Department of Surgery, UMDNJ-Robert Wood Johnson Medical School
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Butler, C. M., Foty, R. A. Measurement of Aggregate Cohesion by Tissue Surface Tensiometry. J. Vis. Exp. (50), e2739, doi:10.3791/2739 (2011).
Rigorous measurement of intercellular binding energy can only be made using methods grounded in thermodynamic principles in systems at equilibrium. We have developed tissue surface tensiometry (TST) specifically to measure the surface free energy of interaction between cells. The biophysical concepts underlying TST have been previously described in detail1,2. The method is based on the observation that mutually cohesive cells, if maintained in shaking culture, will spontaneously assemble into clusters. Over time, these clusters will round up to form spheres. This rounding-up behavior mimics the behavior characteristic of liquid systems. Intercellular binding energy is measured by compressing spherical aggregates between parallel plates in a custom-designed tissue surface tensiometer. The same mathematical equation used to measure the surface tension of a liquid droplet is used to measure surface tension of 3D tissue-like spherical aggregates. The cellular equivalent of liquid surface tension is intercellular binding energy, or more generally, tissue cohesivity. Previous studies from our laboratory have shown that tissue surface tension (1) predicts how two groups of embryonic cells will interact with one another1-5, (2) can strongly influence the ability of tissues to interact with biomaterials6, (3) can be altered not only through direct manipulation of cadherin-based intercellular cohesion7, but also by manipulation of key ECM molecules such as FN8-11 and 4) correlates with invasive potential of lung cancer12, fibrosarcoma13, brain tumor14 and prostate tumor cell lines15. In this article we will describe the apparatus, detail the steps required to generate spheroids, to load the spheroids into the tensiometer chamber, to initiate aggregate compression, and to analyze and validate the tissue surface tension measurements generated.
1. Aggregate preparation for measurement of tissue surface tension.
For adherent cells, spheroids can be formed by using either the hanging drop method or by generating a coherent sheet of cells that can then be cut into 1 mm fragments.
Aggregate formation by the hanging drop method:
Aggregate formation by the cell sheet method:
2. Measurement of aggregate surface tension
3. Representative results:
Below is a table of typical TST results for aggregates of rat prostate fibroblasts (RPF) and rat prostate smooth muscle cells (RPSMC). As can be seen in Fig. 7 aggregates of RPF cells have a surface tension of 22.8 ± 1.1 dynes/cm. Moreover, the mean surface tension values measured after compression 1 and after compression 2 were statistically identical when compared by a paired t-test. We also compared the ratios of σ2/σ1 and F2/F1 to ensure that these aggregates did not obey Hooke's law, as they would if they behaved as elastic solids. As demonstrated in Table 1, the ratio of σ2/σ1 does indeed approach 1.0. Moreover, the ratio of F2/F1 was significantly greater than σ2/σ1 (paired t-test, P < 0.05), further confirming that these aggregates do not obey Hooke's law and in fact behave as liquids. In contrast RPSMCs obeyed Hooke's law. As is evident in Table 1, the ratio of σ2/σ1 is significantly greater than 1 and was not statistically different than that of F2/F1. To further demonstrate liquid-like behavior, we explored the relationship between surface tension (σ) and aggregate volume. As can be seen in Fig. 8, volume is independent of sigma for RPF cells (red regression line, r2 = 0.002), whereas there appears to be some dependence of sigma on volume for RPSMCs (blue regression line, r2 = 0.146). These data further confirm that RPF aggregates behave in a liquid-like manner, whereas those of RPSMCs appear to behave more as elastic solids. Only those mesurements obtained from aggregates behaving as liquids would be used to calculate surface tension.
Figure 1. Overview of the tissue surface tensiometer.
Figure 2. A more detailed view of the tensiometer chamber (right panel).
Figure 3. Schematic view of the tensiometer chamber.
Figure 4. Images of uncompressed (A) and compressed (B) aggregates.
