Simple measurement of the apparent viscosity of a cell from only one picture: Application to cardiac stem cells

Mechanical deformability of cells is a key property that influences their ability to migrate and their contribution to tissue development and regeneration. We analyze here the possibility of characterizing the overall deformability of cells by their apparent viscosity, using a simplified method to estimate that parameter. The proposed method simplifies the quantitative analysis of micropipette-aspiration experiments. We have studied by this procedure the overall apparent viscosity of cardiac stem cells, which are considered a promising tool to regenerate damaged cardiac tissue. Comparison with the apparent viscosity of low-viscosity cells such as immune-system cells suggests that treatments to reduce the viscosity of these cells could enhance their ability to repair damaged cardiac tissue.

Figure 1

Schematic description of the experiments. The cells were detached from the culture substrate by trypsinization and suspended in culture medium, then tested in the following 3 h. (a) Actin filaments (red, Phall. rhod.) and nucleus (blue, DAPI) in an adhered cell. (b) Actin cortex for a detached cell (red, Phall. rhod.). (c) Images at different times for the aspiration test of a human cardiac stem cell, which corresponds to the curve in Fig. 2. (d) Curve showing the differential pressure along time during the experiments.

Figure 2

(a) Representative experimental curve for the aspirated length $x$ (measured from the entrance of the microcapillary to the leading edge of the aspirated cellular material inside the micropipette) vs time for a human cardiac stem cell. (b) Curves length $x$ vs time for all the experiments; the aspiration process is rapid when the volume outside the microcapillary is small, as observed in several curves.

Figure 3

Experimental values of the ratio $V_{\mathrm{in}}/V_{\mathrm{tot}}$ of the cell vs the ratio between initial radius of the cell and radius of the microcapillary for mouse (a) and human (b) cardiac stem cells. The figures show also the theoretical curves obtained by fitting these experimental values (ii) to Eq. (3) and those curves corresponding to the mean viscosity (i) estimated by Eq. (1) from the slopes of the curves $x$ vs $t$ shown in Fig. 2. The definitions of dimensions and volumes are schematically represented in (c); to estimate the viscosity of a cell only the dimensions $R_p,x,d_1,d_2$ need to be measured (see Appendix).

Figure 4

Values obtained for the apparent viscosity by the two methods analyzed: (i) from the slope $dx/dt$ in each experiment, using Eq. (1), and (ii) fitting Eq. (3) to the experimental values $V_{\mathrm{in}}/V_{\mathrm{tot}}$ vs $R_0/R_p$. The figure shows mean values ± standard error.

Figure 5

Theoretical curves given by Eqs. (3), continuous lines, and Eq. (A5), dashed lines, for six different values of the ratio $\Delta {Pt}_e$/mμ. The curves of Eq. (A5) are represented in the interval for which $R_p/R\hspace{0.17em}>\hspace{0.17em}0.4$ and, accordingly, the equivalent curves for Eq. (3) are displayed in the same interval of values $R_0/R_p$. The dotted line shows the boundaries of the region in which we used Eq. (3).