Modeling atomic force microscopy and shell mechanical properties estimation of coated microbubbles

Inferring mechanical properties of the SARS-CoV-2 virus particle with nano-indentation tests and numerical simulations

The pandemic caused by the SARS-CoV-2 virus has claimed more than 6.5 million lives worldwide. This global challenge has led to accelerated development of highly effective vaccines tied to their ability to elicit a sustained immune response. While numerous studies have focused primarily on the spike (S) protein, less is known about the interior of the virus. Here we propose a methodology that combines several experimental and simulation techniques to elucidate the internal structure and mechanical properties of the SARS-CoV-2 virus. The mechanical response of the virus was analyzed by nanoindentation tests using a novel flat indenter and evaluated in comparison to a conventional sharp tip indentation. The elastic properties of the viral membrane were estimated by analytical solutions, molecular dynamics (MD) simulations on a membrane patch and by a 3D Finite Element (FE)-beam model of the virion's spike protein and membrane molecular structure. The FE-based inverse engineering approach provided a reasonable reproduction of the mechanical response of the virus from the sharp tip indentation and was successfully verified against the flat tip indentation results. The elastic modulus of the viral membrane was estimated in the range of 7-20 MPa. MD simulations showed that the presence of proteins significantly reduces the fracture strength of the membrane patch. However, FE simulations revealed an overall high fracture strength of the virus, with a mechanical behavior similar to the highly ductile behavior of engineering metallic materials. The failure mechanics of the membrane during sharp tip indentation includes progressive damage combined with localized collapse of the membrane due to severe bending. Furthermore, the results support the hypothesis of a close association of the long membrane proteins (M) with membrane-bound hexagonally packed ribonucleoproteins (RNPs). Beyond improved understanding of coronavirus structure, the present findings offer a knowledge base for the development of novel prevention and treatment methods that are independent of the immune system.

Quantitative Elasticity Mapping of Submicron Silica Hollow Particles by PeakForce QNM AFM Mode

Silica hollow spheres with a diameter of 100-300 nm and a shell thickness of 8±2 nm were synthesized using a self-templating amphiphilic polymeric precursor, i.e., poly(ethylene glycol)-substituted hyperbranched polyethoxysiloxane. Their elastic properties were addressed with a high-frequency AFM indentation method based on the PeakForce QNM (quantitative nanomechanical mapping) mode enabling simultaneous visualization of the surface morphology and high-resolution mapping of the mechanical properties. The factors affecting the accuracy of the mechanical measurements such as a local slope of the particle surface, deformation of the silica hollow particles by a solid substrate, shell thickness variation, and applied force range were analysed. The Young's modulus of the shell material was evaluated as E=26±7 GPa independent of the applied force in the elastic regime of deformations. Beyond the elastic regime, the buckling instability was observed revealing a non-linear force-deformation response with a hysteresis between the loading and unloading force-distance curves and irreversible deformation of the shell at high applied forces. Thus, it was demonstrated that PeakForce QNM mode can be used for quantitative measurements of the elastic properties of submicon-sized silica hollow particles with nano-size shell thickness, as well as for estimation of the buckling behaviour beyond the elastic regime of shell deformations.

Nanodeformations of microcapsules: comparing the effects of cross-linking and nanoparticles

The mechanical properties of proteinaceous and composite microcapsules loaded with oil were measured by SFM and evaluated using the Reissner model. Comparison of the obtained results reveals significantly higher Young’s moduli of protein capsules due to intermolecular crosslinking. In contrast, conformational restrictions in composite microcapsules inhibit protein crosslinking leading to the reduction of their elasticity.

SFM results for protein and composite microcapsules are evaluated by the Reissner model. Protein capsules show higher Young’s moduli due to crosslinking, which is absent in composite capsules because of restrictions in the protein conformations.

Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy

We introduce a model that describes spherical oscillations of encapsulated microbubbles in an unbounded surrounding fluid. A Rayleigh-Plesset-like equation is derived by coupling the Navier-Stokes equation that describes fluid dynamics with the Navier equation that describes solid dynamics via the internal/external boundary conditions. While previous models were restricted to incompressible isotropic shells, the solid shell is modeled here as a compressible viscoelastic isotropic material and then generalized to an anisotropic material. The exact value of the resonance frequency is calculated analytically, and the damping constant is computed in the approximation of weak damping. A correction of the widely used Church model for incompressible shells is evidenced, and the effects of shell compressibility and anisotropy are discussed.