Wave front engineering for microscopy of living cells.

A new method to perform simultaneously three dimensional optical sectioning and optical manipulation is presented. The system combines a multi trap optical tweezers with a video microscope to enable axial scanning of living cells while maintaining the trapping configuration at a fixed position. This is achieved compensating the axial movement of the objective by shaping the wave front of the trapping beam with properly diffractive optical elements displayed on a computer controlled spatial light modulator. Our method has been validated in three different experimental configurations. In the first, we decouple the position of a trapping plane from the axial movements of the objective and perform optical sectioning of a circle of beads kept on a fixed plane. In a second experiment, we extend the method to living cell microscopy by showing that mechanical constraints can be applied on the dorsal surface of a cell whilst performing its fluorescence optical sectioning. In the third experiment, we trapped beads in a three dimensional geometry and perform, always through the same objective, an axial scan of the volume delimited by the beads.


INTRODUCTION
In recent years, the advance in imaging methods has become apparent in biology, due to the tremendous progress in fluorescence tagging techniques and nano-metric probes. Nowadays, high-spatial and temporal resolution techniques as confocal [1], two-photon [2] total internal reflection microscopy (TIRF) [3] or fluorescence lifetime imaging microscopy [4,5] permit to look at subcellular details and macromolecular organization with sub-micrometer resolution.
The possibility to optically explore the complex mechanisms which regulate cell function in living cells on a nanoscopic scale has generated, in parallel, the need for the development of manipulation techniques with a comparable resolution.
Optical tweezers (OT) enable an all-optical manipulation of matter with micrometer precision, piconewton control of the applied forces and, at present, is one of the most promising manipulation technique operating with minimal invasion in biology [6]. It permits manipulation of micrometric and submicrometric biological samples as viruses, bacteria, DNA and living cells [7][8][9][10]. The movement and force of motor proteins can be measured by attaching micron-sized beads to single motor proteins [11,12]. Cellular force transduction [13][14][15][16][17] or membrane elasticity [18] can be measured by inducing controlled localized forces or tensions via the attachment of beads on cell membranes.
The successive introduction of multi trap [19] optical tweezers has extended these manipulations to different objects simultaneously and recently it has been used to demonstrate multi force optical tweezers [20] where the force of each trap can be adjusted individually .
Furthermore, the recent advent of spatial light modulators, has permitted to evolve from the 'conventional' optical tweezers systems towards the so called dynamical holographic optical tweezers. Here, thanks to the wave-front engineering of the trapping beam, it is possible to generate multiple traps in three dimensional (3D) geometries and to dynamically reconfigure them [21][22][23][24]. Moreover the intensity profile of each spot can individually be modified allowing for complex arrangement of traps based on different modes. For example, the trapping beam can be shaped to generate optical vortices [25,26] which carry orbital angular momentum that can be transferred to the trapped objects. Optical vortices have been demonstrated to be useful to trap reflecting-, absorbing-or low-index-particles and to rotate microscopic objects thus opening new prospectives otherwise not possible with a conventional OT system. A further advance in the development of optical techniques for biological research is represented now by the combination of the progresses made in high temporal-and spatialresolution imaging with those attained in optical manipulation.
Up to date, in most of the OT microscopes a wide field epi-fluorescence scheme is used.
Very recently, to improve the optical resolution, new imaging solutions start to be exploited as presented in Ref. [27]. In this paper the authors measured the mechanical transitions corresponding to single DNA hybrid ruptures by combining TIRF and OT. They simultaneously achieved, in the near-field volume, pN force measurements and single molecule fluorescence detection.
To further exploit the potentiality of an OT system with a high resolution imaging set up, a possibility is to incorporate into the OT microscope a 3D scanning optical technique. However, this combination presents technical challenges when the trapping and imaging beams are combined by the same objective lens. One problem encountered in this configuration is that the axial movement of the microscope objective inevitably displaces the trapping plane of the same amount.
Alternatively, two objective lenses head-on with completely dissociated beam steering optics can be used. This configuration is however incompatible with the possibility to perform differential interference contrast (DIC). Moreover, to optimize both the quality of the optical traps and the optical resolution of the imaging system, oil or water immersion objectives with a high numerical aperture (≥ 1.2) and therefore a short working distance are largely preferred. Therefore, this configuration limits the sample thickness and the possibility to mount on the upper part of the microscope additional tools as micromanipulators or microinjectors, and definitively hamper an easy switch from fluorescence to transmission measurements.
Very recently, M. Goksör and colleagues [28] have combined a trapping-and a multiphoton-beam using a single objective. An external lens has been translated to control the divergence of the trapping laser and optical sectioning has been achieved by moving the trapped object through the image plane. However, this solution is inappropriate for imaging planes axially distinguished from the trapping plane.
One solution to this problem has been presented in Ref. [29], where a confocal and an OT microscope have been combined by coupling the trapping beam into an optical fiber mounted on a translation stage. In this way, the objective displacements have been compensated with a synchronized reverse motion of the trapping plane. However, the system is limited to a single optical trap.
To overcome these limits, in this paper we present an alternative method which consists in shaping the trapping beam via digital addressing a Liquid Crystal Spatial Light Modulator (LC-SLM). The wave front of the trapping beam is modified to compensate the movement of the objective by projecting on the LC-SLM fast moving correctional diffractive optical elements (DOEs). As a result, we can keep the optical traps at a fixed position whilst the objective is moved. The advantage of the proposed technique is that we can fully exploit the benefits of using a holographic optical tweezers system, such as the possibility to generate and move multiple traps, eventually organized in 3D geometries and/or in different modes, in combination with those of a 3D optical scanning technique.
The capability of our system is demonstrated in three different experiments. In a first one, we show that we can decouple the position of a trapping plane from the axial movements of the objective by performing optical sectioning of a circle of trapped beads. In a second experiment, we use a similar scheme to apply mechanical constraints on the dorsal surface of a cell whilst performing 3D optical sectioning of the cell. To this end, the nucleus of HeLa cells have been fluorescently labeled with H2B-GFP and a circular array of micro beads is attached on the dorsal surface of the cell and kept at a fixed position during the fluorescence and transmission sectioning. Finally, we extend our method to a 3D beads volume. Silica beads are organized in a 3D geometry and we show that we can simultaneously control the position of different planes while performing axial optical sectioning.

