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© 2021 by the authors. ; Over the last decades, nanomechanical sensors have received significant attention from the scientific community, as they find plenty of applications in many different research fields, ranging from fundamental physics to clinical diagnosis. Regarding biological applications, nanomechanical sensors have been used for characterizing biological entities, for detecting their presence, and for characterizing the forces and motion associated with fundamental biological processes, among many others. Thanks to the continuous advancement of micro- and nano-fabrication techniques, nanomechanical sensors have rapidly evolved towards more sensitive devices. At the same time, researchers have extensively worked on the development of theoretical models that enable one to access more, and more precise, information about the biological entities and/or biological processes of interest. This paper reviews the main theoretical models applied in this field. We first focus on the static mode, and then continue on to the dynamic one. Then, we center the attention on the theoretical models used when nanomechanical sensors are applied in liquids, the natural environment of biology. Theory is essential to properly unravel the nanomechanical sensors signals, as well as to optimize their designs. It provides access to the basic principles that govern nanomechanical sensors applications, along with their intrinsic capabilities, sensitivities, and fundamental limits of detection. ; This research was funded by the European Union's Horizon 2020 research and innovation program under grant agreement no. 731868—VIRUSCAN. ; Peer reviewed

Resumen del trabajo presentado en la Conferencia Española de Nanofotónica (CEN2021), celebrada de forma virtual del 20 al 22 de septiembre de 2021 ; Vibration modes of biological particles such as proteins, viruses and bacteria involve coherent structural vibrations at frequencies in the THz and GHz domains. These vibration modes carry information on its structure and mechanical properties that play a pivotal role in many relevant biological processes. Despite the rapid advances of optical spectroscopy techniques, detection of vibration modes of single bioparticles has remained elusive. Here we harness a particular regime in the physics of mechanical resonator sensing that serves for detecting them. By depositing single bacterium on the surface of ultra-high frequency optomechanical disk resonators, we demonstrate that the vibration modes of the disk and bacterium hybridize when their associated frequencies are similar (Figure). A general theoretical framework is developed to describe the different regimes that can be found when an analyte adsorbs on a mechanical resonant sensor. The model recovers the classical inertial mass sensing regime as a limit case of a more general problem. Theory, numerical calculations and experiments show excellent agreement, allowing to retrieve the eigenfrequencies and mechanical loss of the bacterium vibration modes. Our method is applied for analysis of the effect of hydration on the vibrational properties of a single bacterium. This work opens the door for a new class of vibrational spectrometry based on the use of high frequency mechanical resonators with the unique capability to obtain information on single biological entities ; This work was supported by the European Union's Horizon 2020 under grants agreement no. 731868 – VIRUSCAN, 681275 – LIQUIDMASS- ERC- CoG-2015 and 770933-NOMLI-ERC-CoG 2017. E. Gil-Santos acknowledge financial support by the Spanish Science and Innovation Ministry through the projects PID2019-109765RA-I00 and RYC2019-026626-I.