Sharper low power STED nanoscopy by time gating

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1 Nature Methods Sharper low power nanoscopy by time gating G. Vicidomini,3, G. Moneron,3, K. Y. Han,3, V. Westphal, H. Ta, M. Reuss, J. Engelhardt, C. Eggeling, S. W. Hell, Max Planc nstitute for Biophysical Chemistry, Department of NanoBiophotonics, Am Fassberg, Göttingen, Germany German Cancer Research Center (DKFZ), Optical Nanoscopy Division, m Neuenheimer Feld 80, 690 Heidelberg, Germany 3 G.V., G.M. and K.Y. H. equally contributed to this wor. Correspondence should be addressed to S.W.H. (shell@gwdg.de) Supplementary Figure Excited-state lifetime τ as a function of the CW- power Supplementary Figure Effective point-spread-function of the g- nanoscope Supplementary Figure 3 Supplementary Figure 4 Supplementary Figure 5 Supplementary Figure 6 Supplementary Figure 7 Supplementary Figure 8 Supplementary Note g- nanoscopy on uorescent beads Resolution increase of g- nanoscopy g- nanoscopy on living cells g- nanoscopy on fixed cell g- FCS of three-dimensional diffusion in solution g- FCS data of two-dimensional diffusion on membranes Theory

2 Supplementary Figure Excited-state lifetime τ as a function of the CW- power. TCSPC measurements on single NV color centers. Each point represents the average of five measurements on five different isolated NV color centers (mean + s.e.m; n = 4). The decrease of τ with P can be described by Eq. 3 (solid line, Supplementary nformation). Excitation: 53 nm, 0 MHz repetition rate and 0 µw average power; : 740 nm, diffraction-limited Gaussian spot.

3 Supplementary Figure Effective point-spread-function of the g- nanoscope. E-PSFs for different CW- powers P (rows) and different detection delays T g (columns) measured for a single isolated NV color center. (a) Fluorescence intensity, (b) ited-state lifetime τ and (c) normalized lateral line profiles of a for T g = 0 ns (blac, CW-) and T g = 5 ns (red, g-). The profiles are well described by Eq. 0 (solid lines, Supplementary nformation). The grey lines show the confocal profile for reference, which is not inuenced by time gating. Scale bar 00 nm.

4 Supplementary Figure 3 g- nanoscopy on uorescent beads. Scanning uorescence images of 40 nm diameter yellow-green beads for confocal (left), g- (middle left) and CW- (middle right) recordings. The insets show a magnified view of the mared areas, renormalized in signal intensity. The right panel depicts normalized intensity profiles along the dashed line of the insets demonstrating the distinction of features as small as ~ 40 nm. Excitation: 485 nm, 80 MHz and 0 µw; : 59 nm, P = 370 mw; gated detection: T g = ns, T = 8 ns. Scale bars µm.

5 Supplementary Figure 4 Resolution increase of g- nanoscopy. Measurements on single isolated NV color centers. (a) Full-width-half-maximum (FWHM) versus contrast: Normalized line profiles of the signal intensity through the point-lie object (Supplementary Fig. for P = 77 mw and T g = 5 ns) were taen to determine the FWHM of the PSF and the image contrast. The image contrast defines the ability to resolve two neighboring objects (separated by the Center-Center Distance) and is given by (max-lmin)/max, where max = is the pea value of the intensity line profiles of the two neighboring objects and lmin is the value of the local minimum between the two peas. Eq. 0 was used to fit (lines) the experimental line profiles (dots) and the value of lmin was determined from the fits. (b) FWHM as a function of CW- powers P for different detection-delays T g (mean + s.e.m; n = 4), and as a function of T g for different P (inset, mean + s.e.m; n = 4). Solid lines show fits of Eq. to the data (Supplementary nformation). The decrease of the FWHM is also shown for CW itation instead of pulsed itation, which coincide with the values of T g = 0 ns (i.e., no gating). (c) Contrast as a function of the distance between two objects for g- (solid lines, T g = 5 ns) and CW- (dotted lines) for P = 77 mw (grey) and 56 mw (red). The curves result from calculations based on the fitted (Eq. 0) experimental data reported in Supplementary Fig. c. The dotted horizontal line (contrast = 6 %) represents the Rayleigh criteria for a proper distinction of alie objects. For g-, already 77 mw are sufficient to resolve 50-nm-apart objects, while > 56 mw are necessary for CW-. The main reason lies in the strong Lorentzian tails of the CW- PSF (compare a), resulting in a much steeper contrastdistance dependence for g-. (d) Decrease of the pea signal (maximum intensity) of the effective PSF due to the time gating as a function of T g for different P, which is well described by exp(t g /τ ) with τ = 3.5 ns,. ns, 0.9 ns and 0.7 ns for increasing P (Supplementary nformation). The decrease of τ for increasing P results from residual intensity in the central minimum of the doughnut-shape CW- beam.