Microscope design
The microscope is based on a standard inverted microscope (Zeiss AxioVert 135) with differential interference contrast (DIC), and epi-fluorescence. The attenuated and expanded (3X) 1064-nm beam of a 10W single-mode CW fiber laser (IPG Photonics YLM-10) is directed onto the LC-SLM, reflected into the side port of the microscope and directed with an IR dichroic mirror to the focusing objective (100x NA-1.3 oil). To allow simultaneous recording of fluorescence and DIC while using the optical traps, the dichroic is positioned above the fluorescence filter block. In this way, the excitation light from a Mercury lamp mounted on the rear port of the microscope is focused into the sample by the same objective used for trapping. Fluorescence from the sample is sent to a high sensitive CCD camera (Cool Snap HQ, Roper) placed at the exit port of the microscope. To obtain DIC images, a polarizer is inserted below the fluorescence block filter and crossed with the DIC analyzer positioned above the microscope condenser.
In order to perform 3D optical sectioning, the objective is mounted on a nanofocusing positioner (PI Instruments, PIFOC 721.10). To improve the resolution, the collected images A spherical wave approach [24,30] is used to calculate phase DOEs which are displayed on the SLM to transform the incoming laser beam into a distribution of laser spots, each with individually specified characteristics and arranged in an arbitrary desired geometrical configurations.
A schematic of the optical set up is presented in Figure 1 Once the two fixed parameters d and f MO are known, Equation 1 permits to derive for each position of the trapping plane, z, the focal length, f SLM . As explained in Methods, we derived the values for d, and f MO by fitting the calibration curve shown in Figure 1(b).
The generation and manipulation of spots in 3D volumes may require to collect images from optical planes different from the objective's focal plane. Therefore we have modified the optical path from the sample to the imaging camera (green lines) by adding a 1:1 telescope (T) in front of the CCD, as shown in Figure 1(a). The telescope, T, and the CCD are mounted on a translation stage that allows us to adjust the position z 1 of the imaging plane by a rigid translation, D, of the telescope T and the CCD (see Methods).
The efficacy of this imaging approach is demonstrated in Figure 1 Figure 4 (a)). The cell nucleus is crossed by the imaging plane towards the end of the scan, as it appear from the fluorescence sequence shown in Figure 4 (b).
Finally, we performed an optical sectioning of beads trapped in the 3D geometry of Figure 1(c). In this case, we wanted to keep constant during the axial scan the position and the 3D shape of the structure. Therefore the movement of the objective has been compensated by calculating, for each step, the DOEs necessary to simultaneously move backwards the three planes of the 3D array of beads. Figure 5 To illustrate the potentiality of our method, we have performed three experiments. In the first, we have shown that we can move the imaging plane in respect to the trapping plane by performing a 3D optical sectioning of a circle of micrometric beads kept by the laser. This approach is very useful for high resolution optical sectioning of motile biological samples such as bacteria, non adherent cells, spermatozoa etc. In this case one can hold the sample with the trapping beam and simultaneously perform the 3D optical sectioning of the trapped object. Moreover, the possibility to generate multi traps allows one to manipulate many samples at the same time and to control their relative position. Consequently one can use this manipulation to study the mutual spatial influence between interacting cells during their optical sectioning. Finally, by modifying the mode of the optical traps one can imagine to extend this technique for optical sectioning of absorbing-, reflecting-or low index-samples.
In the last decade, several experiments have shown that cells can sense mechanical forces coming from their environment. Such mechanotransduction occurs primarily at adhesive contacts where membrane receptors make a physical-chemical link between the extracellular matrix and the cytoskeleton. To dissect these processes, a typical experiment consists in using OT to place microspheres coated with specific extracellular ligands on the dorsal surface of cells and probe the resistance of the receptor-cytoskeleton connection e.g by monitoring the recruitment or activation of specific proteins. [13][14][15][16][17] In the second experiment of this paper, we have shown that we can control the position of a circle of beads on a cell cortex whilst performing optical sectioning through the cell. We can therefore add to previous experimental schemes the possibility to monitor cell reaction to external mechanical constrains on planes different from the plane where the constraints are applied. Consequently one can reconstruct 3D map of cellular mechanotransduction and follow how the effects of mechanical constraints propagate in the cell.
Finally, in the last experiment we have shown that we can control and fix the position of optical traps located on different axial planes while simultaneously performing a 3D optical sectioning of the volume delimited by the planes. With this experimental scheme we can imagine to extend the previous experiment to the case where mechanical constraints are distributed in 3D patterns. As already shown, the rapid refreshing rate of the SLM enables to dynamically adapt the distribution of the optical traps to the cell shape and to hold a 3D volumes of beads on cell cortexes [32]. The combination of a holographic microscope and a 3D optical sectioning technique will allows us to complete this kind of manipulation with the possibility to monitor the effect of a 3D pattern of forces on cellular force mechanotransduction.
As a final remark, we note that a similar approach is not limited to decouple an imaging and a trapping beam, but one can imagine to extend the same method to decouple an imaging path from any perturbation beam e.g a photoactivating-, uncaging-or scissor-laser.

