Measurement of Single Macromolecule Orientation by Total Internal
Reflection Fluorescence Polarization Microscopy
Joseph N. Forkey, Margot E. Quinlan, and Yale E. Goldman
Pennsylvania Muscle Institute and Department of Physiology, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6083
single molecule fluorescence polarization (SMFP) microscopy. The technique uses the unique polarizations of evanescent
waves generated by total internal reflection to excite the dipole moment of individual fluorophores. To evaluate the new SMFP
technique, single molecule orientation measurements from sparsely labeled F-actin are compared to ensemble-averaged
orientation data from similarly prepared densely labeled F-actin. Standard deviations of the SMFP measurements taken at 40
ms time intervals indicate that the uncertainty for individual measurements of axial and azimuthal angles is ;10? at 40 ms time
resolution. Comparison with ensemble data shows there are no substantial systematic errors associated with the single
molecule measurements. In addition to evaluating the technique, the data also provide a new measurement of the torsional
rigidity of F-actin. These measurements support the smaller of two values of the torsional rigidity of F-actin previously reported.
A new approach is presented for measuring the three-dimensional orientation of individual macromolecules using
High-resolution structures of proteins trapped in distinct
static configurations have shown that rotational motions of
compact domains are a common feature of their enzymatic
and energy transducing mechanisms (1–11). In all of these
systems, plausible relationships have been proposed between
the observed rotational motions and the functional output,
buttestingthe structurally derivedhypotheses requires detec-
tion of the timing and extent of the rotations during activity.
Fluorescence polarization on bulk biological samples,
such as suspensions of macromolecules or lipid vesicles, is a
commonly used method to detect rotational motions (12,13).
The signals are typically sensitive to the time course and
extent of motions of the probe molecules. The method is well
suited to detect time-resolved structural changes in organized
systems, such as proteins embedded in lipid membranes (14)
or muscle fibers (15). In these samples having a symmetry
axis, the absolute distribution of probe orientations relative
to that axis becomes available (16). With the recent avail-
ability of probes having known local orientation within the
domain of interest (17,18), the information can be directly
converted into distributions and motions of the local molec-
ular domain. Among techniques available for detecting
protein rotational motions, fluorescence polarization has the
advantages of good sensitivity and time resolution and being
relatively straightforward to set up and interpret.
In bulk experiments, however, relating the information
about protein distributions to the orientation and dynamics of
individual protein molecules is difficult because of averaging
over an unsynchronized population. Abrupt perturbations of
a molecular ensemble, such as temperature or pressure jumps,
or rapid addition of substrate, can partially synchronize the
population, but some important characteristics, such as fast
or backward reaction steps and rare states, are usually not
Single molecule fluorescence measurements have been
used to avoid the complications caused by the ensemble
averaging in measurements on molecular distributions. Where-
as most single molecule experiments have been focused on
detecting the temporally resolved location of individual
molecules, some have used fluorescence polarization to also
determine structural information (e.g., 19–22). Single mole-
cule fluorescence polarization has the potential to bridge
the gap between techniques with atomic spatial resolution
but poor time resolution (e.g., x-ray crystallography) and
those capable of resolving kinetics but giving somewhat
ambiguous structural information (e.g., fluorescence energy
Here, we present single molecule fluorescence polariza-
tion instrumentation that utilizes total internal reflection
(TIR) microscopy. The TIR excitation offers an advantage
over epifluorescence and confocal microscopy of a strong
polarization component along the z axis (optical axis of the
microscope) as well as along the x and y axes, making it
possible to determine the three-dimensional (3D) orientation
(22,23). Analytical techniques are described to determine,
with a temporal resolution of ;1–40 ms, the full 3D orien-
tation of individual fluorescent probes and the extent of their
wobbling motions on the microsecond and subnanosecond
timescales. Comparison of single molecule and ensemble
measurements of rhodamine bound to actin filaments are
Submitted September 23, 2004, and accepted for publication April 27, 2005.
Address reprint requests to Yale E. Goldman, Tel. 215-898-4017; Fax:
215-898-2653; Email: firstname.lastname@example.org.
Joseph N. Forkey’s present address is Precision Optics Corp., Gardner, MA
Margot E. Quinlan’s present address is Dept. of Cellular and Molecular
Pharmacology, University of California San Francisco, San Francisco, CA
? 2005 by the Biophysical Society
Biophysical JournalVolume 89 August 2005 1261–12711261
used to evaluate the accuracy and limits of the technique.
Large rotational motions of the rhodamine probes (40? half-
width of the wobble cone) on the microsecond timescale
confirm other measurements of the dynamics of actin mono-
mers in filaments that have been hypothesized to be crucial
for actomyosin-based motility (24).
Fast skeletal muscle myosin II was purified from New Zealand white rabbit
back muscle as described by Margossian and Lowey (25) with minor
modifications. Myosinwas storedin 0.3 M KCl, 5mM Hepes, pH7.0, 5 mM
NaN3and 50% glycerol at ?20?C for up to 6 months. Actin was also
purified from rabbit muscle according to a protocol similar to Spudich and
Watt (26) as modified by Murray et al. (27). G-actin was stored on ice in
G-buffer (2 mM Tris, pH 8.0, 0.2 mM CaCl2, 0.2 mM ATP, 0.5 mM DTT)
for 3–4 weeks or frozen in liquid N2and stored at ?80?C for up to a year.
