Calibration of Dynamic Molecular Rulers
Based on Plasmon Coupling between
Bjo 1rn M. Reinhard,†,‡Merek Siu,§Harish Agarwal,†A. Paul Alivisatos,|,⊥and
Physics Department, Biophysics Graduate Program, and Chemistry Department,
UniVersity of California, Berkeley, California 94720, and Physical Biosciences
DiVision and Materials Sciences DiVision, Lawrence Berkeley National Laboratory,
Berkeley, California 94720
Received August 12, 2005; Revised Manuscript Received September 9, 2005
Pairs of noble metal nanoparticles can be used to measure distances via the distance dependence of their plasmon coupling. These “plasmon
rulers” offer exceptional photostability and brightness; however, the advantages and limitations of this approach remain to be explored. Here
we report detailed plasmon peak versus separation calibration curves for 42- and 87-nm-diameter particle pairs, determine their measurement
errors, and describe experimental procedures to improve their performance in biology, nanotechnology, and materials sciences.
The characterization of nanometer-sized machines, such as
artificial1and biological motors,2and of transient interactions
between individual macromolecules requires stable and
precise tools to measure absolute distances and distance
changes. However, continuous monitoring of distances is
challenging because of the small size of the systems of
interest (tens of nanometers) and the extremely broad range
of time scales. In cell differentiation and tissue growth, for
example, relevant time scales range from nanoseconds to
hours or longer. Molecular rulers based on single dye pair
fluorescence resonance energy transfer (FRET)3have been
the tool of choice for single-molecule measurements of
distance changes.4-7However, like all fluorescence-based
methods, FRET is constrained by the properties of organic
dyes: a short lifetime (<180 s) when continuously il-
luminated and blinking due to trapping in dark states.8,9
Conventional FRET measurements are also limited to a
distance range of <10 nm,10complicating the investigation
of the structural dynamics of large multicomponent systems
such as the ribosome, the DNA loops formed during
transcriptional regulation by distant enhancers,11and the
folding/unfolding of large proteins or RNAs.
In cases where probes with a diameter of 30-40 nm can
be tolerated, the limitations of FRET can be overcome with
a dynamic molecular ruler based on the distance-dependent
plasmon coupling of two noble metal nanoparticles.12A
particle plasmon refers to the collective oscillation of the
free electrons within a metal nanoparticle.13Noble metal
nanoparticles are efficient light scatterers at their plasmon
resonance frequency. The plasmon resonance frequency
depends on the size14-17and shape of the particles,15-19the
dielectric constant of the metal,13,17,20and the surrounding
medium.16,20-23When two nanoparticles are brought into
proximity (within ∼2.5 times the particle diameter)24their
plasmons couple in a distance-dependent manner.25As the
interparticle distance decreases, the coupled plasmon reso-
nance wavelength red-shifts. The distance dependence of the
plasmon coupling has been investigated at fixed interparticle
distances with different nanostructures such as spherical,26
cylindrical,27,28and elliptical nanoparticles,29trigonal prisms,28
and opposing tip-to-tip Au triangle (bowtie) nanostructures.30
In these studies, nanostructures were fabricated with top-
down fabrication techniques such as electron beam lithog-
raphy and thus had fixed interparticle spacing.
In contrast to the wealth of distance versus plasmon
coupling data available for fixed geometries in optically
homogeneous environments, there is currently very little
information available for dynamic geometries in optically
anisotropic environments. For the plasmon ruler to be a
versatile and robust tool in biology and materials science, it
is essential to obtain a wavelength versus distance relation-
ship that is valid under typical experimental conditions:
illumination by unpolarized light of functionalized particle
dimers randomly oriented in space. Ruler calibration can be
done experimentally (by measuring the resonance wavelength
* Corresponding author. E-mail: firstname.lastname@example.org.
†Physics Department, University of California, Berkeley.
‡Physical Biosciences Division, Lawrence Berkeley National Laboratory.
§Biophysics Graduate Program, University of California, Berkeley.
|Chemistry Department, University of California, Berkeley.
⊥Materials Sciences Division, Lawrence Berkeley National Laboratory.
