Super-resolution fluorescence polarization microscopy

Karl Zhanghao*†, Juntao Gao‡, Dayong Jin¶, Xuedian Zhang*†||†† and Peng Xi*†¶**†† *Department of Biomedical Engineering, College of Engineering Peking University, P. R. China School of Optical-Electronic and Computer Engineering Shanghai University of Science and Technology, P. R. China Department of Automation, Tsinghua University Beijing 100084, P. R. China Bioinfomatics Division, TNLIST MOE Key Laboratory of Bioinformatics and Center for Synthetic & System Biology Tsinghua University, Beijing 100084, P. R. China ¶Faculty of Science, Institute for Biomedical Materials and Devices (IBMD) University of Technology, Australia ||zhangxuedian@hotmail.com **xipeng@pku.edu.cn


Introduction
As a fundamental physical dimension of°uorescence, polarization has been applied extensively in biological researches. Through°uorescence polarization microscopy (FPM), the dipole orientation as well as the intensity of°uorescent probes could be measured. Since the orientation of the°uorescent molecule is related to the tagged biostructures, structural information of cellular organelles or macromolecules can be revealed. Although X-ray crystallography or electron microscopy could elucidate ultra-high resolution of individual proteins or macromolecule assemblies, they require very complex sample preparation unsuitable for live cell imaging. Near-¯eld imaging techniques, such as Atomic Force Microscopy (AFM) could also provide with structural information, which however, is limited only to samples on the surface. FPM is capable of imaging orientations in dynamic samples at the time scale of seconds or milliseconds, thus it can serve as a complementary method for measurement of subcellular organelle structures. Recent decades have seen a variety of application of FPM in the area of cell membrane, biological¯laments including cytoskeleton and DNA¯laments, and other macromolecule assemblies.
The researches of the structure and dynamics of macromolecule assemblies demonstrate FPM as a complementary method with X-ray crystallography or electron microscopy. As an important type of biological macromolecule facilitating selective transport between nucleus and cytoplasm, the structure of nuclear pore complex (NPC) are not completely understood. With FPM, the Y-shaped nuclear pore complex subcomplexes were studied and their relative orientation according to the nuclear envelope plane could be inferred from imaging results. 1 F0F1-ATPase is a kind of enzyme relating to ATP synthesis. It consists of two domains, of which the F1 motor was found to display 120 stepping by FPM. [2][3][4] Lipid membrane is generally locally uniform and provides a quasi-static environment for the°uorescent probes, the orientation of which could be easily measured. [5][6][7] With polarized°uorescence recovery after photobleaching (FRAP), rotational di®usion of the probes could be revealed. 8,9 Molecular orientation disorder in cell membrane has been found due to cholesterol depletion 10 or cytoskeleton perturbation. 11 Monitoring membrane proteins could also be used to observe dynamic protein activation during molecular processes such as calcium°ow or protein interaction. 12 Cytoskeleton provides mechanical support to maintain or deform the cell shape, and is involved in many cell signaling pathways during cytokinesis. It also provides a sca®old to organize the contents of cells in space and for intracellular transport with the motor proteins. Actin was¯rstly to be found to have an organized distribution of probed dipole orientations 13 and was imaged by various FPM techniques. [14][15][16][17][18] Myosin is an important motor protein moving along actin. It exhibits interesting walking pattern with steps and rotation and is an extensively studied system. [19][20][21][22][23][24] Kinesin is another type of motor protein which is bound to microtubules. A highly mobile state and a rigid state of kinesin were distinguished which may relate to ATP and ADP binding. 25 Other types of cytoskeleton are also studied using FPM, including microtubule 17 and septin. 18,[26][27][28][29] Biological¯lamentous structures measured by FPM includes also in vitro DNA¯laments 17,30 and human amyloid¯brils. 31 FPM has been evolving during past decades, from manual or mechanical switching of polarization detection or excitation to simultaneous detection and fast polarization modulation via electro-optic devices. With faster imaging speed and higher imaging quality, FPM has been incorporated with various imaging modalities, such as wide-¯eld, 28,29 confocal, 11,32 two-photon confocal, 10,12,[33][34][35] total internal re°ection°uorescence, 19 FRAP, 8,9 etc. However, as an optical imaging technique, the development of°u orescence polarization microscopy (FPM) is barricaded by the di®raction limit. Compared to the abundant super-resolution techniques on°uorescence intensity imaging, super-resolution techniques in FPM is still in its infancy. In the review, we would rstly summarize current FPM techniques and then introduce recently developed two kinds of superresolution techniques in FPM. We would conclude the review with a comparison of the advantages and disadvantages between various FPM techniques and outlook its application in the future. direction in the molecular structure. Fluorescent dipoles could be used to model excitation absorption or°uorescence emission of chromophores, which remain the same in most cases. 36 When excited by polarized light, the dipoles with their orientations aligned parallel to the electric vector of the polarized excitation would have the highest probability of absorption. The distribution of absorption probability on polarized excitation is proportional to cos 2 , where is the intersecting angle between absorption dipole orientation and polarization direction. Discussion of two-photon or multi-photon absorption is more complex and not included here. 37,38 The emitted°uorescence from dipoles is also polarized, with the highest intensity component of polarization along the emission dipole orientation. The distribution of intensity probability on emission polarization is proportional to cos 2 ′, where ′ is the intersecting angle between emission dipole orientation and the polarization direction of the polarized component of emitted°uorescence.
