Multiplexed temporally focused light shaping through a GRIN lens for precise in-depth optogenetic photostimulation

In the past 10 years, the use of light has become irreplaceable for the optogenetic study and control of neurons and neural circuits. Optical techniques are however limited by scattering and can only see through a depth of few hundreds µm in living tissues. GRIN lens based micro-endoscopes represent a powerful solution to reach deeper regions. In this work we demonstrate that cutting edge optical methods for the precise photostimulation of multiple neurons in three dimensions can be performed through a GRIN lens. By spatio-temporally shaping a laser beam in the two-photon regime we project several tens of targets, spatially confined to the size of a single cell, in a volume of 150×150×400 μm3. We then apply such concept to the optogenetic stimulation of multiple neurons simultaneously in vivo in mice. Our work paves the way for an all-optical investigation of neural circuits at previously unattainable depths.


Introduction
Understanding communication among neurons and how they coordinate and integrate multiple signals is essential for discovering how neural circuits determine brain function and dysfunction. With a still growing toolbox of optogenetic reporters 1,2 and actuators 3,4 , and the parallel development of advanced optical techniques, it is today possible to activate and inhibit neuronal activity with light while optically recording the evoked response. Ultimately this will enable all-optical neural circuit interrogation with single-cell and single-action potential precision, even in deep brain regions 5 .
One-photon (1P) wide field illumination using single optical fibers, enables the simultaneous illumination of large brain regions up to few mm deep and has already permitted to establish the links between neural activity and behaviour in different areas [6][7][8][9][10][11] . This light-delivery approach however lacks spatial selectivity. More sophisticated multi-point photonic probes [12][13][14] achieved selective excitation of single brain layers but still lacked cellular resolution and did not permit concurrent optical recording of functional activity. By using 1P-computer generated holography (CGH) for patterned illumination through a fiber bundle coupled with a small objective, our group previously demonstrated single-and multi-neuron activation together with functional calcium imaging in freely moving mice 15 . However, the large dimension of the micro-objective (<2.5 mm diameter) limited this approach to superficial brain layers and the use of the fiber bundle did not preserve the holographic phase, thus constraining multi-spot generation to a single plane.
Two-photon (2P) excitation 16,17 combined with wave front shaping and opsin engineering allows millisecond manipulation of brain circuits with single cell resolution at multiple planes in three dimensions (3Ds). This was done either by generating multiple diffraction-limited spots that were scanned simultaneously across multiple cell somata [18][19][20] , or by using computer generate holography (CGH) to produce light patterns covering multiple cell somata at once 21 , thus optimizing the temporal precision of the photostimulation 22 . Recently, several research groups [23][24][25][26][27] have shown that using a two-step wave front shaping combined with temporal focusing (TF) [28][29][30][31] it is possible to generate multiple high resolution extended light patterns in 3D, a technique we named multiplexed temporally focused light shaping (MTF-LS). These approaches led to the first demonstrations of neural circuit manipulation in 3D 25,26 , yet the need of using conventional high numerical aperture (NA) objectives limited their use to circuits in superficial (≤ 300 µm) cortical areas or to in-vitro applications.
Micro-endoscopes (MEs), i.e. small optical probes that can be inserted into living tissues, represent a promising solution to extend optical brain manipulation to deeper brain structures.
Most MEs are based on the use of gradient index (GRIN) lenses, which are small cylinders of glass of diameter < 1 mm and length of several centimetres, characterized by a gradual variation of refractive index in the radial direction 32 . In the last 15 years, GRIN lenses were studied and optimized for the 2P imaging of living tissues, e.g. implanted till a few mm deep inside the rodent brain [33][34][35][36][37][38][39][40][41] . In vivo functional calcium imaging was demonstrated through GRIN lenses both in 1P 42 and in 2P excitation [43][44][45][46] . In Ref. 43 , 2P CGH was also performed through a GRIN lens (NA=0.5, diameter 0.5 mm) and a GRIN objective (NA=0.8, diameter 1 mm). Multiple diffraction-limited spots allowed the activity from several neurons to be imaged simultaneously through the GRIN lens. Extended light patterns were also generated through the GRIN objective (10 µm spots with axial resolution of ~ 22 µm). However, CGH was limited to a single plane and extended holographic patterns with single cell axial resolution were only shown through the larger and more invasive GRIN objective. Moreover, no experiment showed so far optogenetic photostimulation through GRIN lenses.
In this work we demonstrate an optical system combining our recent MTF-LS technique 27 with the use of a GRIN lens (NA=0.5, diameter 0.5 mm), and we show that a small ME is suitable for the generation of multiple axially-confined 2P excitation spots matching target somata in 3D. Successively, using this system we demonstrate all-optical control of single or multiple neurons through the ME, by performing in vivo 2P optogenetic stimulation of target cells and reading out their induced activity with 2P calcium imaging. Fig.1 Schematics of the optical setup used in the experiment, comprising a 10 times beam expander, two SLMs, the diffraction grating (G) for TF, the appropriate lenses (L), the 10X, 0.3 NA air objective and the GRIN lens. For optical characterization the sample was a thin layer of rhodamine that was scanned in z for axial resolution measurements.

