Toward single-molecule nanomechanical mass spectrometry
A. K. Naik
*,1
,
M. S. Hanay
*,1
,
W. K. Hiebert
*,1,2
,
X. L. Feng
1
, and
M. L. Roukes
†,1
1
Kavli Nanoscience Institute, California Institute of Technology, MC 114-36, Pasadena, CA 91125
USA
2
National Institute for Nanotechnology, National Research Council of Canada, Edmonton, Alberta
T6G 2M9 Canada
Abstract
Mass spectrometry (MS) provides rapid and quantitative identification of protein species with
relatively low sample consumption. Yet with the trend toward biological analysis at increasingly
smaller scales, ultimately down to the volume of an individual cell, MS with few-to-single
molecule sensitivity will be required. Nanoelectromechanical systems (NEMS) provide
unparalleled mass sensitivity, which is now sufficient for the detection of individual molecular
species in real time. Here we report the first demonstration of MS based on single-biological-
molecule detection with NEMS. In our NEMS-MS system, nanoparticles and protein species are
introduced by electrospray injection from fluid phase in ambient conditions into vacuum and
subsequently delivered to the NEMS detector by hexapole ion optics. Precipitous frequency shifts,
proportional to the mass, are recorded in real time as analytes adsorb, one-by-one, onto a phase-
locked, ultrahigh frequency NEMS resonator. These first NEMS-MS spectra, obtained with
modest mass sensitivity from only several hundred mass adsorption events, presage the future
capabilities of this approach. We also outline the substantial improvements that are feasible in the
near term, some of which are unique to NEMS-MS.
Nanoelectromechanical systems (NEMS)
1
are enabling important emerging applications in
diverse fields ranging from quantum measurement to biotechnology
2
-
9
. In general, the
smaller a device, the more susceptible are its physical properties to perturbation by external
influences. This enhanced sensitivity of NEMS is opening a variety of unprecedented
opportunities for applications such as mass spectrometry, a preeminent methodology for
proteomics
10
,
11
. Furthermore, to reliably detect expression of low level signals and to
understand the fundamental biological processes, it is important to develop techniques
capable of single cell or single molecule analyses
12
,
13
. In this work, the exceptional mass
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†
Corresponding author: roukes@caltech.edu.
*
These authors contributed equally to this work.
Author Contributions:
A.K.N. and M.S.H. fabricated devices, performed experiments, analyzed results and did some simulations.
W.K.H. designed and assembled the system and performed initial experiments. X.L.F. made devices and did the initial phase locked
loop measurements. M.L.R. conceived of the project and provided overall guidance throughout. All authors discussed results and were
involved in the analyses and manuscript preparation.
Supplementary Information accompanies this paper at
www.nature.com/nanotechnology
. Correspondence and requests for additional
materials should be requested to M.L.R.
HHS Public Access
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Nat Nanotechnol
. 2009 July ; 4(7): 445–450. doi:10.1038/nnano.2009.152.
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sensitivity of ultra high frequency (UHF) NEMS resonators
14
-
18
– derived from their
miniscule masses, high frequencies, and high resonance quality factors – is used to
demonstrate a new paradigm for mass spectrometry. Our approach enables the first real-time
detection of individual protein molecules and nanoparticles as they adsorb upon a sensitive
NEMS detector. We use these to carry out an initial form of mass spectrometry based on
discrete adsorption events.
The vibrational frequency of a NEMS resonator is an exquisitely sensitive function of its
total mass. Small variations in mass, for example, from adsorbed addenda, can measurably
alter its resonant frequency. Theoretical calculations for physically-realizable devices
indicate that NEMS mass sensitivity below a single Dalton (1Da=1amu) is achievable
19
,
20
.
Experimental measurements of NEMS mass sensing at the
∼
1000Da level
17
,
21
and, more
recently, below 200Da level
22
,
23
have been demonstrated. Our NEMS-MS paradigm is also
quite distinct from existing approaches to mass spectrometry in that the inertial mass of each
arriving species – atom, molecule, or nanoparticle – is “weighed” as the analyte adsorbs
upon the detector. Hence, a mass analyzer is not needed to pre-separate and aggregate
similar species. In fact, it is possible to contemplate circumventing analyte ionization
entirely if alternative injection and transport methods for neutral species are employed. This
may offer significant advantages for
whole-protein
MS of high-mass species by
circumventing electrostatic fragmentation. It should also dramatically reduce analyte
consumption by permitting the mass detector to be positioned in close proximity to the
protein source. The singular advantage of NEMS-MS is that each NEMS sensor in the
single-molecule limit acts an individual mass spectrometer. This NEMS-based system,
combined with other micro- and nanoscale technology
24
,
25
offers the possibility of compact,
massively-parallel MS, limited only by the number of NEMS mass sensors incorporated on
a chip.
