Detection of channel proximity by nanoparticle-assisted delaying of toxin binding; a combined patch-clamp and flow cytometric energy transfer study

Abstract

Gold nanoparticles of 30 nm diameter bound to cell-surface receptor major histocompatibility complex glycoproteins (MHCI and MHCII), interleukin-2 receptor α subunit (IL-2Rα), very late antigen-4 (VLA-4) integrin, transferrin receptor, and the receptor-type protein tyrosin phosphatase CD45 are shown by the patch-clamp technique to selectively modulate binding characteristics of Pi₂ toxin, an efficient blocker of K_v1.3 channels. After correlating the electrophysiological data with those on the underlying receptor clusters obtained by simultaneously conducted flow cytometric energy transfer measurements, the modulation was proved to be sensitive to the density and size of the receptor clusters, and to the locations of the receptors as well. Based on the observation that engagement of MHCII by a monoclonal antibody down-regulates channel current and based on the close nanometer-scale proximity of the MHCI and MHCII glycoproteins, an analogous experiment was carried out when gold nanoparticles bound to MHCI delayed down-regulation of the K_v1.3 current initiated by ligation of MHCII. Localization of K_v1.3 channels in the nanometer-scale vicinity of the MHC-containing lipid rafts is demonstrated for the first time. A method is proposed for detecting receptor–channel or receptor–receptor proximity by observing nanoparticle-induced increase in relaxation times following concentration jumps of ligands binding to channels or to receptors capable of regulating channel currents.

Appendix

Phenomenological interpretation of the η shielding factor

Analogous problems concerning constrained 3D diffusion of particles in a background of retarding obstacles of various sizes and shapes were treated by theorists modeling phenomena in the field of gel electrophoresis and size exclusion chromatography (Schnitzer 1988; Tong and Anderson 1996). In the case of the close proximity of gold islands and channels, the effective local concentration of toxin around the channels can be reduced by two effects: (1) steric exclusion due to the finite size of the gold beads and the covering antibodies (Schnitzer 1988; Minton 1992; Jürgens et al. 1999), and (2) the reduced diffusion rate of toxin in the gold island due to the increased hydrodynamic interaction caused by the volume confinement (Han and Herzfeld 1993; Tomadakis and Sotirchos 1993; Tong and Anderson 1996; Phillips 2000).

The diffusion current of the toxin can be decomposed into two components: one is parallel to the cell surface; the other is perpendicular to it (Fig. 1A). Because the gold islands are mainly laterally extended, i.e. 2D systems, we expect the lateral component of diffusion to be more effectively reduced than the perpendicular one. Moreover, the binding of toxin to the channel is necessarily preceded by a surface diffusion step or reduction-in-dimensionality (RD) enhancement (Berg and Purcell 1977; Wang et al. 1992; Axelrod and Wang 1994), which further emphasizes the significance of the lateral component of the diffusion current. A semi-quantitative interpretation of the η shielding efficiency can be made, based on the work of Axelrod and Wang (1994) discussing the role of RD enhancement for reaction-limited association of ligands with cell-surface receptors. That binding of toxin to the K_v1.3 channels is reaction limited is justified by the small value of the Damköhler number (D_a<10⁻⁴), calculated by using the values of k_on and the diffusion constant of the toxin, as well as the cell radius given in Materials and methods (Haugh and Lauffenburger 1997). Based on the work of Axelrod and Wang (1994), the following formula can be deduced for the RD enhancement factor of the k_on association constant:

$$ \frac{{k_{{\text{on}}} }} {{k_{{\text{on}}}^{\left( 0 \right)} }} = \frac{{1 + 16\chi _2 D_2 K_{\text{u}} /\left( {3\pi \chi _3 D_3 a_{{\text{cell}}} } \right)}} {{1 + 16\chi _2 D_2 K_{\text{u}} /\left[ {\left( {3\pi \chi _3 D_3 a_{{\text{cell}}} } \right) + 2\sigma k_{{\text{off}}} /(a_{{\text{cell}}} c)} \right]}} $$

(A1)

where D₂ and D₃ designate the 2D (on the cell surface) and 3D (off the cell surface) diffusion constants, χ₂ and χ₃ are the 2D and 3D success probabilities per encounter (orientation factor) leading to binding, K_u is the unspecific equilibrium binding constant of toxin onto the membrane, a_cell is the cell radius, k_off is the dissociation rate constant of the toxin from the channel, σ is the average free path length of the toxin (taken to be equal for 2D and 3D diffusion), c is the toxin concentration, and k_on⁽⁰⁾ is the association rate constant in the absence of surface diffusion of toxin, i.e. at D₂=0. Equation (A1) tells us that surface diffusion can be effective whenever unspecific binding to the surface is strong, i.e. K_u is large (as is the case with the Pi₂ toxin, due to its seven positive charges) and when c is small enough. Additionally, Eq. (A1) reports that gold islands may cause a reduction in D₂ and χ₂ much more than in D₃ and χ₃, because of the large lateral 2D nature of gold islands, and as a consequence the value of k_on should reduce in the presence of gold (using the available data on physical parameters of the Pi₂ toxin, the RD enhancement factor is approximately ~10 at the c=2.5 nM concentration; see Materials and methods). If we write the ratio of the 2D diffusion constant close to or in the gold island relative to that in the absence of gold (or at an infinitely long distance from the gold island) as a product of factors H and S, where H accounts for hydrodynamic effects and S for steric exclusion (tortuosity) effects, the resulting expression is (Phillips 2000):

$$ D_2 /D_{2,\infty } = H\left( {\lambda ,\phi } \right)S\left( {\lambda ,\phi } \right) $$

(A2)

where both H and S are exponential functions of the negative power of the λ and φ quantities, where λ is the ratio of the radius of the toxin and that of the gold bead and φ is the volume fraction excluded by the gold beads in the gold island. At small φ volume fractions, expanding the exponentials in a power series, D₂/D_2,∞ can be approximated by the following formula:

$$ D_{\text{2}} /D_{2,\infty } \approx 1 - F\left( \lambda \right)\phi $$

(A3)

where the F(λ) term is a constant, determined by the toxin size/gold size ratio. If the gold island is modeled by an “equivalent cylinder” of radius R and height h, then the local excluded volume φ can be calculated as follows:

$$ \begin{gathered} \phi {\text{ }} = {\text{volume of beads in the cylinder / volume of cylinder }} \hfill \\ \;\;\;\; = {\text{(}}N \times {\text{4}}r^{\text{3}} \pi /3)/(R^2 \pi h) \hfill \\ \end{gathered} $$

(A4)

where N is the number of gold beads in the island and r is the radius of a gold bead. This expression can be rearranged to the following form, by introducing the interparticle separation d and local surface density ρ=1/d² of gold beads in the island:

$$ \begin{gathered} \phi = (4/3)(r/h)(r^2 \pi )\rho \hfill \\ \;\;\; = {\text{(4}}\pi {\text{/3)}}(r/h)(r/d)^2 \hfill \\ \end{gathered} $$

(A5)

Although Eq. (A1) contains physical constants which can only be approximated, Eqs. (10), (A1), and (A2) show that there exists a formal relationship between the measurable η value and the local surface density (or inter-particle separation) of the gold beads. We should add that besides hindering diffusion, even direct modification of k_on may also occur.