Abstract
The process of cell-sorting is essential for development and maintenance of tissues. Mathematical modeling can provide the means to analyze the consequences of different hypotheses about the underlying mechanisms. With the Differential Adhesion Hypothesis, Steinberg proposed that cell-sorting is determined by quantitative differences in cell-type-specific intercellular adhesion strengths. An implementation of the Differential Adhesion Hypothesis is the Differential Migration Model by Voss-Böhme and Deutsch. There, an effective adhesion parameter was derived analytically for systems with two cell types, which predicts the asymptotic sorting pattern. However, the existence and form of such a parameter for more than two cell types is unclear. Here, we generalize analytically the concept of an effective adhesion parameter to three and more cell types and demonstrate its existence numerically for three cell types based on in silico time-series data that is produced by a cellular-automaton implementation of the Differential Migration Model. Additionally, we classify the segregation behavior using statistical learning methods and show that the estimated effective adhesion parameter for three cell types matches our analytical prediction. Finally, we demonstrate that the effective adhesion parameter can resolve a recent dispute about the impact of interfacial adhesion, cortical tension and heterotypic repulsion on cell segregation.
Highlights
We show numerically for three cell types that the analytically predicted effective adhesion parameter (EAP) guides the asymptotic sorting behavior in the Differential Migration Model (DMM), i.e., the EAP determines the asymptotic value of the normalized sum of heterotypic contacts
The EAP resolves previous discussions about the impact of interfacial tension on cell segregation compared to interfacial adhesion or repulsion [11]: We predict that a higher level of segregation is reached when the EAP is large, which can be achieved by both heterotypic repulsion or differential adhesion
We propose that rather than differentiating between intercellular adhesion and contact tension, the combined effect of intercellular contact on cellular motility, which is quantified by the EAP, should be focused on
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. During the development of multicellular organisms, mechanical forces affect the internal states of cells as well as the interaction between cells, and they are, an integral part of all morphogenetic processes [1]. These forces are typically driven by molecular motors and transmitted via cytoskeleton elements and adhesion molecules within the cells and between them. Molecular motor driven movement and force transmission via adhesion complexes constitute two major self-organizing phenomena that drive tissue morphogenesis
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