Computational analysis of the tether-pulling experiment to probe plasma membrane-cytoskeleton interaction in cells

Tethers are thin membrane tubes that can be formed when relatively small and localized forces are applied to cellular membranes and lipid bilayers. Tether pulling experiments have been used to better understand the fine membrane properties. These include the interaction between the plasma membrane and the underlying cytoskeleton, which is an important factor affecting membrane mechanics. We use a computational method aimed at the interpretation and design of tether pulling experiments in cells with a strong membrane-cytoskeleton attachment. In our model, we take into account the detailed information in the topology of bonds connecting the plasma membrane and the cytoskeleton. We compute the force-dependent piecewise membrane deflection and bending as well as modes of stored energy in three major regions of the system: body of the tether, membrane-cytoskeleton attachment zone, and the transition zone between the two. We apply our method to three cells: cochlear outer hair cells (OHCs), human embryonic kidney (HEK) cells, and Chinese hamster ovary (CHO) cells. OHCs have a special system of pillars connecting the membrane and the cytoskeleton, and HEK and CHO cells have the membrane-cytoskeleton adhesion arrangement via bonds (e.g., PIP2), which is common to many other cells. We also present a validation of our model by using experimental data on CHO and HEK cells. The proposed method can be an effective tool in the analyses of experiments to probe the properties of cellular membranes.

Figure 1

Panel (a) is an illustration of the cochlear outer hair cell tether experiment, with a particular focus on the modeled region (i.e., where the membrane transitions from the tether and reattaches to the lateral wall). Panel (b) is an analogous illustration of the HEK cell tether experiment. TeR, tether region; TrR, transition region; CAR, cytoskeleton attachment region; PM, plasma membrane; DP, detached pillar; AP, attached pillar; C, cytoskeleton.

Figure 2

Illustration of the geometries in the attachment region. The top panel represents the discrete radial pillars of the OHC; the lower panel illustrates the continuous attachment distribution of the plasma membrane to the cytoskeleton in the HEK cell. The connections between the plasma membrane and the cytoskeleton substrate are modeled as Hookean springs.

Figure 3

Surface area void fraction as a function of bond width and edge-to-edge spacing.

Figure 4

Estimation of the adhesion modulus over a range of bond diameters and separation distances.

Figure 5

Panel (a), SEM image of magnetic tweezers tether pulling experiment, where the superimposed white dotted line is our model’s prediction for the shape of a tether pulled from a CHO cell. The SEM image and model parameters are based on CHO cell tether experiments by Hosu et al. Panel (b), standing wave fluorescence microscopy (SWFM) image of HEK tethers, where the white dotted line is our model’s prediction of this tether’s shape. The SWFM image is based on experiments by Gliko et al. Panel (a) source: B. G. Hosu, M. Sun, F. Marga, M. Grandbois, and G. Forgacs, “Eukaryotic membrane tethers revisited using magnetic tweezers,” Phys. Biol. 4, 67 (2007). Panel (b) source: O. Gliko, G. D. Reddy, B. Anvari, W. E. Brownell, and P. Saggau, “Standing wave total internal reflection fluorescence microscopy to measure the size of nanostructures in living cells,” J. Biomed. Opt. 11, 064013 (2006).

Figure 6

The 60 pN holding force membrane shape profiles for the OHC and HEK cell. Panel (a) shows the OHC shape profile over the attachment and detachment zones; Panel (b) shows the HEK shape profile over the attachment and detachment zones; Panel (c) focuses on the attachment zone and includes the shape profile for both cells. The light-gray regions of the profile represent the spatial areas where the membrane is unattached to the cytoskeleton, and the emboldened regions of the profile represent the plasma membrane-cytoskeleton interaction sites.

Figure 7

Panel (a): This figure shows how the maximum deflection, within the attachment region of the cell, varies over a wide range of equilibrium tether holding forces. Panel (b): This figure shows how the detachment radius varies over a wide range of equilibrium tether holding forces.

Figure 8

Effects of varying the bending modulus on the membrane shape profile.: (a) general view and (b) attachment region. The maximum membrane deflection in the attachment region is set at 4 nm, corresponding to an adhesion modulus of $3.18\times {10}^5\text{pN}\mu {\text{m}}^{-3}$. The bending moduli are: 30, 55, and $80k_{B}T$.

Figure 9

This is the free energy stored within the attachment region over a range of forces. Each line is for a different bending modulus: 30, 55, and $80k_{B}T$.

Figure 10

Effects of varying the maximum membrane deflection in the attachment region on the membrane shape profile. The bending modulus remains constant at $55k_{B}T$. The values of maximum deflection in the attachment region are chosen to be 3, 4, and 5 nm, which correspond to adhesion moduli of $4.24\times {10}^5$, $3.18\times {10}^5$, and $2.55\times {10}^5\text{pN}\mu {\text{m}}^{-3}$, respectively.

Figure 11

Modes of free energy stored within the attachment region over a range of forces. Each line is for a different adhesion modulus: $4.24\times {10}^5$, $3.18\times {10}^5$, and $2.55\times {10}^5\text{pN}\mu {\text{m}}^{-3}$.

Figure 12

Membrane shape profiles for various bond spacing in the attachment region. Bond width is constant at 5 nm. Bond spacing is 5, 7, and 9.5 nm, giving adhesion moduli of $2.2\times {10}^6$, $3.11\times {10}^6$, and $4.54\times {10}^6\text{pN}\mu {\text{m}}^{-3}$, respectively. As bond spacing gets larger, the detachment radius gets smaller.

Figure 13

Membrane shape profiles for various bond widths in the attachment region. Bond spacing is constant at 9.5 nm. Bond width is 5 and 10 nm, giving adhesion moduli of $4.54\times {10}^6$ and $2.05\times {10}^6\text{pN}\mu {\text{m}}^{-3}$, respectively. As bond width gets wider, the detachment radius gets larger.

Figure 14

Membrane shape profiles for the continuous distribution with various adhesion moduli. One case uses an adhesion modulus estimate based on HEK tether formation force $\left(1.25\times {10}^6\text{pN}\mu {\text{m}}^{-3}\right)$. The other uses an adhesion modulus based on the adhesion energy value of $3.2\times {10}^5\text{pN}\mu {\text{m}}^{-3}$ from [12].

Figure 15

An illustration of the Gaussian PDF and CDFs based on mean spacing of 5, 7, 9.5, and 12 nm and a standard deviation of 2 nm.

Figure 16

The randomly generated center-to-center spacing between 21 different bonds. We take the mean spacing to be 9.5 nm and the standard deviation to be 2 nm. Data points are the edge-to-edge bond spacing value; solid line is the PDF and CDF functions.

Figure 17

Illustration of the annular spacing between bonds. The gray area represents a membrane-cytoskeleton bond site, and the white areas adjacent to the gray area represent interstitial regions between bond sites.