According to the anisotropy in°uorescent absorption or emission, the dipole orientations of chromophores could be measured. In real conditions, the linker between°uorescent probes and the structure attached is not absolutely¯rm, which makes the dipoles wobbling at a speed much faster than the imaging speed. Thus, the real°uorescent dipoles are modeled with average azimuth and wobbling angle in many researches. 12,17,33 Fluorescence Anisotropy (FA) utilizes the polarization of emitted°uorescence. A typical FA setup consists of linearly polarized excitation and two polarized detections of°uorescence, which are parallel or perpendicular to the direction of the polarized excitation. The parallel and perpendicular detection could be achieved sequentially by changing analyzers in the emission path or simultaneously by polarization beam splitter (PBS), 13 a Wollaston prism 17 or a Thompson prism. 39 The anisotropy and azimuth could be calculated through two relating pixels. Early FA research started from studying the°u orescence polarization of chromophores in solutions, 40 which did not include an objective to collimate the°uorescence. An objective would greatly improve collected signals but may in°uence the°u orescence polarization when numeric aperture (N.A.) is high. A general theory for epi-illumination observation of FA through high N.A. objectives was presented by Axelrod 5 and was applied to measure diIa kind of membrane probeson erythrocyte ghosts. FA was later implemented with total internal re°ection°uorescence microscopy (TIRFM), 19°u orescence recovery after photobleaching (FRAP), 8 etc. Four detection channels could enable 3D orientation detection of°uorescent dipoles instead of only in-plane measurement, 41 or could provide an unbiased measurement of dipole orientations. 16 Based on emitted°uorescence polarization of radiating dipoles, the°uorescent intensity distribution outside the objective image space could also provide orientational information. 42,43 When the dipole lies at an orientation unparalleled to the optical axis, the polarized emission would lead to rotationally asymmetric distribution in the annular image. The orientation could be retrieved from the asymmetric image via pattern analysis or pattern recognition. The orientational information within the defocused pattern is not only limited to in-plane angle but also out-of-focus tilting angle 44 Besides, the dipole orientation is found to strongly relate with the molecular localization position. Later, a similar principle was applied to wide-¯eld epi-°u orescence microscopy and dipole orientations could be measured from the characteristic intensity distribution of the defocused image. 45 A pattern recognition algorithm based on least-squares analysis was developed to¯t the calculated set of master patterns against measured images, which could be applied to determine three-dimensional orientations in defocused single-dipole images. 46 Because of its principle, this technique is termed defocused pattern recognition (DPR) in the review. Based on this principle, Defocused Orientation and Position Imaging (DOPI) measured 3D orientation and stepping behavior of the light-chain domain of myosin V as myosin V moves along actin. 23 While both FA and DPR determine dipole orientations via emitted°uorescence polarization, linear dichroism (LD) is based on the absorption anisotropy of chromophores. LD exploits rotary linear polarized excitation and records the sinusoidal response of the°uorescence. The orientation of°u orescent dipoles could be extracted from the polarization modulation data by curve¯tting or Fourier analysis. Rotary linear polarized excitation could be achieved by passing a circularly polarized light through a rotary polarizer 2 or by passing a linear polarized light through a rotary half wave plate. 12,15,18 Rotary devices are limited in modulation speed and face with averaging e®ects due to their continuous motion. Electro optic devices could provide fast and discrete modulation of lasers, including the Pockel cell, 19 liquid crystal variable retarder, 6,28 electro-optic modulator. 25,30 LD is easy to combine with epi-illumination wide¯eld microscopy and laser scanning confocal microscopy, with additional polarization modulating devices. The polarization of the focal point of confocal illumination is linearly polarized in-plane if the excitation is polarized. 