Multi-color structured illumination microscopy for live cell imaging based on the enhanced image recombination transform algorithm.

Structured illumination microscopy (SIM) has attracted considerable interest in super-resolution, live-cell imaging because of its low light dose and high imaging speed. Obtaining a high-quality reconstruction image in SIM depends on the precise determination of the parameters of the fringe illumination pattern. The image recombination transform (IRT) algorithm is superior to other algorithms in obtaining the precise initial phase without any approximation, which is promising to provide a considerable solution to address the difficulty of initial phase estimation at low-modulation-depth conditions. However, the IRT algorithm only considers a phase shift of π∕2, which limits its applications in general scenarios. In this letter, we present a general form of IRT algorithm suitable for arbitrary phase shifts, providing a powerful tool for parameter estimation in low signal-to-noise cases. To demonstrate the effectiveness of the enhanced IRT algorithm, we constructed a multicolor, structured illumination microscope and studied at super-resolution, the cargo traffic in HRPE cells, and monitored the movement of mitochondrial structures and microtubules in COS-7 cells. The custom SIM system using the enhanced IRT algorithm allows multicolor capability and a low excitation intensity fluorescence imaging less than 1 W/cm2. High-quality super-resolution images are obtained, which demonstrates the utility of this approach in imaging in the life sciences.


Introduction
Over the past several years, exponential growth in the use of super-resolution, fluorescence microscopy has occurred in the field of biological imaging [1]. Among these techniques, structured illumination microscopy (SIM) has attracted considerable interest because of its low light dose and high imaging speed [2]. These characteristics provide a powerful tool for high-speed, live-cell imaging with double the spatial resolution of wide-field fluorescence microscopes [3][4][5].
In SIM, a periodic sinusoidal fringe illumination is adopted to shift the unresolved highfrequency features of the sample to lower frequencies. The super-resolution images can be solved by extracting the high-frequency information. In general, sinusoidal fringe illumination with a spatial frequency close to the cut-off frequency of the microscope is essential to achieve a considerable resolution improvement [6]. The phase-shifted sinusoidal patterns are typically produced by the interference of the ±1-order diffraction beams generated using the ferroelectric liquid crystal on a silicon spatial light modulator (FC-SLM) [7][8][9][10]. To maintain high contrast of the fringe pattern near the diffraction limit, different polarization control mechanisms have been employed to keep the polarization of the incident beams parallel with the orientation of the fringes. In practice, two methods have been used to achieve the fast and precise control of the polarization state. In 2009, Kner et al. employed two ferroelectric liquid crystal phase retarders (FLC) to rotate the polarization of the light and illumination pattern synchronously. However, FLCs have a switching time of over 20ms, which limited the SIM imaging speed to around 50ms per frame [11,12]. To avoid the long switching time of the FLCs, Guo et al. presented a passive polarization control scheme by replacing the FLCs with a homemade, azimuthally patterned, achromatic half-wave plate [13]. Unfortunately, the specially designed half-wave plate requires an experienced manufacturing setup, making it expensive and difficult to access. To circumvent this issue, a simpler and robust approach using an achromatic quarter-wave plate for the isotropic circular polarization for all pattern orientations was presented [14]. The unexpected, relatively lower modulation depth caused by circular polarization increased the difficulty of determining the initial phases for the current reconstruction algorithm, thus limiting the widespread use of this approach.
To overcome the above-mentioned difficulties, we developed an image reconstruction approach for SIM, based on the image recombination transform (IRT) scheme to determine the initial phase at low modulation depth [15]. The utility of this approach was demonstrated by imaging BPAE cells with excitation light intensities as low as 1 W/cm 2 , which is 30 to 100 lower than more commonly used light intensity levels in structured illumination imaging. In SIM, the illumination grating is typically rotated through three orientations separated by 60°for reconstructing the near isotropic resolution image. For each grating orientation, three images at phases 0, 2π/3, and 4π/3 are recorded for most laser interference-based SIM approaches. However, the previous IRT algorithm was originally designed for our SIM setup based on DMD-projection, which only considered a phase shift of π/2 and two orientations separated by 90°, limiting its applications in general scenarios [16].
To address this limitation, we extend the concept of the IRT scheme to arbitrary phase intervals and simplify the process of extracting the high-order spectral components. To test the performance of the algorithm in biological imaging, a light-efficient, multi-color imaging SIM setup, based on the interference of circularly-polarized beams was built. The enhanced IRT algorithm was subsequently employed to obtain the precise solution of the initial phase under the low modulation depth, while imaging sub-cellular structures in eukaryotic cells. Imaging was performed in both static and dynamic scenarios. Results show that individual microtubules derived from the centrosome and Golgi apparatus can be easily resolved as well as their differences in vesicle enrichment and trafficking velocity. Further, mitochondrial cristae structures and the mitochondrial DNA (mtDNA) are also resolved in static images and their dynamic behavior is revealed during mitochondrial fission and fusion.

