Johnson-Kendall-Roberts Theory Applied to Living Cells

Johnson-Kendall-Roberts (JKR) theory is an accurate model for strong adhesion energies of soft slightly deformable material. Little is known about the validity of this theory on complex systems such as living cells. We have addressed this problem using a depletion controlled cell adhesion and measured the force necessary to separate the cells with a micropipette technique. We show that the cytoskeleton can provide the cells with a 3D structure that is sufficiently elastic and has a sufficiently low deformability for JKR theory to be valid. When the cytoskeleton is disrupted, JKR theory is no longer applicable.

Figure 1

(a),(b) Two cells, held under weak aspiration by micropipettes, are placed in contact and 1 s later became adherent. Separation process (c),(d): One cell is held by the right micropipette under strong aspiration. The aspiration applied to the other cell is increased and the right micropipette displaced away. Either the cell leaves the left micropipette (c) or both cells separate (d). In the first case, the cell is reseized by the left micropipette (b), the aspiration incremented, and the right micropipette displaced again. This cycle is repeated until the cells separate and the separation force is deduced from the last aspiration pressures. During the measurements, the pipettes were moved at a velocity of about $20\mu \mathrm{m}/\mathrm{s}$. The whole process of separation lasted 1 min at most. The aspiration level on pressure employed in each cycle was monitored continuously.

Figure 2

Adhesion energy, as deduced from JKR theory [diamonds, Eq. (1)] and spherical shells [crosses, Eq. (2)] as a function of the volume fraction of dextran. Two sizes of dextran molecules ($4.6\times {10}^5$ and $2\times {10}^6\mathrm{M}\mathrm{W}$) were used. The results can be compared to the theoretical ones given by de Gennes [17] (line) and to experimental ones obtained by Evans by contact angle measurements on lipid vesicles [16] (squares).

Figure 3

Parameter $A=\frac{R_m}{2}[-F+3\pi R_m{W}_{\mathrm{a}\mathrm{d}\mathrm{h}}+\sqrt{-6\pi R_m{W}_{\mathrm{a}\mathrm{d}\mathrm{h}}F+(3\pi R_m{W}_{\mathrm{a}\mathrm{d}\mathrm{h}}{)}^2}]$ plotted as a function of $R_c^3$. As indicated in Eq. (5), in the case of JKR theory, the slope gives the elastic modulus. The large error bars are due to the low accuracy in the measurement of the contact radius in optical microscopy. The points are taken from three different experiments at various dextran volume fractions.

Figure 4

Force between two layers of S180 cells deposited on mica surfaces in a SFA function of the parameter $({\delta }^{3}R{)}^{1/2}$ where $\delta$ is the reduction of the two cell layers thickness under compression and $R$ the radius of the substrate. For $\delta$ smaller than the cell size, the slope gives the elastic modulus [3].

Figure 5

(a),(b) Morphology of the cells treated with Lat B during the separation process. Note the difference from Fig. 1. (c) Adhesion energy as it would be obtained through JKR theory [Eq. (1)] as a function of the dextran volume fraction in the presence of $0.1\mu \mathrm{M}$ (filled diamonds) or $1.5\mu \mathrm{M}$ (empty diamonds) latrunculine B. The solid line is the expected value deduced from the applied depletion force [17].