Comparative study of non-invasive force and stress inference methods in tissue

Abstract

Abstract. In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate forceinference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed.

The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing

“…In our previous study, we formulated a Bayesian framework of force inference, in which all the cell junction tensions, differences in pressures among cells, and tissue stress are simultaneously inferred from the observed geometry of cells, up to a scaling factor (supplementary material Appendix S1). We have shown that inferred force and stress values are consistent with those obtained using other methods, such as laser ablation of cortical actin cables, quantification of myosin concentration and photo-elasticity (Nienhaus et al, 2009), and large-scale tissue ablation Ishihara and Sugimura, 2012;Ishihara et al, 2013). The global and noninvasive nature of the Bayesian force-inference method uniquely enables us to quantify space-time maps of force/stress in tissues and to relate the maps to hexagonal cell packing processes.…”

Measuring forces and stressesin situin living tissues

“…However, where such assumptions cannot be applied, the number of unknown forces becomes larger than the number of equations, and more elaborate statistical methods may be required to calculate these forces (Ishihara and Sugimura, 2012;Ishihara et al, 2013). Adding visual measurements of cell-cell junction curvature, which is related to tensions and pressures, increases the number of equations above that of unknown forces, again enabling a direct resolution (Brodland et al, 2014; chapter 18 of Paluch, 2015).…”

“…Most methods reviewed here require models and assumptions to extract measurements of relevant parameters, if necessary through fits of models to data, in particular for laser ablation and force inference experiments (Hutson et al, 2003;Farhadifar et al, 2007;Ishihara and Sugimura, 2012;Brodland et al, 2010Brodland et al, , 2014. Numerical simulations provide benchmark data in controlled conditions, to validate an experimental measurement and test its sensitivity to a parameter or to errors (Landsberg et al, 2009;Ishihara et al, 2013;Brodland et al, 2014;Bambardekar et al, 2015). Finally, comparing experiments with analytical models or numerical simulations enables us to refine the interpretation of experimental results and extract from them more information, such as material properties, or quantities that are not directly accessible to experiments (Farhadifar et al, 2007;Krieg et al, 2008;Rauzi et al, 2008;Mayer et al, 2010;Bonnet et al, 2012;Maître et al, 2012;Sugimura and Ishihara, 2013;Forouzesh et al, 2013).…”

Mechanical Forces and Growth in Animal Tissues

“…The deformations associated with growth in Drosophila imaginal tissues can be quantified using a chronic imaging approach (Heemskerk et al 2014). Force inference via image analysis of cell junctions allows one to measure patterns of mechanical stress, even when the tissue cannot be accessed mechanically (Chiou et al 2012;Ishihara and Sugimura 2012;Ishihara et al 2013). Force sensors based on deformable liquid droplets could also be a method of choice provided they can be delivered in vivo (Campàs et al 2014).…”