Co-Orientation: Quantifying Simultaneous Co-Localization and Orientational Alignment of Filaments in Light Microscopy

Abstract

Co-localization analysis is a widely used tool to seek evidence for functional interactions between molecules in different color channels in microscopic images. Here we extend the basic co-localization analysis by including the orientations of the structures on which the molecules reside. We refer to the combination of co-localization of molecules and orientational alignment of the structures on which they reside as co-orientation. Because the orientation varies with the length scale at which it is evaluated, we consider this scale as a separate informative dimension in the analysis. Additionally we introduce a data driven method for testing the statistical significance of the co-orientation and provide a method for visualizing the local co-orientation strength in images. We demonstrate our methods on simulated localization microscopy data of filamentous structures, as well as experimental images of similar structures acquired with localization microscopy in different color channels. We also show that in cultured primary HUVEC endothelial cells, filaments of the intermediate filament vimentin run close to and parallel with microtubuli. In contrast, no co-orientation was found between keratin and actin filaments. Co-orientation between vimentin and tubulin was also observed in an endothelial cell line, albeit to a lesser extent, but not in 3T3 fibroblasts. These data therefore suggest that microtubuli functionally interact with the vimentin network in a cell-type specific manner.

Fig 1. Steps for obtaining the co-orientation plot.

To compute the co-orientation plot, the images in both color channels are first processed by a filter bank of orientation selective filters (shown here for an orientation scale of 100 nm). This provides orientation space representations of both channels with the evidence per orientation in each pixel. The cross-correlation between these representations then leads to the co-orientation plot showing the correlation c as a function of the distance between localizations and angle between the filaments they belong to.

Fig 2. Co-orientation plot of parallel and unrelated filaments.

(a) Simulated data of parallel filaments in two color channel channels and (b) the corresponding co-orientation plot, showing strong co-orientation at a distance of 50 nm between filaments. The co-orientation plot shows the cross-correlation between the color channels as a function of the distance between localizations in both channels (on the horizontal axis) and the difference in the orientations of the filaments those localizations belong to (on the vertical axis). (c) Simulated data of statistically independent filaments in two color channel channels and (d) the corresponding co-orientation plot, showing no substantial co-orientation.

Fig 3. Orientation scale as a dimension for analysis.

(a) Simulated data of filaments in the green color channel with filaments in the red channel twisted around them. (b) When the orientation is analyzed at a scale of 50 nm, the co-orientation plot shows two peaks at positive and negative angles between the filaments in both channels; (c) for a scale of 500 nm the peaks shift to the center of the plot indicating that the filaments in both channels appear to run in parallel at that scale. The smallest scale for the orientation analysis is determined by the FRC resolutions in both channels, are 34 nm (red) and 36 nm (green).

Fig 4. Statistical significance test results on simulated data.

(a) The normalized anisotropic Ripley’s K statistic K _∥(R) quantifies the co-orientation strength. Rotation over an angle θ of the color channels in Fig 2a relative to each other leads to a rapid decline of K _∥(R); the residual fluctuations can be used to determine that the value K _∥(R) at θ = 0 exceeds the threshold for statistical significance at the 0.01 level (dashed line). (b) The same plot for the data show in Fig 2c indicates that the co-orientation there is not significant for θ = 0.

Fig 5. Co-orientation analysis for experimental data of tubulin and vimentin and of actin and keratin.

(a) and (c) Localization microscopy images of tubulin (red) and vimentin (green) at stable cell edges. The co-orientation plots for the ROIs demarcated by the white circles are shown in (b) and (d), showing clear co-orientation at distances up to 500 nm (with a scale s _o = 200 nm for the orientation analysis; results for (a) for multiple different scales s _o are shown in S5 Fig). (e) Localization microscopy image of actin (red) and keratin (green). The co-orientation plot in (f) for the selected region of interest shows no significant co-orientation.

Fig 6. Visualization of the local co-orientation strength.

(a-c) Localization microscopy images of tubulin (red) and vimentin (green). Blue overlays show the local co-orientation strength K _∥(R) in order to highlight the regions with the strongest local co-orientation. Increasing R causes more filaments that are further apart from each other to contribute to K _∥(R), but also causes K _∥(R) to appear less localized. (d) The same image as (b), but with the cos(2ϕ) weight in the computation of K _∥(R) in Eq 7 replaced by a cos²(ϕ) weight. This provides a visualization in which crossing filaments do not cancel the contributions to the local co-orientation strength of parallel filaments. However, this visualization is also sensitive to regions with mere co-localization where filaments are not aligned.

Fig 7. Co-orientation strength in endothelial and fibroblast cells.

Localization microscopy images of tubulin (red) and vimentin (green) in various cell types. (a) Large SR image of a HUVEC cell, showing that co-orientation is predominantly observed in the peripheral parts (right), and not near the nucleus (left). (b-d) Higher magnifications of comparable peripheral parts of (b) a HUVEC cell showing extensive co-orientation, (c) a EC-RF24 endothelial cell with less, but still significant co-orientation, and (d) a NIH-3T3 fibroblast as an example of a cell-type with very little co-orientation. (e-g) TIRF images corresponding to b, c and d and (h) quantification of the co-orientation strength for the circular ROIs in these three examples for R = 200 nm.