NEMS-based Mass Spectrometry
Typically mass spectrometers comprise three separate components to provide the critical
functions of operation: analyte ionization, analyte separation, and detection. First, analyte
species in the fluid phase are ionized and bare (unsolvated) ions are produced using
electrospray ionization (ESI)
26
,
27
. Second, ion separation is undertaken in vacuum based on
the charge-to-mass (
m
/
z
) ratio of the analytes. Third, detection of clustered groups of these
analytes with similar
m
/
z
is carried out to determine the presence of a given species. Our
new paradigm of NEMS-MS combines the latter two of these functions into one: the NEMS
sensor is employed as both mass analyzer and mass detector. This NEMS mass analyzer/
detector, in this first realization described here, is preceded by well-validated mass
spectrometry components for analyte injection and delivery. Figure 1 schematically depicts
our prototype experimental system that introduces, transports, and measures the mass of
analytes. Protein ions or charged nanoparticles are produced and stripped of fluidic solvent
in the course of ESI. These bare ions traverse through a two-stage differentially pumped
vacuum system and land onto the NEMS mass analyzer/detector situated about 2 meters
away from the ESI source. Two stages of hexapole ion optics
28
driven at radio frequency (an
RF-only hexapole) is used to guide the species to the NEMS with minimal
m
/
z
discrimination, as desired (Supplementary Information). As the individual protein molecules
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and nanoparticles arrive and accrete onto the NEMS sensor, its resonant frequency jumps
downward
abruptly with each individual molecular or nanoparticle adsorption event
(Fig.
2). These precipitous events, which are absent during the control runs (Supplementary
Information), are the hallmark of NEMS mass sensing with single-molecule (-nanoparticle)
sensitivity. They are observed here directly for the first time, and are the centerpiece of this
work.
Each quasi-instantaneous frequency jump provides information about the specific atom,
molecule, or nanoparticle that has just adsorbed onto the sensor. The jump height for each
event – that is, the resonator's adsorbate-induced frequency deviation – depends upon both
the mass of the arriving analyte and its position-of-adsorption upon the NEMS resonator.
This response is characterized by a position-dependent mass responsivity for the NEMS
resonator (Supplementary Information).
Single-Molecule Event Analysis
There are two ways that we can extract the adsorbate mass from the convolved mass- and
position-dependence of these adsorption-induced jumps. The more difficult to achieve, but
conceptually most transparent, is to orchestrate simultaneous measurement of
both
jump-
height and landing position for each species as it arrives, in real time. We shall return to
discuss this option below. For our first proof-of-principle demonstration reported here, we
take a second, simpler approach – that of building histograms of event probability versus
frequency-shift amplitude for small ensembles of sequential single-molecule or single-
nanoparticle adsorption events. Figure 3a shows event probabilities calculated for sequential
adsorption events originating from a
monodisperse
source of nanoparticles and their
subsequent measurement by a NEMS detector. We assume the resonant mass detector to be
a doubly-clamped beam operating in fundamental mode, as in our experiments, and we scale
the results to correspond both to our experimentally-established NEMS mass responsivity
and Au nanoparticles we've employed, which have a nominal
∼
2.5nm radius (see below).
Figure 3a shows both the ideal case (zero nanoparticle size dispersion and perfect mass
sensitivity) as well as more realistic experimental situations that include both the effects of
finite size dispersion and the detector's frequency-fluctuation noise. Together these latter
effects reduce the resolution available in a practical system. It is readily apparent from
Figure 3 that the “canonical” event-probability response is
bicuspid
, with cusps near zero
and at a specific, maximum frequency shift that is associated with adsorption events at the
central, most sensitive region of the beam vibrating in fundamental mode. Below, we shall
employ this characteristic fundamental-mode event-probability shape function to achieve
mass analysis in these first NEMS-MS efforts.
NEMS-MS Spectra
We report here the first NEMS-MS spectra for proteins and nanoparticles. Our analyses are
carried out by observing, for each species introduced by electrospray, several hundred
discrete and abrupt frequency shifts in real time – each associated with an
individual
protein
or nanoparticle adsorption event. Each ESI run is followed by a control run of equal duration
during which the ESI solution pump is shut off to establish the frequency-fluctuation
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background (Supplementary Information). Given the
∼
250 Hz resolution in these
measurements, we construct event probability histograms with 250 Hz bins and, as
mentioned, reject false positives arising from frequency-fluctuation noise by discarding
jumps smaller than 2
σ
(=500Hz).