Image recombination transform algorithm
We have demonstrated the effectiveness of the IRT algorithm in our previous work and predicted its applicability in the interference-based SIM [15]. However, the previous IRT algorithm cannot be extended to the interference-based SIM because it was originally designed for a phase shift of π/2 and two orientations separated by 90°. Here we recombine the complex image and deduce a general form of IRT algorithm suitable for arbitrary uniform phase shifts. The enhanced IRT algorithm is suitable for both DMD-projection and laser-interference-based SIM. Importantly, it maintains the advantages of precise initial phase estimation at low-modulation-depth conditions. In linear SIM, the fluorescence images captured by the detector D(r) can be described by the equation below: Where S(r), I(r), and H(r) denote the specimen distribution, the excitation light, and the point spread function of the microscope, respectively. I 0 , m, and φ represent the illumination intensity, the modulation depth, and the phase of the cosine fringe, respectively. In the frequency domain, the spectrum of the captured picture can be obtained by applying a Fourier transform: Here, is the frequency distribution of the unresolvable high-frequency features of the sample, which is limited by the optical transfer function (OTF). Three raw images with different phase shifts between each are required to reconstruct one SIM image. The unresolved high-frequency features can be solved by There are three pattern parameters p, m, and φ 0 that should be determined to solve the equations. Since the initial phase φ 0 is included in the exponential term of the matrix, it must be precisely determined. To estimate the initial phase, Shroff et al. proposed the phase of peak (POP) algorithm [17]. This was later improved by Wicker with the auto-correlation reconstruction (ACR) algorithm [18]. One drawback of both methods is that they can only find the approximate solution of the initial phase, which requires a high modulation depth of the illumination fringes. However, the high modulation depth condition is often difficult to reach, especially when the fluorescence signal is low. Since the phase shift between two adjacent images is known before reconstruction, we developed a reconstruction approach image recombination transform (IRT) algorithm to obtain a precise solution of the initial phase [15].
Our original IRT algorithm is ideal for DMD-based SIM, which can only employ the phase shift between two adjacent images by π/2. To use the IRT algorithm on the laser interference-based SIM approach, one needs to extend the algorithm to evenly arbitrary phase shifts. We could obtain the expression of the captured images employing an even phase shift of ∆φ in Eq. (1) as We recombine a complex image as And thus The Fourier transform of the complex image is By substituting k=-p into Eq. (6), the complex image becomes Because the sample and symmetrical PSF is a real value, the initial phase can be solved by Compared with the POP and ACR algorithms, the enhanced IRT algorithm provides a precise solution of the fringe initial phase without the assumptions of weak background and high modulation depth, which releases the burden of the polarization control in setup construction.

