Lens-free microscopy for 3D + time acquisitions of 3D cell culture

Thanks to a novel three-dimensional imaging platform based on lens-free microscopy, it is possible to perform multi-angle acquisitions and holographic reconstructions of 3D cell cultures directly into the incubator. Being able of reconstructing volumes as large as ~5 mm3 over a period of time covering several days, allows us to observe a broad range of migration strategies only present in 3D environment, whether it is single cell migration, collective migrations of cells and dispersal of cells. In addition we are able to distinguish new interesting phenomena, e.g. large-scale cell-to-matrix interactions (>1 mm), fusion of cell clusters into large aggregate (~10,000 µm2) and conversely, total dissociation of cell clusters into clumps of migrating cells. This work on a novel 3D + time lens-free microscopy technique thus expands the repertoire of phenomena that can be studied within 3D cell cultures.

Recently the imaging of 3D cell cultures opened a new window onto the study of many cellular processes as nicely reviewed in 1 . 3D + time imaging of 3D cell culture is usually performed through optical sectioning microscopy techniques, e.g. light-sheet microscopy and confocal live-cell microscopy. Light-sheet microscopy is ideally suited to monitor 3D cell culture, it can acquire large volume in reasonable time and with minimal photo-toxicity. However, it requires the sample to be labelled with fluorescent dyes and the geometry of the sample container is constrained. This is not yet the ultimate gentle microscope as defined in 2 , that is needed for the future experimentations. A gentle microscope should be adapted to the sample, without any modification of its environment nor its integrity. In particular it should be compatible with all kind of cell culture container and if possible label-free.
With the aim of developing such a gentle microscope, we developed a novel 3D + time lens-free microscope dedicated to the observation of dynamic biological processes present in 3D cell culture as previously presented in 3 . It is based on the 3D lens-free microscopy setup introduced in 4 which enables a large angular coverage of the 3D scene thanks to its azimuthal acquisition geometry. This setup was modified to perform continuous monitoring inside an incubator at a controlled temperature and humidity 3 . The temperature of the CMOS sensor facing the 3D cell culture is now controlled by means of a laminar air flow which enables to run the image sensor without heating up the cell culture. This allows for the first time 3D + time lens-free acquisitions of 3D cell culture. This microscope works thus directly in the incubator with a regular cell culture container and is able to reconstruct large volumes of label-free 3D cell culture (~5.6 mm 3 ).
The present paper follows our previous work 3 , which introduced the experimental design to perform 3D + time lens-free acquisitions of 3D cell culture. Here we demonstrate the ability of this novel setup to gain insights into a broad range of phenomena only present in 3D environments. We discuss the analysis of two experiments of 3D cell culture of RWPE-1 cells acquired over eight consecutive days. RWPE-1 cells are a model for normal prostate epithelial cell behavior characterized by a polarized acinar morphology in 3D cultures 5,6 . RWPE-1 cells have also been used as a dynamic model of the signaling and interactions between organoids and mesenchyme that are required during organ development 7 . Observing volumes as large as 5.6 mm 3 over several days allows the visualization of a broad range of cell migration patterns discussed in 8,9 , such as the migration of cell leaders, collective cell migration and close-gap branching. We also witnessed interesting new phenomena, such as the cohesive migration of large aggregates of cells, the growth of cell clusters through the aggregation of isolated cells and conversely, the dissociation of cell clusters into clumps of single cells. In addition, we successfully monitored the dynamic evolution of the extracellular matrix on a global scale and we were able to isolate the matrix deformations resulting from traction forces generated by large cell aggregates over long distances, up to 1.5 mm. All these observations demonstrate that many important features of cell migration and cells-ECM (extra cellular matrix) interactions can be conveniently observed with our novel 3D + time lens-free microscope.

