Force-based three-dimensional model predicts mechanical drivers of cell sorting

Abstract

Many biological processes, including tissue morphogenesis, are driven by cell sorting. However, the primary mechanical drivers of sorting in multicellular aggregates (MCAs) remain controversial, in part because there is no appropriate computational model to probe mechanical interactions between cells. To address this important issue, we developed a three-dimensional, local force-based simulation based on the subcellular element method. In our method, cells are modelled as collections of locally interacting force-bearing elements. We use the method to investigate the effects of tension and cell–cell adhesion on MCA sorting. We predict a minimum level of adhesion to produce inside-out sorting of two cell types, which is in excellent agreement with observations in several developmental systems. We also predict the level of tension asymmetry needed for robust sorting. The generality and flexibility of the method make it applicable to tissue self-organization in a myriad of other biological processes, such as tumorigenesis and embryogenesis.

Cell surface fluctuations regulate early embryonic lineage sorting

“…Another suggested mechanical regulator of segregation in developing tissues is differential cell-cell affinity, which is determined by the force balance between cell-cell adhesion, cell surface tensions, and interfacial tension at cell contacts ( Amack and Manning, 2012 ; Chan et al., 2017 ; Maître et al., 2012 , 2016 ) ( Figures 2 A and 2B). Physical modeling suggests that in multicellular systems, differences in cell-cell affinity between two cell types can be sufficient to drive cell sorting ( Revell et al., 2019 ). To analyze differential cell-cell affinity, two quantities describing the contact between two cells in a homotypic doublet of each cell type could be measured.…”

“…To test whether the measured cell-cell affinity parameter is sufficient to account for the segregation of pEPI and pPrE cells, we used a 3D computational model based on the subcellular element method, termed 3D force-based cell-sorting simulation (CS3D, described in Revell et al. (2019) and also in STAR Methods ).…”

“…CS3D also incorporates cell growth and division and enables a multiscale modeling of inter- and intracellular interactions in multicellular aggregates such as the ICM. To score sorting in the aggregates, we established a sorting index ( Revell et al., 2019 ; STAR Methods ). The sorting index has a range of −1 to 1, where −1 indicates pEPI cells on the outside, 0 indicates random cell positioning (no sorting), and 1 indicates pPrE cells on the outside.…”

Cell surface fluctuations regulate early embryonic lineage sorting

“…Physical modelling suggests that in small multicellular systems, differences in cell-cell affinity are sufficient to drive cell sorting (33). Indeed, as we showed previously, differential affinity between two cell types is an excellent predictor of cell sorting (33). Differences in cell-cell affinity can be quantified by differences in contact area or angles ( Fig.…”

“…To test whether the measured affinity parameter is sufficient to account for the segregation of pEPI and pPrE cells, we used a 3D computational model based on the subcellular element method, termed 3D force-based cell sorting simulation (CS3D, described in (33) and also in Supplementary Information). Briefly, each individual cell is modelled as a group of infinitesimal elements, interacting via nearest-neighbour forces.…”