Bleaching-corrected fluorescence microspectroscopy with nanometer peak position resolution

Fluorescence microspectroscopy (FMS) with environmentally sensitive dyes provides information about local molecular surroundings at microscopic spatial resolution. Until recently, only probes exhibiting large spectral shifts due to local changes have been used. For filter-based experimental systems, where signal at different wavelengths is acquired sequentially, photostability has been required in addition. Herein, we systematically analyzed our spectral fitting models and bleaching correction algorithms which mitigate both limitations. We showed that careful analysis of data acquired by stochastic wavelength sampling enables nanometer spectral peak position resolution even for highly photosensitive fluorophores. To demonstrate how small spectral shifts and changes in bleaching rates can be exploited, we analyzed vesicles in different lipid phases. Our findings suggest that a wide range of dyes, commonly used in bulk spectrofluorimetry but largely avoided in microspectroscopy due to the above-mentioned restrictions, can be efficiently applied also in FMS. ©2013 Optical Society of America OCIS codes: (000.2170) Equipment and techniques; (000.4430) Numerical approximation and analysis; (070.4790) Spectrum analysis; (110.4234) Multispectral and hyperspectral imaging; (180.2520) Fluorescence microscopy; (300.6280) Spectroscopy, fluorescence and


Introduction
Fluorescence microscopy has boosted advances in life sciences within the last several decades due to its high sensitivity, applicability to live-cell experiments and ability to visualize the sample [1].Meanwhile, a wealth of molecular information can be provided by fluorescence spectroscopic techniques through excitation/emission spectral shapes, excited state lifetimes, energy transfer efficiencies, rotational and translational correlation times, etc [2].To localize this information within the investigated sample, many combined microspectroscopic techniques have emerged that enable molecular characterization at optical spatial resolution.
Among such hybrid methods, spectral imaging, or fluorescence microspectroscopy (FMS), has seen considerable development in recent years [3,4].It has mostly been used for distinguishing or co-localizing fluorophores with overlapping emission spectra.To this end, several advanced techniques for spectral unmixing have been introduced [5][6][7][8].Conversely, the applicability of these experimental systems to numerous environment-sensitive probes [9] has been largely neglected.Until now only few dyes with large spectral response to local physical/chemical conditions, e.g.Laurdan [10] and 3-hydroxyflavone-based probes [11], have been used for low spectral-resolution ratiometric imaging.
In fluorescence spectroscopy, several fluorophores with smaller spectral shifts have been extensively used.For instance, 7-nitro-2-1,3-benzoxadiazol-4-yl (NBD) enables versatile chemical modifications [12,13] and thus offers ample biological applications, e.g. to sense local polarity, rotational mobility, molecular packing and organization, membrane asymmetry, or temperature [12].To extend FMS to such dyes, we introduced spectral fitting [14,15] using an empirical lineshape function (Section 3 in this paper, which follows the technical details of our work in Section 2).This approach improved spectrum peak position resolution well below filter-width and wavelength sampling step in a similar manner as lateral position determination in particle tracking [16].The analogy [17] enabled us to develop a theoretical estimation for peak position resolution, which was highly consistent with our simulated and experimental data.As presented in Section 4, nanometer precision can be achieved at relatively modest signal-to-noise ratio (SNR) and wavelength sampling steps, which should be attainable by most FMS/spectral imaging systems.
It has long been recognized that results of any multiple-exposure fluorescence experiments are influenced by gradual fluorophore degradation.To overcome the problem, efficient correction algorithms have been introduced for time lapse [18,19], confocal 3D [20,21], and energy transfer imaging [22].For FMS experiments, however, it has only been suggested to avoid sequential wavelength acquisition, realized by narrow-band filters, which yields distorted spectrum lineshape, as shown in Fig. 1(a).Instead, simultaneous wavelength sampling, implemented by diffraction elements, has been recommended [3,23].
To extend the applicability of FMS systems with narrow-band filters (fixed or tunable), which are more affordable and easier to integrate into existing fluorescence microscopes, we have introduced a bleaching correction routine for sequential wavelength sampling [14].As shown in Fig. 1(b), it is based on measuring fluorescence intensity at a chosen reference wavelength several times during the experiment, which enables retrograde correction of the spectral lineshape by accounting for signal decay due to photobleaching.At sufficiently high SNR, the method considerably reduces bleaching-induced artifacts.At lower signal levels, however, some systematic deviations persist, which can be successfully eliminated by stochastic wavelength sampling, presented in Fig. 1(c), and improved spectral fitting [15].
In Section 5, we systematically described and compared both methods for bleaching correction and spectral analysis.We showed that by careful experimental and analytical approach, peak position resolution and accuracy, described above, could be largely maintained even when using photosensitive probes.The applicability of the technique was demonstrated in Section 6 by membrane phase sensitivity of two environment-and photosensitive probes (an NBD-based probe and Laurdan), where spectral shifts as low as 1.5 nm were reliably detected.Additionally, the bleaching correction approach revealed a significant difference in bleaching rate between samples in different lipid phases.Hence, probe photobleaching should not be considered a disadvantage; instead, when properly recorded and analyzed, it represents additional valuable information about local molecular environment that can be exploited for bleach rate imaging [24][25][26].

