Gelastopoulos Alexandros, Kopell Nancy J
Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, 02215, Boston, MA, USA.
Department of Marketing and Management, University of Southern Denmark, Campusvej 55, 5230, Odense, Denmark.
J Math Neurosci. 2020 Nov 17;10(1):19. doi: 10.1186/s13408-020-00096-7.
Neural oscillations, including rhythms in the beta1 band (12-20 Hz), are important in various cognitive functions. Often neural networks receive rhythmic input at frequencies different from their natural frequency, but very little is known about how such input affects the network's behavior. We use a simplified, yet biophysical, model of a beta1 rhythm that occurs in the parietal cortex, in order to study its response to oscillatory inputs. We demonstrate that a cell has the ability to respond at the same time to two periodic stimuli of unrelated frequencies, firing in phase with one, but with a mean firing rate equal to that of the other. We show that this is a very general phenomenon, independent of the model used. We next show numerically that the behavior of a different cell, which is modeled as a high-dimensional dynamical system, can be described in a surprisingly simple way, owing to a reset that occurs in the state space when the cell fires. The interaction of the two cells leads to novel combinations of properties for neural dynamics, such as mode-locking to an input without phase-locking to it.
神经振荡，包括β1频段（12 - 20赫兹）的节律，在各种认知功能中都很重要。神经网络常常会接收到频率与其固有频率不同的节律性输入，但对于这种输入如何影响网络行为却知之甚少。我们使用一种简化但具有生物物理性质的顶叶皮层β1节律模型，来研究其对振荡输入的响应。我们证明，一个细胞能够同时对两个频率不相关的周期性刺激做出反应，与其中一个刺激同相放电，但其平均放电率与另一个刺激相同。我们表明这是一个非常普遍的现象，与所使用的模型无关。接下来我们通过数值模拟表明，另一个被建模为高维动力系统的细胞的行为，可以用一种惊人的简单方式来描述，这是由于细胞放电时状态空间中发生的重置。这两个细胞的相互作用导致了神经动力学特性的新组合，比如锁定到一个输入但不与之锁相。