G-actin was labeled at Cys374with either 1,5-I-AEDANS (N-(iodoacetyl-
N9(5-sulfo-1-napthyl)ethylenediamine, Sigma, St. Louis, MO, No. I8879) or
5-IATR (5-iodoacetamidotetramethylrhodamine, a gift from J. E. T. Corrie,
National Institute for Medical Research, Mill Hill, London) following the
protocol for labeling with pyrenyl-iodoacetamide (28) with minor
modifications. Actin concentration and extent of labeling were determined
using e290¼ 2.66 3 104M?1cm?1for actin (29), e549¼ 9.69 3 104M?1
cm?1and e290/e549¼ 0.21 for ATR (30,31), and e337¼ 6.0 3 103M?1cm?1
and e290/e337¼ 0.21 for AEDANS (32). Labeled G-actin was aliquoted,
rapidly frozen in liquid nitrogen, and stored at ?80?C for up to 1 year. F-
actin with various ratios of AEDANS-labeled, ATR-labeled, and unlabeled
actin was made at a total actin concentration of 1 mM in F-buffer (10 mM
Hepes, pH 7.0, 75 mM KCl, 2.5 mM MgCl2) and stabilized with 5 mM
phalloidin (Molecular Probes, Eugene, OR). Sparsely labeled F-actin was
polymerized with 0.1% ATR-actin, 86% AEDANS-actin, and 14%
unlabeled actin, whereas densely labeled F-actin had 10% ATR-actin,
10% AEDANS-actin, and 80% unlabeled actin. F-actin was stored on ice
and used for up to 1 month.
Labeled actin was held close to the microscope slide surface by binding to
adhered myosin in the absence of ATP. A 10–20 ml flow cell was prepared
using a 25 mm 3 76 mm 3 1 mm thick fused silica slide (Quartz Scientific,
Fairport Harbor, OH), a 22 mm 3 30 mm No.1 glass coverslip (Fisher
Scientific, Hampton, NH), and two pieces of double-sided adhesive tape
(Scotch, ;80 mm thick). All buffers were passed through the flow cell by
capillary action driven by wicking into filter paper; 30 ml of 225 nM full-
length skeletal muscle myosin in high salt buffer (20 mM Hepes, pH 7.0,
5 mM MgCl2, 600 mM KCl, 20 mM DTT) was added first and allowed to
stand for 2–5 min. Next, 30 ml of 100 nM F-actin in F-buffer plus 20 mM
DTT and 1 mM ATP was flowed in and allowed to stand for 5 min. Finally,
120 ml of F-buffer with 20 mM DTT was flowed through. Introducing the
F-actin first in the presence of ATP, and then removing the ATP, aided in
aligning filaments with the flow direction.
The experimental apparatus (Fig. 1) was built around a Nikon TE-300
inverted epifluorescence microscope equipped with a computer-controlled
piezoelectric x-y stage (Polytec PI (Auburn, MA) P-731.20). The excitation
source was a 532 nm frequency doubled Nd:YAG laser (Lightwave
Electronics (Mountain View, CA), Series 142, 220 mW). A rotatable half-
wave plate (Meadowlark Optics, Frederick, CO) and linear polarizer were
used to adjust the laser power. An electro-optical modulator (Conoptics
(Danbury, CT), Pockel cell M370) rapidly switched the beam’s polarization
between vertical and horizontal polarizations, and then a polarizing beam
splitter (PBS; Karl Lambrecht (Chicago, IL) BBPC-12-550nm) directed the
beam alternatively along one of two directions (path 1 and path 2 in Fig. 1).
Extinction ratios better than 1000:1 in this beam path alternation were
necessary to reduce intensity variations at the sample due to interference.
This was accomplished using a feedback system described in the Sup-
Along each path, the laser beam passed through a ‘‘cleanup’’ Glan-
Thompson polarizer (Newport Corp. (Irvine, CA) 10GT04AR.14) and then
through another Pockel cell that rapidly rotated the polarization back and
forth between vertical and horizontal. The beam was directed toward the
sample flow cell by mirrors carefully aligned to reflect in the vertical and
horizontal planes. Each beam passed through a 200 mm focal length
lens, a custom built BK7 glass octagonal prism(ESCO Products, Oak Ridge,
NJ), optical immersion liquid (Cargille (Cedar Grove, NJ) No. 50350, n ¼
1.458), andfinally, intoa 1 mmthickquartzslide.Eachof the focusedbeams
beam was alternately directed along path 1 and path 2.
For each path, the beam passed through a linear
polarizer (P), and then a Pockel cell (PC) to generate
alternating linear polarizations parallel to (p) and
perpendicular to (s) the relevant reflection plane. The
beam was coupled into the quartz microscope slide by
passing through the coupling prism (CP) and through
index matching liquid. At the quartz/water interface,
total internal reflection occurred, sending the beam
back out through the coupling prism to a beam dump
(not shown). The quartz slide was mounted on
a piezoelectric stage (PS). Fluorescence was collected
by a microscope objective lens (OL), passed through
a barrier filter (BF), and imaged by a lens (L).
Depending on the position of a removable mirror
(RM), the fluorescence was imaged either onto an
intensified CCD camera (ICCD) or through a Thomp-
son beam splitting prism (BSP), onto two avalanche
Experimental apparatus. The input laser
1262 Forkey et al.
Biophysical Journal 89(2) 1261–1271
intersected the quartz-water interface, at the bottom of the slide, at an angle
of ;69? relative to the slide normal, an angle greater than the critical angle
for total internal reflection (23,33). The incident laser beam was thus totally
reflected and only an evanescent wave with a 1/e intensity decay constant of
;140 nm was present in the flow cell at the surface of the quartz slide.
The path 1 laser beam is reflected at the quartz-water interface in the x-z
plane, and path 2 in the y-z plane. By time multiplexing the two input paths
at 50 Hz, and the two input beam polarizations for each path at 100 Hz, four
excitation polarizations, labeled s1, p1, s2 and p2, were generated
sequentially. The dwell time at each path and polarization was 9.9 ms,
and 0.1 ms was allotted for switching between them.