Liposome preparation
Giant unilamellar vesicles (GUV) were prepared by the gentle hydration method [28] from DPPC, DOPC, and DPPC + chol (40 mol%), which at room temperature represent gel, liquid disordered, and liquid ordered phase, respectively.To each composition 15 mol% of charged PG lipids were added to induce formation of vesicles.The dry lipid film, formed on the glass tube walls by organic solvent evaporation, was prehydrated for 30 min in water vaporsaturated atmosphere at 60 °C.After the addition of preheated 0.1 M sucrose solution, the sample was left to hydrate overnight at 60 °C.Before measurements, the appropriate amount of SPP268 ethanol solution was added to the GUV suspension for final probe-to-lipid molar ratio of 1:200, while the same amount of Laurdan was added already during the preparation of the dry lipid film.The probe concentration was low enough to prevent aggregation of probe molecules or energy transfer that could affect fluorescence emission spectra.

Spectrofluorimeter measurements
Reference fluorescence emission spectra were measured at Infinite M1000 microplate reader (Tecan, Männendorf, Switzerland) at room temperature.A 96-well black plate was used in the fluorescence intensity top mode.For Laurdan and NBD samples, fluorescence was excited at 370 and 450 nm, and emission spectra recorded from 400 to 550 and from 480 to 650 nm, respectively, both excitation and emission bandwidths being 10 nm.Reference background of 0.1 M sucrose was subtracted from fluorescence emission spectra of the samples.

Quantum-mechanical spectral model -harmonic oscillator
The simplest possible physical model, illustrated in Fig. 2, describes electron transition probabilities from the vibrationally-relaxed excited electron level (0*) into discrete vibrational levels of the ground electron state (n).The probability for the transition P 0*→n can be determined by calculating overlap integrals between the two wave functions.Assuming identical one-dimensional harmonic oscillators, the probability reads [29] ( ) ( ) ( ) where Γ is the Gamma function [30] and Δx represents the spectral asymmetry-inducing expansion of equilibrium intramolecular distance in the excited electronic state.The spectrum (S HO ), expressed by wavelength (λ), can be calculated from the following relations: ( ) d , where E * and E 0 represent energy differences between electronic and vibrational states, respectively, h stands for the Planck constant, and c for the speed of light in vacuum.The obtained spectrum, discrete over n, can be made continuous by allowing n to take any positive real value, reasoning that various electron orbitals and vibrational modes of complex molecules contribute to the overall spectrum, which smears their discrete spectra.The derived lineshape depends on three parameters, E * , E 0 , and Δx, which should suffice to describe peak position, width, and asymmetry of a simple fluorescence spectrum (note that the intensity of the model spectrum should be normalized for each combination of parameters).Any more advanced description, e.g. by taking into account differences in vibrational potential strengths or their anharmonicities, would exceed the prescribed maximal complexity (see next section).Besides, it has been recognized that these additional parameters often induce significant correlations through their similar effect on the lineshape [31].It is interesting to note that the spectrum, given by Eq. ( 1), conforms to Poisson distribution of n given events at Δx 2 /2 mean occurrences [30].In addition, expression (1) is tightly related to distribution χ 2 with k degrees of freedom [30], where Δx 2 directly replaces χ 2 while λ-related n runs over k = 2 (n + 1).Fig. 2. Schematic representation of a transition (red arrow) between two eigenstates of shifted harmonic oscillators (dashed curves represent the potentials).Fluorophore is assumed to relax from the ground vibrational state of the excited electron level (0*) into any vibrational state of the ground electron level (n).Transition probability is proportional to the overlap integral of the corresponding wave functions (ψ n ).Shaded wavy curves represent probability distributions (ψ n 2 ) over the reduced vibrational coordinate x.Symbols ħ and m stand for reduced Planck constant and molecular mass, respectively.

Empirical spectral model -log-normal function
From among several proposed empirical lineshapes [32], we found the intensity-normalized log-normal function (S LN ) [31] the most convenient due to its numerical stability during optimization.The stability was achieved by decoupling parameter influences on main spectral characteristics: peak position (λ MAX ), approximate full width at half-maximum (FWHM, w), and asymmetry (a): .
In contrast to previous applications [33], the asymmetry is defined as a = (w R -w L ) / w, where w R and w L represent partial widths at half maximum right and left from λ MAX , respectively.

