Physics of Nanomechanical Spectrometry of Viruses

Abstract

There is an emerging need of nanotools able to quantify the mechanical properties of single biological entities. A promising approach is the measurement of the shifts of the resonant frequencies of ultrathin cantilevers induced by the adsorption of the studied biological systems. Here, we present a detailed theoretical analysis to calculate the resonance frequency shift induced by the mechanical stiffness of viral nanotubes. The model accounts for the high surface-to-volume ratio featured by single biological entities, the shape anisotropy and the interfacial adhesion. The model is applied to the case in which tobacco mosaic virus is randomly delivered to a silicon nitride cantilever. The theoretical framework opens the door to a novel paradigm for biological spectrometry as well as for measuring the Young's modulus of biological systems with minimal strains.I t is increasingly evident the intimate link between the mechanical properties of biological systems and its role in fundamental biological processes and disease 1 . This link spans from the molecular scale to the tissue scale. For example, the elasticity of cells has become a reliable indicator of cell transformation into cancerous or metastatic cells [2][3] . Similarly, recent reports have demonstrated the biological relevance of the mechanical properties of viruses. Viruses are able to dynamically modulate their mechanical properties in response to external forces, so as to withstand those forces or to ease cell infection 4 . For instance, in the human immunodeficiency and murine leukemia viruses, the stiffness largely decreases during the maturation process, acting as a mechanical switch for the infection process 5 . Strikingly, a single point mutation in the capsid protein of some viruses can significantly change their elasticity 6 . It is therefore fundamental the development of nanotools that enable the accurate quantification of the nanomechanical properties of single biological entities with high throughput. These tools can provide new insights on how the structural conformation, biological function, and mechanical properties of biomolecules and their hierarchical assemblies are related each other. The most prominent method to measure the mechanical properties of biological entities has been so far nanoindentation with the cantilever/tip assembly of an atomic force microscope (AFM) 7 . However, a number of challenges exist with the AFM for the quantification of the mechanical properties. Mainly, the nanoindentation curves strongly depend on the nanometer-scale geometry of the tip/sample contact, which in most of the cases cannot be controlled. Other difficulties include the contribution of the underlying substrate, the effect of adhesion, non-linear loading and the lack of accurate theoretical models.We envisage a novel biological spectrometry technique based on the measurement of several vibration modes of ultrathin micro-and nanocantilevers for the identification of adsorbed biomolecules and biological systems by two coordinates: the mass 8-11 an...

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“…Hence, the resulting frequency shift is the combination of all three mentioned parameters. In addition, the value of frequency shift depends also on the considered vibrational mode through a mode shape [28]. Fig.…”

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