12 Experiments also demonstrated the markedly higher sensitivity of twophoton LD than single photon microscopy. 12,33 To further improve imaging speed together with optical sectioning, LD was also incorporated with a spinning disk confocal microscope. 32 Unlike FA, LD could easily exceed two orthogonal polarized excitations. 7,29 Four polarizations (0 , 45 , 90 , 135 ) 19,28 or more 15 are widely used. Some researchers hold the view that four polarizations are enough for sampling the sinusoidal curve and for an unbiased measurement of the in-plane dipole orientation. 16,28 Eight combinations of polarization could allow unambiguous 3D measurement of dipole orientations. 47 Most FPM could only measure in-plane dipole orientations while some could access out-of-plane tilting angle of dipoles as well. DPR could extract 3D orientation of single dipole when z position information of the dipole is combined. 23,44,45 3D orientation measurement with FA was also proposed. 41,48 LD with epi-illumination could not provide axially polarized excitation, which however, exists in highly inclined thin illumination (HILO) 49 or in the illumination of total internal re°ection microscopy. Such design could be achieved by a rotary combination of a half wave plate and a prism, 3 or polarization modulation with a Pockel cell, as in polTIRF. 19,47,50 LD has also been combined with multi-focus imaging which could achieve 2D orientation measurement and 3D intensity imaging. 26 Polarization Distortion is a general issue in FPM, which requires special attention. Optical elements like lenses, re°ection mirrors, etc. would not bring any distortion, while most polarization distortion is from the dichroic mirror. Other devices like the spinning disk unit,¯bers are alternative sources. Polarization distortion of the dichroic mirror could be approximately compensated by a quarter wave plate 11 or be accurately handled via a Berek's polarization compensator or the Soleil Babinet compensator. 32 System calibration of the polarization distortion could be measured by a polarizer placed on top of the objective when epi-illumination is used. Standard samples with known dipole orientation, such as¯xed single molecules, GFP crystals, 51 in vitro°uorescent labeled actin samples, 52 are perfect for calibrating the system.
Both FA and LD are based on the analysis of the°u orescence polarization, either in excitation or in emission. FA setup seems to be more simple and could achieve simultaneous observation. However, the number of detection channels is usually limited by the total°uorescence signal. FA would also be a®ected by depolarization processes, such as resonance energy transfer, rotational di®usion, etc. Though these properties could provide FA with capabilities to image related phenomenon, they would bring errors in measuring the transition moments of dipoles. In contrast, LD is weakly affected by depolarization processes. It could have more sampling points within one modulation period, though it needs multiple frames for¯nal results. Since FA and LD are separately placed in the detection path and in the excitation path, they are complementary other than being con°ict to each other. In some cases, LD and FA are implemented in the same instruments for speci¯c purposes. 19,47,50

Super-Resolution Techniques in FPM
Ernst Abbe proved that the resolution of optical microscopes would be limited by the optical diffraction, 53 which is about 250 nm in lateral resolution for far-¯eld optical imaging. Super-resolution techniques break the di®raction barrier, which is achieved through intensity on-o® modulation. The modulation could be in a structured manner, such as stimulated emission depletion (STED) 54,55 or (saturated) structured illumination microscopy (SIM), [56][57][58] or in a stochastic manner, such as (f) photo-activated localization microscopy (PALM)/ stochastic optical reconstruction microscopy (STORM). [59][60][61][62] Though a large variety of super resolution techniques have been developed for°uorescence intensity imaging, super resolution FPM is just starting. To achieve super resolution with dipole orientation measurement, one simple thought is to combine FPM with existing super resolution techniques, such as STED, SIM, PALM/STORM, etc.
