Rossbach Philipp, Böhme Hans-Joachim, Lange Steffen, Voss-Böhme Anja
DataMedAssist, HTW Dresden, 01062 Dresden, Germany.
Faculty of Informatics/Mathematics, HTW Dresden-University of Applied Sciences, 01062 Dresden, Germany.
Entropy (Basel). 2021 Oct 21;23(11):1378. doi: 10.3390/e23111378.
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.
细胞分选过程对于组织的发育和维持至关重要。数学建模可以提供分析关于潜在机制的不同假设所产生后果的方法。基于差异黏附假说，斯坦伯格提出细胞分选由细胞类型特异性细胞间黏附强度的定量差异决定。差异黏附假说的一个实现形式是沃斯 - 伯梅和多伊奇提出的差异迁移模型。在该模型中，针对具有两种细胞类型的系统解析推导出了一个有效黏附参数，该参数可预测渐近分选模式。然而，对于两种以上细胞类型时这种参数的存在性和形式尚不清楚。在此，我们将有效黏附参数的概念解析推广到三种及更多细胞类型，并基于差异迁移模型的细胞自动机实现所产生的计算机模拟时间序列数据，通过数值方法证明了三种细胞类型情况下该参数的存在性。此外，我们使用统计学习方法对分离行为进行分类，并表明三种细胞类型的估计有效黏附参数与我们的解析预测相符。最后，我们证明有效黏附参数能够解决最近关于界面黏附、皮层张力和异型排斥对细胞分离影响的争议。