Imaging path
In the presented microscope, it is crucial to have the possibility to focus objects located on plane axially distinguished from the objective's focal plane. To this end, the microscope needed an adaptation of the optical path from the sample to the imaging CCD, as is schematized in Figure 1(a). In a standard microscope, the CCD detection plane would be positioned at the exit port of the microscope, i.e at the optical plane F T L conjugated with the objective focal plane F MO . The image of a sample-object kept at a distance z 1 from F MO would form on an optical plane, F T , shifted by D=M 2 z 1 (M is the magnification of the microscope objective) in respect to the plane F T L , therefore inside the microscope. In our configuration, we transfer the image out of the microscope by using an external telescope T inserted between the exit port of the microscope and the CCD. The telescope is positioned with its first focal plane in coincidence with the position of F T , and its second focal plane in coincidence with the CCD detection plane. The telescope and the CCD are mounted on a translation stage that allows us to select different imaging planes by a rigid adjustment, D=M 2 z, of the component (T+CCD), D=0 being the position in which the first focal plane of the telescope coincides with F T L .

Trapping beam path
As illustrated in Figure 1(a), the SLM is represented by a reflective thin lens and the microscope objective, MO, by its principal planes. The laser beam is reflected and modulated by the SLM in an array of spot focused on the plane F SLM . This plane is imaged by the microscope objective at a distance z from its focal plane F MO . By applying the conjugation equation written in focal coordinates for the MO, we have: where:  Applications" (n. RBAU0157P2).