2.1.

Chemicals

Carboxylate-modified fluorescent microspheres were purchased from Molecular Probes (Eugene, Oregon). Adenosine triphosphate (ATP), dithiothreitol (DTT), and phenylmethanesulfonyl fluoride (PMSF) were from Sigma Chemical (St. Louis, Missouri). All chemicals were analytical grade or ultrapure, if available.

2.2.

Solutions

Rigor solution contains $10\mathrm{mM}$ imidazole, $2.5\mathrm{mM}$ ethylene glycol bis( $\beta$ -aminoethyl ether)-N,N, ${\mathrm{N}}^{\prime },{\mathrm{N}}^{\prime }$ -tetraacetic acid, $2.2\mathrm{mM}$ Mg acetate, $130\mathrm{mM}$ potassium propionate, $0.2\mathrm{mM}$ PMSF, $0.8\mu \mathrm{g}∕\mathrm{mL}$ leupeptin, and $1\mathrm{mM}$ DTT.

2.3.

Sample Preparations

Rabbit psoas muscle fibers were prepared, and the native myosin regulatory light chain (RLC) exchanged with PAGFP-tagged human cardiac RLC (HCRLC-PAGFP) as described.^{1, 2}

Red-orange carboxylate-modified fluorescent spheres had $40\mathrm{nm}$ diam and excitation/emission maxima at $565∕580$ . Sphere concentrations were computed using the formula from the manufacturer and diluted in rigor buffer. We used ${10}^8$ -fold dilutions from stock giving sphere concentration of $1.4\times {10}^{19}\text{spheres}∕\mathrm{mL}$ . All experiments were conducted at room temperature.

2.4.

Coverslip Preparation

Clean No. 1 glass coverslips were sonicated for $10\min$ in ethanol then plasma cleaned (Harrick Plasma, Ithaca, New York) for $15–30\min$ . Plasma-cleaned coverslips were ready for use in the bare glass interface experiments. Plasma-cleaned coverslips were also thin aluminum (Al) film coated by thermal vacuum evaporation at the Mayo Electron Microscope Facility. In some instances, film deposition was limited to half of the coverslip’s top surface by partially covering one coverslip with another during vacuum evaporation. The result was an abrupt edge to the film as viewed in the light microscope. Aluminum film depth was measured with atomic force microscopy by scanning the tip over the edge in the partially aluminized coverslip. Aluminum film depth was estimated to be $20–30\mathrm{nm}$ .

2.5.

Sample Chamber Preparation

Bare glass or Al-coated coverslips were placed on a $(1\times 3)\text{-}\mathrm{in.}$ brass slide with a large hole cut out, permitting the objective from the inverted microscope to contact the coverslip through immersion oil. The Al-coated coverslips had the metal side up. A watertight chamber was constructed on top of the coverslip as described.⁷ The chamber contained either a suspension of nanospheres or a muscle fiber. Nanospheres settled from suspension onto the coverslip, where some of them adsorbed strongly enough to remain after washing out free nanospheres with rigor buffer. Adsorbed spheres were often aggregates with varying emitted intensities. BFP images were from microsphere aggregates.

2.6.

TIR Fluorescence BFP Microscopy

The inverted microscope (Olympus IX71) setup was described previously.¹ Excitation 488 or $514\mathrm{nm}$ light from an argon-ion laser is focused on the BFP of a 1.45-NA objective and incident from the glass side of a glass/aqueous interface at angles greater than critical angle for TIR, ${\theta }_{\mathrm{c}}\approx 61.6\mathrm{deg}$ (see Fig. 1 ). Although light is totally reflected, an evanescent field created in the water medium and decaying exponentially with distance from the interface, excites fluorophores within $\sim 100\mathrm{nm}$ of the surface.⁸ The p-polarized incident light has electric field polarization in the incidence plane and produces an elliptically polarized evanescent electric field. Evanescent intensity is predominantly polarized normal to the interface.⁹ The s-polarized incident light has electric field polarization perpendicular to the incidence plane that is continuous across the interface. In the presence of the metal film, the laser penetrates the interface and creates an evanescent field only when incident at the surface plasmon resonance angle, ${\theta }_{\mathrm{spr}}\approx 64.6\mathrm{deg}$ (see Fig. 1). P-polarized incident light penetrates the interface while s-polarized light is mostly reflected. Experiments with green fluorescent protein (GFP)-tagged muscle fibers use reduced illumination area on the fiber surface accomplished with the laser diameter reducing aperture shown in Fig. 1.