Methods
Cell culture. Experimental setup. 3D objects reconstruction requires to multiply the viewing angles. In our experimental bench (see Fig. 1a The object remains static, while the rotation axis is orthogonal to the sample plane. The illumination is tilted by an angle θ, tuned between 30 and 55°. As the sensor is kept in the same plane, this design is adapted to extended containers such as standard Petri dishes. An air knife blown via a vein carved in the sample holder insures the thermal insulation of the cell culture from the heat produced by the CMOS censor (see Fig. S1a).
Holographic 3D reconstruction. The purpose of the holographic reconstruction algorithm is to recover the 3D scattering potential of the sample from datasets consisting of holographic images recorded at different illumination positions and at different wavelengths. Figure 1d shows an example of 3D holographic reconstruction. For the fully 3D reconstruction, we used two different algorithms based on the Fourier diffraction theorem and the Born approximation of the light propagation. The first 3D reconstruction algorithm is based on the 3D inverse problem approach (see supplementary informations). It gives the best results in terms of contrast and quality 4 . It is, however, time consuming and is used only to reconstruct small region of interests at full resolution (voxel of 1.67 × 1.67 × 1.67 = 4.7 μm 3 ). The second 3D reconstruction algorithm is based on a regularized Gerchberg-Saxton algorithm introduced in 3 in which constraints are applied on the 3D objects 10,11 (see supplementary informations). For the fast reconstruction of volume as large as ~5 mm 3 , we used the regularized Gerchberg-Saxton algorithm at a lower resolution (voxel of 3.34 × 3.34 × 5.32 = 60 μm 3 ), providing sufficient quality results. The assessment of the 3D holographic reconstruction algorithms in terms of position accuracy and capabilities of size estimation has been performed using a reference object made of 10 μm beads embedded into Matrigel. We compared the 3D reconstruction obtained from the lens-free acquisitions with the Z-stack acquisitions obtained with a fluorescence microscope (Zeiss axio Observer Z1, 5x/0.13 N.A.). The 3D lens-free microscope operating with an illumination angles of θ = 45° achieves good position accuracy. We measured on N = 409 micro-beads an overall localization error of 3.8 μm (standard deviation) on the xy plane and 6.4 μm along the z-axis (Supplementary Table 1). Considering the size estimation measured on the 10 μm beads, the full width at half maximum (FWHM) value measured for the xy line profile of 10 μm beads is estimated to 10.5 μm (Supplementary Table 2). But along the z-axis the FWHM is in the order of 50 μm (Supplementary Table 2). The sizing is thus correct in the xy plane but it is strongly overestimated along the z-axis. The performance of the lens-free 3D microscope in terms of position accuracy and xyz-sizing are therefore relatively coarse but sufficient to analyze the dimensions of the cell clusters a relative manner.

Results
First experiment of 3D time-lapse acquisition. The merging of cell clusters into large aggregate. Figure 2 shows the 3D time-lapse acquisition obtained with our lens-free microscope on a 3D cell culture of RWPE-1 (see Movie S1). The dimensions of the 3D reconstructed volume obtained by the regularized Gerchberg Saxton algorithm is 4.86 mm 3 (2.67 mm × 2.67 mm × 0.68 mm) and it is hence possible to monitor hundreds of clusters of cells objects simultaneously (N > 300 Fig. 2c).
Analyzing the dimensions of the cell clusters present in the time-lapse acquisition, we found that the average xy projected area increased from 500 to 710 μm 2 in about 200 hours (see Fig. 2d). A first population of isolated clusters grew via cell proliferation like the one depicted in Fig. 3a but interestingly other clusters increased in size through merging. As a first example,  branches emerged and connected the two aggregates. The aggregate continued to move a little, by 150 μm and accumulated more neighboring cells. This process of cell dynamic clustering is strikingly depicted in Fig. 3h,i and Movie S5 which shows the another accumulation of 25 clusters into one very large aggregate of ~6000 μm 2 . The newly formed aggregate still managed to move as a cohesive group at a speed of 5-10 µm/h. Its course presents speed maxima (~30 μm/h, Fig. 3k) which corresponds to sequence of expansion and contraction. At t 0 + 184h, following a large expansion, we observed a traction force generated by the aggregate onto the ECM. This could be indirectly observed through the displacement of several clusters towards the large aggregate (Fig. 3j). These  tractions forces disappeared as the aggregate released the tensions applied to the ECM and the clusters moved back to their initial positions. The traction forces were generated isotropically and they could be observed up to a distance of 550 μm. A similar observation is shown in Fig. 3e and Movie S3 at t 0 + 120h but at a smaller scale.
Second experiment of 3D time-lapse acquisition. The formation of a complex cellular network. In contrast to the first experiment where we observed cell clusters moving, deforming and merging, in this second experiment we observed the construction of a complex and large cellular network, i.e. a long-scale tubular pattern (see Fig. 4 and Movie S6). In the first hours of the cell culture, we observed the dissociation of cell clusters into clumps of single migrating cells. As a first example, Fig. 5b and Movie S7 show the dissociation at t 0 + 53h of a cell cluster into a fixed cluster and a migrating cluster. The latter moved along a linear path directly toward another fixed cluster at a distance of 450 μm. This path is taken by several cells, migrating between the two fixed clusters in both directions. At t 0 + 120h, the two fixed clusters are finally connected by a branch of 200 μm in length. A second example, in Fig. 5d and Movie S8, depicts the total dissociation of a cluster into four single cells. These cells further migrated along linear paths, they followed each other, sometimes turning back. Importantly they formed trains of cells groups and in a second step, several paths taken by these cells became gradually branches of cells connecting two fixed clusters initially separated by ~300 μm. This phenomenon of dynamic branches formation is best observed when comparing the formation of the cellular network ( Fig. 5a) with the trajectories of the single cells (Fig. 5c). In the cell trajectories time-series, one can observe branches of 100 to 500 μm in length well before the effective formation of the cell branching that occurred 24 to 48 hours later. This phenomenon of dynamic branching happened all over the cell culture and after six days a complex cellular network was formed featuring ~30 aggregates in the range of 50 to 100 μm in diameter (see Fig. 4b) interconnected with branches of 100 to 500 μm in length.
Finally, after 6 days of experiment, the cellular network collapsed as branches of cells and cell aggregates merged together (see Movie S6). Yet, the cellular network did not vanished completely. In sum, we can distinguish three distinct phases in this RWPE-1 3D cell culture experiment that led to a complex cellular network, i.e. a first phase of single cell migration (~96 h), a second phase of interconnection between cell aggregates (~48 h), and a final phase where the cellular network collapsed partially (~60 h).
The generation of long-scale traction forces. In order to better visualize the 3D deformations of ECM present in this second experiment, we inserted 10 µm beads at different depths into the ECM prior to the 3D cell culture. This method is usually performed at the microscopic scale to monitor and quantify the single cell traction forces 12 . Here it was used to show the long scale deformations of the ECM. In the first hours of the experiment, the micro-beads allowed us to observe the intrinsic 3D deformations of the ECM. In the xy-plan, the ECM expanded radially. All the beads moved away from a central point at a speed increasing with the distance to this point (see Fig. 6a). The speed of the beads was about 1 μm/h close to the center of expansion and about 2 μm/h at a distance of approximately 2.5 mm (see Fig. 6a). At t 0 + 90 h, the expansion stopped and the ECM remained stable in the xy-projection. In the z-direction, during the first 24 hours, there was an important ECM expansion of about 100 µm followed by a slow drift which lasted until the end of the experiment (see Fig. 6c). At t 0 + 136h, the collapses of the network revealed significant traction forces that distorted the ECM. We isolated a strong ECM deformations resulting from traction forces generated by the collapse of several cell clusters (see Fig. 6d,e and Movie S9). This traction forces moved the beads by 100 μm (speed of 12 μm/h) at a distance of 350 µm from the cell aggregate. Bead displacement can also be observed 70 μm deep into the matrigel (see Movie S9) and at a large distance of 1400 μm (see Fig. 6e). There is thus an important remodeling of the ECM that occurred during the collapse of the cellular network.

