Selectivity of Ligand-Receptor Interactions between Nanoparticle and Cell Surfaces

Selectivity of interactions between nanoparticles functionalized by tethered ligands and cell surfaces with different densities of receptors plays an essential role in biorecognition and its implementation in nanobiomedicine. We show that the onset of nanoparticle adsorption has a universal character for a range of nanoparticles: the onset receptor density decreases exponentially with the energy of ligand-receptor binding and inversely with the ligand density. We demonstrate that a bimodal tether distribution, which permits shielding ligands by longer nonfunctional tethers, leads to extra loss of entropy at the adsorption onset, enhancing the selectivity.

Figure 1

(a) Simulation snapshots of nanoparticles (with core radius $20a$, containing 64 tethers end functionalized with ligands, $N=32$), created using VMD [41], interacting with normal cells (with low receptor density, receptors are shown as ovals on the part of the cell surface near the nanoparticle) and targeted cells (with high receptor density) together with the general form of the nanoparticle adsorption vs receptor density curve desired for biomedical applications. The onset of adsorption is indicated. (b) Computer modeling data for the absolute value of the free-energy minimum (in units of kT) vs relative receptor density $\rho$ (normalized by the smallest receptor density considered, $1.5\times {10}^{-7}{a}^{-2}$ or $6\times {10}^{-7}{\mathrm{nm}}^{-2}$) for nanoparticles with a core radius of $20a$ (10 nm) containing 128 flexible tethers ($N=32$) end functionalized by ligands for different ligand-receptor binding energies $E_{\mathrm{bind}}$. The inset shows the data in a logarithmic scale for $\rho$ to emphasize the onset of nanoparticle adsorption.

Figure 2

The product of ligand density see Eq. (1) and relative receptor density at the onset of nanoparticle adsorption (logarithmic scale) vs ligand-receptor binding energy for (i) nanoparticles with a core radius of $20a$ (10 nm) containing 128 flexible tethers all end functionalized by ligands for $N=10$ (down triangles), $N=16$ (circles), $N=32$ (squares), $N=64$ (right triangles), 50% functionalized tethers ($N=32$, left triangles), 25% functionalized tethers ($N=32$, spheres); (ii) nanoparticles with core radius of $20a$ (10 nm) with 64 ligated tethers ($N=32$, diamonds; and $N=16$, up triangles); and (iii) nanoparticles with core radius of $40a$ (20 nm) with 256 tethers ($N=32$) among which 64 carry ligands (hexagon).

Figure 3

Computer modeling data for the absolute value of the free-energy minimum vs relative receptor density $\rho$ for nanoparticles with core radius of $20a$ (10 nm) containing 64 ligated tethers ($N=32$) and 64 nonfunctional tethers of different lengths: bimodal nanoparticles ($N=48$ filled circles, $N=64$ filled triangles, $E_{\mathrm{bind}}=14\mathrm{kT}$), monodisperse nanoparticles ($N=32$ for $E_{\mathrm{bind}}=14\mathrm{kT}$ open squares, $E_{\mathrm{bind}}=12.5\mathrm{kT}$ open circles, $E_{\mathrm{bind}}=11\mathrm{kT}$ open triangles). Schematic presentation of the bimodal nanoparticle interacting with a cell surface is shown in the inset.