6 Supplementary Figure 5 g- nanoscopy on living cells. Scanning images of eratin labeled with the uorescent protein citrine in a living PtK cell for confocal (left panel), g- (middle left panel) and CW- (middle right panel) recordings. The insets show a magnified view of the mared areas, renormalized in signal intensity. The right panel depicts normalized intensity profiles along the dashed line of the insets demonstrating the separation of features as small as 60 nm. Excitation: 485 nm, 80 MHz and µw; : 59 nm and P = 00 mw; gated detection: T g =.5 ns and T = 8 ns. Scale bars µm.

7 Supplementary Figure 6 g- nanoscopy on fixed cells. Scanning uorescence images of vimentin filaments in fixed PtK cells labeled with the organic dyes Alexa 488 (a), Oregon Green (b) and Chromeo 488 (c), and of microtubuli in fixed PtK cells labeled with the organic dye Atto 674N (d): confocal (left), CW- (middle right) and g- (middle left) recordings. The insets show a magnified view of the mared areas, renormalized in signal intensity. The right panels depict normalized intensity profiles along the dashed line of the insets demonstrating the distinction of features as small as < 60 nm. Excitation: 485 nm (a,b and c) and 635 nm (d), 80 MHz and 0 µw; : 59 nm (a,b and c) and 760 nm (d), P = 00 mw (a,b and c) and 50 mw (d); gated detection: Tg =.5 ns, T = 8 ns. Scale bars µm.

8 Supplementary Figure 7 g- FCS of three-dimensional diffusion in solution. Dependence of the lateral focal transit time t xy on the CW- power P of the dye Rhodamine 0 in thiodiethanol (TDE) solution, determined by FCS for different T g (mean + s.d.; n = 4). The decrease of t xy follows the confinement of the E-PSF. Excitation: 485 nm, 80 MHz and 8 µw; : 59 nm; gated detection: T = 8 ns.

9 Supplementary Figure 8 g- FCS data of two-dimensional diffusion on membranes. Correlation data of G N (t c ) Atto647N-labelled phosphoethanolanine (PE) and sphingomyelin (SM) diffusing in the plasma membrane of live PtK cells. Normalization at t c = 0.0 ms. The g- (PE: red, SM: light red; P = 50 mw and T g = 3 ns) but not the CW- (PE: blac, SM: grey; P = 50 mw) recordings highlight the difference between the confined diffusion of SM and the almost free diffusion of PE. Lines denote fits using Eq. Online Methods resulting in t xy =.7 ms (PE) and 4.3 ms (SM), α = 0.79 (PE) and 0.67 (SM) for the CW- and t xy = 0.4 ms (PE) and. ms (SM), α = 0.8 (PE) and 0.7 (SM) for the g- curves.

10 SUPPLEMENTARY NOTE Theory Here we present a theoretical model that describes the experimental data of g- nanoscopy. Starting with the underlying photophysics of the uorophore under CW- conditions, we derive an expression for the inhibition of the detected uorescence signal due to stimulated emission and gating, and finally present an expression of the effective point-spreadfunction (E-PSF) of the g- nanoscope. We follow similar approaches as given previously -4. At first we quantify the emitted uorescence, which is proportional to the population of the first ited state. We assume that (i) the uorescence marer can be described by a simple two-level model system consisting of a ground and a first ited state S 0 and S, respectively, i.e., population of, for example, additional dar states are negligible, and that (ii) the probability to ite the marer from S 0 to S with the beam is negligible. n this case, the inetics of S formation is a solution of the equations ds 0 dt ds dt = = S S 0 0 S S S S () where S 0 and S are the probabilities of finding the uorophore in the S 0 and S state, respectively; = /τ is the spontaneous emission rate, given by the ited-state lifetime τ in the absence of light; = σ is the stimulated emission rate given by the stimulated emission cross-section σ and the average intensity of the CW beam ; and = σ abs T r /T p is the itation rate during the pulses (assumed to have rectangular pulses with constant intensity over their duration), given by the absorption cross-section σ abs, the average itation intensity, the lag time between two consecutive laser pulses T r, and the length of the pulses T p. Here, the intensities are given in units photons per area. Usually one experimentally accesses the power P (/) which relates to the maximum intensity of the diffraction-limited Gaussian spot (/) according to = Pλ/(Ahc) with the laser wavelengths λ, the focal area A = π (FWHM/) approximated by the full-width-half-maximum (FWHM) diameter of the focal spots, c the speed of light, and h Planc s constant. To solve Eq. we assume a low repetition rate f = / T r of the itation laser, such that ited uorophores can relax to the ground state before the next pulse arrives. n this case, the initial conditions are the same at the start of every itation cycle, meaning that the study of just a single period is adequate. t = 0 mars the beginning of each pulse (non-equilibrium range). Consequently, S 0 (0) = and S (0) = 0 and the evolution of S (t) is given by S ( t) = ( exp( ( ) t ) ( exp( ( ) T ) exp( )( T t ) P p 0 t T T p p < t T () r n the presence of the ited-state lifetime τ = /( + ) is shortened with increasing or P of the light

