Group for Neural Theory, LNC INSERM U960, DEC, Ecole Normale Supérieure PSL* University, Paris, France.
Center for Cognition and Decision Making, Institute for Cognitive Neuroscience, NRU Higher School of Economics, Moscow, Russia.
PLoS Comput Biol. 2019 May 9;15(5):e1007019. doi: 10.1371/journal.pcbi.1007019. eCollection 2019 May.
Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated in routing information. While multiple cellular mechanisms influence the network oscillatory dynamics and structure the macroscopic firing motifs, one of the key questions is to identify the biophysical neuronal and synaptic properties that permit such motifs to arise. A second important issue is how the different neural activity coherence states determine the communication between the neural circuits. Here we analyse the emergence of phase-locking within bidirectionally delayed-coupled spiking circuits in which global gamma band oscillations arise from synaptic coupling among largely excitable neurons. We consider both the interneuronal (ING) and the pyramidal-interneuronal (PING) population gamma rhythms and the inter coupling targeting the pyramidal or the inhibitory neurons. Using a mean-field approach together with an exact reduction method, we reduce each spiking network to a low dimensional nonlinear system and derive the macroscopic phase resetting-curves (mPRCs) that determine how the phase of the global oscillation responds to incoming perturbations. This is made possible by the use of the quadratic integrate-and-fire model together with a Lorentzian distribution of the bias current. Depending on the type of gamma (PING vs. ING), we show that incoming excitatory inputs can either speed up the macroscopic oscillation (phase advance; type I PRC) or induce both a phase advance and a delay (type II PRC). From there we determine the structure of macroscopic coherence states (phase-locking) of two weakly synaptically-coupled networks. To do so we derive a phase equation for the coupled system which links the synaptic mechanisms to the coherence states of the system. We show that a synaptic transmission delay is a necessary condition for symmetry breaking, i.e. a non-symmetric phase lag between the macroscopic oscillations. This potentially provides an explanation to the experimentally observed variety of gamma phase-locking modes. Our analysis further shows that symmetry-broken coherence states can lead to a preferred direction of signal transfer between the oscillatory networks where this directionality also depends on the timing of the signal. Hence we suggest a causal theory for oscillatory modulation of functional connectivity between cortical circuits.
不同脑区的宏观振荡表现出多种相位关系，这些相位关系在时间上是持久的，并与信息传递有关。虽然多种细胞机制影响网络振荡动力学并构建宏观放电模式，但关键问题之一是确定允许出现这些模式的生物物理神经元和突触特性。第二个重要问题是不同的神经活动相干状态如何决定神经回路之间的通信。在这里，我们分析了在双向延迟耦合的放电回路中出现的锁相现象，其中全局伽马波段振荡是由主要兴奋性神经元之间的突触耦合产生的。我们考虑了中间神经元（ING）和锥体神经元-中间神经元（PING）群体的伽马节律，以及针对锥体神经元或抑制性神经元的相互耦合。使用平均场方法和精确的约化方法，我们将每个放电网络约化为一个低维非线性系统，并得出确定全局振荡相位对输入扰动响应的宏观相重置曲线（mPRC）。这是通过使用二次积分点火模型和偏置电流的洛伦兹分布来实现的。根据伽马类型（PING 与 ING）的不同，我们表明传入的兴奋性输入可以加速宏观振荡（相位提前；I 型 PRC），或者诱导相位提前和延迟（II 型 PRC）。从那里，我们确定了两个弱突触耦合网络的宏观相干状态（锁相）的结构。为此，我们为耦合系统推导了一个相方程，该方程将突触机制与系统的相干状态联系起来。我们表明，突触传递延迟是对称破缺的必要条件，即宏观振荡之间存在非对称的相滞后。这可能为实验观察到的各种伽马锁相模式提供了解释。我们的分析进一步表明，对称破缺的相干状态可以导致振荡网络之间信号传递的优先方向，这种方向性也取决于信号的时间。因此，我们提出了一个关于皮质回路功能连接的振荡调制的因果理论。