Vol. 5, No. 11
10.1021/nl051592s CCC: $30.25
Published on Web 09/29/2005
© 2005 American Chemical Society
for a range of interparticle spacings) or theoretically, by
solving Maxwell’s equations. Here, we present a detailed
experimental and theoretical study of the distance dependence
of the plasmon resonance of single pairs of tethered gold
(Au) nanoparticles with an average diameter of either 42 or
Plasmon Resonance versus Distance Relationship. We
assembled dimers with various interparticle spacings and
measured their plasmon resonance wavelength in a darkfield
microscope using unpolarized white light (Figure 1a). We
used dsDNA spacers of 10 (42-nm particles only), 20, 40,
67, 110, and 250 basepairs (bps) modified with biotin and
digoxigenin at opposing ends to assemble dimers of anti-
digoxigenin and surface-immobilized Neutravidin-coated
gold nanoparticles (Figure 1b). Plasmon rulers are sensitive
analytical tools, and their plasmon wavelength also depends
on the ionic strength of the solution. To eliminate this
influence, we recorded all of the spectra under identical
buffer conditions (10 mM Tris, pH 7, 50 mM NaCl). For
details concerning the synthesis of protein-coated nanopar-
ticles and the directed assembly of plasmon rulers, please
refer to the Supporting Information.
Double-stranded DNA was chosen as a spacer material
because of its stiffness and well-understood synthesis and
functionalization technologies. The interparticle separation,
x, is given by the sum of the end-to-end distance of the DNA
and the thickness of the protein layer used to couple the DNA
to the particles. The end-to-end distance of the DNA was
obtained from its contour length using the wormlike-chain
model31(using a persistence length of 53 nm32and a contour
length per basepair of 0.34 nm), and the thickness of the
protein layer was measured by dynamic light scattering to
be ∼4 nm. Therefore, we added 8 nm to the DNA end-to-
end distances to obtain the interparticle spacing.
We used a very weak criterion for dimer formation: any
scattering source that changed intensity (Figure 1c) and color
(Figure 1d) upon addition of complementary particles (typi-
cally ∼6% of all particles) was considered to be a dimer.
Consequently, the results presented here represent a worst-
case lower bound on the performance of contemporary
plasmon rulers. Simple experimental procedures (described
later) improve the accuracy and reliability of plasmon rulers
As can be seen in Figure 2a and b, the plasmon resonance
distributions blue-shift with increasing interparticle distance.
The distributions for the 87-nm plasmon rulers are consis-
tently broader than those for the 42-nm particles. The average
plasmon resonance peak wavelength, λPR, as a function of x
is plotted in Figure 2c. We included data points for salt-
precipitated 42- and 87-nm dimers at x ) 0 and monomers
Figure 1. Darkfield microscopy of metal nanoparticles. (a) Experimental darkfield setup used for nanoparticle spectroscopy. (b) Directed
assembly of plasmon rulers. First, a Neutravidin-coated nanoparticle is immobilized on a BSA-biotin functionalized surface. Then, a second
antidigoxigenin coated nanoparticle is tethered to the immobilized nanoparticle using dsDNA that is labeled with both biotin and digoxigenin.
(c) Dimer formation leads to a vivid change in color and intensity, which allows detection of assembled plasmon rulers “by eye”. (d)
Spectra before and after dimer formation for 42-nm gold particles (DNA tether length: 67 bps).
Nano Lett., Vol. 5, No. 11, 20052247
(corresponding to infinite separation) at x ) ∞ nm. Our
directed dimer assembly strategy requires dsDNA spacers
and can therefore not generate dimers with zero separation.
Instead we used salt-precipitated “dimers”, which carry
neither proteins nor dsDNA spacers. The salt-induced
precipitation of bare Au nanoparticles cannot be well
controlled. Indeed, there seem to be two separated popula-
tions of resonance wavelengths for salt-precipitated 87-nm
Au nanoparticles, one centered at 635 nm and the other at
685 nm, indicating substantial contributions from larger
The measured resonance wavelength versus distance
relationships are well-fit by simple exponentials (Figure 2c,
continuous lines). Two qualitative trends are apparent. First,
the peak resonance of the 87-nm dimers for all spacer lengths
is consistently further in the red than for the 42-nm dimers.
