Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions

Abstract

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.

Figure 1. 3D Displacement Contours of Migrating Fibroblast.

Surface contour ((a)–(b)) and depth contour ((c)–(d)) plots of the magnitude of the three-dimensional displacement vector ( u ) at two time points and (separated by a 35 min interval) during cell migration. The color bar represents the magnitude of the total three-dimensional displacement vector ( u ) in m, and the cell (green) is superimposed on the three-dimensional contour plots to show its position with respect to the deformation field. The two edges in (c) and (d) are included to show that there are negligible displacements detected from neighboring cells (contours are dark blue).

Figure 2. 3D Traction Contours of Migrating Fibroblast.

Surface contour ((a)–(b)) and depth contour ((c)–(d)) plots of the magnitude of the three-dimensional traction force vector, corresponding to the displacement fields presented in Fig 1. The color bar represents the magnitude of the total three-dimensional traction force vector ( T ) in pN/, and the cell (green) is superimposed on the three-dimensional contour plots to show its position with respect to the traction field. The two edges in (c) and (d) are included to show that there are negligible traction forces detected from neighboring cells (contours are dark blue).

Figure 3. Distribution of 3D Cellular Traction Forces on Polyacrylamide Gels.

Cell-induced surface traction forces contour plot ((a)) at  = 35 min during migration. The color bar represents the magnitude of the three-dimensional surface traction force vector ( T ) in . The pink line depicts the location of the generated one-dimensional plot shown in (b). The location was chosen to show the line profile across a localized force concentration (see Figure S1 for expanded view); (b) illustrates the distribution of the magnitude of the total traction force vector and its in-plane (, ) and normal () components along the selected line-cut highlighted in (a); (c) and (d) display the cell-induced traction force contour and line plot profiles as functions of depth () through the thickness of the gel (see Figure S2 for expanded view); (c) shows the same traction force contours along the long axis of the cell where the color bar represents the magnitude of the three-dimensional traction force vector ( T ) in ; (d) illustrates the distribution of the magnitude of the total traction force vector ( T ) and its in-plane (, ) and normal () components in the thickness () direction.

Figure 4. Distribution of 3D Cellular Tractions on PA Gels.

Cell-induced surface traction forces contour plot ((a)) for the next time point ( = 70 min) during migration. The color bar represents the magnitude of the three-dimensional surface traction force vector ( T ) in . The pink line depicts the location of the generated one-dimensional plot shown in (b). The location was chosen to show the line profile across a localized force concentration; (b) illustrates the distribution of the magnitude of the total traction force vector ( T ) and its in-plane (, ) and normal () components along the selected line-cut highlighted in (a); (c) and (d) display the cell-induced traction force contour and line plot profiles as a function of depth () through the thickness of the gel; (c) shows the same traction force contours along the long axis of the cell where the color bar represents the magnitude of the three-dimensional traction forces in ; (d) illustrates the distribution of the magnitude of the total traction force vector and its in-plane (, ) and normal () components in the thickness () direction.

Figure 5. Time Evolution of 3D Displacements and Tractions of a Migrating Fibroblast.

Time evolution of a successive series of laser scanning confocal cell images (left column) and traction force contours (right column) on the surface during cell migration for a single cell. The cell images on the left represent two-dimensional projections of the confocal volumetric data set showing GFP-actin. The cell-applied surface traction force contours display the magnitude of the three-dimensional traction force vector ( T ) in . The white arrows represent the in-plane traction force components ( and ) only.

Figure 6. Time Evolution of 3D Traction Forces through the Gel Thickness.

Time evolution of cell-induced traction forces as a function of depth () over 70 min along an arbitrary slice below the cell's long axis. The contour plots show the magnitude of the three-dimensional traction force vector ( T ) for a single locomoting 3T3 fibroblast in . The black arrows represent the in-plane traction forces () and normal traction forces (), where the magnitude of the longest arrow during each time increment is equal to the maximum value depicted by the color bar in . The time increment between successive frames is 35 min. The outline of the cell as recorded by confocal imaging is superimposed in green, and the direction of cell migration is from left to right.

Figure 7. Decomposition of the Local 3D Cell Tractions During Locomotion.

Time evolution of cell-induced traction forces (in-plane) and (normal) as a function of depth () over 70 min along an arbitrary slice below the cell's long axis as shown in Fig. 6. The contour plots show the magnitude of the shear traction force components (left column: ; right column: ). The color bar displays all values in . The black arrows on the top of each plot give the general direction of cell-induced traction forces. The time increment between successive frames is 35 min. The direction of cell migration is from left to right.

Figure 8. 3D Traction Force Microscopy Overview.

Schematic overview of the three-dimensional traction force microscopy technique, illustrating the methodology to compute the full-field tractions of migrating cells in all three spatial dimensions.

Figure 9. 3D LSCM Cell Image.

3D LSCM image of a polyacrylamide gel including embedded submicron tracker particles (red) and a fibroblast cell on the surface (blue). The total stack dimensions are 128×128×30 . The rendered cell image has been digitally enhanced in brightness and contrast and superimposed onto the confocal stack to show a clearer image.

Figure 10. LSCM Cross-sectional Image.

Representative LSCM image depicting the surface plane of a three-dimensional image stack, and a cross-sectional view of the scanned volume (inset). The fibroblast cell is showing GFP-actin in green, whereas the 0.5 m fluorescent microspheres are shown in red.