Figure 3b shows an experimental histogram constructed from data obtained by
electrospraying a colloidal solution of gold nanoparticles (Supplementary Information). The
Au nanoparticles employed are characterized by the vendor as having average radius of
2.5nm and standard deviation of “less than” 0.375nm (Sigma-Aldrich). What is ostensibly a
small standard deviation in radius actually corresponds to a rather large spread in
nanoparticle mass; the advertised specifications translate to an average mass of
∼
780kDa
and 1
σ
mass range from 480kDa to 1190kDa. This substantial dispersion, and our finite
frequency-fluctuation noise, together result in significant smoothing of the canonical
bicuspid spectrum expected for the ideal case (Fig. 3a).
Figure 3c shows the residues for a two-parameter least-squares fit of a theoretical event-
probability curve to the experimental histogram data. The two fitting parameters are average
nanoparticle radius and its dispersion; the theoretical curve incorporates the experimentally-
measured frequency-shift resolution of
δ
f
∼
250Hz. With this approach, by recording just
544 individual nanoparticle adsorption events, we resolve an average nanoparticle radius of
2.15nm for the dispersion, corresponding to an average mass of 490kDa, with a standard
deviation of nanoparticle radius of 0.5nm.
Figure 4 shows NEMS-MS spectra obtained for a “nominally pure” solution of the protein
bovine serum albumin (“BSA”, 66kDa) (Supplementary Information). From the standpoint
of MS, pure solutions of protein are the exception rather than the rule
29
,
30
, and the NEMS-
MS spectra of Figure 4 bear out this truism. Protein molecules often aggregate in solution to
form oligomers (Supplementary Information), and each distinct molecular assemblage
present in the sample will produce its own characteristic bicuspid NEMS-MS histogram. A
multi-component solution of such oligomers will thus superpose to produce a complex
spectrum.
The presence of a family of oligomers has two significant effects on the shape of NEMS-MS
histograms. First, the low-frequency-shift cusps for each of the oligomers (occurring at the
same, zero, frequency shift) superpose to produce a single, prominent peak. Second, the high
frequency-shift cusps of the oligomers, which occur at different frequency shifts
corresponding to each specific component's mass, become engulfed in the tails from other
components. This tends to suppress their overall individual prominence. Figure 4a and 4b
illustrate event probabilities as a function of frequency shift for electrosprayed BSA ions
that are transported to the NEMS sensor with a hexapole drive frequency of 1.1MHz. For
comparison, also shown are theoretically expected event probabilities for BSA oligomers,
generated using the experimentally-measured NEMS sensor's mass responsivity of
∼
12
Hz/zg and using a least-squares fit to the data – similar to that employed for the Au
nanoparticle dispersion, but here implemented to extract the spectral weights for the first
five oligomers (Supplementary Information). The spectrum in Figure 4a shows clear peaks
at 3375 Hz and 5875Hz, assigned to BSA trimers and pentamers, respectively. The broadly-
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distributed spectral weight below 2 kHz, arises from monomers and dimers. Note that this
full spectrum has been obtained by recording the individual adsorption of only 578 BSA
molecules.
Prospects for NEMS-MS
We believe these initial results demonstrate the potential of NEMS for mass spectrometry
and provide an unequivocal proof-of-principle for real-time detection of
individual
proteins
and nanoparticles. The full capabilities and sensitivity of the new NEMS-MS paradigm will
more fully unfold in a second-generation realization providing both mass-
and
position-
sensing in real time, for
each
analyte molecule as it arrives. This approach will completely
obviate the need for the histogram-based analyses used in the first demonstrations reported
here. The procedure for simultaneous mass and position sensing exists
31
,
32
, and has been
experimentally proven at the microscale
31
. In automated, real-time form, it involves the
simultaneous excitation, locking, and frequency-tracking of
multiple
vibrational modes of
the resonant NEMS mass sensor. As each analyte adsorbs onto the sensor, it induces a
distinct frequency shift for each of the modes monitored. The combined information from
the
time-correlated
shifts from just two modes provides sufficient information to deconvolve
the adsorbate's mass and position
for each event as it occurs
. Tracking additional modes
over-determines the solution, providing reduced variance in the deduced values of particle
mass and position-of-adsorption. This added technological component will permit the mass
of each arriving molecule to be quantitatively measured in real time as it adsorbs upon the
NEMS, down to the sensitivity limit imposed by the mass noise floor.
