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A repressor-decay timer for robust temporal patterning in embryonic Drosophila neuroblast lineages

  1. Inna Averbukh
  2. Sen-Lin Lai
  3. Chris Q Doe  Is a corresponding author
  4. Naama Barkai  Is a corresponding author
  1. Weizmann institute of science, Israel
  2. Howard Hughes Medical Institute, University of Oregon, United States
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Cite this article as: eLife 2018;7:e38631 doi: 10.7554/eLife.38631

Abstract

Biological timers synchronize patterning processes during embryonic development. In the Drosophila embryo, neural progenitors (neuroblasts; NBs) produce a sequence of unique neurons whose identities depend on the sequential expression of temporal transcription factors (TTFs). The stereotypy and precision of NB lineages indicate reproducible TTF timer progression. We combine theory and experiments to define the timer mechanism. The TTF timer is commonly described as a relay of activators, but its regulatory circuit is also consistent with a repressor-decay timer, where TTF expression begins when its repressor decays. Theory shows that repressor-decay timers are more robust to parameter variations than activator-relay timers. This motivated us to experimentally compare the relative importance of the relay and decay interactions in vivo. Comparing WT and mutant NBs at high temporal resolution, we show that the TTF sequence progresses primarily by repressor-decay. We suggest that need for robust performance shapes the evolutionary-selected designs of biological circuits.

https://doi.org/10.7554/eLife.38631.001

Introduction

Multicellular organisms shape their body plans during embryonic development through parallel processes that occur at different spatial positions and at different times. Spatial coordination of patterning depends on direct cell-cell communication and on long-range signaling by secreted morphogens. By contrast, temporal coordination is often achieved through cell-autonomous processes that measure time-delays (Pourquié, 1998). Molecular circuits implementing biological timers have been described (Murray, 2004; Reppert and Weaver, 2002; Simon et al., 2001), but the basis for their robust functioning is not well understood.

Biological timers play a key role in central nervous system (CNS) development of invertebrates and mammals, where a small pool of progenitors generates a vast amount of neuronal diversity (Grosskortenhaus et al., 2005; Isshiki et al., 2001; Kambadur et al., 1998; Kohwi and Doe, 2013; Kohwi et al., 2011; Li et al., 2013). In Drosophila, NBs delaminate from a ventral neuroectoderm at embryonic stages 9–11 to form an orthogonal two-dimensional grid with 30 NBs per hemi-segment. After formation, each NB undergoes asymmetric cell divisions every ~45 min to produce a series of ganglion mother cells (GMCs), each of which divides into two post-mitotic neurons. The identity of each neuron is determined by the spatial position of the parental NB and by the TTF it inherits from the NB at the time of birth (Doe, 2017; Kohwi and Doe, 2013; Pearson and Doe, 2004). Temporal information is therefore conveyed by the NB cell-intrinsic timer, which drives the sequential expression of four TTFs: Hunchback (Hb), Krüppel (Kr), Pdm (Flybase: Nubbin and Pdm2), and Castor (Cas) (Brody and Odenwald, 2000; Isshiki et al., 2001; Kambadur et al., 1998).

The molecular basis of the NB TTF timer has been characterized: Hb expression is initiated by an external signal, but subsequent dynamics depends on cross-regulation between the TTFs themselves (Cleary and Doe, 2006; Grosskortenhaus et al., 2006; Isshiki et al., 2001; Tran et al., 2010). In addition, the orphan nuclear hormone receptor, Seven-up (Svp), is required to switch off Hb expression, but not for specifying early neuronal fates (Kanai et al., 2005; Kohwi et al., 2011; Mettler et al., 2006; Tran et al., 2010).

The TTF expression sequence is largely independent of the cell cycle: some NBs undergo just one cell division during the Hb expression window, whereas others undergo two or three divisions (Baumgardt et al., 2009; Doe, 2017; Isshiki et al., 2001) indicating that cell division does not direct this temporal transition within the TTF cascade. Consistent with that, mutations that arrest the cell cycle still allow normal TTF expression from Kr onward. Also, NBs can undergo the entire expression sequence when cultured in isolation in vitro indicating TTF timer progression is independent of overall embryo development (Brody and Odenwald, 2002; Grosskortenhaus et al., 2005; Kambadur et al., 1998). While progression along the transcription cascade is largely independent of the cell cycle, these two processes must remain synchronized in order to ensure reproducible NB lineage. How do embryos limit temporal variations that could desynchronize these two largely independent processes?