Comparison of the two spectral models
Both three-parametric spectral models, described above, were used to fit spectrofluorimetric data of NBD-based alkyl chain probe SPP268 in DPPC vesicles.The spectrum was normalized to its maximal signal level, and only data above the signal intensity threshold (I T ) 0.2 were used.The model parameters were optimized by Mathematica's (Wolfram Research, Champaign, IL) Nelder-Mead minimization routine.Standard χ 2 , reduced to the number of points and normalized to the noise level, was calculated as a measure for goodness-of-fit, while the time needed for optimization was monitored to assess computational costs.
Model robustness and consistency were tested by several trivial modifications of the fitting problem: firstly, I T was varied; secondly, wavelength step-size (Δλ) was increased by removing data points; and thirdly, random noise was added to mimic experiments with lower SNR.For a well-posed model, none of the variations should affect the optimized parameters.Therefore, average relative error (δp/p 1 ) of parameters' fitted values (p i ), compared to those obtained for the non-modified spectrum (p i,1 ), was chosen to measure model robustness: ( ) , where i runs over all three parameters for either spectral model.Optimization of parameters was repeated 64 times with noise signal generated each time anew.

Bleaching spectrum model
As the log-normal model was found to be faster and more robust than the quantummechanical one, this lineshape function was further used for numerical simulations and to analyze FMS experiments.Photobleaching was modeled by a mono-exponential decay [34] of simulated intensity with bleaching rate (b), counting the time (t) from the beginning of the experiment.The bleaching spectrum signal (I) was thus described by where I 0 represents maximal signal level of the non-bleached spectrum.The lineshape parameters were obtained by optimized Nelder-Mead minimization [35] of the standard reduced χ 2 , whereas optimal I 0 was determined analytically [15].By the developed algorithm, a typical λ-stack of 512 × 512 images, averaged over 5 × 5 pixels, was analyzed in less than 5 s on a standard quad-core desktop computer.
To characterize more complex spectra due to multi-peak lineshape of the fluorophore in use, presence of multiple dyes, or significant cellular autofluorescence, the procedure allows multicomponent bleaching-corrected optimization to separate the spectral contributions [15].

Numerical comparison of bleaching correction algorithms
Probe photobleaching inevitably distorts sequentially sampled spectra, as shown in Fig. 1(a).To recover the true signal, we have introduced two acquisition schemes: linear wavelength sampling with intermittent measurements at a reference wavelength [14], illustrated in Fig. 1(b), and stochastic wavelength sampling, depicted in Fig. 1(c).Both methods record position-dependent bleaching dynamics that can be used during spectral fitting.
Efficiencies of the two bleaching correction algorithms were first tested numerically.To mimic FMS experiments with a photosensitive NBD probe, synthetic spectra with different SNR levels were generated according to Eq. (3) (I 0 = 1, λ MAX = 535 nm, w = 78 nm, a = 0.24) within the range 515-585 nm.Bleaching rate and wavelength step size were varied; results for b = 0.02/"exposure time" and Δλ = 3 nm are presented.For the linear reference algorithm, six reference data points at 540 nm were also generated; to keep the total number of data the same as for the other two methods, Δλ was increased accordingly.
The generated spectra were fitted 10 4 times with noise signal each time generated anew and with w and a fixed to their true values.For linear acquisition where no specific information about bleaching dynamics was available, b was either set to 0 or optimized.Knowing the original parameter values (p i,0 ), errors of the fitted ones (p i ) were calculated (δp i = |p i -p i,0 |; p i again represents any of the optimized parameters).

FMS setup
NBD-based probe was excited by nonpolarized light from a Xe-Hg source (Sutter Lambda LS, Novato, CA) through 460/60 broad-band filter, while 377/50 was used for Laurdan (all band-pass filters and dichroics were BrightLine from Semrock, Rochester, NY).Fluorescence was detected through 550/88 and 470/100 emission filters for NBD and Laurdan, respectively.For spectral detection a narrow-band liquid-crystal tunable filter (LCTF; Varispec VIS-10-20 from CRi, Woburn, MA) was placed in front of an EMCCD camera (iXon3 897 from Andor, Belfast, UK), allowing sequential acquisition of images at different wavelengths within the transmission range of the emission filter.
For each λ-stack of images, spectra from every volume-element of the field-of-view were extracted.After the dark signal of the camera was subtracted, the spectra were corrected for transmittance of LCTF, which had been calibrated against a set of reference dyes.

FMS experiments with probe SPP268 in solution
Reference FMS experiments for fitting performance tests were conducted at room temperature with 10 −4 M solution of probe SPP268 in DMSO, where NBD experienced a similar polarity as in the membrane.Objectives with 10x (air) and 60x (water immersion) magnification were used to prevent or induce significant probe photobleaching, respectively.Various settings for wavelength sampling step and exposure time were applied to vary SNR and SNR TOT , defined later by Eq. (7).
Spectra from the central region of the image (200 × 200 pix) were analyzed, as outlined above.Since the wavelength scanning range within the transmitting region of the broad-band emission filter (510-585 nm) was smaller than FWHM of NBD spectra, determination of w and especially a from FMS experiments was not efficient.They were therefore determined by fitting the spectrofluorimeter data and then kept fixed at 78 nm and 0.24, respectively, during the optimization of I 0 , λ MAX and b.For measurements at 10x magnification, b was set to 0.
For comparison of the two wavelength acquisition schemes, mean λ MAX and their standard deviations were calculated for each experiment.As the stochastic method yielded very consistent λ MAX values around 543 nm, their average was taken as a reference to determine the errors at each measurement (δλ MAX ).SNR was determined from the brightest image in each λstack as standard deviation of intensity divided by mean intensity value.

