Analysis and Modeling of Early Estradiol-induced GREB1 Single Allele Gene Transcription at the Population Level

Single molecule fluorescence in situ hybridization (smFISH) can be used to visualize transcriptional activation at the single allele level. We and others have applied this approach to better understand the mechanisms of activation by steroid nuclear receptors. However, there is limited understanding of the interconnection between the activation of target gene alleles inside the same nucleus and within large cell populations. Using the GREB1 gene as an early estrogen receptor (ER) response target, we applied smFISH to track E2-activated GREB1 allelic transcription over early time points to evaluate potential dependencies between alleles within the same nucleus. We compared two types of experiments where we altered the initial status of GREB1 basal transcription by treating cells with and without the elongation inhibitor flavopiridol (FV). E2 stimulation changed the frequencies of active GREB1 alleles in the cell population independently of FV pre-treatment. In FV treated cells, the response time to hormone was delayed, albeit still reaching at 90 minutes the same levels as in cells not treated by FV. We show that the joint frequencies of GREB1 activated alleles observed at the cell population level imply significant dependency between pairs of alleles within the same nucleus. We identify probabilistic models of joint alleles activations by applying a principle of maximum entropy. For pairs of alleles, we have then quantified statistical dependency by computing their mutual information. We have then introduced a stochastic model compatible with allelic statistical dependencies, and we have fitted this model to our data by intensive simulations. This provided estimates of the average lifetime for degradation of GREB1 introns and of the mean time between two successive transcription rounds. Our approach informs on how to extract information on single allele regulation by ER from within a large population of cells, and should be applicable to many other genes. AUTHOR SUMMARY After application of a gene transcription stimulus, in this case the hormone 17 β –estradiol, on large populations of cells over a short time period, we focused on quantifying and modeling the frequencies of GREB1 single allele activations. We have established an experimental and computational pipeline to analyze large numbers of high resolution smFISH images to detect and monitor active GREB1 alleles, that can be translatable to any target gene of interest. A key result is that, at the population level, activation of individual GREB1 alleles within the same nucleus do exhibit statistically significant dependencies which we quantify by the mutual information between activation states of pairs of alleles. After noticing that frequencies of joint alleles activations observed over our large cell populations evolve smoothly in time, we have defined a population level stochastic model which we fit to the observed time course of GREB1 activation frequencies. This provided coherent estimates of the mean time between rounds of GREB1 transcription and the mean lifetime of nascent mRNAs. Our algorithmic approach and experimental methods are applicable to many other genes. ### Competing Interest Statement The authors have declared no competing interest.