We outline below the anticipated capabilities of NEMS-MS vis-à-vis other current
techniques.
Mass resolution
Mass resolution in current implementations of MS typically is defined as the ratio of the
m
/
z
value and the width of the mass peaks at half maxima. The best mass resolution is obtained
with Fourier transform mass spectrometry (FTMS) systems which attain mass resolutions of
order 2,000,000 with typical measurement times of about a second. The resolution in FTMS
is high at low
m
/
z
, but becomes progressively worse with higher
m
/
z
. Unlike the current MS
systems which measure the mass to charge ratio, NEMS devices measure the mass of the
molecule directly. Attaining mass sensitivity of 1 Dalton (Da) with a NEMS device
20
will
provide the ability to distinguish two species differing by a single Da. For a 1 kDa molecule,
this would be equivalent to a mass resolution of 1000, however NEMS-MS is capable of
measuring molecules greatly exceeding the 1 MDa, which means state-of-the-art mass
resolution is attainable. With longer measurement times the mass sensitivity can be further
enhanced. The upper limit of the mass sensitivity is set by noise sources such as 1/
f
fluctuations and long term drifts, which always become predominant at long measurement
times. The state-of-the-art of mass sensing with NEMS devices has been improving roughly
by about an order of magnitude per year for the last several years; the current record is
approaching 100 Da
14
,
15
,
17
,
22
,
23
. The ultimate limits imposed by thermodynamically-driven
fluctuation processes have also been theoretically established to be comfortably below 1
Da
19
,
20
for measurement times in the ten millisecond range.
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Mass accuracy
Mass accuracy is the ability of the instrument to accurately establish the absolute mass/
charge (mass in NEMS MS) of the species and is usually expressed in parts per million. A
NEMS device with single Dalton mass sensitivity, calibrated with an appropriate mass
standard, will have a mass accuracy of 100ppm for a 10kDa molecule. In NEMS-MS the
accuracy increases in direct proportion to the the mass of the analyte molecule.
Mass or m/z range
NEMS devices have a exceptionally large mass dynamic range. These devices can easily
measure biomolecules with mass of tens of MDa and still be sensitive enough to detect mass
changes of single Dalton. The upper limit on the mass is set by the mass of the NEMS
device itself. Depending upon the details of adsorption, the properties of the NEMS become
affected only when the mass accreted becomes comparable to that of the device itself. This
translates into an upper mass limit of hundreds of MDa for typical devices
15
,
20
. The lower
mass limit in the case of detection of large biomolecules may ultimately become limited by
the spatial extent of the molecule compared to that of the NEMS sensor.
Scan speed
NEMS devices, in principle, are capable of mass sensitivities of single Dalton for
measurement (integration) times in the tens millisecond range. Additionally, in future
NEMS-MS systems, species of all m/z or masses will be measured simultaneously using
arrays of NEMS devices.
Efficiency of protein transport from the source to the NEMS detector
As mentioned, the NEMS-MS system combines the role of analyzer and the detector into a
single unit. This enables a significant reduction in the distance between the protein source
and the detector, and thus a corresponding improvement in the efficiency of the transport
and capture. In the so-called “nanoESI”-MS systems, for instance, efficiencies as high as
10% have been observed
33
. Loss of analyte molecules arises from a combination of factors
such as incomplete desolvation, transmission losses through the ion optics, and detection
inefficiency. We anticipate that future NEMS-MS systems will be based upon arrays of
NEMS devices to provide maximal capture efficiency.
Parallel processing of the mass information
In NEMS-based MS systems each NEMS device acts as an individual mass sensor. Here the
capture cross sectional area has dimensions of approximately 100nm × 1000nm. This small
cross-section has implications for the parallel-processing abilities of such a system. In 100
seconds, a modest NEMS-MS system consisting of 1,000 devices could
quantitatively
process 1,000 × 100 molecules/sec × 100 sec = 10 million molecules. Integration densities
that greatly exceed this have already been realized
34
. This throughput should be sufficient
for intensive analyses, for example, on individual mammalian cells.
