Fig. 4
Mathematical modeling of transcriptional memory. a Schematic representation of the discrete states (OFF1, OFF2 and OFF3) required to reach transcription (ON state), when coming from an inactive (red stairs) or an active (green stairs) mother nucleus. After mitosis, the probability for a nucleus to initiate the transcriptional activation process from a given state is provided by the parameter p, (p1 = p(OFF1), p2 = p(OFF2) and p3 = p(OFF3)). The distribution of the random time to transcription (t) is modeled as a mixture of gamma distributions, according to the displayed Equation 1, where Cdf is the cumulative distribution function, Γ and γ are the complete and incomplete gamma functions, respectively. The average number of transitions ‘a’ is provided by the sum of weighted probabilities (Equation 2). The time of each jump from one state to another is provided by the parameter ‘b’. Parameters of this model are predicted separately for nuclei coming from active and inactive mothers. The parameter fitting is based on Cdf of the random time to transcription in nc14 (t) (see also Supplementary Equation 1 Supplementary Methods). b Cdf of the random time to transcription in nc14. The origin of time is the end of mitosis nc13 to nc14, (determined by our automatic software, see “Methods” section) added to the time required to detect the first activation (proper to each genotype). Data (cross) are compared to predictions (solid curves) for nuclei, resulting from active (green) and inactive (red) mothers. c, d Mean ‘a’ parameter; error intervals correspond to the variation among optimal and best suboptimal fits (see Supplementary Methods and Supplementary Data 1). e, f Mean ‘b’ parameter; error intervals correspond to variation among optimal and best suboptimal fits (see Supplementary Methods and Supplementary Data 1). g The ratio of parameter ‘a’ in subpopulations from inactive and active mothers is positively correlated (Spearman correlation coefficient = 0.82 p = 0.034) to the average ‘b’ parameter. Predictions of the mathematical model are represented as a black line
