Tailoring the Sensitivity of Microcantilevers To Monitor the Mass of Single Adherent Living Cells

Mass and Stiffness Deconvolution in Nanomechanical Resonators for Precise Mass Measurement and In Vivo Biosensing

Nanomechanical sensors, due to their small size and high sensitivity to the environment, hold significant promise for various sensing applications. These sensors enable rapid, highly sensitive, and selective detection of biological and biochemical entities as well as mass spectrometry by utilizing the frequency shift of nanomechanical resonators. Nanomechanical systems have been employed to measure the mass of cells and biomolecules and study the fundamentals of surface science such as phase transitions and diffusion. Here, we develop a methodology using both experimental measurements and numerical simulations to explore the characteristics of nanomechanical resonators when the detection entities are absorbed on the cantilever surface and quantify the mass, density, and Young's modulus of adsorbed entities. Moreover, based on this proposed concept, we present an experimental method for measuring the mass of molecules and living biological entities in their physiological environment. This approach could find applications in predicting the behavior of bionanoelectromechanical resonators functionalized with biological capture molecules, as well as in label-free, nonfunctionalized micro/nanoscale biosensing and mass spectrometry of living bioentities.

Modeling Nonlinear Dynamics of Functionalization Layers: Enhancing Gas Sensor Sensitivity for Piezoelectrically Driven Microcantilever

This article presents a parametrized response model that enhances the limit of detection (LOD) of piezoelectrically driven microcantilever (PD-MC) based gas sensors by accounting for the adsorption-induced variations in elastic properties of the functionalization layer (binder) and the nonlinear motional dynamics of the PD-MC. The developed model is demonstrated for quantifying cadaverine, a volatile biogenic diamine whose concentration is used to assess the freshness of meat. At low concentrations of cadaverine, an increase in the resonance frequency is observed, contrary to the expected reduction due to mass added by adsorption. The study explores the variations in the elastic modulus vis-à-vis the adsorbed mass of cadaverine and derives the resonance frequency to the adsorbed mass response function. We advance a blended technique involving the analysis of atomic force microscopy (AFM) force-distance (f-d) curves and fitting of the quartz crystal microbalance (QCM) impedance response spectrum to deduce the adsorption-induced changes in the viscoelastic properties of the functionalization layer. The findings obtained are subsequently employed in modeling the response function for a structurally nonhomogenous PD-MC, highlighting the significance of the functionalization layer to the global elastic properties. The structural composition of the PD-MC beam adopted herein features a trapezoidal base hosting the actuating piezoelectric stratum and a rectangular free end with a functionalization layer. The Euler-Bernoulli beam theory coupled with Hamilton's principle is used to develop the equation of motion, which is subsequently discretized into a set of nonlinear ordinary differential equations via Galerkin expansion, and the solutions to the first fundamental mode of vibration are determined using the method of multiple scales. The obtained solutions provide a basis for deducing the nonlinear response function model to the adsorbed mass. The derived model is validated by recorded resonance frequency changes resulting from exposure to known concentrations of cadaverine. We demonstrate that the increase in resonance frequency for low concentrations of cadaverine is due to the dominance of the variation of the elastic modulus of the functionalization layer originating from the initial binder-analyte interactions over damping due to added mass. It is concluded that the developed nonlinear response function model can reliably be used to quantify the cadaverine concentration at low concentrations with an elevated Limit of Detection.

Monitoring the mass, eigenfrequency, and quality factor of mammalian cells

The regulation of mass is essential for the development and homeostasis of cells and multicellular organisms. However, cell mass is also tightly linked to cell mechanical properties, which depend on the time scales at which they are measured and change drastically at the cellular eigenfrequency. So far, it has not been possible to determine cell mass and eigenfrequency together. Here, we introduce microcantilevers oscillating in the Ångström range to monitor both fundamental physical properties of the cell. If the oscillation frequency is far below the cellular eigenfrequency, all cell compartments follow the cantilever motion, and the cell mass measurements are accurate. Yet, if the oscillating frequency approaches or lies above the cellular eigenfrequency, the mechanical response of the cell changes, and not all cellular components can follow the cantilever motions in phase. This energy loss caused by mechanical damping within the cell is described by the quality factor. We use these observations to examine living cells across externally applied mechanical frequency ranges and to measure their total mass, eigenfrequency, and quality factor. The three parameters open the door to better understand the mechanobiology of the cell and stimulate biotechnological and medical innovations.

Hydrodynamic function and spring constant calibration of FluidFM micropipette cantilevers

Fluidic force microscopy (FluidFM) fuses the force sensitivity of atomic force microscopy with the manipulation capabilities of microfluidics by using microfabricated cantilevers with embedded fluidic channels. This innovation initiated new research and development directions in biology, biophysics, and material science. To acquire reliable and reproducible data, the calibration of the force sensor is crucial. Importantly, the hollow FluidFM cantilevers contain a row of parallel pillars inside a rectangular beam. The precise spring constant calibration of the internally structured cantilever is far from trivial, and existing methods generally assume simplifications that are not applicable to these special types of cantilevers. In addition, the Sader method, which is currently implemented by the FluidFM community, relies on the precise measurement of the quality factor, which renders the calibration of the spring constant sensitive to noise. In this study, the hydrodynamic function of these special types of hollow cantilevers was experimentally determined with different instruments. Based on the hydrodynamic function, a novel spring constant calibration method was adapted, which relied only on the two resonance frequencies of the cantilever, measured in air and in a liquid. Based on these results, our proposed method can be successfully used for the reliable, noise-free calibration of hollow FluidFM cantilevers.