Single molecule fluorescence image patterns linked to dipole orientation and axial position: application to myosin cross-bridges in muscle fibers

Abstract

Background: Photoactivatable fluorescent probes developed specifically for single molecule detection extend advantages of single molecule imaging to high probe density regions of cells and tissues. They perform in the native biomolecule environment and have been used to detect both probe position and orientation.

Methods and findings: Fluorescence emission from a single photoactivated probe captured in an oil immersion, high numerical aperture objective, produces a spatial pattern on the detector that is a linear combination of 6 independent and distinct spatial basis patterns with weighting coefficients specifying emission dipole orientation. Basis patterns are tabulated for single photoactivated probes labeling myosin cross-bridges in a permeabilized muscle fiber undergoing total internal reflection illumination. Emitter proximity to the glass/aqueous interface at the coverslip implies the dipole near-field and dipole power normalization are significant affecters of the basis patterns. Other characteristics of the basis patterns are contributed by field polarization rotation with transmission through the microscope optics and refraction by the filter set. Pattern recognition utilized the generalized linear model, maximum likelihood fitting, for Poisson distributed uncertainties. This fitting method is more appropriate for treating low signal level photon counting data than χ(2) minimization.

Conclusions: Results indicate that emission dipole orientation is measurable from the intensity image except for the ambiguity under dipole inversion. The advantage over an alternative method comparing two measured polarized emission intensities using an analyzing polarizer is that information in the intensity spatial distribution provides more constraints on fitted parameters and a single image provides all the information needed. Axial distance dependence in the emission pattern is also exploited to measure relative probe position near focus. Single molecule images from axial scanning fitted simultaneously boost orientation and axial resolution in simulation.

Figure 1. Inverted microscope (Olympus IX71) setup.

Diagram shows excitation and emission detection pathways and double edge arrows indicating translating elements with their approximate spatial resolution. The 488 or 514 nm lines from the argon ion laser (Innova 300, Coherent, Santa Clara, CA) are intensity modulated by the acoustoptic modulator (AOM) then linearly polarized at the Glan-Taylor (P) polarizer. The polarization rotator (PR) uses Fresnel Rhombs to rotate linear polarized light to the desired orientation. The beam enters the microscope, reflects at the dichroic mirror (DM), and is focused on the sample by the objective. The high NA objective (Olympus planapo 60X, NA = 1.45 or TIRF objective) translates along the optical axis under manual control using the microscope focus or with nm precision using a piezo nanopositioner (C-Focus, MCL, Madison, WI). The C-focus translates the objective under computer control and has an alternative feedback mode where it maintains a constant distance between the objective and a set point on the microscope stage. Sphere samples were sometimes mounted on a piezo stage to alter the distance from sample to objective along the optical-axis with nanometer precision when a moving objective was undesirable. Emitted light is collected by the objective, transmitted by the dichroic mirror, then focused by the tube lens (TL) onto the CCD camera with 6.45 µm square pixels (Orca ER, Hamamatsu Photonics, Hamamatsu-City, Japan). In some experiments, a microscope stage with leadscrew drives and stepper motors translate the CCD camera with submicrometer resolution (LEP, Hawthorne, NY).

Figure 2. Ray diagram for object and image axial positions.

Object displacement ε from the objective effective focal point at O gives image displacement δ from the tube lens focal point at I. The CCD axial scan path shows camera translation in image space. BFP is the back focal plane of the objective and L is the tube length. The Tube lens has focal length f_T. Panel A shows point source repositioning relative to a fixed microscope stage due to translation of the objective (Obj) with focal length f_O. Panel B shows an equivalent point source repositioning due to a translating microscope stage.

Figure 3. A translating CCD camera records the axial PSF to calibrate axial image space.

Panel A shows the camera position saw-tooth pattern (solid line) and the fluorescence intensity observed from the point source (▪). The left hand side abscissa scale applies to the saw-tooth curve. The right hand side abscissa scale applies to intensity (▪). Intensity is the sum of photons in 2×2 or 3×3 pixel regions defining the focused point source. Panel B is the camera axial position (independent variable) vs fluorescence intensity (dependent variable) including only the middle portion of the saw-tooth pattern where camera position changes monotonically. The fitted curve is the PSF computed as described in RESULTS. Panel C shows the calibration curve indicating the relationship between δ and ε in Figure 2. The slope of the curve is the axial magnification, M_a.

