Quantification of Depletion-Induced Adhesion of Red Blood Cells

Red blood cells (RBCs) are known to form aggregates in the form of rouleaux due to the presence of plasma proteins under physiological conditions. The formation of rouleaux can also be induced in vitro by the addition of macromolecules to the RBC suspension. Current data on the adhesion strength between red blood cells in their natural discocyte shapes mostly originate from indirect measurements such as flow chamber experiments, but data is lacking at the single cell level. Here, we present measurements on the dextran-induced aggregation of red blood cells using atomic force microscopy-based single cell force spectroscopy. The effects of dextran concentration and molecular weight on the interaction energy of adhering RBCs were determined. The results on adhesion energy are in excellent agreement with a model based on the depletion effect and previous experimental studies. Furthermore, our method allowed to determine the adhesion force, a quantity that is needed in theoretical investigations on blood flow.

Figure 1

(a) Snapshot of a rouleau of seven RBCs in a dextran solution. (b) A sketch of the working principle of SCFS. A single cell is attached to the prefunctionalized cantilever and is lowered onto another cell, which is fixed at the bottom. Both cells are pushed together with an appropriate set point force $F_{\mathrm{set}}$. The adhesion force and adhesion energy are measured while withdrawing the cells.

Figure 2

[(a) and (b)] Effects of BSA treatment (see the text for details). Without BSA treatment, undesired adhesion events occur whose origin is not the investigated depletion effect; e.g., the cells do not hit concentrically, and the lower cell touches the Cell-Tak (i.e., a stronger adhesion force is measured because of the strong adhesiveness of the Cell-Tak). With BSA treatment, the Cell-Tak is completely passivated and the influence of those undesired adhesion events is minimized, as the changes in shape and magnitude of the measured force curve document.

Figure 3

Role of the parameters. (a) Dependence of the measured adhesion energy on the chosen force set point $F_{\mathrm{set}}$. In all measurements, no significant dependence on $F_{\mathrm{set}}$ was observed. (b) Dependence of the measured adhesion energy on the chosen contact time ${\tau }_{\mathrm{set}}$ of both cells. Increasing contact time leads to an increase in interaction energy and error bars (SD). (c) Dependence of the measured adhesion energy on the chosen withdrawal velocity $v$ of the cantilever. At higher velocities in the DEX150 measurements, a dependence on the cantilever velocity was observed, but for moderate velocities this dependence was still less than the error measurement.

Figure 4

(a) Measured adhesion forces of the dextrans in terms of concentrations. The maximum interaction strengths were observed at $2\mathrm{g}/\mathrm{dl}$ (DEX70) and $4\mathrm{g}/\mathrm{dl}$ (DEX150). (b) The dependence of the interaction energy of two RBCs on the concentrations of two dextran types. The solid line represents the curve calculated by Neu and Meiselman [9]. The errors are given in SD. The error bars in the DEX70 measurements are smaller than the symbol size.