Measuring Cell Forces by a Photoelastic Method

INTRODUCTION

Mechanical forces acting on cells affect many processes such as proliferation, cytoskeletal expression (1), and gene activity (2) Often these forces may be applied from external sources, e.g., muscular activity in remote parts of the body. But in addition the cells can act on their near neighbors (3).

Recently a number of novel methods for measuring the forces generated by individual cells have been reported (4–7). These methods, though highly ingenious and useful, measure the forces required either to deform microstructures on the substratum beneath the cell (5,6) or displace marker beads embedded in the substratum close to the cell (7). The possibility exists, as has been allowed by Bershadsky et al. (4), that the heterogeneous mechanical nature of the substratum (pillars or embedded particles) modifies the forces the cell can exert, almost as exercise machines in the gymnasium influence the athlete to develop greater forces. The aim of those measurements has been directed mostly at the questions relevant to cell movement.

But forces between cells are well known to be important in events such as wound healing, especially in contracture and the pulling open of wounds, in development, and perhaps in remodeling of tissues (3).

We describe a new method, based on photoelastic measurements, particularly directed at observing the effects of pairs of cells on each other or on small groups and also providing a method unimpaired by the presence of a heterogeneous substrate. Thus we test whether such substrates with micrometric topographic details modify cell force generation or application. The method has already been used (8) to detect active transverse contractions in fibroblasts in addition to the well-known longitudinal contractions in such cells. It can also detect forces acting between cells when there is microscopically visible separation between them. A further possible advantage of this technique is that observations can be made at fairly short -term and repetitive intervals over long periods, thus revealing whether rapid changes or fluctuations occur.

Measurement of the forces exerted by cells on their surroundings has been achieved by a variety of methods. Basically nearly all these methods set up situations where the cells distort their surroundings in a detectable way and where the situation is sufficiently simple and reproducible to allow calibration of the distortion that a given force applies. Harris (9) introduced the idea of growing cells in a thin membrane and observing the distortion. Those early results were not calibrated but indicated that fibroblasts develop forces sufficient to distort a thin elastic membrane.

Thus it would be appropriate to introduce a method where the substratum is effectively isotropic at least at the start of the experiment. We have grown cells on an isotropic substratum and looked for distortion of that substratum by forces exerted on it by the cells. The method we describe relies on the detection of such distortion by photoelasticity; see Huard (10) for a description of the principles of photoelasticity or Zhao et al. (11) for details of the method applied to strain distribution in a composite material.

MATERIALS AND METHODS

Cells' h-tert fibroblasts (human) (Clontech, UK), B10 D2 (otherwise known as LeII) mouse capillary endothelia (from laboratory stocks), and HGTFN (human granuloma endothelia also derived from laboratory stocks) were grown on the polydimethylsiloxane surfaces which had been coated with appropriate adhesion proteins such as fibronectin for various periods (1–4 days) and the cultures then examined at 37° C with the Polscope microscope.

The Polscope Microscope (CRI International, Woburn, MA) was mainly used with 40× and 100× strain-free objectives. The microscope with its associated software can measure retardances down to 0.1 nm (manufacturer's handbook) and azimuths as well. Pseudocolor images can be obtained which are useful for rapid survey observations and for revealing any mis-set up of the optical system; but for serious observation, images stamped with retardances at various points on the image are most useful. Images of birefringence were obtained after a number of images of the bare poly (dimethyl siloxane) (PDMS) surfaces and a number of phase contrast images of the cells at areas where the birefringence was to be measured. The images of the bare PDMS surface were obtained to check that there was no strain in the substratum in the absence of cells. This check validates the points on the origin in the graph in Fig. 1. The phase contrast images of the sampling areas were acquired so that the exact boundaries of the cell or cells could be established. Three images of each area to be measured were taken in quick succession, one for acquiring the raw birefringence data and two for further processing (for pseudocoloring, obtaining retardance transects across parts of the field, and stamping of calculated retardance values). This method can also be used for measuring forces over a time series. Time- lapse video image sets were acquired over short periods (30– 90 min) to record possible rapid changes in forces.

On many of the images in this work code numbers appear in the bottom right-hand corner: these are the original image filing names from the Polscope. Parts of the date and time may also appear just to the left of the file name.

The images obtained with the Polscope, running in the retardance mode, of isotropic materials were effectively black with a noise level of <0.2%. Each set of measurements made started with a test of isotropic PDMS to show that the noise level met this criterion. When examining cultures of cells on PDMS with the display in the retardance mode, any areas whiter than the noise level indicate birefringence with the whitest parts of the display corresponding to appreciable retardances.

RESULTS

SUMMARY

1. Stresses of ∼ 1–50 pN/μm² are generated around fibroblasts and other cells. Such values are lower than those reported by some other authors.

2. These are often strong on the lateral sides of the lamellopodium as well as in front of it and appear to be associated with transverse contractions in the cell.

3. They are also prominent laterally between fibroblasts along their contact zone.

4. Force generation is removed in 2 min by poisoning the cell's contractile mechanisms and more slowly by cooling the cells.