For particles with a diameter greater than 10 nm, the resonant
peak energy (and therefore the peak wavelength) is expected
to red-shift with increasing size because of electromagnetic
retardation.13Second, the peak wavelengths blue-shift with
increasing interparticle separation because of reduced near-
field coupling, confirming and illustrating the physical
principle underlying plasmon rulers.
The slopes of the λPR(x) calibration curves bracket the
useful dynamic range of the two rulers. The calibration curve
for the 42-nm dimers has a steeper initial slope. Between x
) 0 and x ) 14.7 nm, the average peak wavelength has
already dropped by 58.9 nm. This drop is about 70% of the
total spectral shift ∆λPR between dimers at x ) 0 and
monomers, which resemble noninteracting dimers at infinite
separation. For the 87-nm particles, the average peak
wavelength drops by 27.2 nm between x ) 0 and x ) 14.7
nm, which represents only about 30% of the total spectral
change, ∆λPR. For the largest spacer molecules (x ) 75.3
nm) the measured plasmon wavelengths are still red-shifted
with respect to the isolated monomers for both rulers. This
indicates that there is still nonnegligible plasmon coupling
between the gold particles at these distances. The spectral
gap between monomers and dimers at 75.3 nm is distinctly
smaller for 42-nm dimers (∆λPR) 7.8 nm) than for 87-nm
dimers (∆λPR) 22.7 nm). Because of the steep slope of the
λPR(x) curve at short distances, the 42-nm plasmon ruler can
best detect distance changes at short interparticle distances
(<15 nm). For spacer lengths >20 bps, the slope in the λPR-
(x) calibration curve is steeper for the 87-nm plasmon ruler,
whereas the 42-nm curve has nearly converged. The 87-nm
plasmon ruler thus covers a larger distance range, albeit with
a reduced resolution.
One feature that is absent from our calibration curves
deserves comment. Fromm et al.30demonstrated that for
nanoparticle bowtie structures illuminated with light polarized
along the interparticle axis the resonance shift changes sign
at a critical interparticle distance. In our experiments, red-
shifts with increasing x are not observed, indicating that the
Figure 2. Plasmon resonance vs interparticle separation. Distributions of measured plasmon resonance wavelengths for selected dsDNA
spacer lengths for (a) 87-nm Au plasmon rulers and (b) 42-nm Au plasmon rulers. We included data points for salt-precipitated dimers at
x ) 0. (c) Plot of the average plasmon resonance as a function of spacer length, L, (bottom axis) and approximated interparticle distance
x (top axis) for 42- (red squares) and 87-nm (blue circles) plasmon rulers. The plasmon resonance wavelengths for dimers with infinite
separations ()monomers) are included as open symbols. The reported errors are the standard errors of the mean. The continuous lines show
fits (single exponentials y(x) ) A0*exp(-x/D0) + C) to the experimental data. Best-fit parameters for 42-nm Au particles: C ) 550.87 nm,
A0) 73.48 nm, D0) 10.24 nm; for 87-nm Au particles: C ) 579.66 nm, A0) 74.42 nm, D0) 30.23 nm. The dotted lines represent
T-matrix simulations by Wei et al.29assuming illumination with light polarized along the interparticle axis and dot-dashed lines are T-matrix
simulations assuming nonpolarized illumination.
Nano Lett., Vol. 5, No. 11, 2005
investigated distance range is below the threshold at which
the sign of the coupling reverses for spherical particles.
Simulations of Plasmon Shift versus Interparticle
Spacing. Are our measurements consistent with theory and
previous results? Recently, Wei et al.29obtained the wave-
length versus distance relationships for pairs of bare 40- or
80-nm gold nanoparticles. In their simulations, they assumed
that nE(the refractive index of the particle’s environment)
was 1.5 and that the electromagnetic field was linearly
polarized along a fixed interparticle axis. However, in
potential biophysical or cell biological applications of
plasmon rulers, the orientation of the interparticle axis
relative to the incident light will typically vary with time.
