Meisel Christian, Klaus Andreas, Kuehn Christian, Plenz Dietmar
Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, Maryland, United States of America; Department of Neurology, University Clinic Carl Gustav Carus, Dresden, Germany.
Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, Maryland, United States of America.
PLoS Comput Biol. 2015 Feb 23;11(2):e1004097. doi: 10.1371/journal.pcbi.1004097. eCollection 2015 Feb.
Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system's tendency to recover more slowly from a perturbation the closer it gets to the transition--a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws. Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.
许多复杂系统已被发现会出现临界转变，即所谓的临界点，也就是系统状态突然转变为性质不同的另一种状态。这些变化会对系统功能产生深远影响，范围从可控的状态切换到灾难性的崩溃；因此，能够预测临界转变的信号非常令人期待。为此，研究工作聚焦于利用与系统相关的标记物的定性变化，即系统离转变越近，从微扰中恢复得就越慢，这一现象称为临界慢化。最近对临界慢化标度的研究为理解临界转变提供了一条精细路径：通过标度律来识别转变机制并改进转变预测。在此，我们通过研究哺乳动物皮层神经元的放电转变，首次在一个实际系统中概述并应用了这一策略。动力系统方法已确定了从阈下活动到放电转变的两种稳健机制，即鞍结分岔和霍普夫分岔。尽管理论对接近放电分岔处的临界慢化特征给出了精确预测，但定量的实验证据一直缺乏。通过对锥体神经元和快速放电中间神经元进行全细胞膜片钳记录，我们表明：1）向放电的转变在动态上对应于一个呈现慢化的临界转变；2）标度律表明鞍结分岔控制着慢化；3）这些精确的标度律可用于从有限的观察窗口预测分岔点。据我们所知，这是实验中关于临界慢化标度律的首次报道。它们为一大类神经科学建模提供了缺失的环节，并表明通过将临界慢化标度律作为一种适用于其他复杂系统的策略纳入其中，可以改进对临界点的估计。
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