Single-Cell Optical Distortion Correction and Label-Free 3D Cell

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

pubs.acs.org/NanoLett

Single-Cell Optical Distortion Correction and Label-Free 3D Cell Shape Reconstruction on Lattices of Nanostructures Jürgen Stephan,† Felix Keber,‡ Valentin Stierle,† Joachim O. Rad̈ ler,† and Philipp Paulitschke*,† †

Faculty of Physics and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539 München, Germany ‡ Physics Department, Technische Universität München, 85748 Garching, Germany S Supporting Information *

ABSTRACT: Imaging techniques can be compromised by aberrations. Especially when imaging through biological specimens, sample-induced distortions can limit localization accuracy. In particular, this phenomenon affects localization microscopy, traction force measurements, and singleparticle tracking, which offer high-resolution insights into biological tissue. Here we present a method for quantifying and correcting the optical distortions induced by single, adherent, living cells. The technique uses periodically patterned gold nanostructures as a reference framework to quantify optically induced displacements with micrometer-scale sampling density and an accuracy of a few nanometers. The 3D cell shape and a simplified geometrical optics approach are then utilized to remap the microscope image. Our experiments reveal displacements of up to several hundred nanometers, and in corrected images these distortions are reduced by a factor of 3. Conversely, the relationship between cell shape and distortion provides a novel method of 3D cell shape reconstruction from a single image, enabling label-free 3D cell analysis. KEYWORDS: Single cell imaging, optical distortions, microstructures, three dimensional cell shape, surface reconstruction, localization accuracy

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techniques, where localization with nanometer accuracy through the curved surface of single cells is often needed. Traction-force microscopy19−24 is a commonly used highresolution localization technique, which allows cell forces to be quantified down to the piconewton regime. In general, these forces are calculated from mechanical displacements of defined springs, such as nanowires, pillars, or beads in gel. For thick transparent25,26 or nontransparent samples,27,28 imaging through the cell is typically unavoidable. In these cases the accuracy of force calculation may be impaired, since the optical distortions in the measurement can superimpose the mechanical displacements. In fluorescence localization microscopy and single-particle tracking,2,6,29,30 the imaging is also often done through or into living cells, and localization accuracies in the nanometer range are required. These accuracies can again be limited by optical refraction at the specimen. However, until now optical distortions induced by single cells have not been investigated. Here we present a method for quantifying and correcting optical distortions induced by living single cells growing on a substrate. To this end, a precise lattice of periodically patterned gold nanostructures is utilized as the substrate. With the help of

n the recent past, live-cell imaging techniques such as structured illumination, total internal reflection and light sheet fluorescence microscopy have achieved unprecedented resolution beyond the diffraction limit, yielding insights into intracellular processes at the nanometer scale.1−6 Such techniques rely on precise and accurate localization of single molecules,7 but can be limited by aberrations that arise in the image as a result of light refraction at the boundaries between layers with different refractive indices (RI) within the sample.8−10 Aberrations affect images primarily in two ways. First, deteriorations in the point spread function reduce contrast and resolution throughout the image and thus lower the overall image quality.8,10−13 Second, optical displacements in the image, also known as distortions, constrain the localization accuracy.14 The latter are caused by RI mismatches in the imaging system8,11 and RI inhomogeneities within the sample itself,13,14 which deflect the optical light path, e.g., when imaging through thick tissue. Up to now, the main focus of research has been to improve image quality, and this goal has been achieved with adaptive optics for a variety of thick-tissue microscopy applications.15−18 For thin tissue, such as single cells, aberrations are generally considered to be insignificant for image quality9 and image distortions due to optical deflection are assumed to be small.14 However, this assumption needs critical scrutiny in the context of high-resolution localization © XXXX American Chemical Society

Received: November 2, 2017 Revised: November 21, 2017

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DOI: 10.1021/acs.nanolett.7b04651 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. (a) Schematic diagram of the experimental setup. Bright-field illumination (blue) is used for cell imaging, while epi-illumination (red) is essential for nanostructure localization. (b) Colored scanning electron micrograph of an A549 cell (green) on a surface periodically patterned with gold nanostructures (yellow). Scale bar: 5 μm. (c) Schematic illustration of the optical refraction caused by an adherent cell. The apparent optical displacement D of a structure underneath the cell, caused by refraction, is shown by the path of the refracted ray (red arrow) and the reference ray without a cell (black dotted arrow).

