Time to move on: Modeling transcription dynamics during an embryonic transition away from maternal control

ABSTRACT

In a recent study, we investigated the regulation of hunchback (hb) transcription dynamics in Drosophila embryos. Our results suggest that shutdown of hb transcription at early nuclear cycle (nc) 14 is an event associated with the global changes taking place during the mid-blastula transition (MBT). Here we have developed a simple model of hb transcription dynamics during this transition time. With kinetic parameters estimated from our published experimental data, the model describes the dynamical processes of hb gene transcription and hb mRNA accumulation. With two steps, transcription onset upon exiting the previous mitosis followed by a sudden impact that blocks gene activation, the model recapitulates the observed dynamics of hb transcription during the nc14 interphase. The timing of gene inactivation is essential, as its alterations lead to changes in both hb transcription dynamics and hb mRNA levels. Our model provides a clear dynamical picture of hb transcription regulation as one of the many, actively regulated events concurrently taking place during the MBT.

Introduction

All metazoan embryos must undergo a transition to transfer maternal control of the developmental program to zygotic control.^1-4 In Drosophila, a landmark of this transition period is the mid-blastula transition (MBT) at nuclear cycle (nc) 14, during which numerous molecular and cellular events take place concurrently. For example, many zygotically expressed genes become transcriptionally active for the first time at nc14, whereas other genes that became transcriptionally active prior to this time now experience a shutdown phase.^5-8 Our own analysis of published datasets⁹ identified over 190 zygotically active genes that exhibit characteristics of becoming shut down during nc14.¹ The hunchback (hb) gene, which is required for thoracic development and activated by the maternal morphogenetic protein Bicoid (Bcd),^3,4,10, is among these genes.¹ The shutdown of hb transcription during nc14 is a property that is associated with the MBT, and postponing the MBT to nc15 in haploid embryos leads to a corresponding postponement of hb shutdown.¹ In addition, the dynamics of hb transcription are sensitive to perturbations that alter the potency of its activator Bcd.^1,11

These results suggest that understanding the dynamic regulation of Bcd-activated hb transcription can yield insights into the molecular events during the global changes taking place at the MBT. Here we develop a mathematical model to describe hb transcription dynamics and hb mRNA accumulation in Drosophila embryos, and estimate kinetic parameter values and initial conditions based on our experimental data.^1,11,12 Our results show that: 1) the dynamics of the shutdown phase of hb transcription at nc14 can be recapitulated by a sudden inactivation of a single kinetic parameter k_on, 2) the perturbed behavior of hb transcription can be explained by an altered timing of this event, and 3) promoter switching and k_on shutoff are faster kinetic steps than mature hb mRNA production and decay, rendering the hb mRNA level sensitive to perturbations that alter the k_on shutoff timing. Our results show that, stemming from this quick k_on inactivation, the steady state of hb mRNA concentration (and by inference Hb protein concentration) could not be reached during the MBT. They support the hypothesis that the shutdown of Bcd-activated hb transcription is integral to how patterning decisions are made along the AP axis of the embryo.

Results and discussion

We study the dynamics of hb transcription during the nc14 interphase as the embryo undergoes the MBT. We consider the anterior part of the embryo where the transcribing probability of hb has reached its plateau along the AP axis.^1,11,13-18 We assume that the hb promoter can switch between 2 states, ON or OFF, and only the promoter copies at ON state can produce hb transcripts. The fraction of promoter copies at ON state and the mean changes in promoter state switching and hb mRNA concentration are time-dependent and can be described as,

$$\frac{d{G}_{on}\left(t\right)}{dt}=k_{on}(1-G_{on}\left(t\right))-k_{off}{G}_{on }\left(t\right),$$ (1)

$$\frac{ dR\left(t\right)}{dt}=k_{mRNA}{G}_{on}\left(t-{\tau }_R\right)-\omega R\left(t\right),$$ (2)

where G_on(t) is the fraction of hb gene copies at ON state; R(t) is the concentration of cytoplasmic, mature hb mRNA (in arbitrary units, a.u.); k_on and k_off are kinetic rates (each with a unit of min⁻¹) of switching between ON and OFF states of the promoter; k_mRNA is the maximal rate of hb mRNA production (with a unit of concentration/min) if all gene copies are at ON state; ω is the decay rate of mature hb mRNA molecules (with a unit of min⁻¹); and τ_R is the time delay (min) that results from the elongation, releasing and transporting of mature hb mRNA after the initiation of its production from the active promoters. In order to model the shutdown kinetics of hb transcription during the MBT, the rate k_on follows a step function:

$$k_{on}=\{\begin{array}{ll}k,& t<t_{shutdown,}\\ 0,& t\ge t_{shutdown,}\end{array}$$ (3)

where t_shutdown is the time at which promoters can no longer be switched on.

