Mass and stiffness spectrometry of nanoparticles and whole intact bacteria by multimode nanomechanical resonators

The identification of species is a fundamental problem in analytical chemistry and biology. Mass spectrometers identify species by their molecular mass with extremely high sensitivity (<10−24 g). However, its application is usually limited to light analytes (<10−19 g). Here we demonstrate that by using nanomechanical resonators, heavier analytes can be identified by their mass and stiffness. The method is demonstrated with spherical gold nanoparticles and whole intact E. coli bacteria delivered by electrospray ionization to microcantilever resonators placed in low vacuum at 0.1 torr. We develop a theoretical procedure for obtaining the mass, position and stiffness of the analytes arriving the resonator from the adsorption-induced eigenfrequency jumps. These results demonstrate the enormous potential of this technology for identification of large biological complexes near their native conformation, a goal that is beyond the capabilities of conventional mass spectrometers.

Postprocessing dark field optical microscopy image resulting of the subtraction of the images after and before the experiment (left). Big bumps are impurities produced during the cantilever fabrication and are not labelled. Seven nanoparticles were identified on the cantilever surface in consistency with the observed eigenfrequency jumps. The nanoparticles are numbered in order to correlate with the events identified in graph (a) using the inverse problem algorithm (main text). We confirmed that the identified dark-field spots were real nanoparticles by carrying out SEM characterization of two areas of the cantilever marked in the optical image (right). (c) Comparison between the positions measured by the optical microscope and the positions obtained applying our inverse problem algorithm (symbols). The line depicts the 'perfect' correlation. The positions are normalized to the length of the cantilever.

Capture Efficiency of GNPs
The capture efficiency of the gold nanoparticles defined as the ratio between the number of gold nanoparticles (GNPs) that reach the cantilever surface and the number of GNPs that leave the peek needle was estimated as follows. The GNP flow rate was measured just below the ESI source and also at the cantilever position by placing a Si substrate at both positions and ex-situ counting the nanoparticles that arrive the surface by a home-made dark-field optical microscope equipped with an ultrahigh-definition cooled color camera (DS-RI1, Nikon, Tokyo, Japan). The silicon substrates were previously cleaned with Piranha solution (3 H2SO4 : 1 H2O2).The GNPs on the Si substrates were analyzed by an algorithm written in Matlab (MathWorks®, USA) that identifies the nanoparticles and calculates the radial surface density of GNPs, which approximately follows a Gaussian distribution. Integrating the surface density for all the radii, we estimate that 1564 GNPs/s are emitted by the ESI needle. The flow rate of nanoparticles at the cantilever chamber is of 3.70.3 nanoparticles/s (Supplementary Fig. 1). This is 0.24% of the nanoparticles emitted by the ESI needle. The nanoparticle beam at the cantilever chamber exhibits very low divergence, 0.2 deg, that enables to collect most of the nanoparticles in a reduced area with radius of about 300 ( Supplementary Fig. 1). Accounting for the ratio of the cantilever plan view area to the ion beam cross-section, we estimate an overall collection efficiency of 10 -5 .

Calibration of the density and Young's modulus of the cantilevers
The density and the Young's modulus of the cantilevers were calculated from the frequency and quality factor in air taking advantage of the well-known hydrodynamic effects described by Sader's theory 1,2 . The resonant frequency and quality factor of the cantilever vibrating in air are given by, where is the radial resonant frequency in the fluid, is the density of the fluid, is the density of the cantilever, and ℎ are the width and thickness of the cantilever respectively, Γ ( ) and Γ ( ) are the real and imaginary part of the hydrodynamic function described in reference 1,2 and is the radial resonant frequency in vacuum given by, where is the Young's modulus of the cantilever. We experimentally determine the resonance frequency and quality factor from the frequency spectra of the thermal fluctuations of the microcantilevers in air. We substitute these values and the cantilever dimensions obtained by SEM in supplementary equations (1)-(3) to obtain the density and Young's modulus of the cantilever.
For the cantilevers used for nanomechanical spectrometry of gold nanoparticles, we obtained a density and a Young's modulus of 3374±94 kg/m 3 and 241±22 GPa, respectively. For the cantilevers used for the E. coli measurements, we obtained a density and a Young's modulus of 4127±103 kg/m 3 and 171±13 GPa, respectively.

Theory of the bending stiffness of E. coli bacteria
Since the shape of the E. coli bacteria is cylindrical, we use the model described in reference 3 for the calculation of parameter , where is the angle between the long axes of the bacteria and the cantilever beam, is the ratio between the length and the diameter of the bacteria, is the ratio between the contact width and the bacteria diameter and is the ratio between the diameter of the bacteria and the thickness of the cantilever.