The pattern abnormalities of dendritic spine, tiny protrusions on neuron dendrites, have been found related to multiple nervous system diseases, such as Parkinson’s disease and schizophrenia. The determination of the factors affecting spine patterns is of vital importance to explore the pathogenesis of these diseases, and further, search the treatment method for them. Although the study of dendritic spines is a hot topic in neuroscience in recent years, there is still a lack of systematic study on the formation mechanism of its pattern. This paper provided a reinterpretation of reaction-diffusion model to simulate the formation process of dendritic spine, and further, study the factors affecting spine patterns. First, all four classic shapes of spines, mushroom-type, stubby-type, thin-type, and branched-type were reproduced using the model. We found that the consumption rate of substrates by the cytoskeleton is a key factor to regulate spine shape. Moreover, we found that the density of spines can be regulated by the amount of an exogenous activator and inhibitor, which is in accordance with the anatomical results found in hippocampal CA1 in SD rats with glioma. Further, we analyzed the inner mechanism of the above model parameters regulating the dendritic spine pattern through Turing instability analysis and drew a conclusion that an exogenous inhibitor and activator changes Turing wavelength through which to regulate spine densities. Finally, we discussed the deep regulation mechanisms of several reported regulators of dendritic spine shape and densities based on our simulation results. Our work might evoke attention to the mathematic model-based pathogenesis research for neuron diseases which are related to the dendritic spine pattern abnormalities and spark inspiration in the treatment research for these diseases.

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基于反应扩散模型的神经元树突棘图案形成机理的研究

已经发现树突棘的模式异常，神经元树突上的微小突起与多种神经系统疾病有关，例如帕金森氏病和精神分裂症。确定影响脊柱形态的因素对于探索这些疾病的发病机理，并进一步寻找治疗方法具有至关重要的意义。尽管树突棘的研究是近年来神经科学的热门话题，但仍缺乏对其模式形成机理的系统研究。本文对反应扩散模型进行了重新解释，以模拟树突状脊柱的形成过程，并进一步研究了影响脊柱形态的因素。首先，使用该模型复制了所有四个经典形状的刺形：蘑菇型，粗短型，细型和分支型。我们发现细胞骨架消耗底物的速率是调节脊柱形状的关键因素。而且，我们发现棘突的密度可以通过外源性激活剂和抑制剂的量来调节，这与在胶质瘤SD大鼠海马CA1中发现的解剖结果一致。此外，我们通过图灵不稳定性分析，分析了上述模型参数调节树突状脊柱模式的内在机理，并得出结论，外源性抑制剂和活化剂改变了图灵波长，从而调节了脊柱密度。最后，我们根据模拟结果讨论了几种报道的树突状脊柱形状和密度调节剂的深度调节机理。