  The improved in-vitro regulation of human embryonic stem cell (hESC)
pluripotency and differentiation trajectories is required for their promising
clinical applications. The temporal and spatial quantification of the molecular
interactions controlling pluripotency is also necessary for the development of
successful mathematical and computational models. Here we use time-lapse
experimental data of OCT4-mCherry fluorescence intensity to quantify the
temporal and spatial dynamics of the pluripotency transcription factor OCT4 in
a growing hESC colony in the presence and absence of BMP4. We characterise the
internal self-regulation of OCT4 using the Hurst exponent and autocorrelation
analysis, quantify the intra-cellular fluctuations and consider the diffusive
nature of OCT4 evolution for individual cells and pairs of their descendants.
We find that 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 expression amongst neighbouring cells, we show
that hESCs express similar OCT4 to cells within their local neighbourhood
within the first two days of the experiment and before BMP4 treatment. Our
framework allows us to quantify the relevant properties of proliferating hESC
colonies and the procedure is widely applicable to other transcription factors
and cell populations.
