Ajazi Fioralba, Chavez-Demoulin Valérie, Turova Tatyana
Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100, Lund, Sweden.
Faculty of Business and Economics, University of Lausanne, 1015, Lausanne, Switzerland.
J Math Biol. 2019 Oct;79(5):1639-1663. doi: 10.1007/s00285-019-01406-8. Epub 2019 Jul 24.
We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.
我们对一个随机生长的二维网络进行了分析，该网络模拟了树突和轴突分支的形态生长。从这个模型的随机几何结构中，我们推导出了潜在突触连接的动态图。我们估计了标准网络参数，如度分布、平均最短路径长度和聚类系数，并将所有这些参数视为时间的函数。我们的结果表明，即使是一个只有几个参数的简单模型，也能够代表广泛的架构谱，根据网络发展的时间捕捉著名模型（如随机图或小世界网络）的特性。引入的模型不仅允许进行相当直接的模拟，而且还适合进行严格的分析。这为进一步研究此类网络上突触连接的形成及其可塑性动力学提供了基础。