With this experimental setup, the images of several thousand gold nanostructures in the field of view (66 μm × 89 μm) and up to several hundred structures per cell are recorded and serve as reference points for the localization. Figure 2a shows a

a high-resolution localization microscopy setup, the local cellinduced distortion can be quantified with reference to the fixed underlying lattice. Even for single cells, we find lateral distortions of up to 400 nm. These can severely limit the localization accuracy, and cannot be neglected in highresolution techniques. To overcome this limitation, we propose a novel correction scheme for image distortion, which employs a simplified geometrical optics approach based on the 3D shape of the cell, and enables distortions to be reduced by a factor of 3. Conversely, this approach allows one to reconstruct the 3D morphology of cells from the distortions of the nanostructures. This strategy provides a unique label-free method for 3D cell shape determination, starting from a single two-dimensional (2D) image. To quantify the distortion field (i.e., the spatially resolved distribution of optical distortions) associated with the imaging of single living cells, we use a high-precision and spatially dense lattice as a reference framework.31−33 Such a lattice consists of periodically patterned gold nanostructures imprinted on glass (fused silica) substrates via electron-beam lithography (Supporting Information S1). The circular gold structures have a radius of 225 (or 375) nm, a height of 60 nm and a periodicity of 1.2 (or 2.0) μm and thus are not deformable by cellular forces. Biocompatibility tests of the structured substrates compared to standard cell dishes reveal no changes in cell adhesion, migration, or proliferation. In this work, two human epithelial cell lines (A549 and HuH7) were used. Cells are seeded on the structured glass slides in Leibovitz L-15 medium (Gibco) supplemented with 10% fetal calf serum. The optical microscopy setup is shown in Figure 1a. A Ti-E Eclipse inverted microscope (Nikon Instruments), employed for bright-field and epi-illumination, is equipped with a 100× oil immersion objective (numerical aperture (NA) 1.4) that, in epi-illumination, also functions as a condenser with matching NA. The epi-illumination setup is modified from a fluorescence setup by removing the excitation filter to permit reflection measurements. A SOLA lamp (Lumencore) and an optical filter with a bandpass wavelength centered at 628 nm and a bandwidth of 40 nm is used. The images are acquired with a Clara-E CCD camera (Andor). Samples growing in a Petri dish (ibidi) are mounted upside down on the inverted microscope, thus imaging the gold structures through the cell. Figure 1b shows a scanning electron micrograph of a typical adherent cell with typical widths of 20− 50 μm (heights 5−15 μm) on a periodically patterned, gold nanostructured surface.

Figure 2. (a) Bright-field image of a single adherent A549 cell on a nanostructured substrate. The cell outline is highlighted in green. The lower inset shows the intensity profile of the cross-section corresponding to the red line, while the upper inset shows a closeup. (b) Reflection image of the same sample as in panel a. (c) Vector plot of the distortion field. The vectors point from the original to the displaced positions of the gold nanostructures in the images. The upper inset shows a 2-fold enlargement, the bottom inset shows the scaling vectors. Scale bars: 10 μm.

bright-field image of an adherent A549 cell. This allows for localization of the cell, but is not suited for a comprehensive localization of the gold structures due to the similarity in gray scale intensities between the cell and the structures. This becomes particularly obvious in the close-up and in the plotted intensity profile (e.g., at 5−10 μm) in Figure 2a. However, the gold structures can be localized either by fluorescence labeling or by measuring in reflection mode (epi-illumination), which permits clear differentiation between the gray scale intensities associated with intracellular structures and the underlying nanostructures. In this work, we chose reflection measurements (see Figure 1a), since no additional labeling is needed and the bleaching of fluorophores (which would otherwise limit the observation time) is avoided. A typical reflection image is shown in Figure 2b, where localization of gold structures is achieved even inside the area occupied by the cell (highlighted in the close-up and the intensity profile). To precisely localize the gold structures, rapidSTORM34 is used to automatically fit B


