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

Abstract

Many biological processes, including tissue morphogenesis, are driven by mechanical sorting. However, the primary mechanical drivers of cell sorting remain controversial, in part because there remains a lack of appropriate threedimensional computational methods to probe the mechanical interactions that drive sorting. To address this important issue, we developed a three-dimensional, local force-based simulation method to enable such investigation into the sorting mechanisms of multicellular aggregates. Our method utilises the subcellular element method, in which cells are modeled as collections of locally-interacting force-bearing elements, accommodating cell growth and cell division. We define two different types of intracellular elements, assigning different attributes to boundary elements to model a cell cortex, which mediates the interfacial interaction between different cells. By tuning interfacial adhesion and tension in each cell cortex, we can control and predict the degree of sorting in cellular aggregates. The method is validated by comparing the interface areas of simulated cell doublets to experimental data and to previous theoretical work. We then define numerical measures of sorting and investigate the effects of mechanical parameters on the extent of sorting in multicellular aggregates. Using this method, we find that a minimum adhesion is required for differential interfacial tension to produce inside-out sorting of two cell types with different mechanical phenotypes. We predict the value of the minimum adhesion, 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 biological processes, such as tumorigenesis and embryogenesis.Self-organization is a widely-studied feature of non-equilibrium systems across a great variety of fields [1,2,3]. In Biology, self-organized processes range in length-and time-scales from protein folding [4] to the dramatic murmurations of starlings [5]. Generically, these systems exhibit emergence of macroscopic order 5 from disordered states by the action of simple, local, inter-component interactions. Here we focus on one such a process of self-organization -cell sorting. Cell sorting in a multicellular aggregate (MCA) is critical for normal development of an embryo, and is also at the heart of pathologies such as metastastic growth of tumors. 10The spontaneous separation of mixtures of embryonic cells has long been thought to be driven by cells' differing "affinity" for one another [6]. Two primary drivers have been proposed to facilitate differential affinity: differential adhesion and differential interfacial tension.The differential adhesion hypothesis is a widely studied driver of cell sort-15 ing [7, 8,9]. It asserts that, in an MCA with multiple cell types, those with strong mutual adhesion adhere together better than cells with weaker mutual adhesion. The ...