Elasticity spectra as a tool to investigate actin cortex mechanics

Abstract

Background: The mechanical properties of single living cells have proven to be a powerful marker of the cell physiological state. The use of nanoindentation-based single cell force spectroscopy provided a wealth of information on the elasticity of cells, which is still largely to be exploited. The simplest model to describe cell mechanics is to treat them as a homogeneous elastic material and describe it in terms of the Young's modulus. Beside its simplicity, this approach proved to be extremely informative, allowing to assess the potential of this physical indicator towards high throughput phenotyping in diagnostic and prognostic applications.

Results: Here we propose an extension of this analysis to explicitly account for the properties of the actin cortex. We present a method, the Elasticity Spectra, to calculate the apparent stiffness of the cell as a function of the indentation depth and we suggest a simple phenomenological approach to measure the thickness and stiffness of the actin cortex, in addition to the standard Young's modulus.

Conclusions: The Elasticity Spectra approach is tested and validated on a set of cells treated with cytoskeleton-affecting drugs, showing the potential to extend the current representation of cell mechanics, without introducing a detailed and complex description of the intracellular structure.

Keywords: Actin cortex; Cell mechanics; Cytoskeleton; Force spectroscopy; Nanoindentation; Scanning probe microscopy.

Fig. 1

Overview of a nanoindentation experiment. a Schematics of a nanoindentation experiment performed with a spherical probe of radius R indenting over a compliant material with Young’s modulus E. The main geometrical relationships between the displacement z, indentation $\delta$ and deflection x are indicated. b FluidFM cantilever with attached microbead over a confluent monolayer of HEK-293T cells. c Typical experimental dataset of 127 force-indentation curves obtained on cells. The blue line is the average curve $〈F,(,\delta ,)〉$, and the cyan band is extended over one standard deviation

Fig. 2

Results of ferrule-top nanoindentation experiments on a homogeneous gel. a Picture of the experimental setup, showing the Chiaro nanoindenter with the cantilever holder and optical fiber (white) attached to the z-Piezo (black). The probe with a microbead (transparent) is positioned above the gel and immersed in buffer solution (pink). b Histograms of the Young’s modulus as calculated either with the standard Hertzian fit approach (blue) or based on the average elasticity spectrum (red). Gaussian fit of the histogram values provides (peak position ± SEM) $E=5.2\pm 0.2$ kPa for the Hertz approach and $E=5.6\pm 0.1$ kPa for ES. c Force-indentation results, showing the average force-indentation curve $〈F,(,\delta ,)〉$ (blue) and Hertzian fit (red dashed) from a set of 97 nanoindentation experiments. (d) Elasticity spectra analysis corresponding to the curves in c, showing the average elasticity spectrum $〈E,(,\delta ,)〉$ (blue) and its mean value (red dashed)

Fig. 3

Bilayer model. a Schematics of the geometry of the bilayer model, with an external layer with elasticity $E_0$ and thickness $d_0$ and a bulk substrate with elasticity $E_b$, indented with a sphere of radius R. b Elasticity spectrum (blue dots) calculated from numerical data for a bilayer with $E_0$ = 9.8kPa, $d_0$ = 300nm and $E_b$ = 8.4kPa indicated by the black dotted lines. The solid red line represents the exponential fit that returns the values $E_0$ = 9.77kPa, $d_0$ = 302nm and $E_b$ = 8.39kPa

Fig. 4

Elasticity spectra of single cells. a Schematic of the experimental protocol: a microbead is collected with the FluidFM cantilever and used to indent the cell, described as a double layer with the external AC of thickness $d_0$ and elasticity $E_0$ and the cytosol with bulk elasticity $E_b$. b Experimental set of force–indentation curves $F(\delta )$ obtained on 315 cells. The blue line indicates the average curve and the red dashed line is the best Hertz fit (Eq. 1). c Elasticity spectra obtained by the application of Eq. (5) to the single curves of b. The blue line indicates the average of tghe Elasticity Spectra and the red dashed line is the fit with the exponential bilayer model (Eq. 8)

Fig. 5

Results of the elasticity spectra analysis for control and drug treated HEK-293T cells. The elasticity of the cortex (a), of the cytosol (b), and the thickness of the cortex (c) were calculated for a set of control cells (N = 4 with 13–36 cells each) and after treatment with either 10 μM cytochalasin D (Cyto D, inhibiting actin polymerization, N = 5; 17–33 cells) or 1 μM jasplakinolide (Jaspla, inducing actin polymerization, N = 4; 20–36 cells). Error bars represent the variance of the repeats, calculated over the weighted average