption/desorption cycle on hydrophilic silica surface.
A model was developed for the transport-limited adsorption from flowing solution to enable quantification of adsorbed amount of protein on the surface. In the case of rectangular TIRF flow channel, assuming that laminar flow existed in the channel, an equation for the flowing homogeneous FITC-LDL solution can be expressed as [23,24,25]:
(1)
with the following boundary conditions:
where c is the protein concentration, t is the time, x is the direction of flow, y is the distance from the surface normal to the surface, b is the thickness of the flow channel, co is the bulk concentration of protein solution, Vm is the maximum velocity in flow channel at y = b/2, DLDL is the diffusion coefficient of protein and gamma (lower case Greek gamma) is the wall shear rate given by:
(6)
Here q is the volumetric flow rate of protein solution and w is the width of the flow channel.
As time increases, a concentration boundary layer (often called "unstirred" layer) forms close to the surface. Its thickness, delta is on the order of:
(7)
and the protein concentration profile across this layer develops rather rapidly [26].
At longer times and at y/b << 1, the time dependent term in the equation 1 may be neglected and the equation assumes a following form:
(8)
with the boundary conditions of:
The analytical solution for this classical problem was computed by Leveque [27]: the flux of protein molecules to the surface, dA/dt, which is equal the rate of adsorption of protein to the surface, dGammap/dt, under assumption that all protein reaching the surface adsorb to it, can be expressed as:
(12)
where Gammap (upper case Greek Gamma) is the adsorbed protein concentration and Gamma(4/3) is the gamma function of 4/3.
From the eq 12 one can see that, in the case of the transport-limited protein adsorption and very slow or no desorption, the Leveque equation (eq. 12) predicts the following:
Since the desorption rate of FITC-LDL was indeed found to be very slow, it was safely assumed that the adsorbed amount, , can be calibrated from the initial linear slope of fluorescence increase as a function of time, d(fluorescence)/dt (see Figure 1).
The assumption underlying the proposed calibration of the adsorbed amount is that the flux of the protein to the adsorbing surface, (i.e. that protein adsorption displays a transport-limited rate), is proportional to the slope of experimentally measured FITC-LDL adsorption kinetics by a unique conversion factor.
The Leveque equation used for the calculation of the adsorbed amount of FITC-protein can be expressed as:
(13)
where dA/dt is the flux of protein molecules to the hydrophilic silica surface, q is the experimental volumetric flow rate (in the experiments, q = 0.84 ml/min), b is the thickness of the TIRF flow cell (in the experiments, b = 0.05 cm), w is the width of the TIRF flow cell (in the experiments, w = 0.5 cm), l is the distance from the entrance of the flow chamber to the observation spot (in the experiments, l = 2.8 cm), DLDL is the diffusion coefficient of protein (1.8 10-7 cm2 s-1), and cLDL is the bulk solution concentration of protein.
For the FITC-protein adsorption experiment shown in Fig. 1, computed dA/dt amounted to 1.84 10-3 mg cm-2 s-1 while the slope of fluorescence intensity increase, dF/dt was 18.2 count s-1. The conversion factor which relates the protein flux and the fluorescence increase, Z = (dA/dt)/(dF/dt) was 1.01 10-4 mg cm-2 count-1. This conversion factor was applied to the whole adsorption-desorption cycle. Note that in this quantification scheme it was also assumed that the quantum yield of fluorescence was constant during the process of adsorption.
(Comment: Since the experiment of FITC-LDL adsorption was in fact performed on a octadecyldimethylsilyl-silica gradient surface, all experimental fluorescence adsorption results from one experiment were converted to the adsorbed amount of protein, GammaLDL, by multiplying the recorded fluorescence intensities with the conversion factor Z. The adsorbed amount, quantified through the initial fluorescence rate, was used for the further analysis of protein adsorption kinetics as described in the following section).
Another way to calibrate protein adsorption kinetics is to use radiolabeled protein. It is very unlikely, however, that such labeled protein can be used in any time-resolved experiments. With a very few exceptions, the use of radiolabeled protein excludes the use of surface sensitive techniques like TIRF and requires a longer counting times. It is safe to state that the use of radiolabeled protein is better suited for single point measurements at longer adsorption times. When a protein adsorption kinetics recorded by a spectroscopic technique needs to be quantified, one can design an identical adsorption experiment using radiolabeled protein. In this case, instead of continuously measuring spectroscopic parameter one waits until a pre-determined adsorption time and measures the adsorbed amount using radioactivity detector, or radioactivity imaging technique like autoradiography. In the example shown below autoradiography was used to measure the adsorbed amount of 125I-protein along the octadecyldimethylsilyl-silica (ODS-silica) gradient surface at the end of the adsorption-desorption cycle. Since in the autoradiography experiment the signal from the surface adsorbed 125I-protein could not be recorded independently from the solution 125I-protein signal, the final adsorbed amount of 125I-protein was measured after the unbound protein was washed out of the flow cell. The comparison between two protein adsorption profiles: one from the FITC-protein fluorescence quantitation scheme described above and other measured by autoradiography of adsorbed 125I-protein, produced excellent agreement at both ends of the ODS-silica gradient surface. Hence, the initial assumption that the FITC-LDL adsorption onto the hydrophilic silica surface was transport-limited was proved to be correct.