Fluorescence was collected by a 1003, 1.2 numerical aperture water
immersion objective lens (Leica (Heerbrugg, Switzerland) PL Fluotar) and
passed through two emission filters (Chroma (Rockingham, VT) HQ575/
90M and HQ545LP) to remove background light. The emitted light was
imaged onto an intensified charge-coupled device camera (CCD; Roper
Scientific Princeton Instruments (Trenton, NJ) V/ICCD). Images were
captured and digitized by a frame grabber (Data Translation (Marlboro,
MA), DT3152), displayed on a computer monitor and used to manually
select a location for further data collection. Alternately, the emitted light was
redirected by a mirror (RM; Fig. 1), collimated by a 125 mm focal length
lens, passed through a beam-splitting Thompson polarizer (Karl Lambrecht,
SMTA-12-45) where it was separated into its component polarizations along
projections of the stage x and y axes, and refocused by 125 mm focal length
lenses onto two avalanche photodiodes (APDs; PerkinElmer (Freemont,
CA), SPCM-AQR-16). A piezoelectric stage, under computer control, was
used to align a spot selected from the camera images, with the APDs.
Custom built electronics and a counting board (National Instruments
(Austin, TX), PCI-MIO-16E-4) were used to bin individual photon pulses
into 9.9 ms gates synchronized with the polarization switching. The counts
per gate gave intensities for each combination of excitation and detection
polarization. With the four excitation modes, s1, p1, s2, p2, and the two
detection polarizations, x and y, eight raw polarized intensities, s1IR
y; were measured during each 40 ms
cycle of data collection. For each 40 ms cycle, an estimate of the total
intensity was calculated using the equation ITot¼
empirically using the expressions in Appendix A of the Supplementary
Material (Eq. A.3) to cause this total intensity to be relatively insensitive
to probe orientation. ITot includes probe fluorescence plus background
For visualization of the AEDANS-actin, a 1 mW ultraviolet laser
(355 nm, Uniphase (San Jose, CA), NV-10110-100) was also directed into
the coupling prism and quartz slide at a glancing angle to generate an
evanescent wave. Fluorescence from the AEDANS-actin was passed
. The factor 0.885 was determined
through a 400 nm long-pass filter (Corning GG400) and imaged onto the
intensified CCD camera. Computer-controlled shutters blocked both the
532 nm and 355 nm lasers except during data collection.
For each data spot, images of a single field of view were acquired, first
exciting the AEDANS with the 355 nm laser and then exciting the
rhodamine with the 532 nm laser switching quickly (at 10 kHz) between the
four input polarizations to generate nearly unpolarized excitation. These
images were digitized and overlaid on a computer screen. For each single
molecule measurement on a sparsely labeled filament, a rhodamine spot was
selected based on colocalization with an actin filament aligned along the x
axis. The spot was then shifted in the x-y plane into the point conjugate with
the APDs. The excitation was adjusted to ;20 mW at the sample for
experiments on sparsely labeled filaments, and to 3–30 mW for densely
labeled filaments. Sparsely labeled filaments were interrogated for 250
cycles of the 8 polarized intensities, thereby accumulating 10 s of data. For
densely labeled filaments, a spot near the middle of a horizontal or vertical
filament was selected and interrogated for 50 cycles. Data were collected on
each slide for up to 30 min after preparation. Background intensities were
recorded from nearby filament-free regions.
After data collection on a sparsely or densely labeled F-actin slide,
calibration data, used to calculate the correction factors Cd, X1, X2, and X12
(defined below), were obtained as described in the Supplementary Material
Definition of calibration factors
The four calibration factors X1, X2, X12, and Cdtake into account the
nonideal optical properties of the apparatus and are defined as follows. X1is
the ratio of excitation intensities at the sample for s1 and p1 polarizations,
divided by the ratio expected from the optical arrangement (see the Sup-
plementary Material,AppendixA—Eqs.A.1).X2isthe correspondingfactor
for the s2 and p2 intensities. X12is the ratio of excitation intensities along
path 1 and path 2. Cdis the ratio of sensitivities of the x-polarized and
y-polarized detection paths (including the relative sensitivities of the two
detectors). With these definitions, the raw observed intensities,iIR
readily converted into corrected intensities, iIj (see the Supplementary
Material, Appendix B—Eqs. B.1).
For the experiments reported in this article, the values of X1, X2, X12,
and Cdwere all within ;10% of 1.0. That these values are close to unity
indicates that the alignment of the microscope is close to ideal and that the
optics do not introduce substantial polarization dichroism.
Data analysis for densely labeled F-actin
For each spot measured on a horizontal (parallel to the x axis) or vertical
(parallel to the y axis) densely labeled filament, polarized intensities with
background subtracted were corrected by multiplying or dividing by the
appropriate correction factors (Supplementary Material, Appendix B, Eqs.
B.1), and averaged over 2 s to give eight average polarized intensities,i?I Ij;
per spot. These were used to calculate the following absorptionand emission
Data from the densely labeled F-actin were also analyzed to obtain order
parameters, ÆP2dæ; ÆP2æ; and ÆP4æ; (16) which describe the axial orientation
and motion of the rhodamine probes. The eight raw polarized fluorescence
intensities, including the effects of the high numerical aperture objective,
were transformed into nine low-aperture corrected intensities, xIx;xIy;
xIz;yIx;yIy;yIz;zIx;zIy;zIz; on the assumption that the densely labeled
filaments were cylindrically symmetrical. Here, the first (second) index
indicates excitation (detection) polarization. For a filament oriented along
the x direction, cylindrical symmetry impliesxIy ¼xIz;yIx ¼zIx;yIz¼
zIy; andyIy ¼zIz: For a filament oriented along the y direction, analogous
s1?I Iy?s1?I Ix
s1?I Iy1s1?I Ix
s1?I Ix?p1?I Ix
s1?I Ix1p1?I Ix
p1?I Iy?p1?I Ix
p1?I Iy1p1?I Ix
s1?I Iy?p1?I Iy
s1?I Iy1p1?I Iy
s2?I Iy?s2?I Ix
s2?I Iy1s2?I Ix
s2?I Ix?p2?I Ix
s2?I Ix1p2?I Ix
p2?I Iy?p2?I Ix
p2?I Iy1p2?I Ix
s2?I Iy?p2?I Iy
s2?I Iy1p2?I Iy
Single Molecule Polarized TIRF1263
Biophysical Journal 89(2) 1261–1271
symmetries hold, with each x replaced by y and vice versa. The nine low-
aperture intensities for each spot on a densely labeled filament were ob-
tained by fitting the measured raw polarized intensities, with background
subtracted, to Eqs. C.1 in Appendix C (Supplementary Material). The
expressions used for calculating order parameters ÆP2dæ; ÆP2æ; and ÆP4æ from
the low-aperture polarized fluorescence intensities are listed in Appendix C
The assumption of cylindrical symmetry of the filaments was tested
by relaxing that constraint using one further intensity factor (C0), which
expresses the extent of azimuthal asymmetry around the filament axis
between the otherwise symmetrically related low-aperture intensities. For
example, when the filaments are aligned along the x axis,xIy¼ C0xIz;yIx¼
C0zIx;xIz ¼zIx;yIz ¼zIyandyIy¼ C2
these relaxed constraints averaged 0.87 6 0.04, indicating that the filaments
were nearly cylindrically symmetric.
