Super-resolution spectroscopic microscopy via photon localization

Traditional photon localization microscopy analyses only the spatial distributions of photons emitted by individual molecules to reconstruct super-resolution optical images. Unfortunately, however, the highly valuable spectroscopic information from these photons have been overlooked. Here we report a spectroscopic photon localization microscopy that is capable of capturing the inherent spectroscopic signatures of photons from individual stochastic radiation events. Spectroscopic photon localization microscopy achieved higher spatial resolution than traditional photon localization microscopy through spectral discrimination to identify the photons emitted from individual molecules. As a result, we resolved two fluorescent molecules, which were 15 nm apart, with the corresponding spatial resolution of 10 nm—a four-fold improvement over photon localization microscopy. Using spectroscopic photon localization microscopy, we further demonstrated simultaneous multi-colour super-resolution imaging of microtubules and mitochondria in COS-7 cells and showed that background autofluorescence can be identified through its distinct emission spectra.

Localization precision with respect to NB in SPLM. Black line is the curve calculated by " , where " is the localization precision at NB=1.

Supplementary Notes
Supplementary Note 1

Spectral unmixing
Stochastic blinking events occurring along the same horizontal position within the same frame can cause spectral overlap, which is highly probable in regions with many fluorophores in close proximity. Since the locations of blinking events are unambiguous in the direct image and the spectra from different blinking events are linearly mixed in the spectral image, overlapping can thus be separated with a modified spectral unmixing algorithm 1 . If we have n spectra from same type of dye molecule with emission spectrum s and the ith spectrum ' emitted at ' position with intensity of ' , the observed spectrum S can be expressed as where w is an error term accounting for additive noise (such as sensor noise and model inadequacies).
Supplementary Figure 5 is the flow chart of spectral separation of two identical dye molecules. We simulated the spectral overlapping from two nearby molecules. Background noise was introduced in the image to mimic the SNR of actual fluorescence image. As an optimization process, we applied a linear least-squares solver, a built-in solver in MATLAB, to solve the above equation with a known number of localization events, where ' and ' are free parameters. After conducting unmixing, overlapped spectra can be separated as shown in Supplementary Figure 5. By using positions of two localization events as inherent reference points, we further calibrated their spectra from their pixel coordinates. Finally, spectra were divided by the wavelength dependent system efficiency to recover the actual emission spectra.
Acquiring accurate reference spectra is essential in generating satisfactory spectral unmixing results.
Although the spectral profiles of synthetic dyes and fluorescent proteins are accurately known, they are usually measured from molecule assembles with spectral broadening due to underlying conformational heterogeneity. To obtain the reference spectra for SPLM, we measure the fluorescence spectrum from single molecule emission in the absence of inhomogeneous broadening. It can be easily obtained from frames with sparse single-molecule events. For single molecule spectroscopy, we also have to consider the spectral shift Δ ' from the underlying conformational heterogeneity. The observed spectrum S can be further expressed as where ' is corresponding shift in pixel domain, which can be calculated as Δ ' /0.63nm.
In practical imaging, the blinking density needs to be carefully controlled to avoid a mass number of overlapping spectra, while still maintaining sufficient number of localizations for achieving a satisfactory image quality 2 . Since the stochastic blinking events are also separated in time, mass overlap in single frames is rare. Typically, spectral overlap is from two or three molecules as shown in the statistic analysis in Supplementary Figure 6.
To verify the accuracy of our applied spectral unmixing algorithm in multicolor imaging, we simulated the situation with two types of dyes used in the cellular imaging, namely Alexa Fluor 568 and Mito-EOS 4b. For the case with more than one type of dye molecule, S can be simply expressed as wherer s n is the emission spectrum of type n dye molecule. As shown in Supplementary Figure 7, two blinking events with separation from 0 nm to ±800 nm were used to simulate overlapped spectra in the spectral image. The simulation shows a satisfied result of spectral separation with our modified unmixing algorithm.
Supplementary Note 2

Improving localization precision via spectral regression
The precision of identifying the centroid location (σ) can be approximated by the probability equation 2 = ' 5 + 5 /12 + 8 ' where s i is the standard deviation of the Gaussian fit in x and y direction; N is the number of detected photons; a is the pixel size of the CCD camera; and b is the standard deviation of the CCD background.
As we can see, the localization uncertainty is proportional to the inverse square root of the number of detected photons.
To further validate the resolution improvement with spectral regression, we first performed a simulation in the case of a single molecule and calculated the precision after regression, as shown in Supplementary Figure 11. In general, the regression can be judged by any molecular specific parameter, such as intensity, polarization, anisotropy, and emission spectrum. Since we are considering a single molecule case in this simulation, all blinking events being collected are naturally from the same molecule and no regression is necessary. The feasibility of our spectral regression algorithm will be discussed in the next case of simulation using the line pattern.
In order to examine the localization precision with respect to the number of blinking (NB) from each molecule, we first generated a movie that consisted of NB frames with a pixel size of 100 nm. In each frame, a single blinking event at diffraction-limited resolution (predefined by the objective NA at wavelength of 600 nm) was superimposed on a Gaussian noise background (Supplementary Figure 11a).
The total photon count and noise level were adjusted to match our experimental conditions. After reconstruction using a standard PALM/STORM algorithm, positions of all the collected localizations were plotted as white crosses. Their centroid, which represents the result of the regression, was further plotted as a red cross. As shown in Supplementary Figure 11b, we tested 500 randomly generated cases to evaluate the localization precision of centroids by plotting the histogram along one of the lateral directions (x-axis). When NB=1, the result shows the precision of conventional PLM (37.4 nm) since no regression was used. As NB increases, the localization precision improves, reaching a resolution to 5.1 nm (7.3-fold improvement) when NB=50. In practice, the NB acquired from experiments normally ranges between 10 and 20. Thus the experimental resolution we can typically achieve is between 7.9 nm and 11.7 nm. To achieve even higher resolution, we can prolong image acquisition time and acquire more blinking events from the same molecules if they still generate blinking. These results illustrate the principle of using spectral regression to improve image resolution in SPLM.
Since spectroscopic information provides one of the most important evidence for molecular discrimination, we hereby used SPLM to realize spectral regression to improve spatial resolution. To demonstrate the feasibility and the performance of our spectral regression method for densely labeled molecules, we performed a simulation using a straight-line pattern consisting of randomly arranged molecules with line density of 1 nm -1 . Supplementary Figure 12a shows where is the wavelength; represents the spectral intensity at ; and Δ " is the centroid of the unshifted spectrum.
To perform the appropriate spectral regression, we have to establish reasonable criteria. First, only localizations within the range of localization precision in the zeroth-order image (37.4 nm) were considered. The criteria in the spectral domain were derived from the experimental single molecule spectroscopy data acquired by SPLM simultaneously, as shown in Figure 3e. The spectral shift from the same molecule should be less than 2 nm, which was derived from the maximum standard deviation of spectral variation from the single molecule experiment (Supplementary Figure 10). Based on experimental observation, an acceptable variation of intensity was set to be ±10% of the integrated intensity of the spectrum. All localizations were then judged by these criteria to be clustered and merged as molecules.
Supplementary Figure 12b shows the reconstructed images of PLM and SPLM, where only SPLM uses the spectral regression as mentioned above. Resolution improvement can be clearly observed when NB increases. This is consistent with the previous simulation performed in a single molecule situation.
Additionally, we calculated the resulting resolution of SPLM as a function of NB by averaging images