FMS experiments with lipid vesicles
For easier observation, the chosen GUV suspension was 10x diluted in 0.1 M glucose solution, which caused the vesicles to settle at the bottom of the chamber due to the resulting density difference between interior and exterior of the liposomes.When mixed GUV samples were imaged, the vesicles were additionally immobilized by a transparent hydrogel, composed of an organic gelator [27], which conveniently liquefied upon shaking and solidified in a few minutes.About 60 μl of the sample was transferred into a pool, made from silicone lubrication grease (Klüber Lubrication, Munich, Germany) between a standard microscopy slide and a coverslip.Vesicles were imaged at room temperature by a 60x water immersion objective.For samples with NBD and Laurdan, stochastic wavelength scans from 510 to 582 nm and from 430 to 511 nm with 3 nm step were performed, respectively, using 100-300 ms exposure times and 200-fold electron multiplication of the signal.
For temperature-dependent experiments, the sample was sealed between two coverslips and placed on a microscopy slide with a home-made indium tin oxide (ITO) heating layer and a thermocouple for the feedback to the temperature control unit (ITC503 by Oxford Instruments, Abingdon, UK).
To minimize artifacts due to motion of vesicles during acquisition, images from each λstack were automatically aligned using algorithms built in Mathematica.All images were averaged over 5 × 5 pixels, or 9 × 9 for samples with Laurdan, to achieve the desired spectral resolution.For SPP268, the fitting procedure was the same as in the section 2.10, while for Laurdan w = 50 nm was used and a was allowed for optimization.To visualize the results, images were spectrally contrasted with respect to the optimized λ MAX or b according to the accompanying color legends, while I 0 was coded by pixel brightness [15].Parameter I 0 was used to weight the contribution of each pixel when constructing histograms from subareas of the field-of-view.

Spectral lineshape models
To improve spectral peak position resolution below experimental λ-step and LCTF bandwidth, spectral fitting was applied in analogy with the approach used in particle tracking [16].We searched for an appropriate function that could accommodate to the main characteristics of simple fluorescence emission spectra.To adequately define peak position, width and asymmetry of a potentially noisy distribution without its extreme tails, as usually obtained by FMS, we limited our choice to three-parametric models to ensure the best fitting performance in terms of computation time, stability and parameter correlations.
In the literature, two approaches to describe fluorescence spectra have been used: deriving the spectrum from basic quantum mechanics [29,36], or describing the lineshape by empirical asymmetrical functions [31,32].We therefore tested the most convenient models from both classes: one based on physical description of transitions between harmonic oscillator eigenstates (HO), and the other using a log-normal lineshape (LN).
The two models were applied to fit normalized spectrofluorimeter data of SPP268 in DPPC vesicles, as presented in Fig. 3(a).Since HO model was unable to efficiently describe the spectral tails, only data above the intensity threshold I T = 0.2 were used.Above this threshold, both fitted the part of the spectrum comparably well; if some noise was added to mimic typical FMS data with SNR in the range from 10 to 100, both models achieved perfect accordance with the data with χ 2 -values around 1, as shown in Fig. 3(b).Though, the time needed for optimization, presented in Fig. 3(c), was significantly lower for LN model, which is of high importance as several ten thousand spectra should be fitted from pixels of each FMS λ-stack.For real-time analysis of the latter, we applied an optimized algorithm [35] that sped up the process about 1000-fold.To check model robustness, we monitored average relative error (δp/p 1 ) of the three parameters, compared to the values obtained for the original data set, while varying I T , sampling step (Δλ), and SNR.The variations mimicked measurements of the same sample under different experimental conditions.As neither of the modifications changed the underlying shape of the spectrum, no variations in optimized parameters were anticipated.As The instability of the latter probably originated in considerable interrelations of the parameters' influence on the lineshape, revealed by covariance matrices.We therefore selected the better-posed LN function for our further spectral analysis.

