For a quantitative estimate of cell tractions and contractile forces of single cells in a 3-D extracellular matrix, it seems feasible, at least in principle, to extend the 2-D traction microscopy method described above to the third dimension. The following modifications of the 2-D method described above would be necessary. First, instead of a polyacrylamide hydrogel, a reconstituted connective tissue matrix (e.g., collagen or Matrigel) can be used. Invasive cancer cells are able to spontaneously invade deep into such gels. Second, instead of a single layer of fluorescent beads at the gel surface, they need to be randomly dispersed throughout the matrix. By taking multiple images at different focal depth of the matrix gel, one can then determine the x, y, z position of the fluorescent beads. Third, from changes in the bead position (either measured over time, or after cell treatment with drugs relaxing the contractile forces of cells and inducing cell detachment), certain measures of contractile force generation such as the elastic strain energy can be computed.
There are numerous challenges ahead, however, before such an approach will become a routine tool. First, measurements of the deformation field in 3-D are considerably more difficult compared to a 2-D situation. Image stacks with a z-focus distance of 2 µm between adjacent images over a total z-height of approximately 500 µm need to be recorded. The need for sufficient data storage capacity and long image acquisition time (> 1 min) for a single image stack, and the potentially harmful light exposure, will restrict the measurement time. Computing the x, y and z position for each of the typically far more than 10,000 fluorescent beads within the image stack with an accuracy of better than 30 nm poses additional challenges. Because at least two image stacks are needed to measure cell tractions – one stack each before and after the addition of traction-releasing drugs such as trypsin/EDTA, ML-7, cytochalasin D, or latrunculin A (see ) – it is necessary to identify the same bead in two image stacks, which can be difficult when large deformations have occurred.
Fig. 3 Regulation of contractile forces. Contractile forces are controlled by myosin light chain (MLC) phosphorylation, which in turn depends on the balanced activities of the myosin light chain kinase (MLCK) and myosin light chain phosphatase (MLCP). Force (more ...)
The second challenge is the measurement of the elastic modulus of the 3-D matrix gels. Unlike polyacrylamide gels, collagen gels are not elastic but viscoelastic, they are not linear but stiffen with increasing strain, and they are not amorphous but filamentous. Because of the filamentous nature of collagen gels, it is not even clear to what degree the macroscopic rheological properties that one can measure with a plate rheometer reflect the microscopic properties experienced by the cell.
The third challenge is the computation of the traction field. In the case of 2-D traction microscopy, the gel can be approximated as a semi-infinite solid, and the gel displacements that result from a point traction on the gel surface are described by an analytically known Green’s function (Butler et al., 2002
). In the case of a 3-D gel, the boundary conditions such as the free upper gel surface (usually overgrown with cells that have not yet invaded) and the fixed lower surface, as well as the non-linear rheological properties of the gel need to be considered, and the Green’s function under such conditions is unknown. Moreover, the invaded cell may have generated a path through the gel by secreting matrix-degrading enzymes. Finally, the deformation field of the gel is known only at the locations of the embedded fluorescent beads, which are so sparse (approximately 10–15 µm apart) that the traction reconstruction would severely underestimate the true tractions, although the latter problem may be eased by using the matrix filaments themselves to track the deformation field, as shown in .
Fig. 2 Collagen matrix deformations due to contractile forces. An MDA-MD-231 breast carcinoma cell was allowed to invade into a collagen gel for two days and had reached a depth of approximately 200 µm below the gel surface. The left image shows the (more ...)
One way of overcoming these problems is to use the elastic strain energy stored in the matrix as a robust estimate of contractile cell forces (Butler et al., 2002
). The elastic strain energy can be obtained from the local matrix strain between adjacent fluorescent beads, and only the matrix rheological properties but not the boundary conditions need to be known. Wyckoff et al. (2006)
used glass microneedles to calibrate the gel deformations that arise from a point source, and they estimated that the total traction forces of rat mammary adenocarcinoma cells (MTLn3) are between 10–20 nN. Calibration measurements of the deformation field in collagen gels that result from point forces (generated with magnetic tweezers (Kollmannsberger and Fabry, 2007
)), and measurements in MDA-MB-231 human breast carcinoma cells () show forces that are at least one order of magnitude higher (unpublished). But even 10–20 nN is a substantial force that can significantly enhance the ability of cells to migrate through a dense connective tissue matrix. As such, it is a tenable hypothesis that cancer cells can become more invasive by becoming more contractile. Indeed, this hypothesis is supported by a recent report (Mierke et al., 2007b
). It is, then, also conceivable that pharmacological interventions that alter the contractile properties of cancer cells may offer new therapeutic strategies to reduce cancer cell invasiveness. In the following section, we give a brief outline of the signal transduction pathways that regulate contractile forces in cancer cells ().