0zIz: Values of C0 found using
Data analysis for single fluorophores in sparsely
Traces from individual rhodamine molecules in sparsely labeled actin
filaments were selected for further analysis if they had total intensity, ITot,
typical of single molecules (500–1500 detector counts per 40 ms recording
cycle) and all eight of their raw polarized intensities bleached to background
levels simultaneously in a single step. For traces that exhibited two or more
steps to background, only the steady intensity levels immediately preceding
the final step were analyzed. For each molecule analyzed, the raw polarized
intensities were corrected as shown in the Supplementary Material,
Appendix B, Eqs. B.1, and averaged over the steady interval before
photobleaching. For each molecule, intensity levels measured after photo-
bleaching were temporally averaged to obtain eight background intensities.
In some cases (11 out of 160 analyzed molecules), when a sudden
photochemically induced intensity transition was observed before photo-
bleaching (see the accompanying article (34)), averages were taken
preceding the photochemical event.
For each molecule analyzed, Eqs. A.3 in the Supplementary Material
were fitted to the eight traces of the corrected intensity signals and
background levels to yield angular parameters, u, f, and d, and intensity
factor, K, for that molecule. u and f correspond to the polar angles in the
microscope coordinate system (Fig. 2 a); u is the axial angle relative to the z
axis (normal to the slide surface); f is the azimuthal angle around the z axis;
and d is the half-angle of a cone describing the amplitude of the restricted
diffusion of the fluorophore on a timescale much longer than the 4 ns
fluorescence lifetime and much shorter than the 10 ms data collection time.
A Levenberg-Marquardt algorithm adjusted trial values of u, f, d, and K to
maximize the likelihood that the recorded data, with its Poisson-distributed
uncertainties, described the data (35). A 3 3 3 3 3 matrix of 27 provisional
values for u, f, and d, each of which was set independently to 15?, 45?, or
75?, wasusedas startingvalues.Foreachof the27startingvalues,a x2value
was calculated by summing the squared differences between measured and
best-fit polarized intensities for all of the input/output polarizations and at
each time point. When the best fit had any of the three angles within 3? of
0? or 90?, the next best fit was retained, provided its x2value was not
significantly larger. If the x2value of the next best fit was significantly
larger, or if all 27 provisional values resulted in fits with at least one of
the angles within 3? of 0? or 90?, then the best fit was retained. After fitting,
the data were filtered to remove from further analysis any molecules that,
using the criteria above, resulted in fitted angles within 0.5? of 0? or 90?.
Using these criteria, 12 out of 160 data points were removed from further
analysis. Further details of the fitting algorithm are available by request to
The parameter expressing the extent of subnanosecond probe wobble,
df, (Appendix A, Supplementary Material), was fixed for the analysis at its
value (25?) determined from the densely labeled filament experiments.
When dfwas also made adjustable in fitting data from individual molecules,
its value was similar (see Results). Values for b and a, corresponding to
the axial and azimuthal angles, respectively, relative to the F-actin axis (see
Fig. 2 b), were determined from u and f using a standard Euler rotation
Order parameters for the static axisymmetric distribution of single
molecules, ÆP2sæ and ÆP4sæ, were calculated from the measured b-angles
using the equations
where P2ðxÞ and P4ðxÞ are the second and fourth-order Legendre
polynomials, respectively (16,37). Order parameters describing the ‘‘slow
wobble’’ were calculated using the equations
8cosdð7cos2d ? 3Þðcosd11Þ:
The order parameters ÆP2æ and ÆP4æ determined from the densely labeled
F-actin data (see above) do not distinguish between the static and slow
wobble distributions, but instead are sensitive to the combined distribution.
The corresponding order parameters were determined from the single
molecule data using the relations (16,38)
ÆP2æ ¼ ÆP2sæÆP2pæ
ÆP4æ ¼ ÆP4sæÆP4pæ:
The single molecule data were also combined and analyzed as a virtual
densely labeled filament. For each molecule, eight average intensities were
determined from the data traces after background subtraction and correc-
tion. For each combination of excitation/detection polarizations, the average
intensities from all of the analyzed single molecules were summed to give
the corresponding polarized intensity level expected from a more densely
labeled filament. Absorption and emission polarization ratios as well as
ÆP2dæ; ÆP2æ; and ÆP4æ values were calculated for these summed intensities
following the procedures described above for analyzing intensities from
actual densely labeled filaments.
ordinate system (see Fig. 1). The positive z axis lies along the optical axis
of the microscope and points from the surface of the slide toward the
objective. The x and y axes lie in the reflection planes of beam paths 1 and 2,
respectively, with the positive directions determined by the projections of
the beam propagation directions onto the slide surface. u and f are the axial
and azimuthal angles, respectively, of the rhodamine dipole moment relative
to the laboratory coordinate system. d is the half-cone angle that describes
the motion of the flourophore on a timescale ?4 ns and ?10 ms. (b) Actin
coordinate system. b and a are the axial and azimuthal angles, respectively,
relative to the axis of the actin filament.
