Square Membrane Resonators Supporting Degenerate Modes of Vibration for High-Throughput Mass Spectrometry of Single Bacterial Cells.

In nanomechanical mass spectrometry, sensing devices are commonly placed in the vacuum environment and a stream of analytes is directed toward the sensor surface for measurement. Beam structures, such as double-clamped nanobeams and nanocantilevers, are commonly used due to their low inertial mass and the simplicity of the analytical models for mass extraction. The drawback of such structures is their low capture areas, compromising the capture efficiency and throughput of this technique. Bi-axisymmetric resonators, such as ultrathin square or circular membranes, arise as an optimal geometry to maximize capture efficiency while minimizing the device inertial mass. However, these structures present degenerate mechanical modes, whose frequency perturbations upon analyte adsorption are not well described by commonly used models. Furthermore, prior knowledge of the vibration mode shapes of the sensor is crucial for the correct calculation of the analyte's mass, and the mode shape of degenerate modes may change significantly after every adsorption event. In this work, we present an accurate analytical theory to describe the effect of mass adsorption on the degenerate modes of square membrane resonators and propose two different methods based on the new theory to update the vibration mode shapes after every adsorption event. Finally, we illustrate the problem experimentally obtaining the mass and adsorption position of individual Escherichia coli K-12 bacterial cells on commercial square silicon nitride membranes fabricated with very small tolerances.

High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators.

How bacteria are able to maintain their size remains an open question. Techniques that can measure the biomass (dry mass) of single cells with high precision and high-throughput are demanded to elucidate this question. Here, we present a technological approach that combines the transport, guiding and focusing of individual bacteria from solution to the surface of an ultrathin silicon nitride membrane resonator in vacuum. The resonance frequencies of the membrane undergo abrupt variations at the instants where single cells land on the membrane surface. The resonator design displays a quasi-symmetric rectangular shape with an extraordinary capture area of 0.14 mm2, while maintaining a high mass resolution of 0.7 fg (1 fg = 10-15 g) to precisely resolve the dry mass of single cells. The small rectangularity of the membrane provides unprecedented frequency density of vibration modes that enables to retrieve the mass of individual cells with high accuracy by specially developed inverse problem theory. We apply this approach for profiling the dry mass distribution in Staphylococcus epidermidis and Escherichia coli cells. The technique allows the determination of the dry mass of single bacterial cells with an accuracy of about 1% at an unparalleled throughput of 20 cells/min. Finally, we revisit Koch & Schaechter model developed during 60 s to assess the intrinsic sources of stochasticity that originate cell size heterogeneity in steady-state populations. The results reveal the importance of mass resolution to correctly describe these mechanisms.