The other thought is to exploit the intensity modulation of LD, which modulates the excitation laser and gets a sinusoidal response of the sample. Recently, developed super resolution FPM techniques could be categorized into two group: one is based on intensity modulation of LD 15,18 and the other one is to combine FA with direct stochastic optical reconstruction microscopy (dSTORM) 17 In Ref. 15, Ha¯et al. developed super resolution by polarization demodulation (SPoD) and excitation polarization angle narrowing (ExPAN) which achieved super resolution with neither structured illumination nor special switchable or blinking°u orescent probes. 15 They applied the technique to standard wide-¯eld microscopy and to two-photon scanning microscopy. Two excitation laser beams with rotary polarization were used, with a deexciting stimulated emission beam of always perpendicular polarization to the excitation beam. By doing this, ExPAN could narrow the range of polarization angles that results in e®ective excitation of di®erently oriented molecules. ExPAN could determine the orientation of°uorescent markers attached to structures and measure changes more accurately. Together with SPoD, ExPAN was also demonstrated to bring a better spatial resolution of overlapping°uorescent molecules.
SPoD achieves super resolution imaging by detecting the periodic signals emitted with di®erent phases from di®erent nanoareas under rotary polarized excitation. The rotary polarization of both excitation and stimulated beams is done by passing them through the same rotary half wave plate. The polarization modulation data contains 10 sampling point during each cycle and is demodulated by the sparsity penalty-enhanced estimation by demodulation (SPEED) deconvolution algorithm. The algorithm models each nanoarea as a mean dipole and distinguish neighboring emitters within the di®raction limited area through the di®erent phases of sinusoidal response to rotary polarized excitation, i.e., through di®erent dipole orientations of the mean dipoles. To achieve this, a model of the polarization modulated system is built and penalized maximum likelihood estimation is utilized to estimate original sample information. Fast iterative shrinkage-thresholding algorithm (FISTA) solves the deconvolution problem.
Though SPoD with ExPAN achieved super resolution through polarization demodulation, the information of dipole orientations is lost during the deconvolution process. Hence, SPoD could not be strictly taken as a form of FPM. There also has been an interesting debate on whether polarization modulation adds super resolution or not. 63,64 Super resolution dipole orientation mapping (SDOM) extended SPoD with measurement of dipole orientations, which adds promptly evidence to the debate. 18 Instead of the SPEED algorithm in SPoD, SDOM establishes a polarization-variant model, in which the intensity determines the super-resolution microscopic image using sparsity-enhanced deconvolution, while the phase determines the e®ective dipole orientation of each super-resolved focal volume using least squares estimation, thus fully exploiting the polarization modulation information. The dipole orientations are superimposed onto the image as arrows, whose direction and length denotes e®ective dipole orientation and orientation uniformity accordingly. SDOM achieves comparable intensity resolution compared to SPoD while achieving super resolution dipole orientation mapping as well. The imaging speed of SDOM could be 5 f.p.s and requires low excitation power, making it possible for live cell imaging of yeast.
Both SPoD and SDOM utilize polarization modulation to modulate the intensity of°uorescence. However, it is limited by the small probability that all°uorophores have the same orientation in di®raction-limited zones of labeled samples. When the sample consists of high densities stochastically oriented°uorophores or is highly dynamic in orientation, it would be hard to detect°u orescence modulation. Another super-resolution technique is based on single molecular imaging. Single molecular imaging of°uorescent dipoles in intensity and orientation has long been investigated. 16,19,23,48 For LD single dipole measurement, two or four polarization excitations are modulated for the balance of dipole orientation measurement and imaging speed. 19,47 Simultaneous imaging brings FA the advantage over LD of faster imaging. However, splitting the°u orescent signal into multiple detection channels would reduce the signal-to-noise ratio, thus limiting the number of detection channels. In most cases, two detection channels are used. Four channels could achieve 3D orientation detection 41 or unambiguous measurement of the dipole's average orientation and wobbling angle. 16 However, this only applies to very diluted labeling of°uorophores and could hardly reveal complex bio-structures. This could be solved by polarization-resolved direct stochastic optical reconstruction microscopy (polar-dSTORM), 17 which measures single°uorescent dipoles in one frame, and switches to other dipoles on the ON state stochastically in other frames, accumulating a full picture of the samples from adequate frames.