Coordinate systems. (a) Laboratory (or microscope) co-
1264Forkey et al.
Biophysical Journal 89(2) 1261–1271
Measurement of single molecule 3D orientation
at 40 ms time resolution
Sparsely labeled actin filaments, containing 0.1% ATR-
labeled and 86% AEDANS-labeled actin monomers, were
bound to a myosin coated, fused silica slide and preferen-
tially aligned with the flow direction in the sample chamber
as described in Methods. Fig. 1 of the accompanying article
(34), shows flow alignment of actin similar to that typically
achieved here. Slides were placed on the microscope stage
with the flow direction, and most F-actin filaments, aligned
with the x axis of the microscope coordinate frame (Fig. 2).
Video camera images of the AEDANS and of the rhodamine
fluorescence were used to locate individual rhodamine
fluorophores on single filaments. At this low density of
labeling, single fluorophores were typically separated by
several micrometers, allowing individual spots to be readily
identified. Once a particular fluorophore was selected, sets of
eight polarized fluorescence intensities were collected at
a rate of 40 ms per set for 10 s (see Methods).
The time courses of a typical set of the eight raw polarized
intensities measured from an individual ATR-labeled actin
intensity traces are essentially flat until they simultaneously
bleach to the background level in one step. This behavior
indicates that the detected photons in excess of the backg-
eight intensities that is roughly independent of fluorophore
orientation is shown as the black trace in the fifth panel down
(ITot). As described in Methods, for each data point, the eight
intensities were fitted to the equations in Supplementary
Material Appendix A to determine the 3D orientation in the
microscope coordinate frame, amplitude of slow-wobble
mobility of the fluorophore, and intensity factor IFit(blue
trace in Fig. 3, panel 5). The fitted intensity factor is in good
agreement with ITotminus background. u and f are the axial
and azimuthal angles of the fluorophore’s absorption/
emission dipole moment relative to the optical axis of the
microscope (Fig. 2 a and Fig. 3, panel 6). Because of the
symmetries of the polarizations used, u and f were deter-
mined to within a fourfold degeneracy. Although the mea-
sured values are presented with u and f each between 0? and
90?, the degeneracy indicates that the actual value of f may
be equal to f, 180? ? f, 180? 1 f, or 360? ? f. This
degeneracy, combined with the mirror symmetry of the fluo-
rophore’s dipole moment, implies u could also be equal to
the actin axis (Fig. 2 b and Fig. 3, panel 7). These values are
also reported with each between 0? and 90?. The degeneracy
here indicates a may be a, 180? ? a, 180? 1 a, or 360? ? a,
intensities are relatively constant, the orientation is un-
changed. d is the half-angle of the cone describing restricted
diffusion of the fluorophore on the time scale 4 ns ? t ? 10
ms (slow wobble; Fig. 2 and Fig. 3, panel 8), likely re-
to which the fluorophore is attached. df; the half-angle of the
cone representing restricted diffusion of the fluorophore on
the time scale t ? 4 ns, was fixed at 25? for this analysis.
The angles u, f, and d were also determined for the data
with the fast motion parameter, df; allowed to vary. df
determined this way was 29? 6 11?. Values obtained for the
other adjustable parameters (u, f, and d) were nearly the
same whether df was adjustable or not. However, because
uncertainties on the fitted values of u, f, and d were higher
when dfwas allowed to vary, and because the fitted value of
df reasonably matched the value determined for densely
labeled actin filaments (see below), the main data analysis
fixed dfat 25?.
rhodamine molecule attached to a sparsely labeled actin filament. Raw
polarized fluorescence intensities have units of photocounts per 10 ms gate;
subscripts indicate excitation/detection polarizations as defined in Methods.
ITotis a weighted sum of the fluorescence intensities according to the ex-
determined from the fit to the data (proportional to K—see Methods). The
photobleaching of the fluorophore. Angles are defined as in Fig.2.
Single molecule data. Typical data trace from a single
Single Molecule Polarized TIRF1265
Biophysical Journal 89(2) 1261–1271
For each molecule, average values?b b; ? a a; and?d d were cal-
culated from the temporal traces. The distributions of?b b- and
? a a-values (Fig. 4) show that the?b b-values were more closely
grouped than the ? a a-values, as expected for a population of
fluorophores uniformly distributed around the actin axis. The
mean values of?b b and?d d for 148 individual ATR-labeled actin
monomers were 49.6? 6 0.8? and 37? 6 1?, respectively
(mean 6 SE).
The precision of the angles measured with 40 ms time
resolution was determined by calculating the mean values
and standard deviations from the time-resolved measure-
ments for each individual molecule, as shown in Fig. 4.
There was no apparent correlation between average angle
values and the corresponding standard deviations. For a, b,
u, f, and d measurements, the average standard deviations
were 16?, 9?, 10?, 14?, and 17?, respectively.
To examine the source of noise in the temporal traces
of probe angles, simulated polarized intensities were also
calculated using Eqs. A.3 (Supplementary Material, Appen-
dix A), assuming Poissonian distributed photon shot noise
(39). These simulated intensities were determined for a fixed
value of d (30?) and a range of a, b, u, and f. The root mean-
squared deviations between fits to these simulated intensities
and the corresponding angles were 13?, 7?, 6?, 10?, and 11?
for a, b, u, f, and d, respectively, close to the standard
deviations calculated from the measured single molecule
data. This result indicates that the major source of noise on
the single molecule data was photon shot noise.
(see Methods) were 0.14 6 0.02 and ?0.33 6 0.01,
respectively.The order parameters ÆP2pæ andÆP4pæ describing
the slow-wobble cone were 0.67 6 0.02, and 0.29 6 0.03,
respectively. These values and their products are plotted (see
Fig. 6, black symbols) and are compared below with order
parameters measured on densely labeled F-actin filaments to
estimate accuracy of the measured single molecule angles.