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Figure 3. Correction method and quality of correction. (a) Derivation of cell heights from confocal fluorescence measurement. Scale bar: 10 nm. (b) Cell shape fitted to confocal data (yellow-green with same scale bar as in a) and corresponding translation grid for the remapping (purple). (c) Distortion field (dc) of the corrected image. The top inset shows a 2-fold enlargement, while the bottom inset shows the scaling vectors. (d) Absolute distortion distribution in the original (dm) and the corrected (dc) image. The inset shows a cartoon schematically depicting structure distortions before and after correction. (e) Absolute change in distortion following the correction. We define under-corrected areas as areas where the vectors point in the same direction (|φ| < π/2) before and after correction, and overcorrected areas as areas where they point in opposite directions (|φ| > π/ 2). Blue colors denote under-corrected distortions, while purple colors denote overcorrected distortions.

fluorescence localization and single-particle tracing.29 Our data shows that, due to cell-induced distortions, errors in the relative distance between two nanostructures of up to 13% occur (Supporting Information S4). To summarize, the measured optical displacements show that distortions reduce the accuracy of localization and distance determination, and cannot be considered negligible when imaging through a single cell. To improve distortion-limited accuracies in quantitative localization techniques, we correct the microscope image by performing pixel-wise remapping based on the inverted distortion vector at each pixel. The inverted distortion vector is derived by applying a simplified geometrical optics approach that allows one to link the 3D cell shape and the distortions without the need for a reference framework. The 3D cell shape is accessible by a variety of optical microscopy techniques. Here, we measure it by confocal fluorescence microscopy (see Figure 3a and Supporting Information S5). In the geometrical optics approach, the optical rays that are refracted at the cell boundaries are traced. With the help of two approximations, a differential equation that links the distortions to the 3D cell shape can be formulated: First, since the differences in RI within cells are in general smaller than the RI difference between the cell and the surrounding medium, we approximate the cell as a compartment with a constant RI. Specific considerations on typical RI variations inside a cell are provided in the Supporting Information S6a. The second approximation is that the distortion vector d⃗(x,y) at a certain image position (pixel) is equal to the displacement D⃗ (x,y) of a single specific ray that exits the cell parallel to the optical axis at that position (Supporting Information S6b). This is schematically depicted in Figure 1c, where the rays in the presence (red arrow) or absence (black dotted arrow) of a cell are displaced by a distance D due to Snell’s law.36 The differential equation for dx(x,y) is then given by eq 1. For simplicity we only display the x-component of the distortion vector (for the derivation and the full equation, see Supporting Information S7):

a 2D normal distribution to every single nanostructure and record the center of fit with subpixel accuracy. We determine the optical displacement vector by calculating the difference between the original and the optically displaced image position of each structure in Mathematica. The original position can be obtained from a calculated or an experimental reference framework without any cell. The calculated reference framework is computed based on the periodicity of the fabricated lattice. This procedure yields an average optical displacement detection accuracy down to 11 nm (Supporting Information S2), which is mainly attributable to the precision (typically about 10 nm) attainable with e-beam lithography.35 With an experimental characterization of the reference framework, it is possible to further improve the mean accuracy of optical displacement detection. For this, the exact same gold-structures are imaged in the absence of cells to yield the unbiased positions of the gold structures. Average accuracies of the optical displacement detection down to 1.1 nm are achieved by this means (Supporting Information S2). Figure 2c shows the resulting optical displacement field (= distortion field) induced by a single cell. Absolute values of the measured optical displacement vectors ⎯→ dm range from a few nanometers to a maximum distortion of 240 nm, with an average of the absolute values of the distortions of 85 nm inside the area covered by the cell (Figure 3d). Additional time-lapse measurements of the distortion fields induced by Huh7 cells show even higher optical displacements of up to 400 nm (Figure 5). These distortions are independent from the mode of illumination (trans- or epi-illumination) as they occur due to a change of the imaging light path after the gold structures, which is the same in brightfield-, reflection-, and fluorescence-measurements (Supporting Information S3). To put these results into perspective, the distortions (optical displacements) are compared to observed pillar and nanowire displacements in state-of-the-art traction-force microscopy setups that also image through single cells. Typical reported displacements range from a few 10 nm up to 1 μm,25,27 and are thus in the same order of magnitude as the cell-induced distortions reported here. Distortions can also affect distance measurements between two different read-out points, e.g., in C