Figure 4. Dipole emission basis patterns.

Resolution shown is appropriate for the Olympus IX71, the 60X TIRF objective, and 6.45 µm square pixels. Patterns in the left column depict intensities and are always ≥0. Patterns in the right column have negative values depicted as darker than regions around the edge where values are zero. Positive pattern values are brighter than edge values. Subscripts on I represent the dipole moment components contributing.

Figure 5. Normalized intensity axial dependency.

Intensities , and from eqs. 14 & 15 show peaks for and occur at different axial positions.

Figure 6. Simulated fluorescence emission pattern for a dipole with polar and azimuthal angles (θ_p,φ_p)  =  (28.8,153).

Background fluorescence and camera noise contribute to the Poisson distributed noise of the total signal (top panel, data). The fitted pattern (middle panel, fit) was identified by the GLM, maximum likelihood fitting, for Poisson distributed uncertainties. The residual of the two patterns normalized to fill the 8-bit dynamic range is shown (bottom panel, res).

Figure 7. Model orientation distribution and its representation obtained by different data fitting methods.

Panel A. Orientation distribution for the model (red) with normally distributed dipole polar and azimuthal angles (θ_p,φ_p) covering a 15 degree width with average values (<θ_p>, <φ_p>)  =  (45,120) degrees (Model). The sample set contains 70, (θ_p,φ_p), pairs. Shown in blue is the orientation distribution corresponding to the model but obtained by fitting individual single molecule fluorescence patterns generated from the (θ_p,φ_p) pairs (Smpl. Fit). Depicted in green is the orientation distribution corresponding to the model data but obtained by simultaneously fitting single molecule fluorescence patterns in groups of three from an axial scan series (Ax. Series). Panel B shows the axial distributions for the model (a red single spike at −50 nm), by fitting single molecule fluorescence patterns (blue), and by simultaneously fitting single molecule fluorescence patterns in groups of three from an axial scan series (green).

Figure 8. Single molecule data from muscle fibers.

Single PA-GFP tagged cross-bridges from fibers in rigor from the perpendicular (left) and parallel (right) polarization photoactivated subset. The top images are measured data, middle images fitted data, and bottom images the residuals.

Figure 9. Orientation distribution probability histograms.

Panel A: The orientation distribution for in fiber-coordinates (α,β) for perpendicular polarized photoactivation (red) and parallel polarized photoactivation (blue) detected from PA-GFP tagged muscle fibers in rigor. Panel B: The orientation distribution for in fiber-coordinates derived from simulated data from the model distribution in eq. 17 for β₀ = 47, σ_β = 20, γ_B,0 = 0, and σ_γ = 1 degrees. Simulated data was fitted by the pattern recognition method used to fit the muscle fiber data shown in Panel A.

Figure 10. Polarization ratio histograms.

Polarization ratios derived from the real and simulated data in Figure 9 with dashed lines indicating P_⊥ and solid lines P₇. Panel A: Polarization ratios derived from PA-GFP tagged muscle fibers in rigor from Figure 9A. Panel B: Polarization ratios derived from the simulated data in Figure 9B.

Figure 11. The probe axial spatial distribution probability histograms.

Probe axial spatial distribution from simulated data (Panel A) and data detected from PA-GFP tagged muscle fibers in rigor (Panel B). Simulated data is the same as that used in Figure 9B. Muscle fiber data is the same as that used in Figures 8, 9, 10.

Figure 12. The probe azimuthal orientation distribution probability histograms.

The orientation distribution in the azimuthal angle from probe coordinates, α, for perpendicular or parallel polarization (red or blue) photoactivated PA-GFP tagged muscle fibers in rigor. Angle α is a rotation about the fiber symmetry axis. The probe distribution suggests perpendicular, but not parallel, polarization photoactivation breaks the fiber symmetry.