To approximate our experimental illumination conditions (the
particles’ random orientation in space and the use of
unpolarized light), we simulated the plasmon shift versus
interparticle separation relationship by averaging over a wide
range of incident wave vectors and light polarizations (see
the Supporting Information). In these calculations, we applied
the discrete dipole approximation (DDA)33and the T-matrix
method.34Although the actual experimental geometry is
clearly more complex, we initially approximated the plasmon
rulers by two spherical particles immersed in a homogeneous
solution. This approximation was later relaxed. Figure 3
shows normalized spectra from typical experiments and our
T-matrix simulations for 42- and 87-nm Au plasmon rulers
at selected spacer lengths. The correspondence between
experiment and simulation is very good for the peak width
and shape; for the peak wavelength, correspondence is
reasonable. Differences between experimental and calculated
spectra can be due to the nonspherical shape of the real
probes, formation of multiple tethers between the nanopar-
ticles, as well as simplifications inherent in the T-matrix
simulations. Our calculations also do not account for protein
functionalization of the nanoparticles, the ionic strength of
the buffer, and the blocking reagent applied to the coverslip
To partially account for these features of our experiments,
we performed additional simulations in which nEwas a free
parameter representing a weighted average of the various
materials that surround the particle. The DDA approach
reproduced the overall trend of the experimental data but
because of the high computational cost of this method, we
were unable to produce good fits to the data. We obtained
the best agreement between the simulated and experimental
data using a T-matrix calculation with nE ) 1.6. This
refractive index is reasonable for protein-coated gold nano-
particles. Proteins typically have a refractive index of about
1.6, even when adsorbed.35,36The resulting curves are
included in Figure 2c as dot-dashed lines. We also included
the λPRversus x relationship predicted by Wei et al., assuming
light polarized strictly along the interparticle axis (dashed
lines). For the 42-nm plasmon rulers, our T-matrix simula-
tions and those by Wei et al. show good quantitative
agreement with the experimental data, except for the
precipitated dimers at x ) 0.
For the 87-nm plasmon rulers, both types of calculations
fail to describe the experimental results over the complete
distance range. The Wei et al. curve reports the plasmon
peak due to light polarized along the symmetry axis, and
therefore, driving the parallel mode. However, in our
measured spectra (collected with unpolarized illumination),
the perpendicular mode is present and distorts the spectra
(Figure 3b and c). The perpendicular mode is most prominent
at short interparticle separations, where the Wei et al.
simulations perform most poorly. Our T-matrix simulations
Figure 3. Comparison of measured and simulated spectra. Experimental and T-matrix simulated spectra (dashed line) for 87-nm Au dimers
with (a) infinite separation, (b) 67 bps dsDNA spacer (29.3 nm), (c) 20 bps dsDNA spacer (14.7 nm), and for 42-nm Au dimers with (d)
infinite separation, (e) 67 bps dsDNA spacer (29.3 nm), and (f) 20 bps dsDNA spacer (14.7 nm). For the simulations, illumination with
unpolarized light was assumed.
Nano Lett., Vol. 5, No. 11, 2005 2249
do not fit the data at any separation, even though we averaged
over many polarizations to account for the random orientation
of the particles and the use of unpolarized light. The excellent
fit of the Wei et al. curve to our data at larger separations
suggests that our illumination light was partially polarized
in the focal plane (along the ruler’s symmetry axis) and the
parallel mode thus dominates our signal. Given the geometry
of darkfield illumination and the numerous reflecting surfaces
between the light source and the sample, some degree of
polarization cannot be excluded. In conclusion, the 42-nm
rulers are much more robust toward polarization effects, and
thus should be used in cases where the distance between
particles is the primary desired readout. When larger particles
are used to assemble plasmon rulers, polarization effects must
be carefully accounted for. Of course, polarization sensitivity
also has benefits because it can be used to determine the
relative orientation of a plasmon ruler with respect to the
polarization of the illumination light (via the relative height
and position of the two plasmon peaks).
Measurement Errors. We quantified the magnitude and
the distance dependence of the measurement error inherent
to contemporary plasmon rulers. We fitted single exponen-
tials to the upper and lower error bars of the λPR(x) curves
(Figure 2c) and inverted the resonance wavelength-distance
relationship, yielding the measurement error, ∆x, as a
function of λPR. The absolute spatial resolution of plasmon
rulers is distance dependent and decreases with increasing
interparticle distance, and the relative error, ∆x/x, is smallest
around 15 nm (42-nm rulers) and 30 nm (87-nm rulers)
(Figure 4). The larger rulers should be used in experiments
where the typical separations are larger than the intersection
of the two error curves in Figure 4 (32 nm). The measured
spatial resolution is acceptable for many biophysical and cell
biological applications for separations <25 nm (42-nm rulers)
or <65 nm (87-nm rulers).