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Enhancing NEMS-MS efficiency
Transitioning previous demonstrations of NEMS mass
sensing
, carried out under controlled
laboratory conditions, into practical and useful realizations of NEMS-based biological and
chemical mass
spectrometry
– with the potential to process thousands of proteins in tens of
milliseconds using only picoliters of sample – will require surmounting challenges in
nanoscale systems integration. In future implementations, analytes must be delivered from
aqueous phase, stripped of solvent – then delivered to and captured with high
efficiency
by
the NEMS sensor. More challenging will be attaining high
capture
efficiency; this
necessitates a mass detector with large capture cross-section. Given the minute size of
nanoscale detectors, this will be possible only through use of large sensor
arrays
positioned
in relatively close proximity to the analyte injection point. This will require practical routes
to very-large-scale integration of NEMS. It is also clearly essential to increase sample
throughput in future-generation NEMS-MS systems. The NEMS-MS paradigm is
exceptionally well-suited to these ends: highly multiplexed configurations involving,
potentially, thousands of injectors and detectors can each be co-integrated with microfluidic
pre-analysis and delivery components to create a system capable of efficiently analyzing
minute total volumes down to that of an individual cell. For the foreseeable future, we
believe that the recent advances in top-down wafer-scale nanofabrication processes provide
the only viable avenue to the requisite level of systems complexity. Accordingly, our current
work toward the advancement of NEMS-MS is focused upon NEMS arrays fabricated in this
manner
34
.
Methods
Protein/nanoparticle detection and frequency jump extraction
To accommodate the stochastic sequential arrival of individual protein molecules or
nanoparticles we automate our real-time analysis process. This involves two separate
procedures. First, we continuously track resonant frequency in real time, using a low-noise
UHF phase-locked loop (PLL) while protein ions or charged nanoparticles are injected by
electrospray and delivered to the NEMS sensor by the ion optics. Figure 2 shows a typical
experimental time record of the changes in resonant frequency of a phase-locked NEMS
mass sensor under such conditions.
Note that each abrupt frequency jump downward is the
result of a single protein molecule or nanoparticle landing on the NEMS mass sensor
.
Second, we automate the numerical extraction of the jump heights (frequency shifts) for
each individual adsorption event observed in these time records. Our procedure is to reject
jumps smaller than twice the frequency resolution of the phase-locked NEMS sensor, since
any such smaller events will be increasingly biased by false counts associated with the
“noise floor” set by the frequency instability of the phase-locked NEMS resonator. In our
current measurements this instability is characterized by a typical Allan deviation of
σ
A
(
τ
)
∼
2×10
-7
, for measurement integration times,
τ
, of order several seconds. This corresponds
to a one-standard-deviation frequency resolution of
δ
f
∼
250Hz and mass noise floor of
∼
10kDa in the experiments (Supplementary Information). For the remaining events,
identified by our automated and unbiased numerical procedure as experimentally-significant
(Δ
f
≥ 2 ×
δ
f
), we extract their corresponding jump heights (frequency shifts). This involves
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fitting the time record of each jump to the known temporal step-response function for our
phase-locked NEMS system using a nonlinear least-square fit. The response function is
separately calculated by PLL circuit theory, and has been experimentally verified,
separately, for each NEMS mass sensor employed in this work.
Physisorption
To ensure stable adsorption and immobilization of individual proteins on the NEMS
detector, the detector stage is maintained at a temperature of
∼
40K
in vacuo
. At reduced
temperature, physisorption due to van der Waals forces insures the proteins or nanoparticles
adsorb, and become immobilized, upon the detector's surface. Note that detector cooling is
required primarily for stable protein adsorption, not for enhanced noise performance.
Physisorption is also an ideal method for analyte immobilization in that it is non-specific
and it enables detector “recycling” by periodically warming the NEMS sensor to desorb
accreted species.
Measurement electronics
The detection circuitry utilizes a bridge circuit to null the UHF background near theNEMS
resonance
14
,
16
-
18
and a frequency-modulated, phase-locked loop (FM-PLL) to track the
NEMS resonant frequency in real time
15
. For the very low particle flux employed in this
initial work, a PLL time constant of several seconds ensures each abrupt frequency jump
event is recorded with many data points (Fig. 2, right inset). We determine the temporal
stability of the PLL system and characterize the frequency-fluctuation noise background by
operating in phase-lock over extended intervals (
≫
1000s), both with and without the
activation of ESI. Next-generation NEMS-MS systems, by incorporating recent advances in
NEMS mass sensors
17
, will be capable of significantly enhanced mass sensitivity.
We also monitor ion current reaching the detector stage with a Faraday cup placed in close
proximity to the NEMS detector that is connected to a high-resolution electrometer. In this
first-generation prototype, we do not attempt to demonstrate the potential of high throughput
NEMS-MS; the present system configuration provides a conveniently-infrequent analyte
arrival rate at the NEMS sensor. A typical current of
∼
1pA observed at the Faraday detector
yields about two adsorption events per minute.
