Effect of Sample Heterogeneity on the Interpretation of QCM(-D) Data: Comparison of Combined Quartz Crystal Microbalance/Atomic Force Microscopy Measurements with Finite Element Method Modeling

Abstract

A quartz crystal microbalance was integrated into an AFM in order to monitor the adsorption of biomolecules to the resonator surface with both atomic force microscopy and microgravimetry. The comparison between the two techniques allows the fractional coverage of the surface, theta, to be correlated with the frequency shift of the resonator, deltaf. The adsorbed material was ferritin, which is a spherical protein with a diameter of approximately 12 nm. Even ata coverage below 50%, the protein layer exhibits Sauerbrey-like behavior, meaning that the magnitude in the frequency shift [deltaf] much exceeds the shift in bandwidth and that the normalized frequency shift, deltaf/n (n the overtone order), is similar on the different overtones. The relation between coverage and frequency shift was found to be nonlinear. In order to model this situation, we performed finite element method calculations based on the incompressible Navier-Stokes equation. The comparison between the model and the experiment suggests that the deformation of the protein upon adsorption is small. For low coverage, the volume of the trapped solvent exceeds the volume of the adsorbate itself. The ratio of the two decreases with increasing coverage. This is the cause of the experimentally observed nonlinear relationship between the surface coverage and frequency shift. Comparing frequency shifts at different overtones, one finds that deltaf/n slightly decreases with overtone order. Such a behavior is typically attributed to softness. The model shows that, for the adsorbed spheres, this apparent softness arises through a rocking motion of the spheres at the surface instead of the shear deformation. Also, there is a hydrodynamic contribution (related to roughness) to the overtone dependence of deltaf/n.

Adsorbed liposome deformation studied with quartz crystal microbalance

“…In the case of liposomes adsorbed on the surface (Figure 3), as in many other cases, 20 these two conditions are not satisfied and the QCM signals contain contributions from the thickness of the adsorbed film, which depends on the height of the adsorbed liposomes as well as on the surface coverage (number of liposomes adsorbed per unit area), from the strength of the liposome-surface interactions, and also possibly from the lipid bilayer stiffness. 20,22,[32][33][34] To extract the height of adsorbed liposomes, we plot the ratio of the two measured parameters, − / F, as a function of the frequency shift − F/n. 22 These plots are shown in Figures 3(b) and 3(d) for the measurements done at 10 and 32…”

“…22,32,34 FEM allows the frequency and bandwidth shifts due the stress exerted at the crystal surface by the adsorbed particles that are moved through the surrounding liquid by QCM crystal's oscillatory motion to be calculated via the small load approximation. 21 Stress is calculated from the velocity fields obtained numerically using COMSOL's Incompressible Navier-Stokes Module.…”

Well-defined biomimetic surfaces to characterize glycosaminoglycan-mediated interactions on the molecular, supramolecular and cellular levels

“…The system was operated in flow mode with a flow rate of typically 10 mL/min using a peristaltic pump (ISM935C, Ismatec, Zurich, Switzerland [30,31] as described in detail elsewhere [32]. These thickness values are provided as average ± standard deviation from at least three independent experiments.…”

A Straightforward Detection of HIT Type II via QCM-D

“…An illustration of dissipation versus frequency plot is shown in figure 5. Here it is evident that the dissipation versus frequency plots of all aggregation measurements lie above the bisecting line (the line through origin represents a pure viscosity change 21 indicating that the elasticity contributes to a larger extent than the pure rigid mass deposition. Meaning that the ratio between dissipation and frequency is higher than 1.0.…”