Measuring diffusion and binding kinetics by contact area FRAP

Abstract

The immunological synapse is a stable intercellular structure that specializes in substance and signal transfer from one immune cell to another. Its formation is regulated in part by the diffusion of adhesion and signaling molecules into, and their binding of countermolecules in the contact area. The stability of immunological synapses allows receptor-ligand interactions to approximate chemical equilibrium despite other dynamic aspects. We have developed a mathematical model that describes the coupled reaction-diffusion process in an established immunological synapse. In this study, we extend a previously described contact area fluorescence recovery after photobleaching (FRAP) experiment to test the validity of the model. The receptor binding activity and lateral mobility of fluorescently labeled, lipid-anchored ligands in the bilayer resulted in their accumulation, as revealed by a much higher fluorescence intensity inside the contact area than outside. After complete photobleaching of the synapse, fluorescence recovery requires ligands to dissociate and rebind, and to diffuse in and out of the contact area. Such a FRAP time course consequently provides information on reaction and diffusion, which can be extracted by fitting the model solution to the data. Surprisingly, reverse rates in the two-dimensional contact area were at least 100-fold slower than in three-dimensional solution. As previously reported in immunological synapses, a significant nonrecoverable fraction of fluorescence was observed with one of two systems studied, suggesting some ligands either dissociated or diffused much more slowly compared with other ligands in the same synapse. The combined theory and experiment thus provides a new method for in situ measurements of kinetic rates, diffusion coefficients, and nonrecoverable fractions of interacting molecules in immunological synapses and other stable cell-bilayer junctions.

FIGURE 1

Schematic of contact formation and contact area FRAP. (A) Before contact, the cell surface receptors and bright ligands in the bilayer are uniformly distributed. (B) After a period of contact formation lasting 20–40 min, the receptor and bright ligand accumulation in the contact area reaches equilibrium and remains stable for hours. (C) Patterned photobleaching of the entire contact area converts that bound and free bright ligands into dark ligands. (D) Contact recovery involves exchange of dark free ligands for bright free ligands by diffusion and then replacement of bound dark ligands by bound bright ligands by chemical dissociation and binding.

FIGURE 2

(A) Representative of three independent experiments. Fluorescence intensity integrated over the optical slice height emitted from the Alexa 488-conjugated rabbit anti-DNP IgG molecules in the volume above a 1-μm² area is plotted versus the amount of IgG in the volume above a unit area. The linear relationship between the fluorescence intensity and the number of IgG per unit area provides a calibration curve for determination of site density of IgG bound to the lipid bilayer. (B) Representative of three independent experiments. Fluorescence intensity of Alexa 488-conjugated rabbit anti-DNP IgG bound to bilayers prepared with different dilutions of stock DNP-CAP-PE liposomes. IgG binding increases with increasing DNP concentration nearly linearly when the DNP liposomes is <0.5% but tends to saturate at higher DNP concentrations.

FIGURE 3

Contact area A_c measured by RIM is plotted versus the DNP concentration in the bilayer. A_c increases with increasing DNP concentration nearly linearly when DNP < 0.1% but tends to saturate at higher DNP concentrations.

FIGURE 4

(A) Bond-associated fluorescence intensity versus free ligand-associated fluorescence. (B) Zhu-Golan plot for CD16b^NA2-IgG interaction. B is the density of bound ligands within the contact area, F is the density of free ligands in the bilayer, B/F is the ratio of the density of bound ligands density to free ligand density, and P is the ratio of contact area to full cell surface area. The slope of the linear fit and the x-intercept provide respective estimates for the binding affinity K_a and the receptor density before contact area formation, m_r0 (indicated). The standard deviations of K_a and m_r0 (indicated) are calculated from the 95% confidence interval of the fits.

FIGURE 5

Comparison of measured (dotted line) and fitted (curves) contact area FRAP time courses of (A) CD16b^NA2-expressing CHO cells interacting with bilayers reconstituted with rabbit IgG in four densities (indicated) and (B) CD2-expressing Jurkat cells interacting with bilayers reconstituted with CD58 in three densities (indicated). Representative data are expressed as the spatially averaged, background-subtracted, total ligand-associated fluorescence intensity inside the contact area, FI_in(t)–FI_bdg, normalized by the background-subtracted, free ligand-associated fluorescence intensity outside the contact area before photobeaching, FI_out(0⁻)–FI_bdg. The number of repeats for each ligand density for each system is indicated in Fig. 6 on the top of the parameter value bar for that ligand density for that system.

FIGURE 6

Fraction of nonrecoverable fluorescence f_n for the (A) CD16b^NA2-IgG and (B) CD2-CD58 systems. Results are expressed as mean ± SE of data evaluated from 3–6 (indicated) contact area FRAP time courses measured at the indicated ligand densities.

FIGURE 7

Representative data (points) and model fits (curves) of contact area FRAP (A) and recovery rate (B) time courses for the respective CD16b^NA2-IgG (open circles) and CD2-CD58 (open triangles) systems. The solution of the coupled reaction-diffusion model used in the curve-fitting is described in the companion study (18). The number of repeats for each ligand density for each system is indicated in Fig. 6 on the top of the parameter value bar for that ligand density for that system.

FIGURE 8

Fractional diffusivity inside the contact area, or the ratio of diffusion coefficient inside the contact area to that outside, ξ, for the (A) CD16b^NA2-IgG and (B) CD2-CD58 systems. Results are expressed as mean ± SE. of data evaluated from 3–6 (indicated) contact area FRAP time courses measured at the indicated ligand densities.

FIGURE 9

Off-rate of receptor-ligand dissociation k_r for the (A) CD16b^NA2-IgG and (B) CD2-CD58 systems. Results are expressed as mean ± SE of data evaluated from 3–6 (indicated) contact area FRAP time courses measured at the indicated ligand densities.

FIGURE 10

Free receptor density inside the contact area m_r for the (A) CD16b^NA2-IgG and (B) CD2-CD58 systems calculated using the model (18). Results are shown as mean ± SE of data evaluated from 3–6 (indicated) contact area FRAP time courses measured at the indicated ligand densities.