Quantifying cell-generated forces: Poisson’s ratio matters

Abstract

Quantifying mechanical forces generated by cellular systems has led to key insights into a broad range of biological phenomena from cell adhesion to immune cell activation. Traction force microscopy (TFM), the most widely employed force measurement methodology, fundamentally relies on knowledge of the force-displacement relationship and mechanical properties of the substrate. Together with the elastic modulus, the Poisson’s ratio is a basic material property that to date has largely been overlooked in TFM. Here, we evaluate the sensitivity of TFM to Poisson’s ratio by employing a series of computer simulations and experimental data analysis. We demonstrate how applying the correct Poisson’s ratio is important for accurate force reconstruction and develop a framework for the determination of error levels resulting from the misestimation of the Poisson’s ratio. In addition, we provide experimental estimation of the Poisson’s ratios of elastic substrates commonly applied in TFM. Our work thus highlights the role of Poisson’s ratio underpinning cellular force quantification studied across many biological systems.

Poroelastic osmoregulation of living cell volume

“…In these studies, it is assumed that initial pressurization ramps instantaneously (i.e. rise time t r = 0), while an instantaneous pressure rise assumption is mostly unrealistic under experimental circumstances and may lead to incorrect estimation of the swelling/deswelling poroelastic parameters during a transient osmotic stimulus ( Javanmardi et al, 2021 ). Moreover, active processes at the cell membrane (i.e.…”

Optimal mechanical interactions direct multicellular network formation on elastic substrates

“…Our modeling thus relates network structure to cell contractility, and the prediction can be checked in cell culture experiments on substrates of varying stiffness and Poisson's ratio [48], that combine traction force measure-ment with quantification of network morphology. The presence of substrate deformation-mediated interactions can be checked in a two-cell setup on a micropatterened substrate which allows to observe reorientations of one cell in response to the other, similar to strategies used to examine pairwise interactions during cell motility [56] and cardiomyocyte synchronization [25].…”

“…values could correspond to synthetic hydrogel substrates and the fibrous extracellular matrix, respectively. While hydrogel substrates are nearly incompressible (ν = 0.5), the ECM comprises of networks of fibers which permit remodeling and poroelastic flows leading to reduced material compressibility (e.g., ν = 0.1) at long time scales [48].…”

“…Networks at high ν contain smaller rings than the networks at low ν.Irreversible networks show more smaller rings as noise is not great enough to jostle these compact structures apart to favor more stringy morphologies. (d) Largest cluster size as a function of the fraction of network branch segments removed -a measure of a networks ability to to maintain functionality after being damaged[48]. Networks at the shoulder of the percolation transition exhibit less robustness than those well above the percolation transition for the ν = 0.1 case.…”

Associated changes in stiffness of collagen scaffolds during osteoblast mineralisation and bone formation

“…The set force was 700 nN to ensure an indentation of 10 μm minimum (< 10% of total height of the model). The Hertz model was fitted to the collected force curves to determine the Young’s Modulus E, assuming a Poisson ratio of 0.5 [ 25 ]. Data for each time point was normalised to its corresponding 3D acellular control of either soft or dense collagen scaffolds, as to obtain percentage change (% change = (E-E control )/E control ).…”