Measurement of densely labeled F-actin
Densely labeled F-actin filaments, containing 10% ATR-
labeled and 10% AEDANS-labeled actin monomers, were
bound toa myosin-coatedfused silica slide and preferentially
of the microscope coordinate frame as described in Methods.
Images of the AEDANS or ATR fluorescence were used to
locate individual filaments on the surface. At this density, the
fluorescence intensity appeared uniform along the filaments.
Polarization ratios, as defined in Methods, were calculated
for each spot, and combined into distributions (Fig. 5).
Filaments included in the analysis were oriented within 10?
of the x or y microscope axis, indicated by ‘‘H’’ or ‘‘V’’
If the calibration factors X1, X2, X12, and Cd(Supplemen-
tary Material) are correct, then consideration of the sym-
metries between the different excitation polarizations and
different filament orientations results in the following ex-
Agreement between these equations and the measured
polarization ratios for the densely labeled filaments (Fig. 5)
indicates that the calibration factors have been determined
A simple check of the fidelity of the single molecule
intensity measurements is to sum the polarized intensities
from all 160 individual molecules interrogated in the sparsely
labeled filament experiments as if they were in one ‘‘H’’
-oriented filament. Ratios of these totals are shown as red
dots in Fig. 5 and agree well with the polarization ratios
measured from actual densely labeled filaments.
The orientation distribution of the rhodamine probes on
the densely labeled filaments was described in the form of
ÆP2dæ; ÆP2æ; and ÆP4æ order parameters following the pro-
cedure described in Methods and in Dale et al. (16). As
expected, there was no significant difference between the
order parameter values determined for ‘‘horizontally’’ and
‘‘vertically’’ oriented filaments.
The measured value of ÆP2dæ (second rank order parame-
ter describing subnanosecond wobble) was 0.866 6 0.004
(mean 6 SE; n ¼ 121 filaments). This value corresponds to
single molecule measurements. Histograms show the
distributions of average angle measurements from 148
individual molecules. The associated standard devia-
tions calculated for each molecule are plotted versus
Distribution and standard deviations of
1266 Forkey et al.
Biophysical Journal 89(2) 1261–1271
rhodamine probe motion, on a timescale much faster than its
4 ns fluorescence lifetime, within a hard-edged wobble cone
with half-angle of 25? (16,40). This agrees reasonably
well with the value of 29? 6 11? (corresponding ÆP2dæ ¼
0:8060:13) obtained for dfin the single molecule experi-
ments above.The values ofÆP2æand ÆP4ædeterminedfrom all
denselylabeledactindata were 0.147 60.003 and?0.136 6
0.003, respectively. These order parameters represent the
10 ms) distributions and are plotted in Fig. 6. The description
in Methods (Eq. 4) and Bell et al. (38) indicates that the
products of the order parameters determined from the single
molecule measurements for the different timescales (i.e.,
ÆP2sæÆP2pæ) should be equal to the order parameters de-
termined from the densely labeled filaments (i.e., ÆP2æ). As
shown in Fig. 6, the products of the single molecule order
the densely labeled filaments (diamonds).
Single molecule fluorescence polarization (SMFP) was used
to measure the orientation of individual rhodamine probes
labeling Cys374of actin monomers copolymerized into
filaments with unlabeled actin. The 3D orientation was
measured and reported relative to the microscope laboratory
coordinate frame (u and f), and with respect to the axis of
the actin filaments (b and a). The distributions of these
angles (Fig. 4) for individual molecules spread uniformly
around the actin axis as expected. u should take on values
greater than or equal to b,the axial angle of the probe relative
to the actin. Indeed, here the distribution of u extends from
nearly 90? to a fairly sharp cutoff near the mean measured
value for b (?b b ¼ 50?). f should exhibit values less than or
equal to b, and the measured distribution of f does extend
from very low angles up to a cutoff near?b b: In the actin frame,
the azimuthal angle, a, is distributed fairly uniformly over its
rangeofpossible angles(0–90?),whereas boccupiesasingle
narrow peak close to?b b: All of these distributions are as
expected for the axially symmetric sparsely labeled F-actin.
In addition, the value of?b b; 49.6? 6 0.8?,is close to the value,
45?, that is obtained for the axial angle of the rhodamine
chromophore when the crystal structure of rhodamine-
labeled actin (Protein Data Bank reference 1J6Z (41)) is
aligned with monomers in a model of the actin filament (42),
and the rhodamine dipole moment is assumed to lie between
the carbons bearing its two dimethyl amino groups.
Accuracy and precision of measurements
The standard deviation of the measurements taken every
40 ms for a given molecule is an indication of the precision
of the individual measurements. Here the measurements
have an average standard deviation of 10? for u and 14? for
measurements. The solid triangle and square show (ÆP2pæ;ÆP4pæ) and
(ÆP2sæ;ÆP4sæ); respectively, determined according to Eqs. 2 and 3 from the
distribution of 148 single molecule measurements of b shown in Fig. 4. The
product of these values (see Eq. 4) is shown as the solid circle. The open
circle indicatesthe order parametersdetermined by summingall of the single
moleculeintensities andthenanalyzingthese sums as thoughtheywere from
a densely labeled filament. Dark and shaded diamonds indicate the order
parameters determined for densely labeled horizontally aligned (along the x
axis) and vertically aligned (along the y axis) filaments, respectively. All
physical angular distributions fall within the area bounded by the solid lines.
Comparison of ensemble and single molecule order parameter
plot shows the distribution of polarized intensity ratio measurements (as
defined in Methods) from 76 horizontally oriented (parallel to the x axis)
densely labeled actin filaments. Each green box plot shows the distribution
from 45 vertically oriented (parallel to the y axis) filaments. Large red dots
show the polarized intensity ratios calculated from the sum of polarized
intensitiesmeasuredfrom 160 individual moleculesonsparselylabeled actin
filaments. For each box plot, black dots correspond to the 5–95% range of
the distribution; horizontal lines correspond to the 10–90% range; top and
bottom of the colored box correspond to the 25–75% range; and the line
insideofthe coloredbox correspondsto themedian(50%distributionpoint).
