Before revision:  After cell divisions, OCT4 abundance in the daughter cells fluctuates sub-diffusively, showing anti-persistent self-regulation with a Hurst exponent of 0.38. Auto-correlation analysis shows anti-persistence for five hours or longer in 86\% of cells, on average between three and 12 hours into the cell cycle. The OCT4 fluctuations in five minute intervals follow a Laplace distribution, with BMP4 addition provoking smaller changes and tighter self-regulation, particularly in the differentiated fate group.
After revision:  After cell divisions, OCT4 abundance in the daughter cells fluctuates sub-diffusively, showing anti-persistent self-regulation . We obtain the stationary probability distributions governing hESC transitions amongst the different cell states and establish the times at which pro-fate cells (which later give rise to pluripotent or differentiated cells) cluster in the colony. By quantifying the similarities between the OCT4 fluctuations in five minute intervals follow a Laplace distribution, with BMP4 addition provoking smaller changes and tighter self-regulation, particularly in the differentiated fate group.