Peak position resolution
For FMS experiments with environment-sensitive probes, spectral peak position is often of greatest interest.Hence, we wanted to estimate what is the minimal spectral shift that can be reliably detected.From this viewpoint, the log-normal model turned out to be practical for yet another reason: the simplicity of its analytical form and tight relation to the Gaussian function allowed a straightforward application of the signal resolution theory [17].The uncertainty in peak position determination (σ λmax ) translated into max SNR , ( ) where Δλ stands for the wavelength sampling step; W relates to spectral FWHM as W ≈ w/2.35;SNR depends on the exposure time (t EXP ) and is defined as maximal signal value (I 0 ) divided by noise level for experiments with prevailing contribution of Gaussian background noise, or I 0 1/2 if Poisson shot noise dominates; Δ is a numerical constant that depends on the chosen confidence level -for 0.68 ("1 σ"), it takes values of 1, 2.3, or 3.5 if 1, 2, or 3 parameters are fitted, respectively [37]; F is a dimensionless number, related to the integral of (∂S LN /∂λ MAX ) 2 over the λ-acquisition range (Λ) [17].In our case with Λ ≈2.4 W, F 1/2 took values of approx.0.8 and 1.0 for data with Gaussian and Poisson noise, respectively.We are aware that the original theory was derived for signals of even or odd symmetry [17], which is not strictly true for fluorescence emission spectra.However, the facts that NBD lineshapes exhibit a rather modest asymmetry, and that only about a half of the spectrum was sampled in our experiments, both substantiate our use of Eq. ( 6) as the first approximation.
According to the expression above, one can expectedly enhance the accuracy of λ MAX by lowering Δλ or by increasing SNR, as shown by Fig. 4(a).A decrease in Δλ linearly increases the number of images in the λ-stack (N) and thus linearly prolongs the total experiment duration (t TOT ), which does not affect SNR for filter-based FMS setups with fixed spectral bandwidth.Conversely, SNR is proportional to t EXP 1/2 = (t TOT /N) 1/2 -as long as camera read noise is negligible compared to Poisson shot noise.Hence, considering also the contributing powers of Δλ and SNR in Eq. ( 6), both ways of σ λmax improvement are equally time-effective, showing that all information gathered during t TOT is equivalent.
This can be explicitly shown by introducing the total SNR (SNR TOT ).: which measures the quality of information of the whole FMS experiment.Note that it can only be affected by t TOT , as SNR/t EXP 1/2 depends solely on sample brightness and experimental system characteristics, i.e., illumination level and detection efficiency.Equation ( 7) can be used to substitute SNR and Δλ in Eq. ( 6) with the primary influence on λ MAX resolution, SNR TOT : the λ-stack -can then be optimized to other experimental issues.For instance, sample movement and determination of other spectral lineshape parameters favor smaller Δλ and shorter t EXP , while larger Δλ and higher SNR are preferred for very dim samples to avoid excessive contribution of read noise.Considering σ λmax , the only prerequisite is that the number of measured λ-points is larger than the number of fitted parameters [17].
Within the derivation we assumed a filter-based FMS system with sequential λ-sampling and fixed spectral bandwidth.Nevertheless, Eq. ( 8) holds also for diffraction-based systems with variable bandwidth per spectral channel, as long as the bandwidth does not exceed approx.w/2 and significantly distorts the spectrum shape through convolution.
To verify the relation in Eq. ( 8), we performed FMS experiments with SPP268 in solution, using 10x lens magnification to prevent photobleaching and various wavelength sampling steps and exposure times to influence SNR and SNR TOT .Spectra from pixels across the images in each λ-stack were fitted with w and a fixed to the values obtained from spectrofluorimetric data and b = 0.As shown by Fig. 4(b), the obtained standard deviations of λ MAX distributions (σ λmax ) confirmed that λ MAX precision was mainly determined by SNR TOT , as predicted by Eq. ( 8), which corroborated all the approximations discussed above.For measurements with high SNR TOT where read noise was negligible, very nice accordance with the theory for one-parametric fit was obtained, even though two parameters (I 0 and λ MAX ) were in fact extracted.This indicates that analytical determination of I 0 acted as exact normalization without reducing the information available to λ MAX .The explanation was further supported by results when w was also optimized; in this case σ λmax were slightly higher, conforming to the theoretical curve for two parameters (data not shown).6) for an NBD-like spectrum (w = 78 nm, a = 0.24) sampled at various SNR and wavelength steps (Δλ).One fitting parameter, Poisson noise, and λ-sampling range as in our FMS experiments were assumed.(b) Standard deviations of λ MAX (σ λmax ), obtained from optimizations of experimental spectra across FMS images.These were acquired at various Δλ (see color legend) and exposure times to yield signals of different total SNR (SNR TOT ).Light intensity through 10x objective was low enough to prevent probe photobleaching.The gray line represents the theoretically predicted λ MAX precision, calculated by Eq. ( 8) with the same assumptions as in panel (a).