5. In groups of live cells in cell culture, rapid force changes and readjustments usually take place. In any group of 7– 10 fibroblasts which are not close packed, there will usually be one or more cells that are not exerting mechanical stresses to strain themselves (see video time- lapse sequences).

The strain that the cells cause in the PDMS surface is too small to be easily observable as a dimensional change; but 1 millistrain means that for a typical cell only 20- μm long, the dimensional change is only 20 nm. Cells are sensitive down to at least 50 microstrains (14). A relatively easily measured dimensional change of 2 μm would correspond to 100,000 microstrains.

DISCUSSION AND CONCLUSIONS

The strains in the PDMS substrate due to the activities of cells revealed by polarization microscopy are of course probably rarely uniaxial. Contraction in one axis is likely to lead to relaxation (extension) at 90° to that direction. This can best be seen, in the absence of comparative linear measurements, by azimuth plots (see Fig. 5).

Photoelasticity provides a suitable method for measuring the forces exerted by a cell on an appropriate substratum which should be transparent, isotropic when stress-free, and not too rigid to minimize reactions to stress. Besides, measuring the strain in terms of retardance photoelastic measurements can also indicate the azimuth of the polarization. Photoelastic measurement requires a fairly soft material whose Young's modulus lies in the range 10–10³ kPa. Unfortunately it is not suitable for use of collagen whose intrinsic birefringence is so large that other signals are swamped. Though a signal from areas underneath the cell can be detected, this is usually so complicated by signals from the cytoskeleton that no useful quantitative information can be gained.

The method is ideal for studying interactions between neighboring cells not in optical contact and for measuring smaller forces than can be estimated by other methods. This method also has the advantage that no new physical structure has been introduced that the cells might react to. The methods introduced by Abercrombie et al. (3) and Tan et al. (6) fabricated micropillars on the surface of the culture material, and it is known (15) that cells react to such structures by cytoskeletal reorganization. Since the cytoskeleton is involved in force generation, reorganization could alter the disposition and perhaps the extent of force generation. In the case of the experiments by Dembo et al. (7) where particles were embedded in the substrate, these may have acted to redistribute forces since the force pattern should have changed because the particles could be moved. All this suggests that there is a sensitive feedback mechanical system in the cell. There is, of course, the interesting question of whether the cell is akin to a motor system that increases energy output in response to resistance to motion, a situation found par excellence in a stepping motor. If so, any non-Newtonian behavior or even any constant but unusually high or low rigidity in the substrate will change the force measured. Even the photoelastic method does not escape this source of confusion, but it does allow the hypothesis to be tested.

Force mapping such as we have done does reveal that, with the exception of isolated cells, forces between groups of cells are likely to have complex and rather unpredictable distributions. We probably need to have a parallel model of the principal mechanical components in the cellular system, and this is not merely the distribution of cytoskeletal elements but also the strength with which they bind to each other.

As a culture of cells proceeds by cell division toward confluence, the cell cycle dies down. We cannot observe this by polarization microscopy, but as the cell packing becomes dense though not complete, we can see some tendencies to this end at rather earlier stages in the life of the cell. This fits in well with the observations by Curtis and Seehar (16) that external mechanical stimulation stimulates the cell cycle. In a three- dimensional tissue cells might be expected to exert forces on each other when cell anchoring is not as complete as it may be on a culture plate. An interesting discussion of the likely effects on tissue building of such forces has been published (17).

The force measurements around the periphery of a cell hardly ever fall to zero, whereas some space remains between the cells, suggesting that the cells are well coupled mechanically to the substratum. If the stresses measured by this photoelasticity method are summed up around the cell periphery, the results agree generally with those reported by other methods (5–7).

The tables of cell forces in Bereiter-Hahn (18) and the values quoted by Balaban et al. (5), Tan et al. (6), and Dembo et al. (7) show a wide range of values. However, the following reasons for discrepancies between measurements by this and other methods could be present:

1. The photoelastic method does not allow measurements to be made at the extreme edge of a cell because of diffraction and resolution problems.

2. The values given in the literature correspond to forces measured in focal adhesions (underneath a cell). Our stresses are measured outside (around) the cell, as the measurement underneath a cell could be affected by birefringence from cell components. This fact is likely to contribute to smaller values of measured forces. Vectors can be obtained from the retardance and azimuth measurements.

3. The difference in substrata between the methods may affect the generation of forces by cells (see above).

4. Possibly some variation in force generation will occur between different cell types and at different stages of the cell cycle.

5. Another reason any discrepancy may arise derives from the use of micropillars (5) or embedded particles (7) in much of the work of others. Reports (19–22) on the effects of nanotopographic structures on cell adhesion, shape, and motility show that such structures have extensive effects on these properties, suggesting that force distribution and perhaps magnitude is altered by such substrata.

But it is likely that the main reason for the apparent discrepancy is the fact that the photoelastic method can be used to measure the forces just outside the perimeter of the cell which is several thousands of pixels (hundreds of microns) in extent, whereas those methods that depend on projecting pillars or embedded beads only measure forces at some scores to a few hundred sites. If the stresses are summed for the perimeter, then the forces summed for the two methods may be less discrepant.