Luz Yotam, Shamir Maoz
Department of Physiology and Cell Biology Faculty of Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
PLoS Comput Biol. 2016 Apr 15;12(4):e1004878. doi: 10.1371/journal.pcbi.1004878. eCollection 2016 Apr.
Neuronal oscillatory activity has been reported in relation to a wide range of cognitive processes including the encoding of external stimuli, attention, and learning. Although the specific role of these oscillations has yet to be determined, it is clear that neuronal oscillations are abundant in the central nervous system. This raises the question of the origin of these oscillations: are the mechanisms for generating these oscillations genetically hard-wired or can they be acquired via a learning process? Here, we study the conditions under which oscillatory activity emerges through a process of spike timing dependent plasticity (STDP) in a feed-forward architecture. First, we analyze the effect of oscillations on STDP-driven synaptic dynamics of a single synapse, and study how the parameters that characterize the STDP rule and the oscillations affect the resultant synaptic weight. Next, we analyze STDP-driven synaptic dynamics of a pre-synaptic population of neurons onto a single post-synaptic cell. The pre-synaptic neural population is assumed to be oscillating at the same frequency, albeit with different phases, such that the net activity of the pre-synaptic population is constant in time. Thus, in the homogeneous case in which all synapses are equal, the post-synaptic neuron receives constant input and hence does not oscillate. To investigate the transition to oscillatory activity, we develop a mean-field Fokker-Planck approximation of the synaptic dynamics. We analyze the conditions causing the homogeneous solution to lose its stability. The findings show that oscillatory activity appears through a mechanism of spontaneous symmetry breaking. However, in the general case the homogeneous solution is unstable, and the synaptic dynamics does not converge to a different fixed point, but rather to a limit cycle. We show how the temporal structure of the STDP rule determines the stability of the homogeneous solution and the drift velocity of the limit cycle.
据报道，神经元振荡活动与广泛的认知过程有关，包括外部刺激的编码、注意力和学习。尽管这些振荡的具体作用尚未确定，但很明显，神经元振荡在中枢神经系统中大量存在。这就引出了这些振荡的起源问题：产生这些振荡的机制是由基因硬连接的，还是可以通过学习过程获得？在这里，我们研究在前馈结构中通过尖峰时间依赖可塑性（STDP）过程出现振荡活动的条件。首先，我们分析振荡对单个突触的STDP驱动突触动力学的影响，并研究表征STDP规则和振荡的参数如何影响最终的突触权重。接下来，我们分析一群突触前神经元对单个突触后细胞的STDP驱动突触动力学。假设突触前神经群体以相同频率振荡，尽管相位不同，使得突触前群体的净活动在时间上是恒定的。因此，在所有突触都相等的均匀情况下，突触后神经元接收恒定输入，因此不会振荡。为了研究向振荡活动的转变，我们开发了突触动力学的平均场福克 - 普朗克近似。我们分析导致均匀解失去稳定性的条件。研究结果表明，振荡活动通过自发对称破缺机制出现。然而，在一般情况下，均匀解是不稳定的，突触动力学不会收敛到不同的固定点，而是收敛到一个极限环。我们展示了STDP规则的时间结构如何决定均匀解的稳定性和极限环的漂移速度。
