Resting-state functional magnetic resonance imaging and diffusion weight imaging became a conventional tool to study brain connectivity in healthy and diseased individuals. However, both techniques provide indirect measures of brain connectivity leading to controversies on their interpretation. Among these controversies, interpretation of anti-correlated functional connections and global average signal is a major challenge for the field. In this paper, we used dynamic functional connectivity to calculate the probability of anti-correlations between brain regions. The brain regions forming task-positive and task-negative networks showed high anti-correlation probabilities. The fluctuations in anti-correlation probabilities were significantly correlated with those in global average signal and functional connectivity. We investigated the mechanisms behind these fluctuations using whole-brain computational modeling approach. We found that the underlying effective connectivity and intrinsic noise reflect the static spatiotemporal patterns, whereas the hemodynamic response function is the key factor defining the fluctuations in functional connectivity and anti-correlations. Furthermore, we illustrated the clinical implications of these findings on a group of bipolar disorder patients suffering a depressive relapse (BPD).