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.

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

“…Specifically, the actin cortex's modulus E 0 was estimated to be 5.794 ± 0.095 kPa, the actin cortex's thickness d 0 was found to be 311 ± 3 nm and the bulk modulus E b was found to be 0.539 ± 0.002 kPa (mean ± SD). All values are in accordance with previous experiments performed using AFM on the same cell type 24 , and with values that have been reported in the literature 37 , 38 . Specifically, the actin cortex is expected to be between 300-400 nm for adherent cells 37 , and up to 10 times stiffer than the bulk of the cell 38 .…”

“…Below, the approach is briefly summarized. Full details can be found in the original publication 24 .…”

“…Starting from the Oliver-Pharr model 36 where R is the tip's radius and Λ is a phenomenological parameter, which was determined to be 1.74 from finite element analysis simulations 24 . This procedure has been implemented in the NanoAnalysis software, which allows to fit the average ES with equation ( 3) to obtain an estimate of E 0 , E b , and d 0 (Figure 5BVIII, black dashed line).…”

“…This procedure has been implemented in the NanoAnalysis software, which allows to fit the average ES with equation ( 3) to obtain an estimate of E 0 , E b , and d 0 (Figure 5BVIII, black dashed line). For full methodological details, refer to the original publication 24 .…”

“…To address this issue, instructions for the use of a newly developed open-source software programmed in Python and equipped with a user-friendly graphical user interface (GUI) for batch analysis of F-z curves are provided. The software allows for fast data screening, filtering of data, computation of the CP through different numerical procedures, the conventional computation of E, as well a more advanced analysis named the elasticity spectra 24 , allowing to estimate the cell's bulk Young's modulus, actin cortex's Young's modulus, and actin cortex's thickness. The software can be freely downloaded from GitHub and can be easily adapted to analyze data originating from other systems by adding an appropriate data parser.…”