Bleaching correction algorithms
If fluorescence emission intensities at various wavelengths are acquired sequentially, probe photobleaching significantly distorts the recorded spectral lineshape, as presented in Fig. 1(a) [3,23].Since the acquired spectrum can be equally well described by a range of λ MAX -b combinations, decoupling of the two superimposed effects is numerically ill-posed.To avoid potential misinterpretations of such data, we introduced two wavelength sampling routines that allowed us to purposely record the bleaching dynamics and take it into account during spectral fitting: linear acquisition with reference measurements [14], depicted in Fig. 1(b) and stochastic sampling [15], illustrated in Fig. 1(c).
To evaluate both bleaching correction methods, we first applied them to numerically generated spectra, mimicking FMS experiments with an NBD probe, and compared the errors of fitted values for all optimized parameters -δλ MAX and δb are presented in Figs.5(a) and 5(b), respectively).As predicted, large errors in λ MAX were observed for linear acquisition without any bleaching correction attempt.As w and a were fixed, fitting b from these data on average yielded more accurate results, but with excessively high deviations due to numerical instabilities, outlined above.Conversely, parameters scattered less for the two specialized sampling routines that both nicely replicated the true parameter set at high SNR. Figure 5(b) shows that, at lower SNR, however, the reference method often misestimated the bleaching rate from the six dedicated data points and consequently wrongly determined λ MAX .In contrast, the technique with stochastic sampling, using all data points, resolved the original b value with much better precision and accuracy, leading to more reliable determination of I 0 and λ MAX .
Simulations at various bleaching rates and Δλ always yielded qualitatively similar results.Moreover, even if we deliberately fixed w and a to values that were slightly different than used for data generation, other parameters were still correctly resolved, further confirming the choice of a well-posed spectral model.In addition, the results substantiated our use of values obtained from fitting the spectrofluorimeter data as the best educated guess when w and a could not have been reliably determined from our FMS experiments due to narrow wavelength acquisition range, predefined by the available broad-band emission filter.8) for two-parametric fits with the same assumptions as in Fig. 4. We further tested the numerical results experimentally, again performing FMS measurements on the probe in solution at various wavelength sampling steps and exposure times, but this time using higher lens magnification to induce significant photobleaching.The results confirmed the differences between the two bleaching correction techniques, noted above.Fitting the data recorded by the stochastic acquisition routine gave very consistent λ MAX values across a wide range of SNR, whereas systematic deviations were observed for the reference routine at lower SNR levels, as can be seen from Fig. 5(c).For this reason, the comparison with the spectral resolution theory was meaningful only for stochastically sampled spectra with no systematic errors.As predicted by Eq. ( 8) in shown by Fig. 5(d), the resolution was again found to be mainly determined by SNR TOT and independent of Δλ.The obtained standard deviations were fairly consistent with the peak position resolution theory for two-parametric fits, even though three parameters were obtained (I 0 , λ MAX, b) -as discussed in the previous section, analytical determination of I 0 did not affect the optimization of other parameters.
Finally, we searched for the optimal total duration of an FMS experiment with a photosensitive probe in terms of λ MAX and b accuracy and precision, assuming that one can afford to arbitrarily bleach the sample within one measurement.Fast acquisition, compared to the bleaching rate of a given fluorophore, minimizes the bleaching-induced distortion of the spectrum, but also reduces SNR TOT and thus the resolution of fitted parameters.Oppositely, during a long experiment much of the signal is lost, meaning that further acquisition does not yield any useful information.Our numerical simulations, again applying various Δλ and SNR, showed that parameter reconstruction was the most effective when t TOT ≈1-1.5 b -1 , i.e., when approx.60-75% of the signal was bleached during the experiment.Similar numerical results (84%) have been obtained for optimal unmixing of spectrally-overlapping bleaching probes, assuming a diffraction-based experimental system with simultaneous λ-acquisition [38].