11 τ = /( + ) = /( + σ ) = /( +B P ) (3) B = (σ λ )/(Ahc) relates the power P to the rate of stimulated emission. Our experimental data can well be described by Eq. 3, as given in the Supplementary Fig. for the data of the NV color center (with σ cm (compare reference 5 ), λ = 740 nm, and A = 0-9 cm (FWHM = 30 nm)). Next, we evaluate the inhibition factor η of the g- nanoscope. The inhibition factor is defined as the reduction of the detected uorescence signal under the addition of light relative to the absence of the light T T g, Tg Tg r r (, Tg ) = q S(, t) dt q S( 0 t)dt η (4) where q is the uorescent quantum yield and T g is the starting position of the detection gate. Solving Eq. 4 for T g > T p (or assuming that uorescence emitted during the short period of the itation pulse, usually tens of picoseconds, can be neglected) and assuming a pulse lag time T r > τ one obtains η g (, T ) g ( )( exp( ( + σ ) Tp ) ( + σ )( exp( ( ) Tp ) exp( T σ ) + σ For short pulse lengths T p, the first part of Eq. 5 becomes, i.e., we neglect the stimulated depletion during the itation pulse. n this case Eq. (5) reads η g g ( T ) = exp( T σ ), g g (6) + σ To highlight this equation we briey derive the inhibition factors for other modalities. The inhibition factor of the pulsed modality reads, 3 η ( ) = ( T σ ) ps exp (7) where T is the duration of the pulse. Here we have again regarded only the residual uorescence emitted after the pulse. The inhibition factor of the CW- modality with CW itation is 3, 6 η ( ) CW = (8) + σ This equation holds for low itation intensities avoiding saturation of the S 0 - S transition ( << ). Consequently, the inhibition factor of the g- modality (Eq. 6) is composed of two different terms. Each term represents one step of the experimental time sequence (Fig. b). The first term involves the inhibition of the (uorescent) S state during uorescence collection (t > T g ), and is equivalent to the η CW- of the CW- modality (Eq. 8). The second term (5)

12 involves the inhibition of S before uorescence collection (t < T g ), and is equivalent to η ps- of the pulsed modality assuming T g = T (Eq. 9). For equal intensities, inhibition of uorescence by g- is thus in any case superior over conventional CW- (by the factor η ps- ) and over pulsed (by the factor η CW- ). Note that the high pulse pea intensities usually applied in the pulsed modality (to reach strong inhibition) can now be compensated by time gates T g >> T (usually T ns) thus allowing the use of rather moderate CW laser powers to achieve similar inhibition factors. Note, for T g = 0, i.e., without time-gating, Eq. 6 is equivalent to the inhibition factor of CW- nanoscopy using CW itation (Eq. 8); i.e. as long as the itation power is properly chosen to prevent S 0 - S saturation, the inhibition by CW- light does not depend on whether CW or pulsed itation is chosen, as is demonstrated in the Supplementary Fig. 3b and in previous experiments 5. We now introduce the saturation intensity s = /(σ τ ), which is defined as the intensity at which the detected uorescence signal is inhibited to 50 % of its initial value, η( s, 0) = /. η g (, T ) = exp( T / τ / ) g + / s g ( P, T ) = exp( T / τ P / P ) η g g g s (9) + P / P s This is the final expression of the inhibition factor of g-. As shown in Fig. c, the residual uorescence detected from a single isolated NV center as a function of P or T g can well be described by Eq. 9 (with τ = ns and P s = mw). Given the inhibition factor of g-, we use a similar approach as in reference 4 to describe the spatial distribution h g- (r) of the effective detection volume or E-PSF. h g- (r) h CLSM (r) η(,t g ) is given by the normalized confocal PSF h CLSM (r) and by the inhibition factor η( (r),t g ) of Eq. 9, whose spatial r-dependence is given by the doughnut-lie intensity distribution (r) of the light. n the vicinity of the focal center, the confocal PSF can be well described by a Gaussian with a FWHM d c, i.e., h CLSM (r) exp(-r 4ln()/d c ), and the doughnut intensity pattern may be approximated by a parabola (r) 4 m βr, with m = max( (r)) and β a constant that depends on the shape of the doughnut minimum. Note that in the case of the doughnut-shaped spot P relates to m according to m = P λ /(A hc) with the scaling factor = 0.3. Consequently, the effective PSF of the g- nanoscope reads s h h g g ( r) ( r) r 4ln = exp d c r 4ln = exp d c ( ) + 4βr m s exp 4 ( ) + 4βr 0.3P P s βr τ s T m 4βr exp s g Pτ 0.3P T g (0) The E-PSF of the g- nanoscope is thus governed by three terms: the Gaussian confocal term, the Lorentzian term following from the CW- effect, and finally the Gaussian-shaped term following from the time-gated detection. We note that the first two terms of Eq. 0 represent the E-PSF h CW- (r) of a conventional CW- nanoscope. Hence, compared to a conventional CW- nanoscope the spot size or detection volume is decreased and thus the practical resolution is increased by the introduction of time-gating. Further, while h CW- (r) is Lorentzian-shaped 3, h g- (r) is Gaussian-shaped due to the time-