Optical setup
The optical setup coupling the MTF-LS 27 to a GRIN lens ME is shown in Fig.1. In the optical characterization experiments we used a femtosecond fiber laser (Fidelity 10, Coherent), emitting at 1040 nm. The MTF-LS setup consisted of (1) a first SLM that determined the size and shape of the spot(s) to be generated at the sample plane; (2) a diffraction grating for TF; (3) a second SLM that multiplexed the axially confined spot(s) at arbitrary positions in 3D.
The two SLMs were also used to correct for the aberrations of the system, in particular of the GRIN lens. To do so we maximized the 2P signal from a diffraction-limited spot made at the

MTF-CGH through the GRIN lens.
In a first experiment we used the first SLM (see Fig.1) to generate a simple holographic shape (a 15-µm diameter round spot) that was focused onto the diffraction grating for TF. The second SLM multiplexed the axially confined spot at arbitrary positions in 3D. In Fig. 2a we compare the axial resolution of a 15-µm spot generated through the GRIN lens at the centre of the FOV to the case of a non temporally focused spot of the same size (red) and to that of a spot generated through the 0.3 NA air objective alone (with no GRIN lens) with TF (blue). As the green curve clearly suggests, when TF was not used, the axial resolution, calculated as the full width at half maximum (FWHM) of the curve, was excessively large (~ 80 µm), as a consequence of the relatively small NA of the GRIN lens. When using TF, the axial resolution at the centre of the FOV improved to ~ 20 µm.
In Fig. 2b we compare how the axial resolution of the holographic spots changed as a function of the lateral displacement both in the x (direction of dispersion of the diffraction grating) and in the y (perpendicular to the dispersion) direction (Fig. 2b). From the graph one sees that the axial resolution worsened in the TF direction (i.e. the x direction) when moving away from the centre much faster than for the y direction. This asymmetry, as detailed in the discussion, was not observed in previous experiments 27 , and could be due to a loss of colours through the GRIN lens when displacing the holographic spot in the TF direction. In any case, the temporally focused spots maintained an axial resolution better than 25 µm across 120 µm in the y direction and across 60 µm in the x direction, reaching the value of 35 µm at 60 µm from the centre along x. Comparison of the axial resolutions with TF (28 spots) and without TF (16 spots).
We next used the MTF-CGH system to produce 28 holographic spots in a FOV of 150x150x400 µm 3 through the GRIN lens. spots are focused at different depths. The plot in Fig. 2e compares the axial resolutions of the 28 temporally focused spots with a similar experiment in which we generated a distribution of 16 spots without using TF. The difference between the two cases is striking; the mean axial resolution was 28±7 µm in the former and 82±7 µm in the latter case (the error was calculated as the standard deviation over all the experimental repetitions). From these results one can clearly see that advanced optical methods, here CGH and TF, can be implemented through a GRIN lens ME. Moreover, TF is essential to preserve single cell axial resolution when using low-NA GRIN lenses to create extended 2P excitation spots.