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
Acknowledgments
We gratefully acknowledge support from the NIH under grant R21-GM072898 and, indirectly, from DARPA/MTO
under DOI/NBCH1050001 (MGA program) and SPAWAR/N66001-02-1-8914 (CSAC program). The latter has
enabled development of critical NEMS technology for this work. We thank S. Stryker for expert technical
assistance in constructing the NEMS-MS system; C.A. Zorman and M. Mehregany for custom SiC epilayers used
in our NEMS fabrication; V. Semenchenko, D. A. Van Valen and R. Philips for help with gel electrophoresis, and I.
Bargatin, J.L. Beauchamp, W. Lee, E.B. Myers, and M. Shahgoli for helpful discussions.
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Figure 1. First-generation NEMS-MS system
(a)
Simplified schematic of the experimental configuration (not to scale), showing the fluid-
phase electrospray ionization and injection, the system's two-stage differential pumping, and
its two-stage ion optics.
(b, c)
Progressively magnified scanning electron micrographs
showing one of the doubly-clamped beam NEMS devices used in these experiments. It is
embedded in a nanofabricated three-terminal UHF bridge circuit.
(d)
Magnitude and phase
of the UHF NEMS resonator's response displaying a prominent fundamental-mode
resonance near 428MHz.
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Figure 2. Real-time records of single-molecule adsorption events upon a NEMS mass sensor
(a) This raw experimental data shows the distinctly-different, precipitous resonance
frequency shifts of the NEMS during ESI-induced adsorption of bovine serum albumin
(BSA, 66kDa) and
β
-amylase (200kDa). Each frequency jump downward is due to an
individual protein adsorption event on the NEMS mass sensor. The height of each frequency
jump is a convolved function of the mass of the protein that has adsorbed, and its position of
adsorption upon the NEMS. (b) Raw data from a typical discrete event (blue dots), and a
non-linear least square fit to the system's response (orange line), based on the temporal
response function of the control loop.
(c):
Schematic illustrating single-molecule adsorption
events on a NEMS resonator (orange circles), and the coordinate system used to define its
position-dependent mass responsivity. The device itself is comprised of silicon carbide (dark
grey) with a metallic layers (light gray) on top. The silicon substrate (green) beneath the SiC
is etched to release (suspend) the doubly clamped beam.
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Figure 3. NEMS mass spectrometry of a gold nanoparticle dispersion
(a)
Theoretically expected event probabilities versus frequency-jump amplitudes are shown
for “nominal” 2.5nm radius Au nanoparticles (modeled assuming a 2.15 nm mean radius),
delivered with an average flux that is uniformly distributed over a doubly-clamped beam
having peak mass responsivity
∼
12Hz/zg. Traces show expected results for a monodisperse
ensemble of particles, as well as for several dispersions (characterized by their radius
standard deviations), for the cases of perfect (0Hz) and experimentally-relevant (250Hz)
frequency resolutions.
(b)
Experimentally obtained histogram of adsorption event
probabilities versus frequency-jump amplitude for electrosprayed gold nanoparticles, and
the expected curve for a average radius of 2.15nm and a radial dispersion of 0.375nm (black
trace). Error bars (dark yellow) display the theoretically-expected deviations corresponding
to 544 adsorption events, as registered in this experiment.
(c)
Contour plot showing the
residues for least-square fits to the experimental data using radius and radial dispersion as
the fitting parameter. These data establish the average radius and size dispersion for the 544
nanoparticles measured.
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Figure 4. NEMS mass spectrometry of proteins
NEMS-MS of bovine serum albumin (BSA) enabled by adsorption-event probability
analysis. Experimentally obtained frequency-jump data are binned into 250Hz histograms
commensurate with the experimental mass sensitivity. Applying a 2
σ
detection criterion, we
reject data below 500Hz (blue-shaded regions; see text).
(a)
Expanded view of the low-
event-probability region displaying a clearly detailed decomposition of the simultaneous
contributions from oligomers. The theoretical composite curve (grey) is a weighted
superposition of adsorption probabilities of the intact monomer and a family of its oligomers
deterministically calculated by a least-squares process similar to that of Figure 3
(Supplementary Information).
(b)
Full view of entire data set for the 578 BSA molecular
adsorption events recorded in this experiment. The numerically-determined best-fit
weighting coefficients for the composite curve are displayed in the legend.
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