Aharon Rotem, Janes Peter W, Burgess Anthony W, Hamza Kais, Klebaner Fima, Lackmann Martin
School of Mathematical Sciences, Monash University, Clayton, Victoria, Australia.
Department of Biochemistry & Molecular Biology, Monash University, Clayton, Victoria, Australia.
PLoS One. 2014 Dec 1;9(12):e111803. doi: 10.1371/journal.pone.0111803. eCollection 2014.
Eph receptors, the largest family of receptor tyrosine kinases, control cell-cell adhesion/de-adhesion, cell morphology and cell positioning through interaction with cell surface ephrin ligands. Bi-directional signalling from the Eph and ephrin complexes on interacting cells have a significant role in controlling normal tissue development and oncogenic tissue patterning. Eph-mediated tissue patterning is based on the fine-tuned balance of adhesion and de-adhesion reactions between distinct Eph- and ephrin-expressing cell populations, and adhesion within like populations (expressing either Eph or ephrin). Here we develop a stochastic, Lagrangian model that is based on Eph/ephrin biology: incorporating independent Brownian motion to describe cell movement and a deterministic term (the drift term) to represent repulsive and adhesive interactions between neighbouring cells. Comparison between the experimental and computer simulated Eph/ephrin cell patterning events shows that the model recapitulates the dynamics of cell-cell segregation and cell cluster formation. Moreover, by modulating the term for Eph/ephrin-mediated repulsion, the model can be tuned to match the actual behaviour of cells with different levels of Eph expression or activity. Together the results of our experiments and modelling suggest that the complexity of Eph/ephrin signalling mechanisms that control cell-cell interactions can be described well by a mathematical model with a single term balancing adhesion and de-adhesion between interacting cells. This model allows reliable prediction of Eph/ephrin-dependent control of cell patterning behaviour.
Eph受体是受体酪氨酸激酶中最大的家族，通过与细胞表面的ephrin配体相互作用，控制细胞间的粘附/去粘附、细胞形态和细胞定位。相互作用细胞上的Eph和ephrin复合物的双向信号传导在控制正常组织发育和致癌组织模式形成中起重要作用。Eph介导的组织模式形成基于不同表达Eph和ephrin细胞群体之间粘附和去粘附反应的微调平衡，以及同类群体（表达Eph或ephrin）内的粘附。在这里，我们基于Eph/ephrin生物学开发了一个随机拉格朗日模型：纳入独立的布朗运动来描述细胞运动，并使用一个确定性项（漂移项）来表示相邻细胞之间的排斥和粘附相互作用。实验和计算机模拟的Eph/ephrin细胞模式形成事件的比较表明，该模型概括了细胞间分离和细胞簇形成的动态过程。此外，通过调节Eph/ephrin介导的排斥项，可以调整模型以匹配具有不同Eph表达或活性水平的细胞的实际行为。我们的实验和建模结果共同表明，控制细胞间相互作用的Eph/ephrin信号传导机制的复杂性可以通过一个单一术语平衡相互作用细胞之间粘附和去粘附的数学模型很好地描述。该模型允许可靠地预测Eph/ephrin依赖的细胞模式形成行为的控制。