We hypothesize that reliable progression of the TTF cascade derives from the cell-intrinsic ability of the TTF timer to buffer variation (noise) in its molecular parameters. We therefore used mathematical modeling to analyze theoretically the robustness of the timer mechanism. The TTF-timer is commonly described as a relay of activators (Doe, 2017; Rossi et al., 2017). Its regulatory circuit, however, contains also regulations compatible with a repressor-decay timer, in which TTF starts expressing when its repressor decays to a sufficiently low level. The relative contributions of the activator-relay and the repressor-decay interactions to TTF progression depend on unknown molecular parameters

Our computational analysis revealed that the two mechanisms show different sensitivity to variations in their molecular parameters, with the decay-timer being significantly more robust than the relay timer. This finding motivated us to examine experimentally the relative contribution of the relay and decay interactions to the in-vivo progression of TTF expression. This was done by measuring the TTF dynamics in wild-type and mutant embryos at high temporal resolution. Our results show that removing a relay-controlling factor has limited consequences on the time of induction of the controlled TTF compared to the removal of a decay-controlling factor, indicating that the decay-based interactions dominate the progression of the in vivo TTF timer. We conclude that NB temporal patterning in Drosophila is driven by a timer whose progression is dominated by repressor decay, while activator relay plays a minor role. We propose that the increased robustness of this decay timer, as suggested by our computational analysis, is critical for ensuring the synchrony of this timer with the parallel, yet independent, progression of the cell division cycles.

Results

The TTF regulatory circuit combines activator-relay and repressor-decay interactions

The sequential expression of TTFs within the dividing NB is commonly described as a relay of activators, in which each activator accumulates until reaching a threshold needed for inducing the next activator in the cascade (Doe, 2017; Rossi et al., 2017). Examining the TTF regulatory circuit, however, we noted that in addition to these activator-relay interactions, the regulatory circuit includes two additional interaction types: backward interactions, whereby a TTF inhibits the expression of a TTF upstream in the cascade, and repressor-decay interactions, whereby an upstream regulator represses the expression of a downstream TTF (Figure 1A–B). Therefore, at least in principle, the TTF timer can progress not only through a relay of activators, but also through decay of repressors, where target genes are induced once a repressor decays below some threshold level.

The TTF regulatory circuit combines activator-relay and repressor-decay timers.

(A) The embryonic neuroblast TTF timer: In the Drosophila embryo, NBs express four TFs in a temporal sequence, as shown. We term this sequence the TTF timer. NBs divide asymmetrically to generate GMCs, whose further divisions produce post-mitotic neurons. The identity of both the GMCs and the post-mitotic neurons depends on the TTF expressed at the time of NB division, as shown in panel C, top left. (B) The TTF regulatory circuit: experimentally defined cross-regulation between TTFs include interactions that propagate the cascade through activator relay (blue) or repressors decay (red), and backward interactions (black). (C) Summary of TTF expression in NB7-1 of wild type, mutant, and misexpression genotypes. TTFs are color-coded as in (A). Developmental stages indicated at the bottom and genotypes on the left. Data from (Grosskortenhaus et al., 2006; Isshiki et al., 2001; Tran et al., 2010). (D) Summary of neuronal identity in the NB7-1 lineage of wild type, mutant, and misexpression genotypes. Data from (Grosskortenhaus et al., 2006; Isshiki et al., 2001). (E) TTF timer model reproduces all reported phenotypes: a model was formulated that includes all regulatory interactions shown in Figure 1B. Shown are the simulated dynamics of TTFs expression for a set of experimentally consistent parameters. Progeny identity was defined by the TTFs whose expression exceeded a constant threshold (dashed line) at the time of division (see Supplementary file 2 for mapping of expressed TTFs to neuronal fates). (F) Mutant (top) and constitutive expression (bottom) models using the same parameter set as in 1E (see Materials and methods for details). (G–H) Consistent circuits are distributed through the Decay-Relay timer space: over 106 circuits differing by parameters choice were considered. A subset of ~105 circuits reproduced all experimentally defined phenotypes and are referred to as consistent circuits, or consistent parameter sets. Each consistent circuit was positioned on the Decay-Relay plot (H) based on the changes in Pdm and Cas induction (ind) times following removal of the respective activator-relay or repressor-decay interactions (grey bars, top of G). The density of consistent circuits in the Decay-Relay plot is color-coded. Note the larger density of consistent circuits in the regime of decay-timers. See Materials and methods for details.

