Single molecule imaging simulations with advanced fluorophore photophysics

Advanced fluorescence imaging techniques such as single-molecule localization microscopy (SMLM) fundamentally rely on the photophysical behavior of the employed fluorophores. This behavior is generally complex and impacts data quality in a subtle manner. A simulation software named Single-Molecule Imaging Simulator (SMIS) is introduced that simulates a widefield microscope and incorporates fluorophores with their spectral and photophysical properties. With SMIS, data collection schemes combining 3D, multicolor, single-particle-tracking or quantitative SMLM can be implemented. The influence of advanced fluorophore characteristics, imaging conditions, and environmental parameters can be evaluated, facilitating the design of real experiments and their proper interpretation.


Influence of pH
The reported pKa's of mEos4b in the green and red state are 5.5 and 5.8, respectively. Thus, at pH 8.5 the photoconversion efficiency is decreased and the red-state brightness is increased, while the opposite is true at pH 6.5. SMIS simulations suggest that at 3.5 kW/cm² better NPC images can be obtained at acidic pH. This is explained by the fact that at such readout power density the photon budget per localization is not decreased at moderately low pH ( Supplementary Fig. S4c) because the median on-times are still significantly shorter than the frame time ( Supplementary Fig. S4f). Strikingly, at 0.5 kW/cm² a reverse effect is observed: the image quality is better at pH 8.5. The explanation is that at pH 6.5 substantially more spots are missed (false negatives) during localization, and overall the degraded localization precision and density cannot be compensated for by the higher photoconversion efficiency.

Fermi profiles
Neglecting green-state photophysics, optimized Fermi profiles in principle allow maintaining a constant density of newly photoconverted red molecules along data collection. Their use permits to reduce the localization density (and therefore the numbers of spot overlaps) while maintaining the data collection time, or to reduce the data collection time while maintaining the localization density reached at constant 405-nm power.
The price to pay, however, is a change in red-state photophysics along data collection resulting from the photosensitivity of dark states to 405-nm light 1 . Supplementary Fig. S5 shows that green-state photophysics compromise the possibility to maintain constant photoconversion when Fermi profiles are used, the effect being much more pronounced at 3.5 kW/cm² readout power density. Moreover, Panel 8 in Fig. 1b shows that the application of a Fermi profile while maintaining the data collection time (here 1200 s) is highly detrimental to the quality of the obtained NPC images. The reason is that with such profile (Supplementary Fig. S5e) photoconversion of most green mEos4b molecules by the 405-nm laser is delayed, while photobleaching by the 561-nm readout laser takes place at a constant rate. Hence, the photoconversion efficiency decreases substantially. This effect is much less pronounced at 0.5 kW/cm², and here there is a small gain in using a Fermi profile, attributed to the improved localization sparsity. Interestingly, the best NPC image is obtained at 3.5 kW/cm² using a Fermi profile with reduced data collection time. Here indeed, with no penalty in localization density, mEos4b molecules get photoconverted earlier, reducing green-state photobleaching and increasing the overall photoconversion efficiency. However, the data highlight that in all conditions tested, Fermi profiles result in substantially broader distributions of off-times in the mEos4b red state ( Supplementary Fig. S4e), possibly compromising blinking correction algorithms employed for e.g. molecular counting. S3 which does not absorb cyan light in its non-activated state. This stems from the fact that, during the priming phase, in the absence of 405 nm light, mEos4b gets quickly shelved into its long-lived dark state, which largely protects it from photobleaching ( Supplementary Fig. S8). Artificially removing in SMIS the capacity of green mEos4b to reversibly photoswitch not only results in major photobleaching during the priming phase, but also significantly increases spurious readout photoconversion during that phase, resulting in very poor colocalization ( Fig. 2e and 2f). The SMIS generated datasets also highlight the impact of the different brightness of the simulated fluorescent proteins in the red states (Fig. 2d, Supplementary Fig. S6 and Supplementary Fig. S9). With a reported pKa of 7.9 2 , a high fraction of the Dendra2 red chromophores remain protonated and nonfluorescent, reducing the measured photon budget per localization ( Supplementary Fig. S9) and producing more blurry spots than mEos4b (Fig. 2d). With its lower intrinsic brightness as compared to mEos4b, the photon budget per localization of PAmCherry was also reduced, but this was somewhat compensated by a more complete photoactivation efficiency (Fig. 2f). Finally, as a result of their significantly different effective extinction coefficients, and therefore excitation rates by the 561 nm laser, it is interesting to notice the different levels of triplet state saturation observed in red mEos4b and Dendra2. Whereas there was almost no loss in photon budget due to intersystem crossing to T1 in the case of Dendra2 (~3%), a decrease of ~9% was noticed in the case of mEos4b ( Supplementary Fig. S9).

