Model-free uncertainty estimation in stochastical optical fluctuation imaging (SOFI) leads to a doubled temporal resolution

Technological advances in super-resolution microscopy to study cellular processes

Since its initial demonstration in 2000, far-field super-resolution light microscopy has undergone tremendous technological developments. In parallel, these developments have opened a new window into visualizing the inner life of cells at unprecedented levels of detail. Here, we review the technical details behind the most common implementations of super-resolution microscopy and highlight some of the recent, promising advances in this field.

Design of experiments for the optimization of SOFI super-resolution microscopy imaging

Super-resolution optical fluctuation imaging (SOFI) is a well-known super-resolution technique appreciated for its versatility and broad applicability. However, even though an extended theoretical description is available, it is still not fully understood how the interplay between different experimental parameters influences the quality of a SOFI image. We investigated the relationship between five experimental parameters (measurement time, on-time t _on, off-time t _off, probe brightness, and out of focus background) and the quality of the super-resolved images they yielded, expressed as Signal to Noise Ratio (SNR). Empirical relationships were modeled for second- and third-order SOFI using data simulated according to a D-Optimal design of experiments, which is an ad-hoc design built to reduce the experimental load when the total number of trials to be conducted becomes too high for practical applications. This approach proves to be more reliable and efficient for parameter optimization compared to the more classical parameter by parameter approach. Our results indicate that the best image quality is achieved for the fastest emitter blinking (lowest t _on and t _off), lowest background level, and the highest measurement duration, while the brightness variation does not affect the quality in a statistically significant way within the investigated range. However, when the ranges spanned by the parameters are constrained, a different set of optimal conditions may arise. For example, for second-order SOFI, we identified situations in which the increase of t _off can be beneficial to SNR, such as when the measurement duration is long enough. In general, optimal values of t _on and t _off have been found to be highly dependent from each other and from the measurement duration.

Smoothness correction for better SOFI imaging

Sub-diffraction or super-resolution fluorescence imaging allows the visualization of the cellular morphology and interactions at the nanoscale. Statistical analysis methods such as super-resolution optical fluctuation imaging (SOFI) obtain an improved spatial resolution by analyzing fluorophore blinking but can be perturbed by the presence of non-stationary processes such as photodestruction or fluctuations in the illumination. In this work, we propose to use Whittaker smoothing to remove these smooth signal trends and retain only the information associated to independent blinking of the emitters, thus enhancing the SOFI signals. We find that our method works well to correct photodestruction, especially when it occurs quickly. The resulting images show a much higher contrast, strongly suppressed background and a more detailed visualization of cellular structures. Our method is parameter-free and computationally efficient, and can be readily applied on both two-dimensional and three-dimensional data.

Enhanced temporal and spatial resolution in super-resolution covariance imaging algorithm with deconvolution optimization

Based on the numerical analysis that covariance exhibits superior statistical precision than cumulant and variance, a new SOFI algorithm by calculating the n orders covariance for each pixel is presented with an almost 2n -fold resolution improvement, which can be enhanced to 2ⁿ via deconvolution. An optimized deconvolution is also proposed by calculating the (n + 1) order SD associated with each n order covariance pixel, and introducing the results into the deconvolution as a damping factor to suppress noise generation. Moreover, a re-deconvolution of the covariance image with the covariance-equivalent point spread function is used to further increase the final resolution by above 2-fold. Simulated and experimental results show that this algorithm can significantly increase the temporal-spatial resolution of SOFI, meanwhile, preserve the sample's structure. Thus, a resolution of 58 nm is achieved for 20 experimental images, and the corresponding acquisition time is 0.8 seconds.

SOFIevaluator: a strategy for the quantitative quality assessment of SOFI data

Super-resolution fluorescence imaging techniques allow optical imaging of specimens beyond the diffraction limit of light. Super-resolution optical fluctuation imaging (SOFI) relies on computational analysis of stochastic blinking events to obtain a super-resolved image. As with some other super-resolution methods, this strong dependency on computational analysis can make it difficult to gauge how well the resulting images reflect the underlying sample structure. We herein report SOFIevaluator, an unbiased and parameter-free algorithm for calculating a set of metrics that describes the quality of super-resolution fluorescence imaging data for SOFI. We additionally demonstrate how SOFIevaluator can be used to identify fluorescent proteins that perform well for SOFI imaging under different imaging conditions.

