We found that the height of the peak of the power spectrum of autocorrelation functions and phase coherence is correlated with barrier heights of the landscape and provides quantitative measures of global stability of the system under intrinsic fluctuations. Therefore, the probabilistic flux may provide an origin of chaotic behavior. Indeed, some studies have found shifts in phase on this basis 2830. This phase shift could result in higher intertrial phase coherence several cycles after the stimulus ceases. As the amplitude of the TNF input increases, the flux contribution, from the total driving force, increases and the system behavior changes from one to two cycles and ultimately to chaotic dynamics. By virtue of receiving an external input, the phase of any oscillator will most likely be shifted by some nonzero amount, and therefore will be altered by the input. As the external noise increases, relevant barrier heights decrease, and the flux increases. The landscape attracts the system into a “double ring valley,” and the flux drives the system to move cyclically. We found that the landscape and flux jointly govern the dynamical “mode-hopping” behavior of the NF-κB regulatory system. Barrier heights from landscape topography provide quantitative measures of the global stability and transition feasibility of the double oscillation system. The potential landscape of the NF-κB system exhibits a “double ring valley” shape. phase of the LFP oscillations recorded superficially. We used a truncated moment equation approach to calculate the probability distribution and potential landscape for gene regulatory systems. feedback they occurred less often during perfnce of re- petitive wrist flexion. We employed a landscape and flux approach to study the stochastic dynamics and global stability of the NF-κB regulatory system. However, the underlying mechanism of this noise-induced “cellular mode-hopping” behavior remains elusive. To our knowledge, this is the first evidence for genetic influences on task-related functional brain connectivity assessed using direct real-time measures of. It was suggested that noise facilitates the switch between different oscillation modes. We conclude that theta-band synchronization of brain oscillations related to negative feedback reflects genetically transmitted differences in the neural mechanisms of feedback processing. Recently, a “mode-hopping” phenomenon has been observed in a NF-κB gene regulatory network with oscillatory tumor necrosis factor (TNF) inputs.
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