Supplementary Note 3 (Application 3, Fig. 3) Discrepancy between simulated and experimental dSTORM data
Although a clear decrease in apparent labeling efficiency is observed as the 647 nm laser power density is increased (Fig. 3e), in line with increasing saturation of the triplet state ( Supplementary Fig. S11, Supplementary   Fig. S12a) from which photobleaching occurs due photon reabsorption in T1, a significant decrease is also observed at the lowest power density, also seen at the ensemble level ( Supplementary Fig. S12b). Also, while the number of photons per localization decreases at high power densities, as experimentally observed, it does not rise as high as expected at lower densities (Fig. 3f). Similarly, the number of localizations per fluorophore drops, as expected, at high densities but plateaus and even decreases at lower densities (Fig. 3e), and a similar trend occurs for the global photon budget per molecule ( Supplementary Fig. S12d). The highest discrepancy between the simulated and experimental data concerns the on-times ( Supplementary Fig. S12c) which tend to rise in SMIS simulations instead of globally decreasing in the experimental case as the 647 nm laser power density increases.

Discussion on the photophysical model of Cy5
To investigate the possible origin for partial disagreement between the SMIS simulations and the experimental data, we attempted to modify some of the interconversion rates and quantum yields in the Gidi et al model 3 .
First, the decrease in labeling efficiency at low power observed in the SMIS data could be assigned to thermal recovery from the SRadduct state, which reduces the duty cycle of Cy5 switching at such low power. Thus, we assumed that in the in cellulo environmental conditions, the thermal recovery from SR-could be slower by a factor of ~4. Then, to increase the contrast in photon budget between low and high intensities, we reasoned that S4 the triplet state saturation could be higher than predicted by the Gidi et al model in the experimental data, for example due to a slightly underestimated pH or concentration of -mercaptoethanol. We also assumed that the ~4-fold superior rate of adduct formation from the singlet state, as compared to the triplet state, measured by Gidi et al 3 could be significantly lower in cellular conditions. The modified interconversion rates and quantum yields (Supplementary Table S6) provided the titration data reported in Fig. 3e-f (dashed lines). A more consistent labeling efficiency at the lowest power density was retrieved (Fig. 3e), as well as a better qualitative trend in terms of localizations per fluorophore (Fig. 3e) and photon budget ( Supplementary Fig. S12d). However, the number of photons per localization (Fig. 3f) and the on times ( Supplementary Fig. S12c) still deviated from the experimental data.
We reasoned that if the main dark state responsible for adduct formation and photobleaching has a lifetime inferior to the shortest frametime in the titration series (which is the case for the s-lived triplet state), a reduction of the on times as laser illumination is augmented can only be reached if T1 saturation is lower than ~50% at the highest intensity (Supplementary Note 1). Such a condition, however, would be incompatible with the high contrast observed throughout the titration series in effective labeling densities, photons per localization and localizations per fluorophore. Thus, we conclude that a long-lived (ms) dark state is likely involved in controlling Cy5 photobleaching in dSTORM experiments. In fact, hints towards the existence of such a state has been provided experimentally 4,5 , and a very long-lived triplet state had to be invoked by Diekmann et al 6 to explain their data using a simple photophysical model. Yet, T1 cannot be ms-lived under dSTORM conditions.
Another argument in disfavor of the s-lived T1 being the pivotal dark state is the huge photobleaching quantum yield >> 10 -3 required in SMIS to explain the experimental data. The long-lived dark state could possibly involve one of the anionic or cationic radical states, or be generated from the cis state of Cy5, but the conclusion is that, despite its sophistication, the model of Gidi et al still appears insufficient to explain the experimental dSTORM data. More complex schemes could be tested with SMIS, but the nature of the presumed long-lived dark state remains to be elucidated.