An extended quantitative model for super-resolution optical fluctuation imaging (SOFI)

Super-resolution optical fluctuation imaging (SOFI) provides super-resolution (SR) fluorescence imaging by analyzing fluctuations in the fluorophore emission. The technique has been used both to acquire quantitative SR images and to provide SR biosensing by monitoring changes in fluorophore blinking dynamics. Proper analysis of such data relies on a fully quantitative model of the imaging. However, previous SOFI imaging models made several assumptions that can not be realized in practice. In this work we address these limitations by developing and verifying a fully quantitative model that better approximates real-world imaging conditions. Our model shows that (i) SOFI images are free of bias, or can be made so, if the signal is stationary and fluorophores blink independently, (ii) allows a fully quantitative description of the link between SOFI imaging and probe dynamics, and (iii) paves the way for more advanced SOFI image reconstruction by offering a computationally fast way to calculate SOFI images for arbitrary probe, sample and instrumental properties.

Synergizing superresolution optical fluctuation imaging with single molecule localization microscopy

Single-molecule-localization-microscopy (SMLM) and superresolution-optical-fluctuation-imaging (SOFI) enable imaging biological samples well beyond the diffraction-limit of light. SOFI imaging is typically faster, yet has lower resolution than SMLM. Since the same (or similar) data format is acquired for both methods, their algorithms could presumably be combined synergistically for reconstruction and improvement of overall imaging performance. For that, we first defined a measure of the acquired-SNR for each method. This measure was ∼x10 to x100 higher for SOFI as compared to SMLM, indicating faster recognition and acquisition of features by SOFI. This measure also allowed fluorophore-specific optimization of SOFI reconstruction over its time-window and time-lag. We show that SOFI-assisted SMLM imaging can improve image reconstruction by rejecting common sources of background (e.g. out-of-focus emission and auto-fluorescence), especially under low signal-to-noise ratio conditions, by efficient optical sectioning and by shortening image reconstruction time. The performance and utility of our approach was evaluated by realistic simulations and by SOFI-assisted SMLM imaging of the plasma membrane of activated fixed and live T-cells (in isolation or in conjugation to antigen presenting cells). Our approach enhances SMLM performance under demanding imaging conditions and could set an example for synergizing additional imaging techniques.

Reduced Fluorescent Protein Switching Fatigue by Binding-Induced Emissive State Stabilization

Reversibly switchable fluorescent proteins (RSFPs) enable advanced fluorescence imaging, though the performance of this imaging crucially depends on the properties of the labels. We report on the use of an existing small binding peptide, named Enhancer, to modulate the spectroscopic properties of the recently developed rsGreen series of RSFPs. Fusion constructs of Enhancer with rsGreen1 and rsGreenF revealed an increased molecular brightness and pH stability, although expression in living E. coli or HeLa cells resulted in a decrease of the overall emission. Surprisingly, Enhancer binding also increased off-switching speed and resistance to switching fatigue. Further investigation suggested that the RSFPs can interconvert between fast- and slow-switching emissive states, with the overall protein population gradually converting to the slow-switching state through irradiation. The Enhancer modulates the spectroscopic properties of both states, but also preferentially stabilizes the fast-switching state, supporting the increased fatigue resistance. This work demonstrates how the photo-physical properties of RSFPs can be influenced by their binding to other small proteins, which opens up new horizons for applications that may require such modulation. Furthermore, we provide new insights into the photoswitching kinetics that should be of general consideration when developing new RSFPs with improved or different photochromic properties.

Correcting for photodestruction in super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging overcomes the diffraction limit by analyzing fluctuations in the fluorophore emission. A key assumption of the imaging is that the fluorophores are independent, though this is invalidated in the presence of photodestruction. In this work, we evaluate the effect of photodestruction on SOFI imaging using theoretical considerations and computer simulations. We find that photodestruction gives rise to an additional signal that does not present an easily interpretable view of the sample structure. This additional signal is strong and the resulting images typically exhibit less noise. Accordingly, these images may be mis-interpreted as being more visually pleasing or more informative. To address this uncertainty, we develop a procedure that can robustly estimate to what extent any particular experiment is affected by photodestruction. We also develop a detailed assessment methodology and use it to evaluate the performance of several correction algorithms. We identify two approaches that can correct for the presence of even strong photodestruction, one of which can be implemented directly in the SOFI calculation software.

Effect of probe diffusion on the SOFI imaging accuracy

Live-cell super-resolution fluorescence imaging is becoming commonplace for exploring biological systems, though sample dynamics can affect the imaging quality. In this work we evaluate the effect of probe diffusion on super-resolution optical fluctuation imaging (SOFI), using a theoretical model and numerical simulations based on the imaging of live cells labelled with photochromic fluorescent proteins. We find that, over a range of physiological conditions, fluorophore diffusion results in a change in the amplitude of the SOFI signal. The magnitude of this change is approximately proportional to the on-time ratio of the fluorophores. However, for photochromic fluorescent proteins this effect is unlikely to present a significant distortion in practical experiments in biological systems. Due to this lack of distortions, probe diffusion strongly enhances the SOFI imaging by avoiding spatial undersampling caused by the limited labeling density.