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Figure 4. Validation of the 3D reconstruction method. (a) Reconstructed shape of the cell depicted in Figure 2a. (b) Micrographs of the labeled cell at different cross-sectional levels (c1−c3). The red lines correspond to the reconstructed height, while white areas show high fluorescence intensity in the confocal measurement.

⎛ ⎛ ⎛ ⎛ ⎛ dh(x , y) ⎞⎞ n ⎞ dx(x , y) = ⎜⎜tan⎜⎜ −sin−1⎜⎜sin⎜tan−1⎜ ⎟⎟ × 1 ⎟⎟ ⎝ d x ⎠⎠ n 2 ⎠ ⎝ ⎝ ⎝ ⎝ ⎛ dh(x , y) ⎞⎞⎞ + tan ⎜ ⎟⎟⎟ × h(x , y) ⎝ dx ⎠⎟⎠⎟⎠

the cell, where the greatest distortions occur, and these areas tend to be slightly under-corrected. Note that there are no distinctly visible correction errors induced in the cell center, were the nucleus is located, which confirms the constant RI approximation. No free fitting parameters are used, as the correction solely relies on eq 1, the confocal data, and literature values. The correction approach dispenses with the use of a reference framework. It therefore enables distortion correction for techniques that cannot practically implement a reference framework, like traction-force microscopy, but also for fluorescence methods that image at various planes inside the cell. The correction by a factor of 3 also improves the localization accuracy in these techniques by the same amount. This improvement is comparable in magnitude to image quality improvements due to adaptive optics in thick tissue imaging16 and does not require extensive computing. One further advantage of the derived relation is that eq 1 and the measured distortion field can also be used for fast 3D cell shape reconstruction without the need for labeling. For the 3D reconstruction, the initial value problem (eq 1) needs to be solved for the cell height h(x,y) for the measured distortion field. The mathematical procedure is provided in Supporting Information S9. Figure 4a depicts the 3D reconstruction from the distortion data for the cell shown in Figure 2. Figure 4b shows a comparison of the reconstructed (red) and confocal (white) cell shapes in three equidistant cell cross sections (c1− c3). The reconstructed cell heights overlap well with the outlines of the raw confocal data. The two methods exhibit a close shape and volume resemblance (Supporting Information S10), showing only a 3% volume difference. The quality of agreement is particularly striking, given that no free fitting parameters are used for the 3D reconstruction and only a single 2D image is required. Since the proposed 3D cell shape reconstruction is label-free and relies only on a single shot 2D image, it offers the advantage of low system requirements in comparison to confocal microscopy. Furthermore, the cell function is not impaired by markers39 and the method thus provides a tool for cell volume studies40−43 on long time scales, since it is not limited by, e.g., bleaching of fluorophores or long exposure times. Supplementary Video V1 is computed from a measured time-lapse series of the cell-induced distortion field over a period of 4.5 h with 8.000 frames. Figure 5a shows three representative frames of the distortion field induced by three cells at the beginning of this time-lapse series. Due to the high

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(1)