Fig. 1

Lens L focuses 488 or $514\mathrm{nm}$ of light from an argon-ion laser at the BFP of a 1.45 NA oil-immersion objective. The light is incident from the glass side of the glass/aqueous or glass/metal-film/aqueous interface at angles greater than critical angle, ${\theta }_{\mathrm{c}}\approx 61.6\mathrm{deg}$ , or equal to the surface plasmon resonance angle, ${\theta }_{\mathrm{spr}}\approx 64.6\mathrm{deg}$ . The excitation aperture reduces the illuminated area in the sample plane.

Fluorescent spheres or HCRLC-PAGFP exchanged muscle fibers in aqueous buffer solution make contact with the TIR-supporting glass or metal-film substrate and are illuminated by the evanescent field. Excited fluorescence is collected by the objective and spectrally filtered using a rhodamine (fluorescent spheres) or fluorescein (GFP-tagged fibers) filter set. Figure 2 shows the optical setup.

Fig. 2

Optical setup for conventional and BFP pattern imaging. The object (black arrow) is at the object plane (OP), OBJ is objective, SP is the plane where the BFP pattern (double arrow) is observed, TL is tube lens, RL is a removable lens, CCD is the image plane for the camera, and $f_{\mathrm{TL}}$ is the tube lens focal length. Light emitted by the object at OP emerges from the back of the objective in parallel rays. RL is removable (bidirectional arrow) to facilitate BFP (RL in) or object (RL out) imaging.

The BFP lies within the Olympus objective and is not readily accessible, hence, we image the intensity pattern at the BFP from a sample plane (SP) between the BFP and tube lens (TL). Imaging an object at SP (light double arrow) rather than the BFP changes the image size at the CCD plane. SP is not telecentric, implying an object displaced laterally changes the position of its intensity pattern at SP (the pattern at a telecentric plane is not translated when the object moves laterally). All experiments were conducted with the object at the center of the field. A single molecule from a muscle fiber was centered in the field, but most of the background fluorescence was intentionally displaced from the center likewise displacing its BFP pattern at SP. The background BFP pattern displacement enhances our ability to separately identify BFP patterns for the single molecule and background. The removable lens (RL) is positioned to form a real image of SP at the CCD plane by placing a translucent ruler at SP and adjusting RL position until a real image of it is formed at the CCD plane. The RL is conveniently removable (indicated in Fig. 2 by the two-directional arrow) to facilitate conversion between BFP and normal imaging.

2.7.

Emission Near an Interface

When a dipolar is near a conducting or dielectric planar interface, the radiated fields are significantly altered.⁵ An emitting fluorophore has a dipolar emission field that is the superposition of propagating transverse waves forming the far-field and nonpropagating longitudinal (evanescent) waves forming the near field. The near field is not detected unless perturbed by a nearby interface creating detectable propagating transverse waves. Converted near-field propagating waves appear in the glass medium at angles beyond ${\theta }_{\mathrm{c}}$ for the dielectric interface or at ${\theta }_{\mathrm{spr}}$ for the metal-coated interface. We refer to either emission mode as supercritical angle fluorescence (SAF).¹⁰ Oil immersion objectives with $\mathrm{NA}\gtrsim 1.3$ capture SAF. Subcritical angle fluorescence (UAF) is from far-field emission. Figure 3 shows emission near a bare glass (left) or metal-film (right) interface and indicates the critical angle, ${\theta }_{\mathrm{c}}$ , and surface plasmon resonance (SPR) angle, ${\theta }_{\mathrm{spr}}$ . The objective lens subtends a polar angle appropriate for a $\mathrm{NA}=1.45$ objective.

