Viscoelastic Properties of Confluent MDCK II Cells Obtained from Force Cycle Experiments

Abstract

The local mechanical properties of cells are frequently probed by force indentation experiments carried out with an atomic force microscope. Application of common contact models provides a single parameter, the Young’s modulus, to describe the elastic properties of cells. The viscoelastic response of cells, however, is generally measured in separate microrheological experiments that provide complex shear moduli as a function of time or frequency. Here, we present a straightforward way to obtain rheological properties of cells from regular force distance curves collected in typical force indentation measurements. The method allows us to record the stress-strain relationship as well as changes in the weak power law of the viscoelastic moduli. We derive an analytical function based on the elastic-viscoelastic correspondence principle applied to Hertzian contact mechanics to model both indentation and retraction curves. Rheological properties are described by standard viscoelastic models and the paradigmatic weak power law found to interpret the viscoelastic properties of living cells best. We compare our method with atomic force microscopy-based active oscillatory microrheology and show that the method to determine the power law coefficient is robust against drift and largely independent of the indentation depth and indenter geometry. Cells were subject to Cytochalasin D treatment to provoke a drastic change in the power law coefficient and to demonstrate the feasibility of the approach to capture rheological changes extremely fast and precisely. The method is easily adaptable to different indenter geometries and acquires viscoelastic data with high spatiotemporal resolution.

Buckling of epithelium growing under spherical confinement

“…Deviations from these values are penalized by harmonic spring energy terms with constants K and ! for the area and the length, respectively ( Fig 4A and SI) (17)(18)(19). In addition, large bending deformations of the monolayer are penalized by a harmonic spring energy term with constant c b (SI).…”

Viscoelasticity in simple indentation-cycle experiments: a computational study

“…More advanced approaches involve algorithms for the fitting of the force curves to the preselected viscoelastic models [5,15,16] or algorithms for the direct reconstruction of the relaxation function. In both cases, however, it is useful to obtain experimental curves in a wide range of indentation rates, and thus, it is useful to know how the curves should look for different viscoelastic models.…”

“…For a single springpot element (Power-law rheology model), we will use the Young's relaxation function in the form of ( ) 1   − = E t E t . The analytical solutions for the Ting's equations for triangular indentation were obtained previously by Bruckner et al [15]. The 1 () tt function for the triangular ramp is:…”

“…Most of them are using modifications of the testing protocol by including constant stress or constant strain phases and oscillatory indentation. However, there are also methods to extract viscoelastic properties directly from the simplest indentation experiment presenting a cycle of approach (deepening into the sample) and retraction of the indenter [5,[15][16][17]. Indentation of a viscoelastic body presents a complex problem with time-varying boundary conditions.…”

Single-cell immuno-mechanics: rapid viscoelastic changes are a hall-mark of early leukocyte activation

“…In fact their ratio = ′′ ′ , the loss tangent, lies within a narrow range of 0.1-0.3 20,30,45,46,[56][57][58][59] . This implies that the stiffer the cell, the more viscous it is.…”