Here n1 and n2 are the RIs of the surrounding medium and the cell, respectively, which are taken from established literature (surrounding medium: n1 = 1.3437 and A459 cell: n2 = 1.3638). Furthermore, h(x,y) is the cell height at the point of refraction and dh(x,y)/dx denotes the tangent of the angle α at that point, whereas α is the angle between the surface normal and the incident light ray. These parameters are obtained by fitting a 2D polynomial to the confocal data (Figure 3b). To correct image distortions, each image pixel is translated in accordance with the inverted distortion vector −d ⃗ (x,y) at that pixel (purple translation grid in Figure 3b). The translation operation is done using the remap function in the OpenCV library, and results in the corrected image (see Supporting Information S8). To quantify the quality of the correction, the corrected image is analyzed with the same reference framework as the original image. This is depicted in Figure 3c. Compared ⎯→ to the measured displacement vectors dm in the original image → ⎯ (see Figure 2c), the corrected displacement vectors dc in the corrected image are distinctly reduced in the area occupied by the cell. The reduction is depicted quantitatively in the optical displacement distribution in Figure 3d. The effective mean distortion induced by the cell, as well as the width of the distortion distribution, is reduced by as much as a factor of 3, from 85 nm to 27 nm and from 52 nm to 17 nm, respectively. To evaluate the correction for systematic errors the angle φ between the corrected and measured distortion vectors (Inset Figure 3d) is analyzed. We define the distortion at a structure as → ⎯ being under-corrected if the vector dc points in same direction ⎯→ as dm (|φ| < π/2) and overcorrected if it is pointing in the opposite direction (|φ| > π/2)). In Figure 3e the absolute change in vector length through the correction dφ = ⎯→ → ⎯ || dm| − | dc|| is depicted for each structure, using a separate color scale for under-corrected (blue) and overcorrected (purple) structures (for details, see Supporting Information S8). The largest corrections are achieved at the border region of D


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Figure 5. Time series of the distortion field induced by HuH7 cells on a lattice of gold nanostructures. The structure periodicity is 2 μm and the interval between frames is 30 min. (a) Vector plots of the optical nanostructure displacements. The vector lengths are enhanced relative to the spatial distance. A scale vector is plotted at the top right. (b) High-contrast plots shown in panel a with absolute vector lengths as color scale. Scale bars are 10 μm. (c) Reconstructed 3D time-lapse frames from the distortion data in panel a.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +49 89 2180 5793. ORCID

Jürgen Stephan: 0000-0002-1774-9603 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the Federal Ministry of Education and Research of Germany (BMBF) as part of the project “Validation of the Technological Innovation Potential of Scientific Research − VIP”.

signal-to-noise ratio between the cell and the background, the distortion measurement also enables a high-contrast 2D visualization of the cells by using a color scale for the absolute vector lengths (Figure 5b). In the Supporting Video V1 and Figure 5c, the cells are reconstructed in 3D, and typical changes of the cell contour during cell migration, such as leading-edge lamellipodia and cell contraction at the trailing edge,44 as well as cell division, are observed. In conclusion, we have precisely quantified the optical distortion field induced by single adherent cells with nanometer scale accuracy. In contrast to common assumptions, we find distortions of up to 400 nm, which thus significantly impair the accuracy of localization techniques. The correction method presented here offers an easily implemented way to reduce these distortions in single-cell images by a factor of 3, and hence improve localization accuracy in traction-force and fluorescence localization microscopy. We further described how the method can be used to reconstruct 3D cell shape from the distortion data, allowing quantitative 3D shape information to be acquired from a single 2D image. This in turn provides a fast, label-free method that can record the 3D cell shape and volume over time and is capable of resolving rapid changes, which could be used to study the 3D cell shape in response to substrate stiffness (e.g., on elastic hydrogels). Together, these findings highlight the potential that lies in utilizing distortions, which can be advanced in resolution and accuracy by employing densely spaced point emitters, e.g., through single-molecule nanopatterning.45 This would open up the possibility for, e.g., label-free, high-resolution, cell morphology or surface roughness measurements or investigation of smaller prokaryotic cells. Reconstruction and distortion quantification applications are furthermore not limited to single cells but can also be envisioned in the broader context of reconstruction and characterization of transparent 3D objects like microlenses or 3D gels.

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S1: sample fabrication; S2: accuracy assessment; S3: illumination independence; S4: relative distance error assessment; S5: 3D cell shape with confocal microscopy; S6: distortion correction approach; S7: equation derivation; S8: remapping, corrected image, and correction analysis; S9: 3D reconstruction process; S10: comparison of reconstruction and confocal data (PDF) Video V1: time-lapse 3D cell reconstruction (AVI)

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04651. E


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Single-Cell Optical Distortion Correction and Label-Free 3D Cell

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