Fig. 3

Far- and near-field emission from dipole $\mu$ transmits the interface and propagates into the glass medium at angles beyond critical angle, ${\theta }_{\mathrm{c}}$ , for the dielectric interface or at the SPR angle, ${\theta }_{\mathrm{spr}}$ , for the metal-coated interface. SAF is supercritical angle fluorescence referring to any near-field light that propagates into the region defined by $\theta >{\theta }_{\mathrm{c}}$ . The objective lens drawn subtends a solid angle appropriate for a $\mathrm{NA}=1.45$ objective. The BFP and laser beam for TIR excitation are also shown.

The interface also affects total radiated power. Hellen and Axelrod pointed out that, for a fluorophore under steady illumination, the dissipated power must equal the absorbed power, implying that a fixed power, rather than a fixed amplitude, dipole radiator is the appropriate model for probe emission near an interface.⁵ An important consequence of the power normalization is that the metal film totally quenches fluorescence from probes within $\sim 10\mathrm{nm}$ of the interface. Hellen and Axelrod also pointed out conditions where reflection coefficients for the conducting interface need to incorporate nonlocal effects due to the dipole’s near-field coupling to surface waves whose wavelengths do not satisfy the condition of being much greater that the mean free path of conducting electrons in the metal. They use reflection coefficients derived from quasistatic semiclassical infinite barrier (SCIB) theory.¹¹ The SCIB correction, inserted when large wavenumber radial waves of the dipole’s near-field contribute to energy dissipation, is largest for dipoles very near to the metal film $(\lesssim 5\mathrm{nm})$ and affects total power dissipated by the dipole.

The high-NA collection of light in a microscope objective mixes light contributions from emitter dipole Cartesian components due to the collection of light from a large solid angle surrounding the dipole. The Cartesian dipole moments produce differently polarized light that is combined by the objective such that their individual contributions cannot be separated using an analyzing polarizer. Separating the contributions into the Cartesian components of the dipole moment is the basis for fluorescence polarization measurement of dipole orientation. Axelrod described the solution to the problem in a homogeneous medium.⁶

We address the probe emission perturbation by the interface and the complications for polarized light collection by a high NA objective in the dipolar emission intensity from single probes. Our computations give the two-dimensional intensity pattern in the objective BFP for comparison to experiment and show the effect of probe orientation on the pattern.

Computation and display of BFP intensity patterns were performed using software written for Mathematica (version 6.0, Wolfram Research, Champaign, Illinois).

3.1.

Two-Dimensional BFP Intensity

A dipole in aqueous medium near to a bare glass or metal-film-coated glass interface emits light part of which transmits to the glass side and is collected by the objective. Figure 4 shows the spatial relationship of the dipole moment, interface, objective, BFP, SP, pattern mask (MA), filter set (FS), and analyzing polarizer (AP).

Fig. 4

The spatial relationship of the dipole moment $\mu$ , interface ( $xy$ plane), objective, BFP, sample plane (SP), pattern mask (MA), filter set (FS), and analyzing polarizer (AP). The bare glass or metal-film-coated glass side of the interface lies in the $z<0$ half-plane and the aqueous side in the $z⩾0$ half-plane. The $u$ - and $v$ -auxiliary lines lie in the $xy$ plane. Dipole $\mu$ is at the focal point of the objective with $z$ -axis position $z_0$ and orientation in the microscope fixed frame given by $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ . Heavy arrows delineate an emitted light ray path. The ray is incident on the objective with propagation vector $\mathbf{s}$ and emerges in image space at distance $f{n}_{\mathrm{o}}\sin \theta$ from the $z$ -axis, where $f$ is the objective focal length and $n_{\mathrm{o}}$ is the refractive index for the objective and immersion oil. Coordinates $(f{n}_{\mathrm{o}}\sin \theta ,\varphi )$ define the observation point at the BFP or SP.

