Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of two or more morphogens described by a reaction–diffusion system of equations. In this work we suggest another mechanism of the emergence of spatial distributions in biological tissues based on local cell communication and global inhibition, and described by a nonlocal reaction–diffusion equation. Instability of the homogeneous in space solution leads to the emergence of stationary pulses and not of periodic solutions as in the case of Turing instability.

中文翻译：

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论生物模型中空间分布出现的新机制


各种生物因子的不均匀分布对于组织生长控制、形态发生或肿瘤生长至关重要。第一个描述这种分布出现的模型是由 A. Turing 提出的，用于解释生长中的胚胎中的细胞分化。在这个模型中，由于反应-扩散方程组描述的两个或多个形态发生素的相互作用，出现了空间溶液的扩散驱动的不稳定性。在这项工作中，我们提出了基于局部细胞通讯和全局抑制的生物组织中空间分布出现的另一种机制，并由非局部反应-扩散方程描述。空间均匀解的不稳定性导致平稳脉冲的出现，而不是像图灵不稳定性那样出现周期性解。