MTF-MS through the GRIN lens.
As described in Ref. 27 , the MTF-MS method relies on a mixed phase/amplitude shaping approach, capable of simultaneously producing different speckle-free shapes, with an overall better axial resolution with respect to MTF-CGH, and to independently multiplex them at the sample plane. Here we used MTF-MS in two different configurations (Fig. 3): in the first one we generated a mixture of round and stars (for a total of 20 spots) (Fig. 3a,b); in the second one we generated 16 identical round spots (Fig. 3c). In Fig. 3a we show the lateral view (xz plane) corresponding to the case of two different shapes, whereas in Fig. 3b and c we show the projections along the z direction in the case of two and one shapes respectively. As expected, in both cases, we could generate a 3D distribution of shapes with improved axial resolution and intensity homogeneity with respect to Fig. 2. As summarized in Fig. 3d, the axial resolution was around 22±6 µm in the case of a single shape and 26±7 µm when using two different shapes. As discussed later, contrary to previous results through a normal objective 27 , when using the GRIN lens we could not easily generate more than two shapes, probably due to the larger aberrations of the system. In the in vivo experiments, we mounted the GRIN lens ME on a microscope already equipped for 2P optogenetic stimulation and 2P scanning imaging, described in Ref. 50 . In this case, we used a more basic version of the holographic setup shown in Fig. 1, comprising only one After viral infection of ReaChR at the depths of ~250 µm and ~500 µm in the mouse primary visual cortex (V1), we performed acute craniotomy and removed the dura mater to expose the brain in anesthetized mice. All the in vivo experiments were performed in the anesthetized mouse V1 using the GRIN lens to image and photo stimulate through the craniotomy. By moving the objective and the GRIN lens together with a z motor we could change the focus of the system from the brain surface down to ~250 µm deep (when the GRIN lens was in contact with the brain surface), possibly deeper if the GRIN lens slightly penetrated the brain.

All-optical control of neuronal activity through GRIN lens in vivo
Through the GRIN lens, we were able to resolve on average 34±3 individual cortical neurons in a FOV of 150×150 µm 2 (mean±s.e.m., 9 FOVs). As Fig. 4a shows, we observed GCaMP6s fluorescence changes in single (5 FOVs) or multiple (5.2±0.7 cell, 5 FOVs) target neurons by stimulating with 10 light-pulses at a repetition rate of 11.84 Hz, through 12-µm diameter circular holographic spots at a threshold illumination intensity (defined as the intensity resulting in ≥0.5 activation probability in target cells, see Methods) of 0.39±0.09 mW/µm 2 .
The imaging power was kept at 90±14 mW, using a scanning speed of 5.92 or 11.84 Hz.
Higher imaging powers led to an increased GCaMP6s fluorescence in cytosol, probably due to the slow channel kinetics of ReaChR 47 .
To examine the spatial selectivity of photostimulation, we determined the relationship between the activation probability (see methods) of non-target cells and their distance to the target cells 50 . We found the critical distance where non-target cells displayed 50% of target cells' activation probability at the threshold stimulation intensity (see methods) to be 18 µm for single-cell activation (4 FOVs) and as 72 µm for multi-cell activation (5 FOVs) (Fig. 4b).
Of note, for 2 FOVs in multi-cell activation experiments, non-target cells displayed >0.9 activation probability at the threshold stimulation intensity up to 100 µm away from a target cell, which implied neuronal network activation, thus reducing the spatial selectivity of photoactivation.
In sum, we demonstrated in vivo all-optical control of a single and multiple neurons through a GRIN lens. Out-of-target activation could result from a combination of neurite activation, smaller FOV and the relative low NA of the GRIN lens.

Discussion
In this work we developed a ME, based on the combination of MTF-LS with a GRIN lens, for the 2P excitation of multiple targets in 3D and we combined it with functional imaging to enable cell-targeted all-optical interrogations of deep brain regions in vivo.
Using the TF technique and holographic multiplexing we could generate 3D distributions of extended excitation spots over a total FOV of ~ 150x150x400 µm 3 , keeping at the same time an axial resolution better than 30 µm. Importantly, our results demonstrate that the TF effect is maintained through the GRIN lens, despite its larger aberrations 51 . As shown in Fig. 2 Compared to a MTF-LS conventional microscope, the use of a GRIN lens imposes few limitations ( Fig. 2 and 3). First, we observed an asymmetric deterioration of the axial resolution when moving holographic spots in the x,y plane. Precisely, the axial resolution worsened more in the TF (x) than in its perpendicular direction (y) (Fig. 2b), a feature we did not observe when using a conventional high NA objective 27  Out of target activation can thus be prevented by using somatic opsins and possibly GRIN lenses with a bigger FOV or by further improving the axial resolution, e.g. by using higher NA GRIN lenses.
In the present study, we have limited the demonstration of all-optical neuronal control to a single-plane. The combination of MTF-LS with several volumetric imaging implementations as upstream divergence control 20,21 remote focusing 54 or extended depth-of-field scan 55 will enable to extend these demonstration to multiple planes. The use of chronic implantation of GRIN lenses (as shown for example in 43,46 ) will also enable to extend this approach to the optical manipulation of deeper brain regions.