What limits our ability to extract absolute distances from
plasmon rulers? In principle, there should be no variation of
the plasmon peak position for a given set of conditions. In
practice, however, each particle dimer will differ from all
other dimers, introducing measurement uncertainty. Numer-
ous sources of dimer-to-dimer variations exist, including
variation of the number of DNA tethers between the two
particles and the precise diameter and shape of each particle.
The interparticle distance will decrease with increasing
number of tethers. Under our experimental conditions, the
number of dsDNA molecules bound to the functionalized
nanoparticles is roughly 200 per 42-nm particle (Supporting
Information Figure S1). This corresponds to an average
surface coverage of 1 dsDNA molecule per ∼25 nm2. Given
this dsDNA density, the formation of multiple tethers
between the nanoparticles cannot be excluded. Any variation
of the number of tethers between the particles will broaden
the distribution of the measured resonance wavelengths at a
given spacer length. Because this error source is asym-
metrical, that is, it can only decrease the interparticle spacing,
the overall effect of multiple tethering will be to red-shift
the average plasmon peak.
Particle heterogeneity is another major source of measure-
ment uncertainty because the size and shape influence a
particle’s scattering spectrum and the surrounding field
density. For example, triangular- and pentameric-shaped
nanoparticles have different plasmon resonances than spheri-
cal particles.14Our commercially obtained “40”- and “80”-
nm-diameter nanoparticle preparations had an actual diameter
of 41.7 ( 3.1 nm and 86.9 ( 5.5 nm (Figure 5a and c), as
judged from transmission electron microscopy (TEM) analy-
sis of ∼125 particles per nominal diameter. Moreover, most
particles are ellipsoidal with aspect ratios of ∼1.06 (Figure
5b and d); the TEM images also reveal that triangular and
pentameric shapes occur in nonnegligible amounts (tri-
angles: 3.3% (42 nm), 6.6% (87 nm); pentamers: 5.3% (42
nm), 4.8% (87 nm)) (Figure 5e). Thus, sphere-sphere dimers
are likely to constitute ∼80% of all dimers, and sphere-
triangle and sphere-pentamers about 10%.
To estimate the contribution of particle heterogeneity to
the width of the plasmon peak distributions (Figure 2a and
b), we performed DDA simulations of plasmon coupling
between the most likely contaminants (sphere-triangle and
sphere-pentamer dimers). We held the particle volume fixed
at the volume of an 80-nm sphere and the interparticle
spacing to 19.1 nm and varied the shape. Compared to the
peak plasmon of a sphere-sphere dimer, the peak plasmon
of a sphere-triangular prism dimer was blue-shifted by 22
nm, and the peak plasmon of a sphere-pentagonal prism
dimer was blue-shifted by 25 nm. The blue-shifting of the
plasmon peak in these assemblies is expected because the
coupling between two plasmons depends on the degree to
which their normal modes overlap: any departure from an
ideal sphere-sphere case will degrade coupling, blue-shifting
the plasmon peak.
Concluding Remarks. Taken together, the experimental
calibration experiments, the calculations, and the TEM
Figure 4. Distance dependence of the relative error, ∆x/x, of two
types of plasmon rulers. 42-nm Au plasmon rulers have the best
spatial resolution at an interparticle separation of around 14 nm,
87-nm Au plasmon rulers exhibit highest resolution at 30 nm. The
error curves intersect at x ) 32 nm. At distances below this
threshold, the 42-nm plasmon rulers are more precise than the 87-
nm plasmon rulers.