In our experiments,^1,11-13 we used an intronic probe to monitor specifically the transcription status near the Bcd-activated P2 promoter of hb (Fig. 1A, left). In this setting, the actively transcribing hb copies can be detected as bright fluorescent dots, referred to as intron dots (Fig. 1A, right). The relation between intron dots and activate gene promoters can be described as:

$$\frac{\rho (t)}{2}=G_{on}(t-{\tau }_1),$$ (4)

where ρ(t) is the average number of detected intron dots per nucleus in the anterior part of embryos that have an estimated average developmental time t upon entering the nc14 interphase; and ρ(t) is twofold of G_on(t) since each nucleus contains 2 copies of the gene (see Methods); τ₁ is the average time delay between the switching ON of a promoter copy and its detection as an intron dot inside the nucleus (Fig. 1A, left). The overall process of gene transcription studied in this report is illustrated in the flow chart (Fig. 1B).

Figure 1.

Modeling hb transcription. A) Shown are a schematic diagram of the hb gene (left) and the detection of hb intron dots in wt embryos (right). The hb intron is located close to the P2 promoter (145 bp downstream) and, thus, the transcription status at this intronic location can be expressed to infer the promoter state (depicted by a shade area in the diagram). Our experimental data analyze transcription initiated exclusively from this promoter because the embryonic region selected for data analysis is devoid of the parasegment 4 (PS4) stripe expression, which is initiated from another promoter further upstream (P1, not shown in the diagram).^22,23 The images shown on the right are from 2 wt embryos, with an estimated time of ∼3 min (top) or ∼8 min (bottom) into the nc14 interphase. Note the abundance of bright fluorescent dots (referred to as intron dots) for the embryo at ∼3 min and a diminishing number of such dots in the embryo at ∼8 min. Images are reproduced from Liu and Ma.¹² B) Flow chart of the current model. The hb gene is either active (ON) or inactive (OFF), with k_on and k_off as the kinetic rates of promoter switching. Only the hb gene copies at ON state could produce mature mRNA and intron dots (as part of nascent transcripts) with the respective time delays shown. The produced mature mRNA is constantly degraded with a rate ω, and the degradation product is indicated with the small dots.

With the above model and an estimated set of parameters (Table 1), we simulated the dynamics of activated genes (G_on(t), Fig. 2A) and the cytoplasmic hb mRNA concentration (R(0), Fig. 2B) for wild type (wt) embryos. The simulation starts at the entry into the nc14 interphase (t=0). At this point, we assume all genes are inactive (G_on(0) = 0), because all transcription activities would have been shut off during the previous mitotic division.^12,14,17-19 We also assume the level of hb mRNA is non-zero, reflecting its accumulation from previous transcription at earlier nuclear cycles.^20,21 This initial level of hb mRNA is also estimated from the observed data using estimated parameters. Comparing model simulation with our data¹² suggests a sudden shutoff of gene activation at 2.6 ± 0.1284 min (mean ± sd) upon entering the nc14 interphase. Without such shutting off, the activated genes would remain at its plateau instead of the experimentally observed decreases (Fig. 2A, dashed line). In addition, mRNA concentrations would have reached a much higher level approaching its steady-state without this k_on shutoff (Fig. 2B, dashed line).

Table 1.

Estimated values of kinetic parameters of the wild type system.

Parameter (unit)	Mean ± standard derivation
kon (min−1) (prior to shutdown)	0.5 ± 0.0056
koff (min−1)	0.4 ± 0.0032
ω (min−1)	0.09 ± 0.0059
kmRNA (min−1)	16 ± 1.0054
τ1 (min)	0.4 ± 0.225
τR (min)	4.7 ± 0.2759

Figure 2.

