In order to better understand neurodegenerative diseases, characterization of neuronal activities at different regions correlated with the resting state brain activity, which indicates the normality of the spontaneous cognition, to sustain the memory of the brain is needed. The signaling dynamics of these neuronal activities are determined by the so-called default mode network consisting of nodes overlapped with the major functional regions of the brain for task-driven cognition and links among the nodes with correlation coefficients. In the case that the brain's signaling system is an integrated network system, which integrates several sub-systems - molecular, cellular, and cognitive networks, and the signaling network of the brain exists as a complex network that systematically determines the function of the brain, how can the coupling relationship among these interacted sub-systems be modelled and quantitatively analyzed. To answer this question, we propose a new modeling method based on the framework of a systems approach extended from probabilistic computational neuro-genetic modeling (pCNGM), which maps individual neuronal signals at molecular level to the brain's signals at regional level. We use the extended pCNGM model where a new theoretical-physics-inspired data structure is used to quantitatively analyze the region-level correlation of the brain which indicates a kind of synchronization and is used as an indicator of quantitative analysis of neuro-dynamics. The results show that the coupling constrained by structural dynamics with quantum effects embedded in the brain's network plays a pivotal role in the synchronization among regional nodes within the brain's spontaneous signaling network.