The essential step in the determination of Young’s modulus is the appropriate calibration of the cantilever spring constant and the photodetector sensitivity. The calibrated load force F is used in the fitted equation:
where a is proportional to Young’s modulus value. Thus, the errors introduced by discrepancies in both cantilever spring constant and photodetector sensitivity influence strongly the accuracy of the elastic modulus determination. The maximum error can be estimated by
As an example estimation, for particular, typical case, uncertainties in spring constant introduce roughly 10% of total error, while the photodetector sensitivity part adds additional 14%.
Variability stemming from cell-related factors
Cells are highly dynamic in their properties. Therefore, usually, discrepancy arising from the applied calibration methodology can be less significant as compared to variations of Young’s modulus stemming from cell-related factors, such as culture conditions (culture medium composition), density of cells, confluence on a substrate, the number of passages, the day of measurement after the passage, etc. Despite extensive research showing mechanical differences between normal and pathological cells, there is a little information devoted to systematic studies showing the effect of cell-related factor on single-cell biomechanics. Some examples are mentioned below and summarized in Fig. 4.20.
The influence of medium composition on mechanical properties of non-malignant (MCF10A) and metastatic (MDA-MB-231) breast cancer cells has been reported in the work of Nikkhah et al. . Five different compositions were investigated, i.e., medium Ml—RPMI supplemented with 10% FBS; M2—RPMI supplemented with 5% FBS; M3—RPMI supplemented with 5% FBS and 20 ng/ml epidermal growth factor; M4—DMEM:F12 supplemented with 5% FBS; and M5—DMEM:F12 supplemented with 5% horse serum, 20 ng/ml epidermal growth factor, 100 ng/ml cholera toxin, 0.01 mg/ml insulin and 500 ng/ml hydrocortisone (Fig. 4.22, prepared using the data published in ).
Figure 4.20 The elastic properties of breast cancer cells, determined for various medium composition: Ml—RPMI supplemented with 10% FBS; M2—RPMI supplemented with 5% FBS; M3—RPMI supplemented with 5% FBS and 20 ng/ml EGF; M4—DMEM:F12 supplemented with 5% FBS; M5— DMEM:F12 supplemented with 5% HS, 20 ng/ml EGF, 100 ng/ml CT, 0.01 mg/ml INS and 500 ng/ml HC (FBS—fetal bovine serum; EGF—epidermal growth factor, HS—horse serum, CT—cholera toxin, INS—insulin, and HC— hydrocortisone).
The effect of medium composition on single-cell elastic properties is more dominant for non-malignant MCF10A breast cell lines as compared to the results obtained for metastatic MDA- MB-231 cells. Elastic modulus of non-malignant breast cells changes from 1.11 ± 0.85 kPa to 0.72 ± 0.54 kPa (decrease of about 35%). In case of metastatic MDA-MB-231 cells the modulus changes from 0.50 ± 0.35 kPa to 0.37 ± 0.25 kPa (~26%). These results strongly suggest the use of similar medium composition in studies aiming at the comparison of properties of various cell lines (or consider the effect of medium composition if it is not possible to use the same culture medium or use reference cell lines). Simultaneously, such studies could be accompanied by fluorescent images of actin cytoskeleton to bring conclusion whether culture medium composition changes the actin filament organization that is manifested in alterations of mechanical properties of single cells.
Some research demonstrates also the effect of cellular microenvironment on mechanical properties of single cells (Fig. 4.21).
IC IN PCPNCCCN 1C IN PCPNCCCN 1C IN PCPN 1C IN PCPN
Figure 4.21 Bright-field images of cells in culture: (a) A small colony or monolayer. (b) Several individual cells (the arrows indicate a cell placed inside (1), and at the periphery (2) of a monolayer of cells, as well as an isolated cell (3)). (c) Elastic modulus (mean ± standard error of the mean), determined for normal (HMEC), immortal, tumorigenic, and metastatic cells measured in various conditions: I—isolated single cell; P—cell located at the periphery of a monolayer; C—cell measured inside of a monolayer (close to its center) and distinct places within the cell: C—cytoplasm; N—nucleus (re-printed from ).
For example, a recent study by Guo et al. reported the effect of neighboring cells on elastic properties of normal (human mammary epithelial cells, HMEC cells), immortal (derivatives of HMECs that were transfected with hTERT), tumorigenic (HMLER cells—HMECs cells taken at 23 population doubling time) and metastatic (MDA-MB-231 breast cancer) cells . Depending on the place of measurement within a single cell and the density of cells, distinct elastic moduli are observed. Normal (HMEC) and immortal cells are stiffer than both tumorigenic and metastatic cells. They show larger Young’s modulus values, ranging from 0.60 ± 0.05 to 1.13 ± 0.06 kPa, while the elastic modulus for tumorigenic and metastatic cells varies from 0.38 ± 0.03 to 0.66 ±
0.03 kPa. The tumorigenic cells seem to be the most deformable cells among the four studied types of breast cells (E = 0.49 ± 0.11 kPa versus E = 0.58 ± 0.05 kPa for tumorigenic and metastatic breast cells, respectively). Noteworthy, there is a small difference between modulus determined from areas above the nucleus and the cytoplasm (not exceeding 15%). Among four studied cell lines, only normal cells (HMEC) show a strong dependence on the cellular microenvironment. The largest Young's modulus is observed for cells located at the center of a monolayer where the neighboring cells influences strongly the mechanical properties (the elastic modulus almost doubled its value).
Most of animal cells are cultured at temperature of 37°C that resembles physiological conditions. On the other hand, majority of scientific papers report the elasticity measurements carried out at room temperature that varies, usually, between 20 and 22°C. Few reports show rather inconsistent effect of temperature on elastic properties of living cells. For example, NIH3T3 fibroblasts seemed to be unaffected within the temperature range 31-37°C, whereas the increase to 43°C causes sudden drop of modulus value. The 7-4 cells behaved differently. For them, a modulus maximum at 37°C was observed .
Another cell-related parameter influencing cell mechanical properties is the number of passages carried out before the measurements. In general, for immortalized cell lines, no differences are reported (see, e.g., ). However, for such cells, the cytoskeleton organization was probably preserved from one passage to another. One could expect some variations for normal and primary cell lines, whose doubling time is limited. In such case, the alterations in elastic properties for large number of passages are almost directly related to changes in actin cytoskeleton structure and cells state. Close to the maximum number of possible passages, cells are not dividing and their morphology is clearly distinguishable as compared to cells after first few passages.