Fig 1.
Registration of a signal of interest captured by a live cell movie using a co-imaged location fiducial.
a) Illustration of the cell registration pipeline. Top row: The pipeline establishes a frame-by-frame diffeomorphism between all images of a location fiducial time lapse sequence and a reference frame. Without loss of generality, all analyses in this paper rely on the center frame of the sequence as the reference frame. Bottom row: The diffeomorphic functions are applied to remapping a signal of interest from the original movie to a new movie with a rigid geometry defined by the location fiducial reference. The temporal dynamics of the signal of interest is conserved by the remapping process. b) Application of the pipeline to a cell undergoing symmetry breaking, i.e. it transforms from a round geometry to a geometry with front (F)-back (B) polarity (see annotation in the center frame of the remapped Actin signal). The data includes a Halo-CAAX and mNG-Actin time lapse sequence as a location fiducial and as the signal of interest, respectively. Colored points in the center frame of the remapped Actin signal indicate the three positions at which mNG-Actin time-series are sampled in d. c) Cell edge color-coded from blue (early time points) to red (late time points) in the geometry of the original movie (left) and in the geometry of the reference frame (right). With the exception of two regions with strong, intermittent ruffling activity (arrowheads), the registration produces a stationary cell edge. d) The registration of the time lapse image sequence in a spatially stationary reference frame permits straightforward sampling of time-series of the signal of interest. The traces indicate mNG-Actin signal fluctuations at stereotypical sites of interest: Red–retraction fibers, Blue–transverse arcs, Black–lamellipodia. All scale bars 10 μm.
Fig 2.
Computational elements for the remapping process.
a) Extraction of the mask gradient ∇fmask. Based on a cell mask, we calculate for each pixel the distance to the nearest cell boundary element for both the cell-interior and cell-exterior spaces. The gradient on this distance field defines ∇fmask. b) Diffeomorphism constraint. From left to right, illustrations of interpolation fields, where edges indicate the sampling position of an input image to remap onto a target. The mesh diagram shows displacements as deviation from a square mesh (1st diagram from left). A diffeomorphic transform (2nd diagram) is represented by a deformed mesh. A break in diffeomorphism (3rd diagram) is represented by crossings of mesh edges. By sorting the mesh coordinates in sequential order, breaks in diffeomorphism can be reverted (4th diagram). c) Effect of algorithm components on cell edge registration. Accuracy of registration over n iterations is indicated by the area of mismatch (green and purple) between the moving cell and the target cell image, normalized by the target cell perimeter. Removing the mask regularization and topological constraint enforcing diffeomorphism reduces both the rate of convergence and the final accuracy. The dashed line indicates the iteration stop for a visualization of the registration results (bottom row). The proposed algorithm gives a near pixel perfect registration of the two images. Removing the mask regularization largely reduces the rate of convergence. Removing both mask regularization and topological constraint causes failure in the capture of small protrusions.
Fig 3.
Impact of location fiducial on remapping accuracy.
a) Overlay of two frames separated by 8 minutes of the total Actin channel (top) and a high intensity component (defined by manually selected intensity cutoff) emphasizing Actin fibers (bottom). b) Qualitative comparison of the remapping quality for both Actin signals of interest using the lowpass-filtered Actin image (top row left), Profilin (top row middle), and Vasp as location fiducials. There were minimal differences in the registration quality in both the total Actin (middle row) and Actin fiber (bottom row) components of the Actin signal of interest. c) Definition of the half-distance transform used as a ground truth for performance evaluation. First, we estimate the diffeomorphic map between moving frame (t = 1) and target frame (t = 3). We then asked how well a half diffeomorphic map matches the middle frame (t = 2) under the expectation that the mapping between moving and target frames follows a linear deformation path. d) Quantification of subcellular remapping accuracy (sum of squared distance (SSD) between target and remapped images) using the to-target and half-distance transforms for indicated location fiducials. The SSD between untransformed moving and target frames is computed as a baseline. Box plots illustrate 25th, 50th, and 75th percentile of n = 116 moving/target frame pairs pooled from m = 4 movies. Whiskers indicate the 5th and 95th percentile. P-values are calculated by one-way ANOVA testing. Overall, there were only small differences in accuracy between the choices of location fiducials. e, f) Comparison of time-series sampling using a fixed grid of probing windows in the reference frame of a full cell registered movie vs. using edge-tracking probing windows. e) Snapshots of the actomyosin organization in a U2OS cell at an early (top left) and later (top right) stage before symmetry breaking. The cell displays characteristic transversal arcs behind a thin lamellipodia layer at the periphery. Towards the symmetry breaking event, the arcs begin to dissolve. In between, the transversal arcs follow the displacement of the cell edge. We detected these arcs using an intensity filter (red regions bottom row). Overlaid to the segmented arcs region is a grid of 0.6 μm wide (at initial time point) and 0.6 μm deep edge-tracking probing windows. Highlighted in blue, 5th layer of probing windows, which sample the transverse arcs in early time points (left). In late time points the windows fall outside the arc region. f) Sampling of the transverse arcs by the 5th layer of probing windows that are either tracking the cell edge in the original movie or fixed after remapping the movie to a reference frame (left). Space vs time heatmaps of the samples (right, top & bottom). The maps show the presence (white) or absence (orange) of transverse arcs. Edge-tracking windows have frequent “drop-outs” (black) in layers further away from the cell periphery. Window “drop-outs” (black) are persistent in time when the movie is remapped. All scale bars 10 μm.