Demonstration of application: lipid phase sensitivity
To demonstrate the use of stochastic bleaching correction FMS algorithm and the applicability of high spectral peak position resolution, we chose a well-known and controlled model system: spectral response to local polarity of a photosensitive NBD-based probe SPP268 was used to distinguish DPPC and DOPC GUV samples.Due to different structure of the two lipids and consequently different packing of the molecules in the bilayers, the two membranes are at room temperature found in gel and liquid disordered membrane phases, respectively [39], exhibiting different polarity profiles across the bilayer [40].Since the applied fluorophore is located in the headgroup region, as depicted by the inset in Fig. 6(a), where polarity differences between phases are much smaller than in the membrane core [40], only minor variations in fluorescence emission spectra were expected [12].As shown by Fig. 6(a), spectrofluorimeter measurements of bulk samples indeed showed a red shift of 3 nm for the probe in DOPC compared to DPPC sample, which was in accordance with the expected higher local polarity [41] due to increased hydration of the outer membrane region [42].
The small spectral difference was unmistakably resolved by FMS on individual vesicles.Figure 6(b) confirms that the influence of strong photobleaching was effectively fitted, resulting in clearly distinguishable spectral differences between GUV in Fig. 6(c).The observed shift around 2 nm was nicely revealed by nanometer λ MAX resolution, estimated from histogram widths.Quantitative accordance with spectrofluorimetric data as well as with FMS measurements on separate GUV suspensions (data not shown) enabled us to unambiguously determine the composition of the two vesicles: DPPC for the smaller (labeled as "1") and DOPC for the larger liposome ("2").
Besides the spectral shift between the vesicles in different lipid phases, the method revealed a significant difference in bleaching rate, which was also in agreement with the known probe behavior.In a more polar environment, fluorescence emission spectrum of NBD shifts to higher wavelengths and lifetime decreases [41].According to the linear relationship between fluorescence lifetime and bleaching rate [34], the probe in DOPC should thus bleach slower.The relation was confirmed by lower b, obtained with bleaching-corrected FMS analysis for vesicle "2", as is apparent from Fig. 6(d).In addition to spectral information, the procedure therefore provides the functionality of bleach rate imaging [24][25][26], representing a simple alternative to fluorescence lifetime imaging [26,34].To corroborate the results further, we measured FMS signal after having induced a phase transition of DPPC vesicles from gel to liquid disordered phase by heating the sample from approx.35°C to approx.45 °C, as presented by Figs.7(a) and 7(b) (the transition occurs around 41 °C [39]).In accordance with temperature-dependent spectrofluorimetric data (not shown), λ MAX red-shifted for about 1.5 nm, as can be observed from the histograms.Figure 7(c) revealed that upon cooling, one vesicle was found to undergo the transition earlier than the other, but the change in mean λ MAX was expectedly reversible, as is seen in Fig. 7(d).As a reference, we checked that no detectable effect of heating was observed for DOPC samples which do not exhibit a phase transition in this temperature region [39].We tested the method also by using another commonly used environment-and photosensitive probe, Laurdan.Between the two lipid phases, observed above, its spectrum shifts for about 50 nm [43], which can be easily distinguished by broad-band filters.We therefore chose a more challenging combination -gel and liquid ordered phase, realized by DPPC and DPPC + chol (40 mol%) GUV, respectively, where λ MAX difference is expected to be around 3 nm [43].Spectrofluorimetric data in Fig. 6(e) indeed confirmed the small spectral shift and indicated the need for fitting of another parameter, asymmetry (a), during FMS analysis.After reliably eliminating the distortions due to photobleaching, presented in Fig. 6(f), FMS again revealed the expected difference in λ MAX , as demonstrated in Figs.6(g) and 6(h).The detected spectral shift agrees with the data presented above and previous observations [43].Therefore, the presented bleaching-correction technique is applicable to a variety of established environmentally sensitive but fast-bleaching dyes, which can now be exploited also in FMS.
It is again worth noting that the experiments with lipid phase detection, conducted above, exemplified a well-defined model system to characterize the presented technique.Such experiments should serve as a reference for the method when investigating more complex biological systems [14], as demonstrated in Fig. 8 by a mixture of cells with uni-and multilamellar DOPC vesicles in the presence of cell medium.The agreement of the detected λ MAX of the liposomes with the values obtained in Fig. 6(c) confirms the repeatability of results, substantiates the robustness of the method, and corroborates the reliability of the small relative spectral shift for the probe in cell membranes.To identify the molecular source of the latter, however, several additional reference experiments should be performed, since in such complex environments, various factors could influence the shape of the recorded spectra, e.g.polarity, pH, presence of certain molecules, probe aggregation, etc.To decouple such effects, it is extremely valuable to simultaneously measure several spectral properties of the dye [9].Lineshape parameters and bleaching rate, provided by bleaching-corrected FMS, could be further complemented by polarization dependence that can reveal probe conformation coexistence [15], or by fluorescence lifetime, anisotropy, energy transfer, etc.To obtain even more in-depth information about particular lipid phase properties, it is also advisable to use other complementary methods, such as infrared spectroscopy [42,44] or Raman-based imaging, e.g.coherent anti-Stokes Raman scattering imaging [45] and tipenhanced Raman scattering imaging [46].These label-free techniques are especially valuable when putative effects of probes are being evaluated and when chemical identification of membrane components is needed.Nevertheless, fluorescence methods are invaluable for many biological and biophysical applications due to their high sensitivity and applicability to live 3D samples.As such, bleaching-corrected FMS could complement the information obtained by other techniques that are required to adequately characterize complex systems.

Conclusion
Within this work we systematically evaluated our recently developed experimental and analytical FMS methods.We first demonstrated the convenience and robustness of the chosen log-normal spectral fitting function that enables nanometer peak position resolution at relatively modest experimental cost in terms of SNR and wavelength sampling.The results obtained for numerically generated and experimental spectra were corroborated by accordance with theoretical peak position precision that we derived from previous work on instrumental resolution.We showed that accuracy and precision of peak position determination were largely maintained even for photosensitive dyes if bleaching correction algorithms were applied.Especially at low SNR levels stochastic wavelength sampling was found to be more efficient than the linear sampling with reference measurements.
To demonstrate the reach of the technique, we applied it to distinguish lipid vesicles in different phases with two commonly used environment-sensitive dyes, NBD and Laurdan, that shifted their spectral maxima for 1.5-3 nm.The results showed that peak position resolution, characteristic for spectrofluorimetric measurements on bulk samples, could readily be achieved at micrometer spatial scale by conventional FMS/spectral imaging systems.By this a whole new range of probes with desired biochemical characteristics, but weaker environmental response, could be exploited to characterize more complex biological systems, provided adequate reference measurements.Moreover, to distinguish various environmental effects, environment-dependent photosensitivity can be simultaneously used for bleach rate imaging, which was in our case provided automatically by bleaching-corrected FMS.

