Two- and three-dimensional de-drifting algorithms for fiducially marked image stacks
Introduction
Traction force microscopy (TFM) is well accepted as a tool for uncovering connections between cellular force generation and cell-cell interactions, biochemical processes of locomotion, and cell adhesion and migration (Abu Shah and Keren, 2013, Abuhattum and Weihs, 2016, Roy et al., 2002). The gels used in TFM are typically elastic or viscoelastic, synthetic or biopolymer, two-dimensional (2D) substrates on which cells adhere, grow, differentiate and migrate (Abuhattum et al., 2015, Butler et al., 2002, Discher et al., 2005, Plotnikov et al., 2014, Teo et al., 2015). For example, TFM has revealed that cells with higher metastatic potential apply ‘stronger’ adhesive (lateral) forces that evolve over time (Kraning-Rush et al., 2012, Massalha and Weihs, 2017). However, metastatic invasion occurs in a three-dimensional (3D) microenvironment. Thus, it is important to evaluate the 3D tractions that cells apply to their 2D or 3D microenvironments (Jorge-Peñas et al., 2017, Kaytanlı et al., 2020, Koch et al., 2012, Legant et al., 2010, Maskarinec et al., 2009). Aptly, we have observed that highly metastatic cells can rapidly deform initially flat gels in 3D (Dvir et al., 2015, Kristal-Muscal et al., 2013, Merkher and Weihs, 2017). This combination of two- and three-dimensional (2D/3D) forces results from the cells’ invasive capacity and can provide an indication to their in vitro (Alvarez-Elizondo and Weihs, 2017) and in vivo metastatic risk (Merkher et al., 2020). Notably, evaluation of the cell-induced 3D tractions requires a different algorithmic approach (Koch et al., 2012, Mierke et al., 2008).
The time-evolution of tractions in 3D systems is typically evaluated with time-lapse imaging of several fields of view (FOV). Potential long-time drift at a specific location may be minimized by equilibrating the microscope elements prior to imaging. Upon return to a location, a uniform, apparent 2D/3D shift of the imaged region and objects therein may be observed, which is termed drift. Drift can occur from small inaccuracies in motion of automated/manual mechanical controls. For example, microscope stages used to move laterally between FOVs are typically accurate to about ±1 μm upon return; objective lens (e.g. in confocal system) are moved vertically in each FOVs and accuracy on return is on a similar scale, being up to ±5 μm. That drift affects the accuracy of return to a location, yet does not affect the quality of the acquired images; this differs from drift occurring during image acquisition, e.g. due to unstable electrical, thermal, or vibrational effects that are typically prevented by appropriate insulation. The resulting shift in location upon return, the drift, must be removed prior to any quantitative, comparative analysis of images at a single FOV, e.g. between different time points. If drift is not removed an artefactual displacement of the particle locations will be detected that may be incorrectly attributed to cell-applied forces.
To date, several methods for correcting drift have been published in the context of 2D/3D traction microscopy. Methods typically utilize cross-correlations between pair of 2D images, e.g. with a fast Fourier transform (Plotnikov et al., 2014) or particle image velocimetry (Soine et al., 2015). Ensembles of 3D bead trajectories in a silicone gel have been corrected in all three directions using a reference bead far from any cell effects (Colin-York et al., 2019); that approach requires immobility of the reference bead, or at least its placement on glass (on a different focal plane) or within an unchanging (e.g. synthetic, non-degradable) gel. In 2D traction force microscopy, which typically uses synthetic, non-degradable polyacrylamide (PAM) or polydimethylsiloxane silicone (PDMS) gels, lateral drift is typically removed by cross-correlating images of beads immobilized on the glass substrate underlying the gels (Massalha and Weihs, 2017, Style et al., 2014, Teo et al., 2015); the determined drift is subtracted from the imaged beads at the top layer of the gel, where cells are seeded. This has been translated into 3D, for example, by focusing separately on each 2D slice within a 3D stack of a synthetic, unchanging PDMS gel (Soiné et al., 2016). A different approach may be required for the z-drift removal, however, especially if the substrate structure may change over time, for example due to cell degradation, e.g. in collagen gels, or swelling that may change the absolute location of a gel layer of interest. A rigid registration method has also been proposed for removing z-drift, using unique fiber-structures of a collagen gel observed by confocal reflectance (Steinwachs et al., 2015). We propose a different approach to remove the vertical z-drift of images, based on the distribution of particles in the entire imaged stack; this can account for changes in the gel structure and does not necessitate immobile beads at a distant location.