Fig 4.
Analysis of spatial coherence in diffuse molecular signals.
a) Select frames of a movie visualizing the activation of the GTPase Cdc42 (middle) and its upstream GEF Asef (bottom) using multiplex FRET-based biosensors. Shown are normalized FRET-ratio signal indicating local activation of the molecues. For registration the donor signal of the Cdc42 biosensor is used as the location fiducial (top). b) Remapped, normalized FRET-ratio signals for the same time points as in a). c) Spatial coherence of the Cdc42 donor (left), Cdc42 FRET-ratio (center), and Asef FRET-ratio (right) time-series extracted from the remapped (top) and raw time-lapse sequences. d) Distributions of average spatial coherence of the Cdc42 donor, Cdc42 FRET-ratio, and Asef FRET-ratio time-series. Box plots illustrate 25th, 50th, and 75th percentile of average values in for m = 4 movies. Whiskers indicate the 5th and 95th percentile. P-values are calculated by one-way ANOVA testing. Scale bars 10 μm.
Fig 5.
Profilin dynamics in live cells show patterns in local time-series coherence.
Raw intensity vs local time-series coherence scores of diverse Profilin probes. The computation of reliable coherence scores is enabled by the remapping of the movie into a spatially stationary reference frame. a) Control experiment using an mCherry cytoplasmic volume marker. As expected, coherence of a diffuse signal is high across the entire cell footprint. For remapping, a Halo-CAAX tag membrane marker was used as the location fiducial. b) Cell undergoing drug-induced symmetry breaking, which expresses SNAP-Profilin at endogenous levels. For remapping, a Halo-CAAX tag membrane marker was used as the location fiducial. c) WT EGFP-Profilin (top) and R88E mApple-Profilin mutant (bottom) concurrently expressed at low concentration from a leaky CMV100 promotor in a Profilin knockout cell. For remapping, the lowpass-filtered Actin-SNAP signal was used as the location fiducial. WT and R88E Profilin display distinct coherence patterns. d) Quantification of subcellular heterogeneity of the signals observed in a-c using the Gini coefficient. Dots indicate values for individual cells. All scale bars 10 μm.
Fig 6.
Co-expressed wildtype and mutant Profilin exhibit different relationship to Actin dynamics.
a-d) Signal transforms to relate Profilin organization to Actin dynamics. The transforms are enabled by remapping the movie into a spatially stationary reference frame. U2OS cells expressing a) Actin-SNAP with b) entropy of the Actin signal, c) WT EGFP-Profilin, and d) R88E mApple-Profilin. The remapping was accomplished using lowpass-filtered Actin as a location fiducial. To reduce perturbation by overexpression, the two Profilin constructs were expressed in a Profilin null background. Panels in (c) and (d) display the dynamics of the diffuse image signals as local time-series coherence scores over a rolling window of 25 time points (250 s). The SNAP-Actin signal consists of various filament forms as well as a diffuse background of monomers. The mixture makes a direct cross correlation to other molecular processes difficult to interpret. We therefore extracted the entropy over a rolling window of 25 time points, which indicates relative stability of Actin structures (high entropy delineates regions of high polymer turnover and/or concentration variation). e) Cross correlation of Actin entropy and Profilin coherence in subcellular regions defined by distance from the cell edge. We performed this analysis on 3 zones: 0–1.2 μm from the cell edge (top row) roughly corresponding to the thin lamellipodia, 3.6–6 μm from the cell edge (mid row) roughly corresponding to transverse arcs, and 8.4–12 μm corresponding to perinuclear regions. As a control we also calculated the cross correlation between Actin entropy and the coherence of an mCherry volume marker (right column). WT Profilin and Actin show a significant correlation only in the band 0–1.2 μm from the edge, confirming the biochemical function of Profilin as a promoter of Actin polymerization. The correlation collapses for R88E Profilin, which is deficient in Actin binding (boxed). The coupling between Profilin and Actin dynamics is absent in regions more distal from the cell edge. All scale bars 10 μm.
Fig 7.
Cell symmetry breaking reveals polarization dependent organization of Profilin coherence a) Time course of a drug-induced symmetry breaking experiment, following the protocols published in [39]. 500 s prior to imaging cells seeded on glass slides are treated with 25 μM Blebbistatin. During the initial phase after drug induction the cells exhibit a stable morphology (not filmed). The remainder of the displacement time course (total cell edge displacement integrated over the cell boundary) displays distinct phases of cell morphodynamic activity, as indicated. Symmetry breaking occurs 150–250 s into the movie. b) Remapped mNG-Actin signals at four select time points. See Fig 1b for the original image sequence. The cell registration relied on Halo-CAAX as a location fiducial. c) Actin entropy computed over a rolling window of 25 time points. d) Profilin time-series coherence score computed over a rolling window of 25 time points. Both the Actin entropy and Profilin coherence reveal a shift in high values away from the cell front to the cell center and back during the symmetry breaking process showing that Profilin organization is responsive to changes in subcellular Actin polymerization. See text for further discussion. All scale bars 10 μm.