SIM setup
The schematic diagram of the SIM system is illustrated in Fig. 1. Four laser sources with wavelengths of 405, 488, 561, and 638nm (L4cc, Oxxius Inc., France) are used to enable multi-wavelength excitation. The expanded and collimated beam enters a polarized beam splitter (PBS) and an achromatic half-wave plate (HWP) and is then modulated by the FC-SLM (QXGA-3DM-STR, Forth Dimension Displays Ltd, UK). After being modulated by FC-SLM, the exiting light is diffracted into different orders. The ±1-order diffraction orders are selected by a mask and pass through a polarization rotator consisting of a ferroelectric liquid crystal variable retarder (FLC, LVR-200-VIS, Meadowlark Optics Inc., US) with an achromatic QWP. The purpose of the FLC is to compensate for the additional phase difference induced by the dichroic mirror. The linearly polarized light is converted to circularly polarized by the QWP, which produces an equal contrast of sinusoidal fringes in all three orientations on the sample. The light then passes through a 4f system consisting of lens 2 and lens 3 and is focused by a 100× objective (Apo TIRF, NA1.49, Nikon Inc., Japan). The ±1-order diffraction beams interfere at the focal plane to produce sinusoidal patterns on the specimen. The sample is mounted on a motorized XY and piezo Z-axis translation stage (PZ-2150-XYLE-FT piezo Z system, Applied Scientific Instrumentation Inc., USA) that can be moved axially in steps of 1 nm. The fluorescence signal is reflected by a dichroic mirror (LF488/561, Semrock Inc., USA) and collected by a tube lens. An sCMOS camera with a maximum full-frame rate of 100 fps (Orca Flash4.0, Hamamatsu Inc., Japan) is used to capture the images. The system is synchronized by a NI-DAQ (USB-6003, National Instruments Inc., USA) with custom-developed software written in C++.
Generally, a laser interference SIM system requires that the polarization direction of the two linearly polarized interference beams be carefully adjusted to obtain optimal modulation depth [19]. To achieve this, circularly polarized light is produced by passing the linearly polarized light through the QWP (Fig. 1). Using the isotropic circular polarization for all pattern orientations has the advantage of high efficiency and wide spectral range, while the maximum modulation depth of the circularly polarized interference fringe is only 1/3. An additional phase shift can be induced by the dichroic mirror (DM). Heintzmann et al. used two identical dichromatic reflectors to ensure the polarization state [20]. In the setup shown in Fig. 1, the FLC is precisely positioned and its fast axis and voltage are carefully regulated during the experiment. To prove the effectiveness of the proposed method, we traced the polarization states of the laser along the optical path. Without the FLC, the ellipticity of the laser light before and after the DM is 0.927 and 0.205, respectively. With the help of FLC, the ellipticity is 0.938 after DM.

COS-7 cells (CV-1 in
Origin with SV40 genes, derived from the kidney of the African green monkey) were obtained from the American Type Culture Collection. Cells were cultured in Dulbecco's modified eagle medium (Life Technologies) supplemented with 10% fetal bovine serum, and 1% each penicillin/streptomycin in a 5% CO2 humidified incubator at 37°C. Cells were seeded onto 35 mm glass-bottom microscope dishes (Cellvis) and cultured for an additional 12-18 h before the experiments. To label mitochondrial DNA, COS-7 cells were transfected with 2 ug TFAM-mCherry in Opti-MEM medium (Invitrogen) containing 5 µl Lipofectamine 2000 reagent (Invitrogen), according to the manufacturer's instructions. To label mitochondria, cells were incubated with 500 nM MitoTracker Green FM (Thermo Fisher Scientific, M7514) in DMEM at 37°C for 30 min and washed with PBS for 3 times.

Comparison of algorithms
To assess the functionality of the SIM system employing the enhanced IRT algorithm, we imaged fixed BSC-1 cells from the African green monkey, which are fluorescently stained to highlight microtubules with Cy5-phalloidin, mitochondria with Tom-20-Atto488, and nuclear DNA with DAPI. The super-resolution SIM images of the microtubules, mitochondria, and nucleus are sharper than those captured using wide-field, which makes it easier to discern fine details ( Fig. 2(a)). When the POP algorithm was used to process the raw data, some unwanted residues appear in the Fourier spectrum as indicated by the red circles, resulting in some artifacts in the reconstructed image (Fig. 2(c) for the image and 2 g for the spectrum). The ACR algorithm provides an improvement in artifact suppression and the residual fringes are hardly seen in its reconstructed image (Fig. 2(d)). However, there still exist a few extra components in the Fourier spectrum, leading to a reduction in image quality (Fig. 2 h). In contrast to the POP and ACR algorithms, here is no artifact with the IRT and there are no residues apparent in the corresponding Fourier spectrum (Fig. 2(e) and (i), respectively). To compare the algorithms quantitatively, we used NanoJ-SQUIRREL, which is an ImageJbased analytical approach that provides a quantitative assessment of super-resolution image quality [21]. The software analyzes these images with two metrics, the resolution-scaled error (RSE) and the resolution-scaled Pearson coefficient (RSP). The RSE represents the root mean square error between the reference and SIM image and the RSP represents the Pearson correlation coefficient between two images.
To compare algorithms, the BSC-1 cells were imaged with four different illumination intensities of 0.1, 1, 5 and 10W/cm 2 . Then, image reconstruction was performed with each of the three algorithms and the error maps from the 1W/cm 2 light dose are presented in Fig. 3(a) using the first widefield image used as reference. This visual comparison highlights discrepancies and artifacts between the SIM and widefield images, where the IRT algorithm provides the minimum artifacts compared with POP and ACR. In the quantitative metrics in Fig. 3(b), the RSE of the POP and ACR algorithms increases rapidly when the illumination intensity below 1 W/cm 2 , while the IRT algorithm retains a relatively low RSE over the whole range of the illumination intensity. When the illumination intensity was increased to 5W/cm 2 , the RSE of each of the three algorithms is almost the same. Similar results were obtained when the RSP metrics were compared (Fig. 3(c). Consequently, and consistent with the super-resolution image comparison in Fig. 2, the IRT algorithm produces superior quality reconstructed SIM images.