Here, we have developed a de-drifting algorithm to remove the vertical and lateral drifts from 3D image stacks. Our vertical and lateral de-drifting algorithms may be applied together or independently; confocal time-series images typically require 3D de-drifting. We develop the de-drifting algorithms using experimentally obtained 3D confocal image stacks of cells seeded on 3D collagen gels with embedded fluorescent beads as fiducial markers. We then demonstrate the application and necessity of the de-drifting algorithms on simulated image stacks and experimental microscopy images.
Section snippets
Cell culture and imaging
Cells from a metastatic breast cancer cell line, MDA-MB-231 (ATCC, Manassas, VA), were cultured in Dulbecco’s modified Eagle’s medium (DMEM, Life Technologies, Carlsbad, CA) supplemented with 10% FBS (Thermo Scientific, Waltham, MA), and 1% each penicillin streptomycin and L-Glutamine (Biological Industries, Israel). Cross-linked collagen gels were prepared by mixing equal amounts of Type I rat tail collagen (Merck-Millipore, USA) and Bovine dermis collagen (Matrix Bioscience, Germany) in
Results
To test the de-drifting algorithm, we generated image stacks of grid-ordered dots, to simulate fluorescent beads in a gel, with an identifiable pattern for template matching (see Figure S1). Then we added drift to one stack and compared to an unmodified stack (Fig. 2A), to e.g. match comparison of two time-points. Drift was added above and below the length-scale of the inter-bead distance (4 pixels), i.e. 5 and 2 pixels. The de-drifting algorithm successfully corrected the drift, as
Discussion
We have presented a novel approach to remove vertical drift, followed by lateral de-drifting using cross-correlation. Drift has previously been shown to have deleterious effects on traction microscopy results (Style et al., 2014). As demonstrated in the current work, drift can produce stress patterns that may appear physical, leading to flawed analysis. Hence, removal of drift prior to further analysis, e.g. traction microscopy, is crucial.
The de-drifting algorithms presented here are
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors have no conflicts of interest to declare.
Acknowledgements
The work was partially supported by the Montreal Biomedical Research Fund. Confocal microscopy was performed at the facilities of the Lorry I. Lokey Interdisciplinary Center for Life Sciences and Engineering at the Technion-IIT and was partially supported by the Russel Berrie Nano Institute at the Technion-IIT.
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2021, Journal of BiomechanicsCitation Excerpt :We evaluated the time-evolution of strain energies applied by cancer cells adhering onto 1.8 kPa crosslinked collagen gels, as compared to simulations. To demonstrate that the volume-of-effect of single cells locally interacting with the gel should be detectable on the cells’ length-scale via 3D traction microscopy, we simulated spheroidal deformations with inverse-distance decay (Wiener et al., 2020) applied on initially evenly spaced markers (Fig. 1A), which induced symmetric displacements (Fig. 1B), and a spherical strain energy field centered around the deformation (Fig. 1C). The total SE increased with volume of integration until plateauing at the effective volume-of-effect of the perturbation (Fig. 1D); we identify linear segments in scatter-plotted data using our custom, automated tool (Umansky and Weihs, 2012).
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Current address: Faculty of Medicine, Technion-Israel Institute of Technology, Haifa 3525433, Israel.