Figure 5. The Laplace Equation.
Figure 6. Diagram of a liquid droplet compressed between two parallel plates to which it adheres poorly, at shape equilibrium. R1 and R2 are the two primary radii of curvature, at the droplet's equator and in a plane through its axis of symmetry, respectively. R3 is the radius of the droplet's circular area of contact with either compression plate. H is the distance between upper and lower compression plates. X is one side of a right-angled triangle with hypotenuse R2 extending to a point of contact between the droplet's surface and either compression plate.
|σ1(dynes/cm ± SEM)||σ2(dynes/cm ± SEM)||Pσ1 vs σ2||σ1,2(dynes/cm ± SEM)||σ2/σ1||F2/F1||Pσ2/σ1 and F2F1|
|RPF||22.6 ± 1.7||22.9 ± 1.4||> 0.05*||22.8 ± 1.1||1.04 ± 0.04||1.47 ± 0.06||< 0.05|
|RPSMC||15.0 ± 2.8||23.0 ± 3.2||0.039||NA||1.9 ± 0.3||1.6 ± 0.1||0.16*|
Figure 7. TST measurements and confirmation of aggregate liquidity for aggregates of rat prostate fibroblasts and smooth muscle cells.
Figure 8. Relationship between sigma and volume for aggregates of RPF (red line) and RPSMCs (blue line).
Measuring aggregate cohesion by TST is relatively straightforward. There are, however, key steps that must be mastered in order to generate useable TST data; 1) aggregates must be "healthy". This can be controlled by ensuring that aggregate formation begins with cells that are at optimal confluence prior to detachment. Aggregate size and time in culture must also be controlled to minimize the development of a necrotic core within the aggregate; 2) Another parameter that can influence TST measurements is the degree of adhesion of the aggregate to the upper or lower compression plates. Accordingly, the optimal concentration of poly-HEMA used to coat the plates must be empirically determined for each type of aggregate; 3) While it is preferable that pre-compression aggregates should be as spherical as possible, it is not strictly necessary. Some aggregates, particularly ones that are held together weakly, tend not to form perfect spheres. The explanation for this is that in order to completely round-up cells must expend energy by moving and re-arranging. If the amount of energy required to round-up into a sphere exceeds the energy minimization of becoming spherical, the aggregates will tend to stall at some sub-spherical shape. In our experience, such aggregates upon becoming compressed, resist the compressive force to an extent that the sides of the aggregate form semi-circles, exactly as they would do if starting from a perfect sphere; 4) It is also important that the compression plates are parallel to one-another. This is best accomplished by ensuring that the nickel-chromium wire is straight and that the instrument is level and plumb. If these measures are adhered to, tissue surface tensiometry is relatively simple and can generate very useful information on mechanical properties of tissues and of their underlying molecular determinants.
Other methods for measuring aggregate cohesion exist, some that eliminate the need for specialized equipment such as the Cahn electrobalance. One such method aspirates a spheroid into a pipette of much smaller diameter than that of the spheroid, with a constant suction pressure. The viscoelastic properties of the tissue are deduced from the variation of the strain by measuring the change in length of the cellular material as it flows inside the pipette18. While useful, this method may have limitations as to the range of surface tensions in which it can be applied. Very weak aggregates would likely be destroyed as they are aspirated into the pipette, whereas aggregates that are held together very strongly may not be aspirated at all. Parallel plate compression has measured surface tensions as low as 0.33 ± 0.02 dynes/cm for zebrafish germ layer ectoderm treated with E-cadherin morpholino3 to as high as 20.1 ± 0.5 dynes/cm for aggregates of embryonic chick limb bud mesoderm2, demonstrating its general utility over a broad cohesion range for several embryonic systems.
No conflicts of interest declared.
|water bath/shaker||New Brunswick Scientific|
|10 ml round-bottom flasks||Bellco Glass|