Nizhny Novgorod State University, Nizhny Novgorod, Russia.
Saint-Petersburg State Electrotechnical University (LETI), Saint-Petersburg, Russia.
PLoS One. 2019 Jun 27;14(6):e0218304. doi: 10.1371/journal.pone.0218304. eCollection 2019.
Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.
在分离的神经元培养物中，活神经元网络因其在各种实验条件下产生高度稳健的时空活动模式的能力而广为人知。这些模式通常被视为神经元瀑，满足幂律缩放，并因此在生命系统中体现出自组织临界性。一个关键问题是如何以具有生物学意义、数学上可处理且足够广泛的方式来解释和建模这些模式，以解释神经元的异质性和复杂性。在这里，我们推导出并分析了一个简单的网络模型，该模型可能是对这个问题的回应。我们的推导基于几个关于孤立神经元输入-输出行为的基本现象学观察。该模型的一个独特特征是，在最简单的描述水平上，它仅包含两个变量，即网络活动变量和对应于维持活动所需能量的外生变量，以及几个参数，如网络连接和信号传输效率。信号传输的效率由现象学能量变量调制。引人注目的是，这个简单的模型已经能够解释发育中的神经元培养物中网络尖峰和爆发的出现。模型行为和预测与已发表的关于培养神经元的实验证据一致。在更大的细胞自动机尺度上，引入依赖能量的调节机制会导致整体模型行为，可以将其特征化为在网络渗流转变的边缘上平衡。处于这种状态的网络活动表现出满足标度瀑条件的群体爆发。这种网络状态是自我可持续的，代表了全局网络范围过程和单个元素自发活动之间的能量平衡。