Heavy arrows delineate an emitted light ray path. It leaves the dipole, refracts at the interface and at the objective, then emerges in image space propagating parallel to the $z$ -axis. The ray is incident on the objective with propagation vector $\mathbf{s}$ and emerges in image space at distance $f{n}_{\mathrm{o}}\sin \theta$ from the $z$ -axis, where $f$ is the objective focal length and $n_{\mathrm{o}}$ is the objective and immersion-oil refractive index. Coordinates $(f{n}_{\mathrm{o}}\sin \theta ,\varphi )$ define the observation point at the BFP. We computed the intensity at SP using the method outlined previously¹ and based on the original work of Hellen and Axelrod.⁵

A fluorescent object translated laterally from the center of the visual field produces the BFP pattern like the centered object implying multiple single molecules in the field produce a summed BFP pattern. The pattern image at SP however is translated with object translation. The translated image is approximated using a coordinate transformation that accounts for the changed light collection geometry but not for the changed light refraction at the objective. The latter would be needed to interpret the translated BFP pattern quantitatively.

An object translated a lateral distance $L$ from at the visual field center is one focus of an ellipse with the other focus at the visual field center. The semimajor axis $\left(a\right)$ and eccentricity $\left(e\right)$ for the ellipse are

Computed BFP intensity patterns are averaged over square regions to imitate pixilation by a CCD camera. Pixels correspond to $6.45\times 6.45\mu {\mathrm{m}}^2$ regions in image space as appropriate for our CCD camera (Hamamatsu, Orca ER).

Figure 5 compares computed BFP intensity patterns for a bare glass interface with a dipole at $z_0=50\mathrm{nm}$ and orientation ${\theta }_{\mathrm{p}}=\pi ∕3$ , and ${\varphi }_{\mathrm{p}}=0$ (top) or $\pi$ (bottom). Patterns for dipole orientation ${\varphi }_{\mathrm{p}}$ have a reflection symmetry axis along a line at $\varphi ={\varphi }_{\mathrm{p}}$ ; hence, we can compare patterns with a half-plane representation. All patterns show an intense circular band where critical angle light intersects the BFP (arrows). Light falling outside the band is SAF, and light falling within the band is UAF. Figure 5a shows the intensity pattern without the AP. The two dipoles $({\theta }_{\mathrm{p}}=\pi /3$ and ${\varphi }_{\mathrm{p}}=0\text{or}\pi )$ are subtly distinguished in the pattern mainly with UAF intensity near the equatorial (horizontal line bisecting the circular pattern). Figures 5b and 5c show the BFP patterns after analyzing polarizer (AP) insertion for active axis at two perpendicular directions indicated by the white arrows in the right bottom corners. The patterns distinguish the ${\varphi }_{\mathrm{p}}=0$ or $\pi$ dipoles in both SAF and UAF intensity but SAF is the more characteristic indicator of dipole orientation.

Fig. 5

Computed BFP intensity patterns for a bare glass interface for dipoles at $z_0=50\mathrm{nm}$ and orientation ${\theta }_{\mathrm{p}}=\pi ∕3$ , and ${\varphi }_{\mathrm{p}}=0$ (top), or $\pi$ (bottom) with $x$ -axis indicated and $z$ -axis pointing into the page. All patterns show an intense circular band where critical angle light intersects the BFP (arrows inside ring). Light falling outside the band is SAF, and light falling within the band is UAF. (A) shows the intensity pattern without the AP. Dipoles with $+x({\varphi }_{\mathrm{p}}=0)$ and $-x({\varphi }_{\mathrm{p}}=\pi )$ components (and with ${\theta }_{\mathrm{p}}=\pi ∕3$ ) are distinguished in the pattern mainly with UAF intensity near the equatorial (horizontal line bisecting the circular pattern). (B, C) show the BFP patterns after analyzing polarizer (AP) insertion for active axis at two perpendicular directions indicated by the white arrows in the right bottom corners. The patterns distinguish dipoles equivalent except for the $+x({\varphi }_{\mathrm{p}}=0)$ and $-x({\varphi }_{\mathrm{p}}=\pi )$ components in both SAF and UAF intensity. BFP patterns in (A) and (B) differ at 10:30 and 4:30 o’clock where (A) is brighter in the UAF and SAF regions.

