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At low dose Jagged acts synergistically with Delta to enable more robust lateral induction pattern formation. It also helps to suppress the possibility of obtaining an antihexagon pattern and increases the order in the patterns. 

Abstract Recent years have seen a tremendous growth of interest in understanding the role that the adaptive immune system could play in interdicting tumor progression. In this context, it has been shown that the density of adaptive immune cells inside a solid tumor serves as a favorable prognostic marker across different types of cancer. The exact mechanisms underlying the degree of immune cell infiltration is largely unknown. Here, we quantify the temporal dynamics of the density profile of activated immune cells around a solid tumor spheroid. We propose a computational model incorporating immune cells with active, persistent movement and a proliferation rate that depends on the presence of cancer cells, and show that the model able to reproduce semi-quantitatively the experimentally measured infiltration profile. Studying the density distribution of immune cells inside a solid tumor can help us better understand immune trafficking in the tumor micro-environment, hopefully leading towards novel immunotherapeutic strategies. 

The first stage of the metastatic cascade often involves motile cells emerging from a primary tumor either as single cells or as clusters. These cells enter the circulation, transit to other parts of the body and finally are responsible for growth of secondary tumors in distant organs. The mode of dissemination is believed to depend on the EMT nature (epithelial, hybrid or mesenchymal) of the cells. Here, we calculate the cluster size distribution of these migrating cells, using a mechanistic computational model, in presence of different degree of EMT-ness of the cells; EMT is treated as given rise to changes in their active motile forces ( μ ) and cell-medium surface tension (Γ). We find that, for ( μ > μ min , Γ > 1), when the cells are hybrid in nature, the mean cluster size, N ¯ ∼ Γ 2 . 0 / μ 2 . 8 , where μ min increases with increase in Γ. For Γ ≤ 0, N ¯ = 1 , the cells behave as completely mesenchymal. In presence of spectrum of hybrid states with different degree of EMT-ness (motility) in primary tumor, the cells which are relatively more mesenchymal (higher μ ) in nature, form larger clusters, whereas the smaller clusters are relatively more epithelial (lower μ ). Moreover, the heterogeneity in μ is comparatively higher for smaller clusters with respect to that for larger clusters. We also observe that more extended cell shapes promote the formation of smaller clusters. Overall, this study establishes a framework which connects the nature and size of migrating clusters disseminating from a primary tumor with the phenotypic composition of the tumor, and can lead to the better understanding of metastasis.