13 gated detection. Our experimental E-PSFs are well described by Eq. 0 as shown in the Supplementary Fig. for the data of the NV color center (with P s = mw, τ = ns and d c = 86 nm). Following Eq. 0, the FWHM d of the g- nanoscope can be approximated by d d ( ( )) + dc + / ln c β ς ξ () where ς = m / s = 0.3P /P s denotes the saturation factor of the depletion and ξ = T g /τ includes the effect due to time-gating. Eq. clearly states that the spatial resolution of a g- nanoscope is tuned by two parameters, the CW- intensity m (d ~ / ς) as for CW- nanoscopy, and the time-delay T g (d ~ / (ς ξ)). However, it is less the absolute values of τ and T g that govern the resolution increase by g- but rather their ratio ξ = T g /τ. Eq. fits our NV color center data well as exemplified in the Supplementary Fig. 3b (with β = nm -, d c = 87 nm, P s = mw and τ = ns). For FCS, the focal transit time t xy is proportional to d, i.e. t xy ~ d c /( + β d c ς (+ξ/ln()), which fits our g- FCS data - but not the non-gated CW- FCS data (due to the focal pedestal, i.e., its non-gaussian shape) - as exemplified in Fig. 3a (with β = nm -, d c = 40 nm, P s = 5 mw, 6 mw and 9 mw respectively for T g = 3 ns, ns and ns and τ = 3.9 ns) indicating free Brownian diffusion of the lipids in the supported lipid bilayer. t is important to note that the advantage of enhancing the resolution by increasing the timegate T g has to be carefully weighed against the reduction of the pea signal ~exp(-ξ), which in the presence of noise would result in a decrease of the signal-to-noise ratio in the image. This is well confirmed by our observations (Supplementary Fig. 4d). The g- approach can be extended to three-dimensions by appropriate engineering of the beam, 7 or to two-photon itation nanoscopy 8, 9 An important factor for a proper implementation of g- is the instrument-responsefunction (RF) of the system, particularly the RF of the detector. Many single-photon-counting (SPC) devices show a delay in their temporal response which depends on the signal intensity (see, for example, appnote_pdm_im.pdf), i.e., one would have to adapt the gating to the instantaneous count rate. With the eption of the FCS experiments on the membranes, which rendered homogeneous intensity traces (i.e. no response jitter), we have used only SPC devices which do not exhibit such bias. Additionally, the temporal width of the system RF should be short enough to ensure a precise time discrimination, especially for marers with short ited-state lifetimes τ. The measured values of the FWHMs of the RFs of the system that have been applied in our wor were ~30 ps for the APD configuration (~ 400 ps in the case of the FCS measurements on the membranes) and ~30 ps for the PMT configuration. t is also important to control the width of the time-gate T. Late photons arriving after T + T g following the itation pulse are discarded as well. These photons tend to originate from dar counts of the SPC device, direct itation from the CW- laser, or other sources of bacground and give rise to a decreased of the signal-to-bacground and signal-to-noise ratios, especially at low repetition rates f of the itation laser.

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