Discussion
In the present paper, we demonstrated the capability of lens-free 3D microscopy to perform 3D + time acquisitions of 3D cell culture. Acquiring a volume as large as ~5.6 mm 3 over several days, allowed us to observe the broad spectrum of migration mechanisms previously discussed in 8,9,13,14 , whether it is single cell migration, collective migrations of cells, and cell branching. In addition, we observed the cohesive migration of a large aggregate of cells (~10,000 µm 2 projected area) that confirms the prediction that an isolated cells monolayer may acquire a global polarity and consequently performs a persistent random walk 15 . We also observed the sprouting of cells, i.e. short-range dispersal of cells. This mechanism described in a model discussed in 16 supports a faster rate of tumor growth.
We have also observed the formation of a complex cellular network of several mm 3 , i.e. a long-scale tubular pattern made of large cell aggregates connected by cell branches and surrounded by voids. This spongy structure has its origins in the cell migrations patterns that occurred during the early days of the cell culture. The paths taken by the migrating cells have indeed settled the interconnection between the different aggregates. In particular, we observed total dissociations of cell clusters into clumps of migrating single cells that provide simultaneously a path and the cell material to form new branches. This is a novel process which, is geometrically distinct from the "budding" and "clefting", the two processes that usually describe branching morphogenesis 17    also be viewed as a new invasive phenotype, the study of which should lead to a better understanding of tumor initiation and metastasis. Finally, we also studied the deformations of the ECM. We first observed intrinsic deformations of the ECM. The speed of these deformations are in the range of 1 to 2 µm/h. This is not negligible and it should be taken into account when measuring the speed of single cells in 3D cell culture. We were also able to isolate ECM deformations resulting from traction forces generated by cell aggregates. Importantly, we observed ECM deformations at two different scales, namely local ECM deformations generated by an aggregate which favor close-gap branching and large scale deformations that occurred during the collapse of the cellular network. The latter generated traction forces over long distances, up to 1500 µm. To our knowledge, this is the longest reported ECM deformation. Long-range traction forces have already been discussed but for smaller lengths of ~600 µm in 18,19 . 3D + time lens-free microscopy is thus a unique mean to capture in time the dynamic and multi-scale interplay between complex cellular self-assembly and ECM remodeling at different scales. These are important observations, as the dysregulation affecting ECM may contribute to pathologies such as inflammation 8 , age-related diseases 20 or cancer 21,22 .

Conclusion
In this paper we demonstrate that the novel 3D + time lens-free microscopy is a unique and powerful technique providing insights into spatial and temporal aspects of 3D cell cultures. Compared to other 3D microscopy techniques, such as confocal microscopy, 3D digital holographic microscopy, and light-sheet microscopy which provide much better resolution and specificity due to fluorescence labelling, our 3D lens-free microscopy technique favours ease of use, label-free experimentation and the acquisition of large field of view 3D + time datasets. To our knowledge, our technique is the only one able to reconstruct large volumes of 3D cell cultures (~5.6 mm 3 ) by phase contrast imaging.