4Pi-RESOLFT nanoscopy

By enlarging the aperture along the optic axis, the coherent utilization of opposing objective lenses (4Pi arrangement) has the potential to offer the sharpest and most light-efficient point-spread-functions in three-dimensional (3D) far-field fluorescence nanoscopy. However, to obtain unambiguous images, the signal has to be discriminated against contributions from lobes above and below the focal plane, which has tentatively limited 4Pi arrangements to imaging samples with controllable optical conditions. Here we apply the 4Pi scheme to RESOLFT nanoscopy using two-photon absorption for the on-switching of fluorescent proteins. We show that in this combination, the lobes are so low that low-light level, 3D nanoscale imaging of living cells becomes possible. Our method thus offers robust access to densely packed, axially extended cellular regions that have been notoriously difficult to super-resolve. Our approach also entails a fluorescence read-out scheme that translates molecular sensitivity to local off-switching rates into improved signal-to-noise ratio and resolution.


Supplementary Methods
Switching patterns for 3D point scanning nanoscopy Off-switching patterns used for point scanning fluorescence nanoscopy are characterized by a local intensity minimum at the focal center, flanked by preferably steep gradients. This shape is usually generated by phase modulation of a high-angle focused wavefront, e.g. by means of a phase mask at (or imaged to) the back pupil plane of the objective lens, and/or by control of the phase between the counter propagating wavefront caps that form a 4Pi focus. The following patterns are of particular relevance in context of 3D nanoscopy: The 'z-donut' 1 (Supplementary Figure 1a) is generated by single-lens focusing of a top-hat shaped wavefront, and was the first switching pattern reported for STED microscopy. By itself, it is a rather inefficient pattern for 3D switching, as most of its intensity is concentrated in two lobes above and below the focal plane, and gradients close to the focal center are comparatively low. These properties, however, make it ideally suited for side-lobe suppression in a two-focus setup (Figs. 1a, 3e).
The '3D-donut' 2 (Supplementary Figure 1b) results from 4Pi focusing of a circularly polarized beam that has been imprinted with an azimuthal phase ramp oriented in countersense to the rotation of the field vector. It represents a very narrow single-focus 3D configuration for ON-state confinement that becomes virtually isotropic at high focusing angles. The precise axial-to-lateral aspect ratio also depends on the distributions of orientation and mobility of the fluorophore dipoles, as the lateral and axial confinement is mediated by orthogonal field components (h ax , h lat , Supplementary Fig. 1b). Secondary minima down to zero intensity are present above and below the focal plane and result in areas of little to no side-lobe suppression.
The 'aberrated 3D-donut' (Supplementary Figure 1c); a 3D-donut that has been modified by a further quarter-wave retardance added to each initial wavefront over a top-hat profile, in order to create a single-focus 3D switching pattern with raised secondary minima and thus improved suppression of on-axis lobes. With respect to a pure 3D-donut, light is diffracted outwards, which flattens gradients by about a factor of 0.5. Just as in case of the z-donut, implementation of the modified phase mask involves a more elaborate alignment due to its dependence on the pupil diameter, which can be facilitated by the use of adaptable phase retarders (e.g. spatial light modulators 3,4 ).
Expression plasmids for Dronpa-M159T targeted to mitochondria were constructed from the mitochondrial targeting sequence from subunit VIII of human cytochrome c oxidase (from vector pDsRed1-Mito, Clontech).

Cell culture and sample preparation
HeLa (human epithelial carcinoma) and CV-1 (cercopithecus aethiops monkey kidney) cells were cultured under constant conditions at 37°C and 5 % CO 2 in DMEM (high glucose, Invitrogen, Carlsbad, California) containing 5 % FCS (PAA, Pasching, Austria), 100 µg ml -1 streptomycin, 100 U ml -1 penicillin, 15 µg ml -1 phenol red (all Biochrom, Berlin, Germany) and 1 mM pyruvate (Sigma, St. Louis, USA). Prior to transfection, cells were seeded onto 'small' coverslips (No. 0, 18 mm x 18 mm, hand-selected thickness 100 µm ±2 µm, Marienfeld, Lauda-Königshofen, Germany) in 6-well plates. On the following day, the cells were transfected with plasmid DNA using Turbofect (Thermo Scientific, Waltham, USA) according to the manufacturer's instructions. 24 hours past transfection, the coverslips were washed for 5 minutes in HDMEM and subsequently covered with 150 µl of a diluted suspension (5 % v/v in HDMEM) of 10 µm beads (FluoSpheres, yellow-green, 10 µm, for blood flow determination, Life Molecular Probes) that stick to the sample and act as spacers. After 5 minutes of incubation, the coverslips were briefly rinsed with HDMEM to remove non-adherent beads, and immersed into imaging medium for another 20 minutes. For paraformaldehyde (PFA) fixation, the respective samples were incubated for 5 minutes in 4 % m/m PFA solution and washed twice in PBS before the immersion medium was applied. 'Small' cover glasses are then stacked on top of their 'large' counterparts, with cells and beads facing inside. The resulting sandwich is gently weighted down in order to bring glass and spacers into contact, sealed by epoxy resin (UHU Plus Sofortfest, UHU, Bühl, Germany), and finally glued into the sample holder (Fig. 1b) using nail polish.