https://doi.org/10.7554/eLife.38631.002

The activator-relay and repressor-decay regulations could both contribute to the progression of the TTF timer. Alternatively, one timer type could dominate. The relative contribution of the different regulations to the initiation of TTFs expression depends on the in vivo parameters, whose values are not known and are difficult to measure. We therefore examined whether the in vivo parameters can be distinguished computationally.

We formulated a model of the TTF timer that includes all experimentally described interactions, capturing their strengths by 17 independent parameters. Main parameters in this model include TTF degradation rates, TTF production rates, and the expression thresholds defining the minimal TTF expression levels required for activating or repressing the controlled TTF and to confer neuronal identities (Supplementary file 1). The model is summarized by four ordinary differential equations (ODEs), whose solution simulates the temporal dynamics of the four TTFs. Note that model dynamics depends on the choice of the kinetics parameters (Supplementary file 1). Further, varying parameters qualitatively changes the regulatory network by varying the relative influence of the different interactions on TTF temporal dynamics. This allows us to capture a wide range of networks, ranging from decay dominant ones, through any mixed models, to relay dominant networks all the while taking into account all experimentally observed TTFs and cross-regulations (Supplementary file 1).

To define parameters consistent with the in vivo dynamics, we compiled phenotypes of mutant embryos, focusing on the best characterized NB7-1 lineage (Figure 1C–D). Available data describes which TTF(s) are expressed by the dividing NB, within the GMCs, and by the post-mitotic neurons (Grosskortenhaus et al., 2006; Isshiki et al., 2001). This data is of low temporal resolution and cannot be used to define the precise durations at which each TTF is expressed. Still, this data provides the basic constraints with which our model should comply: the temporal sequence at which TTFs are expressed in our simulations should be consistent with the temporal sequence for wild type, mutant, and misexpression embryos as emerges from reported data (Figure 1C–D, Supplementary file 2). We therefore define consistent parameter sets as parameter sets for which the solution of model equations meets the above requirements by exhibiting the correct TTF expression sequence in WT and all mutants.

Screening a wide range of parameters, each defining a different circuit, we detected a large number of parameter sets that were consistent with the reported phenotypes (Materials and methods, Figure 1E–F). To examine if these consistent sets favor an activator-relay or a repressor-decay timer, we focused on the last two TTFs (Pdm and Cas) for which activating and repressing interactions were described (Figure 1B). We examined how their induction time changes when specifically removing either the activator-relay or the repressor-decay interaction (Figure 1G). These values – the changes in TTFs induction times when removing either the activator-relay or the repressor-decay interactions – were used to calculate a decay significance and relay significance score for each parameter set (Materials and methods). Based on these significance scores for the two respective timers, we positioned each consistent circuit within a Decay-Relay timer space (Figure 1H). In this analysis, we removed the repression of Cas by its immediate repressor (Kr), but left the repression by Hb intact, reasoning that Hb had already decayed at the time of Cas expression.

We observed a higher density of consistent circuits in the region of repressor-decay timers. However, a large number of consistent circuits were equally dependent on both the relay and the decay interactions, and some were driven primarily by relay (Figure 1H). We conclude that the available data is not of sufficient resolution to distinguish whether the in vivo parameters progress the TTF timer through an activator-relay or a repressor-decay timer.