Nano Lett., Vol. 5, No. 11, 2005
analyses of particle shapes reveal that plasmon rulers are
already a useful material for single-molecule biophysics and
nanotechnology. Even with a loose selection criterion for
particle dimers and employment of heterogeneous off-the-
shelf particle preparations, distances between 1 and 80 nm
can be measured with a time resolution <50 ms (with 80-
nm particles) and with absolute distance errors ranging from
<1 nm to around 20 nm. Because of the steep slope of the
λPRversus x relationship for 42-nm plasmon rulers, this ruler
is most sensitive in the distance range between 0 and 20
nm; significantly larger distances can be measured with
poorer spatial resolution. The λPRversus x relationship for
Figure 5. Heterogeneity of nanoparticle preparations. Size distributions for particles with nominal diameters of (a) 80 nm and (b) 40 nm
obtained with transmission electron microscopy (TEM). Differences in diameter measured along two perpendicular axes for (c) 80-nm and
(d) 40-nm Au nanoparticles. (e) TEM pictures of selected shapes found in the nanoparticle preparations.
Figure 6. Improved procedure for use of plasmon rulers in single-molecule biophysics and nanotechnology. (a) First, a color CCD camera
should be used to identify individual particles, as judged by their scattering intensity and color (blue circles). (b) Then, complementary
particles should be introduced into the flow chamber, and scattering sources whose color and intensity changed should be located (red
circles). (c) Finally, spectra for candidate plasmon rulers should be recorded, allowing identification of well-behaved plasmon rulers by
comparison of its spectrum with a simulated or empirically obtained standard spectrum. All of these steps can be fully automated via
suitable image processing software and a nanopositioning three-axis stage.
Nano Lett., Vol. 5, No. 11, 20052251
87-nm plasmon rulers is less steep, allowing the measurement
of larger distances and distance changes, albeit with a reduced
resolution. The accuracy of absolute distance measurements
is limited principally by size and shape heterogeneity of the
nanoparticles and the possibility of multiple tether formation
The accuracy of plasmon rulers should improve more than
4-fold for the 42-nm particles and more than 10-fold for the
87-nm particles by employing a simple enrichment and
validation procedure (Figure 6) that exploits a fundamental
advantage of single-molecule approaches: ruler assembly can
be monitored step by step, and at each stage, the nascent
ruler can be compared to a predefined standard such as a
simulated spectrum or empirically obtained standard spec-
trum. This procedure involves, per field of view, the
acquisition of two color images, some simple image process-
ing, and the subsequent acquisition of scattering spectra
(Figure 6). Given our present setup and frame rates, and
assuming the use of custom software and a commercial three-
axis positioning system or a slitless spectrometer, we estimate
that this procedure should identify 1-3 well-behaved plas-
mon rulers per field of view per minute. This approach is
conceptually identical to the one that has been refined over
the past decade for single-molecule fluorescence experiments
in which only FRET pairs fulfilling certain stringent criteria
(e.g., anticorrelation of donor and acceptor emissions and
single-step bleaching) are subject to further analysis.
To take full advantage of the long distance range of the
plasmon ruler, synthetic strategies have to be developed to
lower the surface density of tethering biopolymers and to
improve the size and shape homogeneity of the nanoparticles.
Both of these issues do not present fundamental limitations
of the technique. Already, 10-nm gold nanoparticles can be
functionalized routinely with a single DNA molecule,37and
new promising synthetic approaches to better size and shape
control, like the polymer-mediated polyol process, are being
Acknowledgment. We acknowledge financial support
from the Deutsche Forschungsgemeinschaft (B.M.R.), a
Howard Hughes predoctoral fellowship (M.S.), and a NSF
Graduate Research Fellowship (H.A.). This work was
supported in part by the Director, Office of Energy Research,
Office of Science, Division of Materials Sciences, of the U.S.
Department of Energy under contract no. DE-AC02-
05CH11231 and by the NIH National Center for Research
Resources through the University of California, Los Angeles,
subaward agreement no. 0980 G FD623 through the U.S.
Department of Energy. We are also grateful to Bruce Draine
and Michael Mishchenko for making their DDA and T-
matrix code publicly available and to Phillip Geissler for
his generous allowance of computational time on his cluster.
We thank Aleksandra Radenovic for taking the TEM images
and Hari Shroff for helpful discussions.
Supporting Information Available: Materials and meth-
ods, determination of the DNA coverage of Neutravidin gold
nanoparticle conjugates, and Figure S1. This material is
available free of charge via the Internet at http://pubs.acs.org.
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