Estimation of the dependence of Cy5 on times as a function of laser power density
Here, we show that, using the Cy5 photophysical model of Gidi et al 3 with the short-lived triplet state as the main source of photobleaching , a decrease in on times as the laser power density increases is incompatible with a high contrast in the number of emitted fluorescence photons between high and low intensity lasers.
The rate of triplet state formation is given by: where is the excitation rate of the singlet state and is the quantum yield of intersystem crossing. The characteristic time spent in the singlet state before intersystem crossing is = 1/ . The rate for combined sulfur adduct formation and photobleaching from the triplet state is given by = + × where is the thermally induced rate of sulfur adduct formation, is the excitation rate of the triplet state and is the photobleaching S5 quantum yield from that state. The number of accesses to the triplet state to achieve a transition to either the sulfur adduct or the photo bleached state can then be estimated by: with being the triplet state lifetime. As ≫ 1 when is in the microsecond range, we can estimate the ontime in [s] as: Now let's convert the on-time in units of frametimes, keeping in mind that frame times are adjusted to obtain a constant illumination dose. At a given laser power density, the frame time can thus be written: where is the number of excitation of the singlet state per frame. Therefore, the on-time in units of frametimes can be expressed as: At low laser power density, there is little photobleaching from the triplet state and we have ≈ .
Thus the on time [ ] reduce to: with being the characteristic time before switching to the triplet state and , the excitation rate under low intensity illumination. In contrast, at the highest laser power density, photobleaching predominates so that Now the ratio of the on times at low and high laser eliminations is given by: At low intensity, we have ⁄ ≪ 1 , as there is low triplet state saturation. Thus, the expression above simplifies to: For / > 2 and ≈ 3, as observed experimentally, we arrive at the following constraint: This condition implies a rather low triplet state saturation of < 50% of the highest illumination power density, which is incompatible with the high contrast in photon detection between low and high laser intensities.

SMIS SPT data with a 5 ms frametime
Reducing the total frame time to 5 ms, the expected 2-state model was now retrieved with highest probability in the absence of fast exchange ( Supplementary Fig. S17b). However, in the presence of fast exchange, a wrong 3-state model was again found, this time because the fast exchange rate becomes close to the inverse of the shortened frametime. Suppressing sensitivity of vbSPT to the fast exchange process required raising the rates to values as high as 100,000 s -1 (Supplementary Fig. S17b). Of note, with mEos3.2, at 5 ms frame time, the localization precision limits the accuracy of the slow diffusion coefficient retrieval and no improvement is obtained by either of the techniques presented above ( Supplementary Fig. S18-19).

Supplementary Table S6
Phototransformation quantum yields and thermal rates used for Alexa647 (Application 3, modified parameters)

Objective transmission efficiency [%]
25.8   &: Quantum yields are only indicative, as phototransformation rates are dictated by the product q× were  is the associated extinction coefficient at the considered wavelength. *: Values in parentheses refer to thermally induced relaxation rates S16  Fig. S1 Ground-truth photophysical behavior of mEos4b in SMIS simulations employing the model of Fig. 1a. The case of the simulation in Fig. 1c, Panel 2 is shown (3.5 kW/cm², pH 7.5). PDF: probability density function. P-value: probability of bleaching normalized by the probability of transitioning to either bleached or blinked states.

Supplementary Fig. S2
Blend images obtained by combining rendered NPC images shown in Fig. 1c and a ground truth NPC image assuming 100% labeling efficiency and Nup96 Gaussian spots of ~10 nm fullwidth at half maximum (FWHM). The panel numbers shown correspond to those in Fig. 1c. Red color is a marker for incomplete labeling due to lack of mEos4b photoconversion or detection. Green color is a marker for degraded localization precision.