Temporal control of gene expression by the pioneer factor Zelda through transient interactions in hubs

Pioneer transcription factors can engage nucleosomal DNA, which leads to local chromatin remodeling and to the establishment of transcriptional competence. However, the impact of enhancer priming by pioneer factors on the temporal control of gene expression and on mitotic memory remains unclear. Here we employ quantitative live imaging methods and mathematical modeling to test the effect of the pioneer factor Zelda on transcriptional dynamics and memory in Drosophila embryos. We demonstrate that increasing the number of Zelda binding sites accelerates the kinetics of nuclei transcriptional activation regardless of their transcriptional past. Despite its known pioneering activities, we show that Zelda does not remain detectably associated with mitotic chromosomes and is neither necessary nor sufficient to foster memory. We further reveal that Zelda forms sub-nuclear dynamic hubs where Zelda binding events are transient. We propose that Zelda facilitates transcriptional activation by accumulating in microenvironments where it could accelerate the duration of multiple pre-initiation steps.

(b) Immunostaining using anti-GFP and anti-Ser5-P Pol II in GFP-zld embryo from the end of mitosis between nc12 and nc13 to nc14 showing that Zelda comes back very quickly in the nucleus at the end of mitosis compared to Ser5-P Pol II. Scale bars represent 10μm.
(c) Living eGFP-bcd/+;His2Av-mRFP/+ embryo imaged by confocal microscopy from interphase of nc13 to early interphase of nc14. Successive representative maximum intensity projected Z-stack images are shown at the indicated timings. Scale bars represent 20μm.
(d) Average intensity profiles for nucleoplasmic GFP-Zelda (dark green) and nucleoplasmic eGFP-Bicoid (light green) measured from a nc13 embryo transitioning into nc14. An automatic tracking of fluorescence from a minimum of 87 nuclei generated these profiles, error bars represent SD. Synchronization of the developmental timing was done using the time frame where mother nuclei are splitting into two daughter nuclei, using His2Av-mRFP staining.    given by a mixture of gamma distributions with shape parameters 1, 2, 3, ... and scale parameter , whose cumulative distribution function (cdf) reads: We define the following parameters of the mixed distribution that can be computed empirically from the mean and the variance, the first two moments of the distribution, are as such: Using Supplementary Equation 2 we find that: showing that the parameter 'a' represents the average number of transitions and, equivalently, the mean shape parameter of the mixed gamma distribution, whereas 'b' is the mean transition time.
In the case of three jumps, the model has three independent parameters b, p 1 , p 2 . shows that F r depends on the rescaled argument t/b, also on p 1 , p 2 . Therefore T 50 /b=ψ where ψ does not depend on 'b' but depends on p 1 , p 2 . By sampling uniformly the possible values of p 1 , p 2 we showed (see Supplementary Fig. 4) that ψ depends on p 1 , p 2 essentially via 'a', and that the following approximate relation holds: where, for the three jumps model, ψ(a) = 0.085a 4 -0.78a 3 + 2.
Furthermore, because M(t) is a Markov chain, each of the vectors X ij (t) = (X 1j (t), X 2j (t), X 3j (t), X 4j (t)) satisfies the following system of ordinary differential equations (master equation):  respectively. We noticed that the post-mitotic ratio is smaller than the pre-mitotic value (which is 3), the reduction resulting from mitotic transitions between nonproductive states. Furthermore, we computed the dependence of the post-mitotic ratio on the transition time 'b' and showed that this ratio increases with 'b', it is equal to one for small 'b', and it is larger than one for large 'b'. This result is robust with respect to the simulation parameters. The free parameter in the simulation is the ratio of transition times for upward and backward transitions during mitosis. The theoretical curve in the Fig. 4g was obtained when backward transitions are two times slower than upward transitions.

Data analysis and parameter estimates for modeling
Data analysis and parameter estimates were performed using MATLAB and Optimization Toolbox Release 2013b, The MathWorks, Inc., Natick, Massachusetts, United States.
The time origin was first set at the end of mitosis. The deterministic waiting time T 0 was estimated as the time between the end of mitosis and the time when the first nucleus from a large population is activated. This estimate is accurate for a large number of nuclei, because the probability p 0 that T r is close to zero was supposed to be non-zero. The estimate is more accurate when the number of nuclei is large (by the law of large numbers) and when the number of transitions is small (because p 0 is high for a gamma distribution with small shape parameter, as it is the case when the number of transitions is small). Then the origin of time was set at T 0 and T r was determined for all nuclei. Parameters 'a' and 'b' were first, roughly estimated with the formulas in Supplementary Equation 3. We found that 'a' is not higher than 3, which allowed us to restrict the analysis to only three unidirectional transitions.
The empirical cumulative distribution function of T r was estimated using the Kaplan-