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

Abstract

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.

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

“…The experiment consists in nebulizing bacteria from a solution by means of the electrospray ionization technique. This nebulization enters the spectrometer and is guided through different vacuum stages to the sensor surface . Five different eigenfrequencies of the sensor are tracked continuously using the laser beam deflection method (Supporting Information Section S2) so every time a bacterium reaches the sensor surface, we observe abrupt changes in these eigenfrequencies.…”

“…In this work, we consider the case of a stressed membrane where the bending energy can be neglected, which is the most common case found in practice. For such a membrane, the different eigenfrequencies associated to the out-of-plane vibrations can be expressed as a function of two natural numbers ( m , n ) as f m , n = m 2 + AR 2 n 2 2 L x σ ρ where σ and ρ are the stress and density of the membrane, respectively. The mode shapes associated to these eigenfrequencies are given by ψ m , n ( X , Y ) = 2 sin ( m π true( X − 1 2 true) ) sin ( n π true( YAR − 1 2 true) ) where X = x / L x and Y = y / L x are the coordinates normalized to the length of the membrane.…”

“…Note that we assume that the potential energy of the membrane is not altered upon analyte adsorption, which is a very good approximation for the case of stressed membranes . Applying the Rayleigh–Ritz principle, the total kinetic energy must be equal to the total potential energy, giving as a result the equation for the system ( ω 2 false( M δ ij + normalΔ M ij false) − M Ω ij ) A i A j = 0 …”

“…If we know the frequencies before and after the adsorption, and the mass and position of the adsorbed particle, we can use eq to update the mode shape for the next event. The calculation of the mass and position of the adsorbed particle can be made by the inverse problem described elsewhere . The only difference is that for the modes that have degeneration, we must use eq instead of eq .…”

“…Another solution is to optimize the size and shape of the resonator to maximize the covered area of the cross section of the particle beam. In this regard, if the particle beam is symmetric (a circular beam is the most common), the optimum shape of the resonator should have an aspect ratio close to one, such as circular or square, covering as much area as possible . At the same time, the thickness of the resonator must be as low as possible to not compromise the mass sensitivity.…”