The Role of Glycocalyx in Nanocarrier-Cell Adhesion Investigated Using a Thermodynamic Model and Monte Carlo Simulations

Abstract

We present an equilibrium model for quantifying the effect of glycocalyx in mediating the interaction of functionalized nanocarriers with endothelial cells. In this model, nanocarrier adhesion is governed by the interplay between three physical parameters, namely, glycocalyx resistance, flexural rigidity of receptors, and receptor-ligand bond stiffness. We describe a procedure to rationally determine the values of these crucial parameters based on several independent (single molecule and cell-based) characterizing experiments. Using our model and independent derivation of the parameter values in conjunction with Monte Carlo simulations, we describe the binding of nanocarriers to endothelial cells at equilibrium. We show that we can quantitatively reproduce the experimental binding affinities with zero fitting to binding data. Additionally, our simulations provide quantitative descriptions for the multivalency in nanocarrier binding, as well as for the degree of clustering of antigens. Our study identifies two interesting parameters: glycocalyx resistance and antigen flexural rigidity, both of which reduce binding of nanocarriers and alter the sensitivity of the nanocarrier binding constant to changes in temperature. Collectively, our model, parameter estimations, simulations, and sensitivity analyses help provide unified molecular and energetic analyses of the nanocarrier binding process.

Figure 1

Schematic of the microscopic model for nanocarrier binding to endothelial cells.

Figure 2

Regression of the glycocalyx model (eqs 3 and A2-2) to the experimental data of Mulivor provides an avenue to estimate the glycocalyx sprint constant k_glyx reported in Table 1.

Figure 3

Effect of ICAM-1 diffusion on nanocarrier multivalency: a visual comparison of data from Tables 2 and 3.

Figure 4

Effect of ICAM-1 diffusion on nanocarrier binding energy: a visual comparison of data from Tables 2 and 3.

Figure 5

(a) Radial distribution function of diffusing antigens on the cell surface in the presence (solid line) and absence (dotted line) of bound nanocarriers. Simulations are performed with 640 antigens/μm² and 50 nanocarriers at 4 °C. (b) Percentage of probability of spatial occupancy of surface antigens in the absence of bound nanocarriers. (c) Percentage of probability of spatial occupancy of surface antigens in the presence of bound nanocarriers. A visual comparison of parts b and c clearly indicates clustering of antigens only in the presence of bound nanocarriers.

Figure 6

Effect of bond stiffness (k) on nanocarrier (a) multivalency and (b) binding energy for diffusing ICAM-1. The presence of glycocalyx does not affect the multivalency, although it increases the (negative) binding energy. Simulations are performed for 2000 antigens/μm².

Figure 7

Effect of ICAM-1 flexural rigidity on nanocarrier (a) multivalency and (b) binding energy for nondiffusing ICAM-1. The presence of glycocalyx does not affect the multivalency, although it increases the (negative) binding energy. Simulations are performed for 2000 antigens/μm².

Figure 8

Difference of lnK_D of binding at 37 and 4 °C plotted against the glycocalyx spring constant k_glyx. The difference between lnK_D at 37 and 4 °C decreases with increasing glycocalyx resistance, thus reducing the temperature dependence of the binding process.