The panels demonstrate that an important degeneracy in dipole moment orientation is lifted by BFP imaging. In conventional microscope fluorescence polarization, the dipole orientations $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ , $({\theta }_{\mathrm{p}},\pi +{\varphi }_{\mathrm{p}})$ , and $(\pi \text{-}{\theta }_{\mathrm{p}},\pi +{\varphi }_{\mathrm{p}})$ will produce equal intensities. The high-NA objective collects Cartesian dipole component products ${\mu }_x{\mu }_y$ , ${\mu }_x{\mu }_z$ , and ${\mu }_y{\mu }_z$ in addition to the usual products ${\mu }_x^2$ and ${\mu }_y^2$ collected at low NA. The BFP pattern shows the functional dependence on $\varphi$ . The combination (high NA and $\varphi$ dependence in the BFP pattern) removes the $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ , $({\theta }_{\mathrm{p}},\pi +{\varphi }_{\mathrm{p}})$ degeneracy, but $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ , $(\pi \text{-}{\theta }_{\mathrm{p}},\pi +{\varphi }_{\mathrm{p}})$ degeneracy remains. Conventional object imaging microscopy sums intensity uniformly over $\varphi$ reducing to zero weights for the ${\mu }_x{\mu }_y$ , ${\mu }_x{\mu }_z$ , and ${\mu }_y{\mu }_z$ products thereby removing their contribution from detected intensity. Figure 4 shows the position of the mask within the microscope, which can be configured to nonuniformly sample contributions from different $\varphi$ ’s reinstating ${\mu }_x{\mu }_y$ , ${\mu }_x{\mu }_z$ , and ${\mu }_y{\mu }_z$ sensitivity in the total detected intensity. Figure 6 shows angle $\varphi$ and BFP subdivision into four quadrants. Emitted light propagates toward the viewer and the excitation TIR laser beam propagates into the page. Emitted light is blocked from propagating beyond the BFP in the shaded region. The presence of the mask removes the $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ , $({\theta }_{\mathrm{p}},\pi +{\varphi }_{\mathrm{p}})$ degeneracy. With the mask from Fig. 6, collected intensities for the system depicted in Fig. 5a with $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})=(\pi ∕3,0)$ and $(\pi ∕3,\pi )$ have relative values of 1 and 0.6, respectively. Under the same circumstances, the intensity ratio for the systems depicted in Figs. 5b and 5c [the intensity collected in Fig. 5b divided by the intensity collected in Fig. 5c] is 1 and 2.3 for $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})=(\pi ∕3,0)$ and $(\pi ∕3,\pi )$ , respectively.

Fig. 6

Variable $\varphi$ and the BFP subdivided into four quadrants of the $xy$ plane. Emitted light propagates toward the viewer and the excitation TIR laser beam propagates into the page. Emitted light is blocked from propagating beyond the BFP in the shaded region.

3.2.

Quantitative BFP Pattern Modeling

Small aggregates of fluorescent nanospheres were adsorbed onto Al-coated or bare glass coverslips then illuminated under TIR. Figure 7a compares experimental (top half) and computed (bottom half) BFP patterns for the nanospheres near the Al-coated interface. The inner ring appears at ${\theta }_{\mathrm{c}}$ (inner arrow, bottom left) position and the outer ring at the ${\theta }_{\mathrm{spr}}$ position (outer arrow bottom left).

Fig. 7

(A) contains experimental (top half) and computed (bottom half) BFP patterns for nanospheres near the Al-coated interface. The inner ring appears at the critical angle, ${\theta }_{\mathrm{c}}$ , position (inner arrow) and the outer ring at the surface plasmon resonance angle, ${\theta }_{\mathrm{spr}}$ , position (outer arrow). (B) compares equivalent projections of the experimental and computed patterns. The computed pattern uses the parameters indicated in (B).

Figure 7b compares experimental and computed patterns showing good alignment of peaks. The parameters needed in the fitting are the dielectric constants for water, glass, and aluminum; the thickness of the metal film $d$ ; the distance of the dipole from the interface $z_0$ ; and the orientation of the dipole $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})$ . The dipole orientation was assumed to be perpendicular to the interface $({\theta }_{\mathrm{p}}=0)$ due to the apparent cylindrical symmetry of the rings. We did not investigate other polar angles with cylindrical symmetry imposed by averaging over ${\varphi }_{\mathrm{p}}$ . Dielectric constants were taken from Ref. 5 while parameters $d$ and $z_0$ were varied to find a suitable fit.