Model-generated G_on(t) and R(t) profiles in wt and perturbed systems. A) Shown is a simulated G_on(t) profile for the wild type (wt) system, superimposed with experimental data (mean and sd). For comparison, a simulated G_on(t) profile without shutdown is shown (dashed line). B) Shown is a simulated R(t) profile for the wt system, superimposed with experimental data (mean and sd). Note the initial drop of the cytoplasmic hb mRNA level in this simulated profile. This is reflective in part of τ_R (see text and Fig. 1). For comparison, a simulated profile without shutdown is also shown (dashed line). C) Shown are simulated G_on(t) profiles for the 2 perturbed systems (dmpd and sumo), superimposed with experimental data (mean and sd). A simulated profile of the wt system is also shown for comparison. D) Shown are simulated R(t) profiles of the wt and perturbed systems. Note the peak mRNA levels in perturbed systems relative to the wt system; these predicted properties are qualitatively similar to those observed experimentally.^1,11

Our recent studies^1,11 have identified 2 mutations [dampened (dmpd) and Bcd sumoylation-defective (sumo)] that lead to altered dynamics of hb transcription at nc14, and we suspected that these mutations only changed the timing of k_on shutoff. To test this hypothesis, we changed only t_shutdown in our model, and compared the consequential simulation with the observed data.^1,11 The comparison suggests that altering the shutoff timing alone is sufficient to explain the altered dynamics of hb transcription in the mutants (Fig. 2C). In addition, alterations of the shutting down time lead to changes in the expression profiles of hb mRNA (Fig. 2D), and increase or decrease of the mature hb mRNA levels has been observed in each of these mutants, respectively.^1,11 Our analysis suggests that in comparison to the wt system (2.6 ± 0.1284 min), the dmpd mutation causes a premature gene shutdown (2.2 ± 0.0428 min), and the sumo mutation results in a delayed inactivation (3.6 ± 0.0583 min).

The shutdown of hb transcription modeled in our current study depicts a sudden, decisive event among the numerous events that are concurrently taking place during the MBT. It is well documented that hb transcription from the P2 promoter in the anterior part of the embryo that we study is dependent on the Bcd input.^22-25 The dmpd mutation disrupts a Bcd-interacting nuclear co-activator,¹¹ whereas the sumo mutation affects the sumoylation status of Bcd.^1,26 Thus both of these mutations affect the ability of Bcd to activate transcription. As suggested recently,¹⁵ the activation of hb transcription (k_on) can be modeled as function of Bcd concentration and Bcd occupancy at the hb enhancer located upstream of the P2 promoter. It has also been argued that DNA binding of Bcd itself is not weakened as hb transcription experiences its shutdown during nc14.¹⁵ Thus, one could speculate that a MBT-mediated “disruptive force” might disrupt a functional interaction(s) between the enhancer-bound Bcd molecules and the transcription machinery at the P2 promoter. In other words, this inactivation acts on a step(s) of transcription beyond enhancer binding of Bcd molecules. This suggestion is consistent with the experimental observation that hb shutdown is a sudden event that is independent of the AP position in the embryo, i.e., independent of Bcd concentration.^1,12 Although our detected intron dots track closely the P2 promoter state (Fig. 1), they are not direct measurements of G_on(t). Hence it remains to be resolved precisely which step(s) of transcription is subject to MBT-mediated shutdown.^27-31

The shutdown of hb transcription at nc14 has been proposed to be a key aspect of the regulatory logic of the gap gene network.¹² The nc14 interphase is a time during which gap genes begin to experience an intensifying cross-regulation among themselves in pattern formation.^21,32,33 The quick shutdown of hb transcription (<3 min into the nc14 interphase as estimated in our model; Table 1) provides a mechanism for hb P2 promoter to respond to the Bcd gradient as its primary input in forming an expression boundary in a Bcd concentration-dependent manner.³ This relatively reliable input-output relationship between Bcd and hb transcription has been suggested to be important for AP pattern formation in a manner that is robust to embryo size variations.^3,34-38

The estimated parameters in our current study are consistent with existing estimates and yield new insights into transcription regulatory mechanism during embryonic development. For example, our estimated k_on (prior to shutdown) and k_off are both fast, as those at earlier nuclear cycles reported by Xu et al.,¹⁵ despite the significant differences in our experimental and modeling approaches. On the contrary, hb mRNA decay is significantly slower and hb mRNA is relatively more stable (1/ω = 11 min). Importantly, our results also reveal a time delay τ_R of 4.7 ± 0.2759 min. This delay is longer than the anticipated minimal elongation time of 2.4 to 3.3 min computed by dividing the 3.6 kb hb gene length from its P2 promoter with the estimated elongation rate of 1.1 to 1.5 kb/min.³⁹ The additional delay of 1.4 to 2.3 min might represent time needed for mRNA maturation, release and cytoplasmic transport as reported recently.⁴⁰ Since hb mRNA concentration changes much more slowly than the promoter status (Fig. 2A, B), patterning decisions along the AP axis of the embryo are likely made before hb mRNA and Hb protein can reach their steady states during the MBT. This conclusion is supported by a systematic analysis of model behavior when individual parameters are altered (Fig. 3). This also underscores the importance of the precise timing in hb shutdown as being tightly coupled with the progression of the MBT. As shown experimentally^1,11 and in our simulations (Figs. 2 and 3), altering the shutdown timing even slightly can lead to altered mature mRNA levels that can have developmental consequences.