Live cell imaging
Mitochondria and microtubules play an important role in cellular biology by supplying energy and transporting vesicles, respectively. However, they are difficult to track using traditional microscopy because of the sensitivity to phototoxicity, high density, and as they are highly dynamic structures [22,23]. Here we prepare two kinds of samples to demonstrate the performance  . Red curve and green curve, Gaussian fitting curves of velocity distribution on GaMTs or non-GaMTs, respectively (n = 14 MTs). The peak of red curve (472.1 ± 33.6 nm/s) and peak of purple curve (227.86 ± 44.31 nm/s). ***P < 0.001, unpaired t-test. of the SIM system and enhanced IRT algorithm: mitochondria with mtDNA and microtubules with cargo in transit.
Mitochondria are dynamic structures undergoing changes in shape, mtDNA distribution, fusion and fission [24]. COS-7 cells have large mitochondria and have been used in numerous studies to follow mitochondrial dynamics [13]. However, the mitochondrial structure is sensitive to light illumination. A phototoxic reaction will destroy the fine structure thus it is challenging to image these organelles at super-resolution [25,26]. Therefore, imaging was done using a light dose lower than 1W/cm 2 with images reconstructed using the IRT algorithm. Results show that as expected, mitochondrial proteins and DNA can be discerned (Fig. 4(a)). Second, dynamic behavior was monitored for more than 400 frames, permitting visualization of mitochondrial fission and fusion, as well as changes in the position of the mtDNA (see also Visualization 1). Image analysis reveals mitochondrial tubulation occurring with tubules extending from either the tip or side areas at velocities of 1-3 µm/sec, and in addition, some mtDNA nucleoids were observed to rapidly traffic towards the tubulation tips at velocities ranging from 1 to 3 µm/sec ( Fig. 4(b)-4(e)). For the nucleoid in Fig. 4(b), its velocity allowed it to catch up to the slowing down tubule tip, while for the second nucleoid in Fig. 4(c), its velocity matched that of the tip. This behavior is consistent with the active transportation model for mtDNA [27,28] Microtubules derived from the Golgi (GaMTs) have been implicated to play critical roles in persistent cell migration. However, the MT network density is extremely high near the Golgi region [29]. Therefore, MT-dependent trafficking has not been visualized in real-time and at super-resolution. To visualize vesicle trafficking on individual MTs, dual-color imaging of MAP4-GFP (microtubules) and Ecadherin-mCherry (cargo) fusion proteins in HRPE cells was performed ( Fig. 5(a)).
To study vesicle movement on GaMTs, we classified GaMTs and non-GaMTs ( Fig. 5(b)), as described previously [30]. We then superimposed MT tracks with vesicle trajectories and analyzed vesicle velocity in both MT groups. Results show that the velocity of vesicles along the GaMTs is on average, two-fold faster than vesicles along the non-GaMTs. (Figure 5(c) and Visualization 2).

Conclusion
By pairing the enhanced IRT algorithm with a light-efficient structured illumination microscope, exquisite, multi-color super-resolution images of dynamic processes in live cells can be readily obtained. This occurs due to the superior performance of the IRT algorithm in image reconstruction that provides a simple and robust operation producing higher quality SR images compared to other reconstruction algorithms. This has enabled the imaging of microtubule-dependent trafficking in live cells at super-resolution.