Reaction–Diffusion Model-Based Research on Formation Mechanism of Neuron Dendritic Spine Patterns

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.