To preserve high signal-to-noise ratio for single molecular localization, two emission detection channels were used, which allows in-plane orientation measurement only and omits the wobbling information of single dipoles. The designed algorithm estimates both the azimuth and the position of the single molecules in each frame, which provides accurate localization and orientation measurement. With single molecular detection in polar-dSTORM, the dipole information measured includes the average orientation of the dipole and the wobbling aperture angle. The average orientation of the dipole could be measured directly from the°uorescence anisotropy in each frame, while the wobbling aperture angle is statically calculated from nearby localized emitters. Previous FPM images could only o®er an average of orientation information over many molecules, which would lose information on individual wobbling behaviors at some extent. It was found that the average orientation may remain the same in ordered and disordered system while their wobbling angle varies. Polar-dSTORM was applied to nanoscale orientational order imaging of biological¯laments, including dsDNA, actin, and microtubule, providing quantitative results of point orientation and wobbling angle. Since the imaging time of polar-dSTORM takes 2-40 min and statistical calculation of molecules detected during the period is used, it¯ts better for stationary samples. The speci¯c sample preparation of polar-dSTORM also limits the application of live cells.

Discussion and Conclusion
Di®raction limited FPM techniques are generally applied to imaging bulk samples with organized distribution of dipole orientations. Taking the study of septin for example, both early research and FluoPolScope could only reveal the 90 rotation of the¯lament direction. [27][28][29] As for the intermediate state, during which the¯lament direction transits, they could hardly do anything and requires higher resolution imaging. 65 What's worse, the results true for the bulk sample, may be completely wrong for single°uorescent probes, 17,18 making the measurement results unreliable.
Single molecular dipole imaging could achieve both position tracking and dipole orientation measurement of single molecules at microseconds time scale. The localization precision could be as high as several nanometers. It achieved great success in studying the rotational walking of motor protein myosin 19,23,47,50 and the step rotation of ATPase enzyme. 2,3,65 Whereas, single dipole imaging is limited particle tracking or samples with dilute labeling. It lacks the power to reveal samples with complex structure. Polar-dSTORM solves this by on-o® modulation of the°uorescent probes and acquisition adequate frames for a reconstruction of super resolution image. The imaging resolution of polar-dSTORM is high, with localization precision of tens of nanometers. Single dipole average orientation is directly measured separately and the wobbling angle is statistically calculated from neighboring emitters. The drawback of polar-dSTORM is long imaging time of 2-40 min, which requires a stationary sample during the imaging period. The sample preparation of dSTORM also makes it hard for live cell samples.
SDOM has achieved super resolution dipole orientation mapping with a spatial resolution of 150 nm and sub-second temporal resolution. It has been applied to both¯xed cell and live cell imaging, which shows great advantages over di®raction limited FPM techniques on both revealing sub-di®ractional structures and measuring local dipole orientations. In comparison with polar-dSTROM, SDOM still measures average dipoles and could not separate the signal of the wobbling of single°uorophores from the variation of orientation distribution of°uorophores with the resolvable area. Same with SPoD, the power of SDOM would be weakened if the°uorescent probes are distributed too homogeneously or too dense. A comparison of actin imaging results among SDOM, polar-dSTORM and instantaneous FluoPolScope are displayed in Fig. 4. Summary of more representative FPM techniques is included in Table 1, together with related literatures and their characteristics.
Thanks to the intrinsic polarization of chromophores,°uorescence polarization reveals the structures and functions of the biological macromolecules. With incorporation with various optical imaging modalities, FPM has played an irreplaceable role in   solving many questions. Fast and noninvasive imaging of the samples makes it a complementary tool for X-crystallography which typically applies to individual proteins, or sub-complexes, or EM which requires invasive sample preparation, or AFM which could measure the surface of the sample. Compared to these methods, the speci¯c labeling of the°uorescent probes provides better focus on the structure of interest. As the development of FPM techniques, its power has spread from uniform oriented°u orophores to°uorescent dipoles with organized orientation or on complex bio-structures. The detection accuracy has improved from measuring the bulk volume polarization to sub-di®raction area measurement and single dipole measurement. Imaging resolution of FPM matters not only for intensity image but also for the accuracy of dipole orientation detection. Recently developed super resolution FPM techniques still have their limitations though demonstrating great successes in their imaging results. Spatial 3D super resolution FPM techniques and 3D orientation measurement of°uorescent dipoles are still missing. In the future, we anticipate more inventions which could achieve both high-resolution measurement and fast temporal resolution, allowing imaging samples of live cells. This may be done by introducing existing super resolution principles into FPM, or by better exploiting the intensity°uctuation with polarization modulation, or other alternative means.

Acknowledgments
This work is supported by the National Instrument Development Special Program (2013YQ03065102), the Natural Science Foundation of China (614-75010,