The ‘‘H’’ and ‘‘V’’ superscripts correspond to polarization ratios measured
on horizontal (vertical) actin filaments.
Polarization ratios for densely labeled F-actin. Each blue box
Single Molecule Polarized TIRF1267
Biophysical Journal 89(2) 1261–1271
f. These levels of statistical uncertainty are low enough to
make this SMFP technique useful for detecting and quan-
tifying motions within many protein systems. For example,
the technique was used to detect structural changes in
myosin V during processive motility, where calmodulin light
chains tilted by ;45? (or, likely, 75?, taking symmetries into
account) each time the molecule stepped along actin (22).
X-ray crystallography studies have implied similar or larger
domain rotations in many other systems including DNA
polymerase (43), F1-ATPase (3,6), the potassium ion chan-
nel (10,11,14), and translation elongation factors (44).
The standard deviations on the measured angles were
close to those predicted by a computer simulation that as-
sumed statistical uncertainties under similar recording con-
ditions were dominated by photon shot noise in the signal
and background intensities. This implies that similar pre-
cision could be achieved on shorter timescales, provided that
comparable counts per measurement interval were main-
tained by increasing the excitation laser power. Maintenance
of the angular precision by increasing laser intensity
proportional to the measurement frequency should hold
until the intensity becomes large enough to saturate the
fluorophore, (e.g., the time between excitations is compara-
ble to the fluorescence lifetime). Saturation would occur with
rhodamine at an excitation intensity ;100-fold higher than
that used here. Thus, submillisecond time resolution should
be achievable, although with a corresponding reduction of
the observation time (;5 s in the present experiments) due to
To test the accuracy of the SMFP measurements and to
determine whether any major artifacts caused systematic
angular deviations, the angles and mobilities measured on
a series of single molecules were compared to ensemble
measurements on heavily labeled, similarly aligned actin
filaments. Also, in the absence of systematic errors in the
single molecule technique, ratios of summed single molecule
intensities should be equivalent to ratios of multi-molecule
intensities, as was found (Fig. 5).
The ensemble experiments cannot be used to measure the
detailed distribution of molecular b-angles, but they pro-
duce two order parameters of that distribution, ÆP2æ and ÆP4æ:
The orientation distribution described by ÆP2æ and ÆP4æ
slower than the fluorescence lifetime (4 ns). SMFP measure-
ments, on the other hand, determine both of these b-distri-
butions, so these order parameters can be calculated directly.
As described in Methods and in Bell et al. (38), the
aggregate order parameters equivalent to ÆP2æ and ÆP4æ
measured by the ensemble experiment can be calculated by
multiplying the order parameters (ÆP2pæ and ÆP4pæ) derived
from the extent of microsecond motions (d) in the SMFP
experiment by those describing the static distribution (ÆP2sæ
and ÆP4sæ). As seen in Fig. 6, the products of the order
parameters (ÆP2sæÆP2pæ and ÆP4sæÆP4pæ) measured with SMFP
are indeed close to ÆP2æ and ÆP4æ; respectively, determined
from the ensemble measurements. The slight differences
between the SMFP products and the ensemble order
parameters are difficult to interpret directly in terms of angle
differences since the ensemble measurements do not directly
report individual angles or their distributions. However, if
the distributions of b are modeled as either single Gaussian
profiles or maximum entropy distributions (45) for both the
sparsely and densely labeled filaments, the difference
between ÆP2æ and ÆP4æ from the ensemble measurements
and ÆP2sæÆP2pæ and ÆP4sæÆP4pæ from SMFP, corresponds to
a difference in the peak angles of the Gaussians or maximum
entropy distributions of ;2?. This comparison indicates that
systematic errors in the single molecule measurements com-
pared to the ensemble measurements are very low.
Comparison with other single
Single molecule methods, particularly mechanical measure-
ments using optical traps and single molecule fluorescence
imaging techniques, have opened a new and powerful
avenue for investigations of biophysical systems. These
techniques reveal details of the functionally relevant mech-
anisms by directly measuring the trajectory of reactions and
by avoiding averaging of populations that inevitably ob-
scures some information (see Introduction, and Forkey et al.
(23) and references therein). Orientations of single fluoro-
phores have been measured by a number of novel polarization-
sensitive microscopies. Several groups have reported the use
of polarizations in the plane of the microscope slide (i.e., in
the x-y plane) to measure the orientation, f, of the projection
of a single fluorophore’s dipole onto the x-y plane (20,21,46–
53). To determine the axial angle, u, as well, Bopp et al.
(19,54) and Empedocles et al. (55) used unique fluorophores
with cylindrically symmetric degenerate dipole moments.
Dickson et al. (56) and Bartko et al. (57,58) used the effect of
spherical aberration on the shape of a single fluorophore’s
point spread function to estimate both u and f. Although
these approaches have yielded a wealth of new information
about the motions of individual macromolecules, none is
ideally suited to measuring the 3D orientation with mil-
lisecond time resolution of an individual conventional fluo-
rophore having a nondegenerate dipole moment.