Fig. 1 .
Fig. 1.Schematic presentation of the effect of probe photobleaching on fluorescence emission spectrum, recorded with different sequential wavelength (λ) acquisition schemes: (a) Linear λsampling yields a distorted spectrum (solid circles and line in the bottom panel), compared to the expected spectrum (dotted line in the bottom panel).(b) Occasional measurements of signal at a reference λ (green points) additionally record the intensity decay rate that can be taken into account during spectral fitting.(c) Stochastic λ-sampling stores the information about bleaching dynamics together with spectral lineshape into the "saw-tooth" signal, which is due to random jumps of λ measurement points while intensity decays in time (t).

Fig. 3 .
Fig. 3. Comparison of the two lineshapes for spectral fitting: quantum-mechanical harmonic oscillator model (HO, black symbols) and empirical log-normal function (LN, red symbols).(a) Best fits (solid lines) to the spectrofluorimetric data of SPP268 in DPPC GUV (gray open circles) above the intensity threshold 0.2 (dotted line).(b) Goodness-of-fit (χ 2 ) and (c) time needed for optimization (t) for spectra with different levels of added noise (SNR).To measure model robustness, average relative error (δp/p 1 ) of the fitted parameters, compared to the values obtained for the original data set, was monitored when varying (d) intensity threshold (I T ), (e) wavelength step (Δλ), and (f) SNR.Columns and error bars represent mean and standard deviation of the corresponding values, respectively, for 64 repeats of parameter optimization with noise signal generated each time anew.

Fig. 4 .
Fig. 4. (a) Theoretical peak position uncertainty (σ λmax ), calculated according to Eq. (6) for an NBD-like spectrum (w = 78 nm, a = 0.24) sampled at various SNR and wavelength steps (Δλ).One fitting parameter, Poisson noise, and λ-sampling range as in our FMS experiments were assumed.(b) Standard deviations of λ MAX (σ λmax ), obtained from optimizations of experimental spectra across FMS images.These were acquired at various Δλ (see color legend) and exposure times to yield signals of different total SNR (SNR TOT ).Light intensity through 10x objective was low enough to prevent probe photobleaching.The gray line represents the theoretically predicted λ MAX precision, calculated by Eq. (8) with the same assumptions as in panel (a).

Fig. 5 .
Fig. 5. Comparison of wavelength sampling schemes for bleaching correction: linear without correction, linear with fitted b, linear with reference, and stochastic (see color legend in panel b).When spectral data were numerically generated (λ MAX = 535 nm, w = 78 nm, a = 0.24, b = 0.02/"exposure time"; Δλ = 3 nm, Λ = 69 nm), errors of the fitted values for (a) λ MAX and (b) b were monitored.For clarity of presentation, the data sets were slightly shifted along SNR-axis.Experimental FMS spectra of SPP268 solution were measured with either bleaching correction acquisition routine at various settings for exposure time and Δλ to influence SNR and SNR TOT .Photobleaching was induced by 60x magnification lens.From the results of optimization for all pixels in each λ-stack, (c) mean λ MAX were compared to a reference value.(d) Standard deviations of λ MAX are plotted against theoretical prediction (gray line), calculated by Eq. (8) for two-parametric fits with the same assumptions as in Fig.4.

Fig. 6 .
Fig. 6.(a) Fluorescence emission spectra of SPP268 (inset) in DPPC and DOPC vesicles (blue and green line, respectively), acquired separately on a spectrofluorimeter at room temperature.(b) Representative FMS spectra, distorted due to photobleaching (circles of the appropriate colors), of the two GUV samples.Solid and dashed lines represent the model fit and bleachingcorrected spectral reconstruction (BC), respectively.Spectra were extracted from the two red points in colored images, spectrally contrasted according to (c) spectral peak position (λ MAX ) and (d) bleaching rate (b).Blue and green rectangles mark the areas from where the correspondingly-colored histograms of the optimized parameter values from each liposome were constructed.Similar analysis was performed also for GUV from DPPC and DPPC + chol (40 mol%) and labeled with the probe Laurdan: (e) Spectrofluorimetric data and the structure of the probe (inset).(f) Typical FMS spectra, extracted form the two red points in λ MAXcontrasted images for a representative (g) DPPC and (h) DPPC + chol vesicle.

Fig. 7 .
Fig. 7. Spectrally contrasted images of SPP268-labeled DPPC vesicles in (a,d) gel phase, (b) liquid disordered phase, and (c) around the phase transition.Upon cooling, vesicle "1" underwent the phase transition earlier than vesicle "2".The histograms show the distribution of λ MAX for the two vesicles, marked with the accordingly-colored rectangles in the images above.

Fig. 8 .
Fig. 8. (a) Fluorescence intensity image of cells MCF-7 (at the bottom of the image), mixed with uni-and multilamellar vesicles DOPC (top), which were all labeled with the NBD-based probe SPP268 in the presence of cell medium.Cell cultivation and handling were the same as in our previous work [14].(b) Spectrally contrasted image and histograms of λ MAX values from the two marked areas, as obtained from stochastic λ-sampling and bleaching-corrected FMS analysis.The measured autofluorescence was low enough not to affect the analysis and results.