A combined experimental atomic force microscopy-based nanoindentation and computational modeling approach to unravel the key contributors to the time-dependent mechanical behavior of single cells

Abstract

Cellular responses to mechanical stimuli are influenced by the mechanical properties of cells and the surrounding tissue matrix. Cells exhibit viscoelastic behavior in response to an applied stress. This has been attributed to fluid flow-dependent and flow-independent mechanisms. However, the particular mechanism that controls the local time-dependent behavior of cells is unknown. Here, a combined approach of experimental AFM nanoindentation with computational modeling is proposed, taking into account complex material behavior. Three constitutive models (porohyperelastic, viscohyperelastic, poroviscohyperelastic) in tandem with optimization algorithms were employed to capture the experimental stress relaxation data of chondrocytes at 5 % strain. The poroviscohyperelastic models with and without fluid flow allowed through the cell membrane provided excellent description of the experimental time-dependent cell responses (normalized mean squared error (NMSE) of 0.003 between the model and experiments). The viscohyperelastic model without fluid could not follow the entire experimental data that well (NMSE = 0.005), while the porohyperelastic model could not capture it at all (NMSE = 0.383). We also show by parametric analysis that the fluid flow has a small, but essential effect on the loading phase and short-term cell relaxation response, while the solid viscoelasticity controls the longer-term responses. We suggest that the local time-dependent cell mechanical response is determined by the combined effects of intrinsic viscoelasticity of the cytoskeleton and fluid flow redistribution in the cells, although the contribution of fluid flow is smaller when using a nanosized probe and moderate indentation rate. The present approach provides new insights into viscoelastic responses of chondrocytes, important for further understanding cell mechanobiological mechanisms in health and disease.

Finite Element Models of Osteocytes and Their Load-Induced Activation

“…Thus, different non-linear models can be used to accurately describe osteocyte behavior under dynamic loading. This is commensurate with studies that use visco-hyperelastic, poro-hyperelastic or even poro-visco-hyperelastic descriptions of cell behavior [ 90 , 91 ]. Sophisticated continuum models are useful to accurately quantify the stiffness of healthy and diseased cells [ 92 ] However, they fall short in describing mechanosensing.…”

Finite element simulation for the effect of loading rate on visco‐hyperelastic characterisation of soft materials by spherical nanoindentation

“…Viscous properties were also considered in other works, Liu et al , proposed a viscoelastic finite element method (FEM) model, which accounted for both cell elasticity and viscoelasticity for cell AFM nanoindentation [21]. An approach of experimental AFM nanoindentation and FEM modelling was proposed by Florea et al , viscohyperelastic model was employed in their study for parameter analysis of fluid flow through the cell membrane [22]. The geometry of AFM tip is one of the most important factors in the proper characterisation of mechanical properties of cell [23].…”

Sensing and Modelling Mechanical Response in Large Deformation Indentation of Adherent Cell Using Atomic Force Microscopy

“…The horizontal axis data is denoted the Z-axis location of the AFM probe, and a negative value indicates the location is above the petri-dish surface referenced by the previous scanning result. The stress-relaxation behaviour of the deformed biological cells causes the discrepancy of the detected forces before and after the pause [28].…”

“…Apart from nano-indentation, various forms of mechanical stimuli, such as indentation, compression and elongation, were simulated by the hyperelastic models [22][23][24][25][26][27]. Many other non-linear elastic theories, such as viscoelastic and poroelastic, have also been investigated to characterize the time dependent stress-relaxation behaviour of the cell during nano-indentation [28]. Because of the versatility of the multi-layer hyperelastic model in describing the mechanical response of living cells under mechanical stimuli [25][26][27], it is adopted in this paper to simulate the continuum components of the cell during central indentation.…”