We find that fitted $d\approx 23\mathrm{nm}$ falls within the experimentally determined Al-film depth of $20–30\mathrm{nm}$ . Fitted dipole position $z_0\approx 454\mathrm{nm}$ is beyond the expected penetration depth of the TIR evanescent field of $\sim 100\mathrm{nm}$ . The discrepancy suggests that the nanosphere aggregate frustrates TIR of the incident beam to propagate excitation into the aggregate.

Figure 8 compares experimental (top half) and computed (bottom half) BFP patterns for the nanospheres aggregate near a bare glass interface. The broad bright ring begins at the critical angle position but continues into the SAF region, indicating probes are emitting very near to the interface. The faint ring patterns seen in the UAF region not reproduced in simulation are probably caused by diffraction of scattered excitation laser light contaminating the image from fluorescence. The same uneven background effect probably produces the faint dark band in the outermost SAF region also not reproduced in simulation. The experimental BFP emission pattern is heterogeneous in $\varphi$ and slightly more intense at the meridian (vertical line bisecting the circular pattern) than at the equatorial line and qualitatively similar to the computed pattern where $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})=(\pi ∕3,\pi )$ and $z_0=0\mathrm{nm}$ .

Fig. 8

Experimental (top half) and computed (bottom half) BFP patterns for the nanospheres aggregates near a bare glass interface. The broad bright ring starts at the critical angle, ${\theta }_{\mathrm{c}}$ , and continues into the SAF region indicating probes are emitting very near to the interface. The computed pattern uses $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})=(\pi ∕3,\pi )$ and $z_0=0$ .

Figure 9a shows a HCRLC-PAGFP exchanged muscle fiber in rigor at a bare glass interface and under TIR illumination. Emission is dominated by a single photoactivated PAGFP. Background light is from many unphotoactivated HCRLC-PAGFPs in the fiber emitting at $\sim 1\%$ the efficiency of the photoactivated molecule with $488\text{-}\mathrm{nm}$ excitation. The exciting TIR laser aperture is closed down (Fig. 1) to minimize the area illuminated around the photoactivated molecule. Further reduction in aperture size unacceptably reduced fluorescence intensity from the photoactivated single molecule. The single dominant photoactivated HCRLC-PAGFP was positioned at the center of the microscope field of view and at the lower edge of the illuminated region such that the majority of background emission originated from the top portion of the field of view.

Fig. 9

(A) A HCRLC-PAGFP exchanged muscle fiber in rigor at a bare glass interface and under TIR illumination. The single dominant photoactivated HCRLC-PAGFP is at the center of the microscope field of view and at the lower edge of the illuminated region. (B) The BFP image from (A) and simulated BFP image from an object at the center plus an object translated upward from center of the field of view (right and left hemicircles, respectively). The single dominant photoactivated HCRLC-PAGFP emission in the fiber image maps to the centered ring at the outer edge of the BFP pattern. Background in the fiber image maps to the downward translated broad BFP ring pattern.

The right side of Fig. 9b shows the BFP image from Fig. 9a. The left side of Fig. 9b shows the simulated BFP image from two objects, one at the center and another translated upward from center of the field of view. An object translated laterally produces a laterally translated BFP image at SP. The object translated upward produces the simulated light ring translated downward in correspondence with the broader observed light ring at the BFP. In the fiber image, background is centered upward from the single molecule source but is distributed over the whole illuminated region producing the translated and diffuse light ring in the BFP image. Simulating the distributed background sources over the whole illuminated region is prohibitively computer time consuming and was not attempted.

The object at the center of the field produces the centered simulated light ring in correspondence with the centered observed light ring in the BFP image. The translated background BFP image allows observation of the centered object over about half of the BFP image. The single-molecule source BFP image diminishes at the equator, indicating an oriented single molecule. The simulated ring is identical to that in the lower part of Fig. 5a, where $({\theta }_{\mathrm{p}},{\varphi }_{\mathrm{p}})=(\pi ∕3,\pi )$ and $z_0=50\mathrm{nm}$ .