Park Seong Hyun, Lefebvre Jérémie
University of Toronto, St. George, 40 St. George St., M5S 2E4, Toronto, Canada.
Krembil Research Institute, University Health Network, 60 Leonard Avenue, M5T 2S8, Toronto, Canada.
J Math Neurosci. 2020 Sep 16;10(1):16. doi: 10.1186/s13408-020-00091-y.
White matter pathways form a complex network of myelinated axons that regulate signal transmission in the nervous system and play a key role in behaviour and cognition. Recent evidence reveals that white matter networks are adaptive and that myelin remodels itself in an activity-dependent way, during both developmental stages and later on through behaviour and learning. As a result, axonal conduction delays continuously adjust in order to regulate the timing of neural signals propagating between different brain areas. This delay plasticity mechanism has yet to be integrated in computational neural models, where conduction delays are oftentimes constant or simply ignored. As a first approach to adaptive white matter remodeling, we modified the canonical Kuramoto model by enabling all connections with adaptive, phase-dependent delays. We analyzed the equilibria and stability of this system, and applied our results to two-oscillator and large-dimensional networks. Our joint mathematical and numerical analysis demonstrates that plastic delays act as a stabilizing mechanism promoting the network's ability to maintain synchronous activity. Our work also shows that global synchronization is more resilient to perturbations and injury towards network architecture. Our results provide key insights about the analysis and potential significance of activity-dependent myelination in large-scale brain synchrony.
白质通路形成了一个由有髓轴突组成的复杂网络，该网络调节神经系统中的信号传递，并在行为和认知中发挥关键作用。最近的证据表明，白质网络具有适应性，并且髓鞘在发育阶段以及之后通过行为和学习以活动依赖的方式进行自我重塑。因此，轴突传导延迟会不断调整，以调节在不同脑区之间传播的神经信号的时间。这种延迟可塑性机制尚未整合到计算神经模型中，在这些模型中，传导延迟通常是恒定的或被简单地忽略。作为适应性白质重塑的第一步，我们通过使所有连接具有适应性的、相位依赖的延迟来修改经典的Kuramoto模型。我们分析了该系统的平衡点和稳定性，并将我们的结果应用于双振荡器和大维度网络。我们的联合数学和数值分析表明，可塑性延迟作为一种稳定机制，促进了网络维持同步活动的能力。我们的工作还表明，全局同步对网络架构的扰动和损伤更具弹性。我们的结果为大规模脑同步中活动依赖的髓鞘形成的分析和潜在意义提供了关键见解。