Figure 3.

Evaluation the impact of individual parameters for transcription. Shown are model-generated G_on(t) and R(t) profiles when an individual parameter is systematically changed while holding other parameters as in the wt system. Panels A and B show the effect of pre-shutdown k_on (varied from 0.1 to 0.9/min) on G_on(t) and R(t), respectively. Panels C and D show the effect of k_off (varied from 0.1 to 0.9/min) on G_on(t) and R(t), respectively. Panels E and F show the effect of t_shutdown (varied from 1 to 20 min) on G_on(t) and R(t), respectively. In these 2 panels, the dashed lines represent system properties without shutdown (see also Fig. 2A, B).

Methods

Experimental data

In our experiments, we have measurements of the average number of intron dots per nucleus in the anterior part of the wt,¹² dmpd¹¹ and sumo mutant¹ embryos. These results were collected in embryos that had been grouped into ∼1 min intervals, representing ∼1 min time series within the nc14 interphase. Consistent with our model assumption (Eq. 4) that has also be used in previous studies,^15,41 the maximal number of intron dots detected in individual nuclei very rarely exceeded 2 under our experimental setting.^1,11-13 For wt embryos,¹² we also have time series measurements on the average of hb mRNA levels in ∼5 min intervals representing the first ∼25 min of nc14. The estimated average developmental time of the embryos for these measurements is 2.5, 7.5, 12.5, 17.5, and 22.5 min into the nc14 interphase.

Mathematical modeling

First, we solved Eq. 1 with the initial condition G_on(0)= 0 and used this analytical solution to estimate the shutdown time t_shutdown, the kinetic rates (k_on and k_off) and the parameter τ₁ with the experimental data obtained from wt embryos. As k_on is a step function, the analytical solution is in 2 following forms in respect to the time variable:

$$\begin{array}{l}{G}_{on}(t)=\frac{k_{on}-k_{on}{e}^{-(k_{on}+k_{off})t}}{k_{on}+k_{off}},t<t_{shutdown},\\ G_{on}(t)=G_{on}(t_{shutdown})e^{-k_{off}(t-t_{shutdown})},t\ge t_{shutdown},\end{array}$$ (5)

Here, $G_{on}\left(t_{shutdown}\right)=\underset{t\to t_{shutdown}}{\lim }{G}_{on}\left(t\right)$ approaching from t = 0. Assuming the average number of intron dots detected at any time is a random variable following lognormal distribution, log N(${\displaystyle \mu , \sigma }$) with 2${\displaystyle \mu }$ and 2${\displaystyle \sigma }$ being the mean and standard derivation of the observed average number of intron dots detected per nucleus within 3–12 embryos at different times, we applied the Maximum Likelihood Estimation to fit the curve of G_on(t) for the wt system (Fig. 2A). Second, we generated G_on(t) profile by the estimated parameters from the previous step and fed it into the differential equation (Eq. 2) to estimate the other parameters for the wt system: ω, k_mRNA and τ_R by the Euler Method. Since we do not have data for the level of hb mRNA at the beginning of nc14, we backward-estimated the initial condition R(0). Third, we used the measured average number of intron dots per nucleus in dmpd and sumo mutants to re-estimate the time of shutdown for each of these mutant systems, respectively. Our experimental settings were maintained across these measurements, and we assumed τ₁ to be the same. As explained in main text, we only estimated t_shutdown for the 2 mutants while keeping the rest of the parameters (k_on, k_off and τ₁) at their estimated values obtained from the first step. After the estimation the timing of shutdown for the mutant systems, we generated their corresponding G_on(t) profiles (Fig. 2C). Last, we assigned the estimated values for all the parameters in Eq. 2 from the second step and fed 2 of the G_on(t) profiles in Eq. 2 to simulate the hb mRNA profiles for both wt and mutant systems (Fig. 2B, D). The estimated initial condition R(0) from the second step was used for all systems.

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Funding

This work was supported in part by 1R01GM101373 from NIH and IOS-0843424 from NSF (to JM) and start up support from the University of Cincinnati (to TZ and to YX).

Author contributions

JL generated data; YX analyzed data and performed simulations; JL, YX, TZ and JM conceived the study, developed the model, interpreted the results, and wrote and approved the paper.