Main optical layout and data acquisition
The microscope was assembled according to Supplementary Figure 4. Light pulses from a Ti:Sapphire laser (Chameleon-XR, Coherent, Santa Clara, CA) were used for two-photon activation of fluorescent proteins at 780 nm. Light for 3D deactivation (3d) and read-out at 491 nm emanated from a diodepumped solid state laser (Cobolt Calypso, Cobolt, Vretenvägen, Sweden). A further diode laser (Cobolt MLD, 488nm, Cobolt, Vretenvägen, Sweden) provided a 488 nm beam for the auxiliary deactivation of side-maxima (zd). Individual phase masks were used to imprint phase patterns onto the beams (PP3d: vortex phase plate, VPP-1A, RPC Photonics, Rochester, NY. PPzd: top-hat phase plate, MgF 2 deposited onto fused silica, custom built in our optics workshop), that were subsequently imaged to the back pupil (BP) of each objective lens (1.20 NA HCX PL APO, 63x, Leica Microsystems, Wetzlar, Germany) in order to generate the desired focal light patterns (Supplementary Figure 1). Scanning of the sample was implemented by a galvanometric beam scanner (Yanus IV, TILL Photonics, Gräfeling, Germany), located at a conjugated plane with respect to both BP planes, and a piezo driven sample stage (P-541.ZCD, Physik Instrumente, Karlsruhe, Germany) with added optical stabilization (Fig. 1b).

4Pi unit operation
The construction of the 4Pi unit was geared to combine convenient handling with minimal drift during measurements. Its geometry and material composition (Supplementary Figure 5) were chosen such that the thermal expansion of corresponding components cancels out at the focus position in order to minimize thermal drift. The rigidity of each objective lens was increased by a lens cage (L 1,2 ) that fixes the movable lens cap to its base.
Optical contact between each objective lens and the sample was established by a droplet of refractive index liquid (Series AAA, n D = 1.350, Cargille Laboratories, Cedar Grove, NJ, USA). The individual PSFs of each objective lens as well as their joint 4Pi PSF were deduced from images of fluorescent reference beads inside the sample. The initial alignment of the unit (Supplementary Figure 5) adhered to standard procedures 8 and involves minimizing the PSF extends by means of the correction collars (C 1,2 ), straightening of the PSFs by collinear alignment of the objective lens and sample axes (θ 2 , θ S ), and coarse superposition of the fields of view (FOV) of both lenses (∆X,Y,Z FOV ).
During routine operation, the upper objective mount was detached in order to change the sample, and subsequently reattached with about 2 µm accuracy, which lies well within the travel of the lower objective piezo stage (30 x 30 x 10 µm, P-733.3DD, Physik Instrumente, Karlsruhe, Germany) used for FOV fine control (∆xyz FOV ). Sample orientation (θ S ) and coarse axial position (Z S ) were realigned as necessary. Axial travel of the goniometer platform could be locked against the outer frame by four clamp screws (L) for improved long term stability. An automated online (drift) correction for the 4Pi phase ( 4Pi ) and diverging FOV was implemented as a Python script within the data acquisition framework. Scanning was periodically switched from the region of interest (ROI) to the location of predefined, 100 nm reference beads, in order to assess the current 4Pi and FOV mismatch. The corresponding corrections were then applied to the main 4Pi beam splitter (MBS, Supplementary  Figure 4) and ∆xyz FOV , and scanning of the ROI finally resumed.
A notable feature of the optical layout of the 4Pi unit (Supplementary Figure 4) is the suppression of the transmitted light. In a typical 4Pi arrangement, light that is focused on the sample is usually picked up and re-collimated by the opposing objective lens, and therefore directed towards the detector where it needs to be filtered out in order to prevent it from generating image background.
Here, due to the polarization state of the transmitted light, it is already attenuated by a factor of 10 -1 -10 -2 at the polarizing beam splitter adjacent to the respective objective lens (Supplementary Figure 4, 4Pi unit, hollow and solid beam paths), which relaxes the requirements on further filters.