Genetically encoded biosensors for visualizing live-cell biochemical activity at super-resolution

Compartmentalized biochemical activities are essential to all cellular processes, but there is no generalizable method to visualize dynamic protein activities in living cells at a resolution commensurate with their compartmentalization. Here we introduce a new class of fluorescent biosensors that detect biochemical activities in living cells at a resolution up to three-fold better than the diffraction limit. Utilizing specific, binding-induced changes in protein fluorescence dynamics, these biosensors translate kinase activities or protein-protein interactions into changes in fluorescence fluctuations, which are quantifiable through stochastic optical fluctuation imaging. A Protein Kinase A (PKA) biosensor allowed us to resolve minute PKA activity microdomains on the plasma membrane of living cells and uncover the role of clustered anchoring proteins in organizing these activity microdomains. Together, these findings suggest that biochemical activities of the cell are spatially organized into an activity architecture, whose structural and functional characteristics can be revealed by these new biosensors.

Live-cell monochromatic dual-label sub-diffraction microscopy by mt-pcSOFI

We present mt-pcSOFI, live-cell monochromatic sub-diffraction imaging and illustrate the method with existing RSFPs and the newly developed ffDronpa-F.

Complementarity of PALM and SOFI for super-resolution live-cell imaging of focal adhesions

Live-cell imaging of focal adhesions requires a sufficiently high temporal resolution, which remains a challenge for super-resolution microscopy. Here we address this important issue by combining photoactivated localization microscopy (PALM) with super-resolution optical fluctuation imaging (SOFI). Using simulations and fixed-cell focal adhesion images, we investigate the complementarity between PALM and SOFI in terms of spatial and temporal resolution. This PALM-SOFI framework is used to image focal adhesions in living cells, while obtaining a temporal resolution below 10 s. We visualize the dynamics of focal adhesions, and reveal local mean velocities around 190 nm min⁻¹. The complementarity of PALM and SOFI is assessed in detail with a methodology that integrates a resolution and signal-to-noise metric. This PALM and SOFI concept provides an enlarged quantitative imaging framework, allowing unprecedented functional exploration of focal adhesions through the estimation of molecular parameters such as fluorophore densities and photoactivation or photoswitching kinetics.

Live cell super-resolution imaging requires a high temporal resolution, which remains a challenge. Here the authors combine photo-activated localization microscopy (PALM) with super-resolution optical fluctuation imaging (SOFI) to achieve high spatiotemporal resolution and quantitative imaging of focal adhesion dynamics.

Statistical precision in super-resolution optical fluctuation imaging

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by calculating the spatiotemporal cross-cumulants of independent stochastic intensity fluctuations of emitters. Ideally, SOFI eliminates any noise that is not correlated over time, but in practice, due to limited data lengths, the statistical uncertainty of cumulants will affect the continuities and homogeneities of SOFI images. Since the variance and signal-to-noise ratio (SNR) characterize cumulant statistical uncertainty, we determined theoretical expressions for these based on a single dataset. From a simulation of temporal fluctuations of blinking fluorescent emitters, we calculated the quantitative relation between the SNR of cumulants and multiple parameters of the blinking signal, such as the on-time ratio, acquisition frame to average blinking rate ratio, sequence length, and photon amplitude, which not only provides a physical interpretation for SOFI phenomena but also theoretical guidance to achieve optimal practical outcomes.

Superior performance with sCMOS over EMCCD in super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) is a fast and low-cost live-cell optical nanoscopy for extracting subdiffraction information from the statistics of fluorescence intensity fluctuation. As SOFI is based on the fluctuation statistics, rather than the detection of single molecules, it poses unique requirements for imaging detectors, which still lack a systematic evaluation. Here, we analyze the influences of pixel sizes, frame rates, noise levels, and different gains in SOFI with simulations and experimental tests. Our analysis shows that the smaller pixel size and faster readout speed of scientific-grade complementary metal oxide semiconductor (sCMOS) enables SOFI to achieve high spatiotemporal resolution with a large field-of-view, which is especially beneficial for live-cell super-resolution imaging. Overall, as the performance of SOFI is relatively insensitive to the signal-to-noise ratio (SNR), the gain in pixel size and readout speed exceeds the loss in SNR, indicating sCMOS is superior to electron multiplying charge coupled device in context to SOFI in many cases. Super-resolution imaging of cellular microtubule structures with high-order SOFI is experimentally demonstrated at large field-of-view, taking advantage of the large pixel number and fast frame rate of sCMOS cameras.