标题： 细胞动力学中趋触性和趋化性的关系 显示英文标题

标题： Relationship between haptotaxis and chemotaxis in cell dynamics

摘要： 具有长突起的细胞（如神经元）通过接触其他细胞进行交流并适当排列的现象被称为通过贴壁趋性的细胞分选，这一现象由涉及非局部对流的偏微分方程描述。 相比之下，通过化学物质与其他细胞交流并适当排列的细胞现象被称为通过趋化性的细胞分选，通常由 Keller-Segel 模型等趋化系统建模。 尽管贴壁趋性和趋化性之间存在明显差异，但常常观察到相似的行为。 本研究探讨了贴壁趋性和趋化性在细胞分选现象中的关系。 具体来说，我们分析了针对贴壁趋性的非局部聚集模型与 Keller-Segel 型趋化系统之间的联系。 通过展示特定核近似下的收敛性，我们展示了这些不同的机制如何导致可比的动力学行为。 本研究为理解贴壁趋性和趋化性在细胞分选现象中的相互作用提供了数学框架。 显示英文摘要

摘要： The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial differential equations involving nonlocal advection. In contrast, cell phenomena where cells communicate with other cells via chemical substances and arrange themselves appropriately are termed cell sorting through chemotaxis, typically modeled by chemotactic systems such as the Keller--Segel model. Although there are clear differences between haptotaxis and chemotaxis, similar behaviors are often observed. In this study, we investigate the relationship between haptotaxis and chemotaxis in cell sorting phenomena. Specifically, we analyze the connections between a nonlocal aggregation model for haptotaxis and a Keller--Segel type chemotaxis system. By demonstrating convergence under specific kernel approximations, we show how these distinct mechanisms can lead to comparable dynamic behaviors. This study provides a mathematical framework for understanding the interplay between haptotaxis and chemotaxis in cell sorting phenomena.