The present technique utilizes an evanescent wave
generated by totally internally reflected excitation beams
with temporally modulated polarization. The p-polarization
(electric field parallel to the scattering plane) generates an
electric field with a strong polarization component along the
z axis. Such polarization is not available with excitation light
propagated along the microscope optical axis. Comparison
of the fluorescence between intervals of excitation with
this z polarized evanescent wave versus that with x- and
y-polarization provides robust discrimination between probe
absorption dipoles aligned near the optical axis from those
1268 Forkey et al.
Biophysical Journal 89(2) 1261–1271
nearer the x-y plane. The z-polarized evanescent wave has
a small (;5%) component along the x axis as well (for path
1 excitation; see Fig. 1), but this effect is easily accounted
for in the analysis (Methods and Supplementary Material,
Appendix A). The s-polarized excitation beam produces
a purely y-polarized evanescent wave (for path 1). SMFP is
only sensitive to the angle of the detected single fluorophore
and is relatively insensitive to lateral motions, laser intensity
variations, and mechanical vibrations. As implemented here,
the detected angles are ambiguous with respect to reflection
across the x-y, x-z, and y-z planes. Some of these symmetries
could be removed, however, by directing or polarizing the
illumination along intermediate axes (59,60). The ability of
this new technique to measure both the axial and azimuthal
angles on a millisecond timescale, or better, makes it a
powerful tool for real-time investigations of biological
In addition to reporting the 3D orientation averaged over
the measurement time, this SMFP technique also enables
determination of the extent of motion (d) on the timescale
shorter than the measurement time (10 ms here), but longer
than the fluorescent lifetime (4 ns for rhodamine). Pre-
sumably, rotational motions on this microsecond timescale
are due to thermal motions of the protein subunits. A con-
ventional fluorescence polarization measurement made on an
ensemble of molecules is not capable of separating the effect
of motion on this timescale from that of a broad static
orientation distribution. Thermal motions on this timescale
have been implicated in a number of important biological
processes, including the movement of molecular motors
such as myosin and kinesin (61–63) and the movement of a
cellular leading edge by actin polymerization (64). Although
more complex pulse-probe techniques (38,65) do make
rotational motions on the microsecond timescale accessible
in bulk samples, interpretation of these measurements is
complicated by the presence of the ensemble. Such compli-
cations are not present in the single molecule experiments
Motions of actin monomers in a filament
Previous measurements (reviewed in Egelman (24)) of actin
motions on the microsecond timescale were obtained with
ensemble measurements using electron paramagnetic reso-
nance, saturation transfer electron paramagnetic resonance
(66–68), transient absorption anisotropy, and transient
phosphorescence anisotropy (69,70). These measurements
indicate substantial intrafilament torsional motion on the
100 ms timescale, and imply a filament torsional rigidity of
roughly 2 3 10?27Nm2. Static electron micrographs show
a large component of rotation between successive monomers
in filaments (on the order of 5–6?) beyond that associated
with the average twist of the filament helix, implying similar
values for torsional rigidity (71,72). In contrast, single
molecule in vitro measurements, relying on imaging of
rotations of beads attached to individual actin filaments
(73,74), suggest that the torsional rigidity is more than an
order of magnitude larger, roughly 5 3 10?26Nm2. This
result would imply much smaller relative rotational motions
between adjacent actin monomers in the filament. Although
it is possible that labeling of Cys374or incorporation of
phalloidin may modify the torsional rigidity of F-actin, there
is no correlation between these variables and the different
torsional rigidities reported in the references cited above. In
fact, Yoshimura et al. (69) found no difference in measured
torsional rigidity between filaments that were phalloidin
stabilized, and those that were not.
An accurate measurement of the torsional rigidity and the
associated thermal motions of individual actin filaments is
important for understanding the contribution of such motions
to the interaction of F-actin with other proteins. For instance,
it has been shown that under some conditions in an in vitro
motility assay, myosin applies a rotational torque to actin
filaments (60,75), and that binding of cofilin/ADF to actin
filaments changes the helical periodicity (76). If thermal
motions in the isolated filament easily access torsional
angles similar to those promoted by actin-binding proteins,
then accessory proteins, or even a motor, may stabilize an
otherwise transient structure of the filament. However, if the
isolated filament is stiffer, then the binding proteins must
actively generate a torque.
The average half-width of wobbling rotational motions of
the rhodamine fluorophore on the microsecond timescale (d,
formally 4 ns ? t ? 10 ms) measured here was 37?. The
torsional rigidity implied by this extent of wobble depends
on the separation between attachment points of the actin to
the slide surface, through individual myosin molecules. If the
torsional rigidity were 5 3 10?26Nm2, a rotational motion of
amplitude ;40? would occur if the attachment points were
;34 mm apart (74). This distance is much longer than the
typical filament used and would lead to large lateral motions
of the filaments (77), which were not observed at the myosin
densities used to secure the filaments to the surface. By
contrast, a lower torsional rigidity, i.e., 2 3 10?27Nm2, as
deduced from the ensemble probe and electron microscopy
studies, would imply a separation of ;1.4 mm between
attachments. This separation is consistent with the firm as-
sociation of the filaments with the surface and lack of lateral
motions observed with our standard method of attachment.
The measurements reported here, therefore, support the
lower of the two previously published values for torsional
A factor that might cause error in the measurements
reported here is that the labeled actin monomers were as-
sumed to undergo centrosymmetric wobbling motion about
an average orientation. There is some evidence that the
dynamic motions within actin are anisotropic (74). Other
potential artifacts of ensemble experiments using extrinsic
probes, however, such as inhomogeneous length distribution
in the sample or azimuthal rotations of the whole filament, do
Single Molecule Polarized TIRF1269
Biophysical Journal 89(2) 1261–1271
not apply to the measurements reported here on individual
actin filaments attached to the surface. Concerns regarding
sample preparation for electron microscopy are also not
relevant to the current measurements. In the works cited
above that found much higher tortional rigidity, the small
beads used to report the rotational mobility of actin filaments
were either close to a surface (74) or trapped in an optical
tweezer (73). Either of these geometries may have restricted
the motions of the beads, although both groups considered
this possibility and controlled for it. Therefore the reason for
their outlying value for torsional stiffness is not known.
The current measurements, then, in addition to validating
the new SMFP technique, provide strong support for the low
actin filament torsional rigidity values obtained from many
previous studies, while avoiding potential concerns about
ensemble averaging and sample preparation.
An online supplement to this article can be found by visiting
BJ Online at http://www.biophysj.org.
We thank Eric Gallo, Joby Geevarghese, Ilya Gertsman, Jason Goldman,
Scott Manz, and Joe Pili for technical assistance; Dr. Martin Pring for help
with the fitting and statistical analysis; and Drs. Robert E. Dale, E. Michael
Ostap, and Henry Shuman for useful discussion regarding the results
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