Animal preparations
All

Holographic stimulation and calcium imaging through GRIN lens in vivo
The in vivo endoscope system was integrated to an existing custom-made 2P all-optical system thoroughly described in 50 . Specifically, a 0.5 NA GRIN lens was positioned by means of a custom-designed holder underneath a 10x microscope objective coupled with a SLMbased 2P patterned photostimulation and a 2P galvo-based scan imaging system. The GRIN lens holder was composed of kinematic mounts allowing X,Y,Z translation and rotation of the pitch and yaw axes of the GRIN lens, thus ensuring GRIN lens alignment to imaging and photostimulation paths. GRIN lens holder and objective were jointly connected to an axial motor allowing beam refocusing in the sample.
Initially, GRIN lens and objective were axially translated towards the head of the mouse till the image of brain surface appeared. That set the zero position of the GRIN lens, where its tip was at a distance of 250 µm (i.e., the optical system's working distance) away from the brain surface. To perform all-optical experiments on a sub-population of cortical neurons coexpressing the opsin ReaChR and the calcium sensor GCaMP6s located up to 250 µm below the brain surface (i.e. layer 2/3), we axially refocused the GRIN lens/objective system like with an ordinary 2P objective microscope until at the brain surface.
For acute in vivo experiments, mice were anesthetized with isoflurane (as described above) and the skull was exposed after subcutaneous application of lidocaine. A custom-made headplate was attached to the skull using dental cement (Unifast Trad, GC). A circular craniotomy of 2-3 mm diameter was made over the injection site and the dura mater was removed.
Two-photon imaging of GCaMP6s calcium signal and the fluorophore labelling of dTomato was carried out by exciting with a scan beam provided by a Ti:Sapphire laser emitting at 920 nm (Coherent Chameleon Vision II). SLM-based patterned photostimulation was provided by using high-energy fiber laser-pulses at 1030 nm (Satsuma HP, Amplitude Systemes).
Target cells were selected based on a high-resolution reference image (512×512 pixels) of the red channel collecting signal from ReaChR-dTomato. Through single or multiple circular holographic spots of 12-µm diameter, the target somata were simultaneously illuminated with 10 holographic light-pulses of 5 or 10 ms at 11.84 Hz. Concurrently, the neuronal population activity of GCaMP6s calcium signal in a 150×150 µm 2 FOV was monitored by scanning at a frame rate of 5.92 or 11.84 Hz with 128×128 pixel resolution.
During all-optical experiments, the photostimulation laser induced artefactal excitation of fluorophores, which appeared as consecutive lines of bright pixels. The image frames of GCaMP6s signal from regions-of-interest (ROIs) that were affected by stimulation artefacts were removed in post-processing.

Data analysis
Image analysis was performed by using ImageJ and MATLAB (Mathworks). ROIs covering individual target and non-target cell somata were manually selected in ImageJ based on both red (ReaChR-dTomato) and green (GCaMP6s) channels. The time-lapse fluorescent signal of GCaMP6s from all ROIs was exported in MATLAB. Image frames from ROIs that are affected by the photostimulation artefacts were removed in analysis. For each ROI, the relative percentage change of GCaMP6s fluorescence was computed as ΔF/F=(F-F 0 )/F 0 , where F 0 was the average raw fluorescence signal 3-0.2 s before photostimulation started. A cell was considered activated if the average ΔF/F 1 s after the last illumination onset was significantly larger compared to that 1 s before the first illumination onset (right-tailed paired t-test with a significance level of 0.05). The relationship between activation probability and distance-to-target was determined similarly as previously described 50 . Specifically, the threshold stimulation intensity was determined when the activation probability of target cells >=0.5. The average values of activation probability at different distance-to-target were described by fitting with an exponential function.