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Extending single-molecule microscopy using optical Fourier processing.

Backer AS, Moerner WE - J Phys Chem B (2014)

Bottom Line: A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope.Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane.Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computational and Mathematical Engineering and ‡Department of Chemistry, Stanford University , Stanford, California 94305, United States.

ABSTRACT
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

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Rotational mobilitymeasurements with a bisected pupil. Adaptedfrom ref (71) withpermission. (a) The “rotation within a cone” model:A molecule is assumed to have a mean orientation described by thepair of angles {Θ, Φ}, and may rotate to any orientationwithin the cone specified by the angle α. (b) Diagram indicatingthe regions of an image that are summed when the linear dichroism(LD) and lobe asymmetry (LA) of a molecule are calculated. (c) Histogramsof simulated single molecule images (blue) indicate that rotationalmobility is high. Experimentally acquired data (red) most closelymatches simulation using α = 75°. Note that as rotationalmobility increases, standard deviations σLA and σLD, of histogrammed data decrease. (d) Super-resolution imagescolor coded according to LD and T-channel LA.
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fig11: Rotational mobilitymeasurements with a bisected pupil. Adaptedfrom ref (71) withpermission. (a) The “rotation within a cone” model:A molecule is assumed to have a mean orientation described by thepair of angles {Θ, Φ}, and may rotate to any orientationwithin the cone specified by the angle α. (b) Diagram indicatingthe regions of an image that are summed when the linear dichroism(LD) and lobe asymmetry (LA) of a molecule are calculated. (c) Histogramsof simulated single molecule images (blue) indicate that rotationalmobility is high. Experimentally acquired data (red) most closelymatches simulation using α = 75°. Note that as rotationalmobility increases, standard deviations σLA and σLD, of histogrammed data decrease. (d) Super-resolution imagescolor coded according to LD and T-channel LA.

Mentions: In the previous subsection, our analysisignored the dipolar features of single-molecule images, discussedat great length in sections 4 and 5. Is this omission justifiable? Previous studieshave suggested that fitting simplistic model functions that do notproperly account for dipole emission to single-molecule images cancause systematic localization errors.73 This effect is accentuated by slight microscope defocus (/d/ ≤ 250 nm), which can induce mislocalizations onthe order of 200 nm.74 These huge localizationerrors are most prominent when asymmetric features arise in the acquireddata, due to molecules with transition dipole moments tilted awayfrom both the optical axis and the plane of the microscope coverslip(Θ ∼ 45°). A number of studies have sought to mitigatethese errors61,75 and benchmark the effects oforientation upon localization precision limits.76 In previous work, we demonstrated that the three-dimensionalpositions of molecules immobilized in a polymer could be accuratelyinferred by first estimating their dipole orientation and subtractingthe respective systematic localization error using a lookup-table.69 However, such effort may not always be necessary.In biological specimens, molecules labeling structures often undergosome degree of rotational motion, depending upon the specific probe,and the labeling method employed. As a molecule’s rotationalmobility increases, its fluorescence image will appear as that ofa superposition of immobilized dipoles. The molecule will thus resemblean isotropic emitter, mitigating any localization errors introducedby orientation. To characterize rotational mobility, it is often assumedthat a molecule is free to rotate about a fixed axis, within a conedefined by an angle α (Figure 11a).77 This model may be augmented with rotationaldiffusion and excited state fluorescence lifetime data, making itpossible to estimate the amount of rotational freedom necessary tomitigate localization error. Our calculations indicate that if α≥ 65°, lateral localization errors are bounded to fewerthan 10 nm.78


Extending single-molecule microscopy using optical Fourier processing.

Backer AS, Moerner WE - J Phys Chem B (2014)

Rotational mobilitymeasurements with a bisected pupil. Adaptedfrom ref (71) withpermission. (a) The “rotation within a cone” model:A molecule is assumed to have a mean orientation described by thepair of angles {Θ, Φ}, and may rotate to any orientationwithin the cone specified by the angle α. (b) Diagram indicatingthe regions of an image that are summed when the linear dichroism(LD) and lobe asymmetry (LA) of a molecule are calculated. (c) Histogramsof simulated single molecule images (blue) indicate that rotationalmobility is high. Experimentally acquired data (red) most closelymatches simulation using α = 75°. Note that as rotationalmobility increases, standard deviations σLA and σLD, of histogrammed data decrease. (d) Super-resolution imagescolor coded according to LD and T-channel LA.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4317050&req=5

fig11: Rotational mobilitymeasurements with a bisected pupil. Adaptedfrom ref (71) withpermission. (a) The “rotation within a cone” model:A molecule is assumed to have a mean orientation described by thepair of angles {Θ, Φ}, and may rotate to any orientationwithin the cone specified by the angle α. (b) Diagram indicatingthe regions of an image that are summed when the linear dichroism(LD) and lobe asymmetry (LA) of a molecule are calculated. (c) Histogramsof simulated single molecule images (blue) indicate that rotationalmobility is high. Experimentally acquired data (red) most closelymatches simulation using α = 75°. Note that as rotationalmobility increases, standard deviations σLA and σLD, of histogrammed data decrease. (d) Super-resolution imagescolor coded according to LD and T-channel LA.
Mentions: In the previous subsection, our analysisignored the dipolar features of single-molecule images, discussedat great length in sections 4 and 5. Is this omission justifiable? Previous studieshave suggested that fitting simplistic model functions that do notproperly account for dipole emission to single-molecule images cancause systematic localization errors.73 This effect is accentuated by slight microscope defocus (/d/ ≤ 250 nm), which can induce mislocalizations onthe order of 200 nm.74 These huge localizationerrors are most prominent when asymmetric features arise in the acquireddata, due to molecules with transition dipole moments tilted awayfrom both the optical axis and the plane of the microscope coverslip(Θ ∼ 45°). A number of studies have sought to mitigatethese errors61,75 and benchmark the effects oforientation upon localization precision limits.76 In previous work, we demonstrated that the three-dimensionalpositions of molecules immobilized in a polymer could be accuratelyinferred by first estimating their dipole orientation and subtractingthe respective systematic localization error using a lookup-table.69 However, such effort may not always be necessary.In biological specimens, molecules labeling structures often undergosome degree of rotational motion, depending upon the specific probe,and the labeling method employed. As a molecule’s rotationalmobility increases, its fluorescence image will appear as that ofa superposition of immobilized dipoles. The molecule will thus resemblean isotropic emitter, mitigating any localization errors introducedby orientation. To characterize rotational mobility, it is often assumedthat a molecule is free to rotate about a fixed axis, within a conedefined by an angle α (Figure 11a).77 This model may be augmented with rotationaldiffusion and excited state fluorescence lifetime data, making itpossible to estimate the amount of rotational freedom necessary tomitigate localization error. Our calculations indicate that if α≥ 65°, lateral localization errors are bounded to fewerthan 10 nm.78

Bottom Line: A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope.Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane.Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computational and Mathematical Engineering and ‡Department of Chemistry, Stanford University , Stanford, California 94305, United States.

ABSTRACT
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

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