A repressor-decay timer is more robust than an activator-relay timer

To determine whether an activator-relay or repressor-decay timer best explains the observed, we measured the robustness of consistent circuits, namely their sensitivity to variations (noise) in their biochemical parameters. We expected this sensitivity to differ between different circuits, and perhaps also between the timers whose progression is dominated by the activator relay, or repressor-decay interactions. We previously compared the robustness of a one-step timer encoded by an activator accumulation or a decay of a repressor (Rappaport et al., 2005). This comparison was done by considering circuits that (1) have the same decay rate and (2) require the same time transitioning between two given thresholds, thereby controlling for the effects of changing kinetic constants. As we showed, the repressor-decay timer necessarily shows higher robustness under these conditions (Rappaport et al., 2005). The reason for this differential robustness is easily appreciated: the time at which a protein decays between two thresholds is only moderately (logarithmically) sensitive to the values of these thresholds (Figure 2A–C). In contrast, the time to increase protein levels between two thresholds depends at least linearly, and typically significantly stronger, on thresholds values (Figure 2A–C)

Figure 2 with 2 supplements see all
Repressor-decay timer is more robust than an activator-relay timer.

(A–C) Robustness of single-step timers: a single-step timer can be implemented by the accumulation of an activator (A) or by the decay of a repressor (B). In the accumulation of an activator scenario (A), activator production is initiated at t = 0. Once it accedes the threshold Tr, target genes are induced. In the decay of a repressor scenario (B), production of a repressor is stopped at t = 0. Once repressor levels have decayed below Tr, target genes would no longer be inhibited. The temporal dynamics of the regulatory proteins are shown in (A–B) for reference parameters (solid line) and following two-fold reduction in regulator production rate (dashed line). Timer output is defined by the time-delay from the onset of the dynamics until the regulator reaches the indicated threshold Tr. The change in this output following two-fold change in production rate is indicated (black double arrow), and is shown in (C) for different threshold values. See also analytical analysis in (Rappaport et al., 2005). (D) Illustration of robustness score calculation. Parameter sets were scored for robustness by measuring timer sensitivity to moderate (20%) variations in production parameters (see Materials and methods). When testing set robustness, we solved model equations for all combinatorial combinations of adding or subtracting 20% to all the TTFs production rates. For each noise combination, we compared all TTF expression phase durations to those of the original set solution. If a noise combination yielded phase durations which are all within 10% distance of the respective original durations, the noise combination was considered 'close' to the original. A robustness score was then calculated as the percentage of 'close' noise combinations. An example for a specific parameter set: left- production rates color coded by TTF, right – simulation of Pdm dynamics. Upper: original parameter set, below: two noise combinations:#1 and #N (- sign and lighter shade for reduced production rate, + sign and darker shade for increased production rate). For #1, the perturbed dynamics are 'close' to the original while for #N, a substantial error in phase duration, ΔtNPdm, occurred and dynamics are not 'close'. Formula at the bottom of the panel indicates that the robustness score for the original set is a function of all noise combinations 1,2,…,N and durations of all TTF expression phases. (E) Distribution of robust circuits in the Decay-Relay timer space. Consistent circuits were positioned on the Decay-Relay plot based on both Pdm and Cas induction, as is Figure 1H, and their robustness scores (see Materials and methods), averaged over closely positioned circuits, were color-coded. Considering the positioning of all circuits in the Decay-Relay timer space based on Pdm and Cas separately (Figure 2—figure supplement 1) and based on both TTFs combined (Figure 2E), high robustness scores were found in the region of repressor-decay timers.

https://doi.org/10.7554/eLife.38631.003

We measured the robustness of each of our consistent circuits identified above by scoring the ability of the circuit to buffer the temporal durations of TTF expression phases against moderate (~20–40%) variations in TTF production rates (Figure 2D and E, Figure 2—figure supplement 1) (see Materials and methods). In our model, introducing fluctuations in TTF production rate captures also fluctuations in thresholds values, as circuit function depends on the ratio of TTF levels to their activation thresholds. Finally, degradation rates were kept constant, as they define the time scale of timer dynamics and equally affect all circuits (Rappaport et al., 2005 and data not shown).

To rigorously distinguish whether robustness correlates with a specific timer type, we considered again the positioning of all circuits in the Decay-Relay timer space (c.f. Figure 1H). Unlike the simple case of the one-step timer, here we did allow some range of possible dynamics, to account for the low temporal precision of the experimental data. This does not affect our ability to compare the consistent circuits since these differences in dynamics are not correlated with location in Decay-Relay space (Figure 2—figure supplement 2). High robustness scores were found in the region of repressor-decay timers, while activator-relay timers were significantly less robust (Figure 2E, Figure 2—figure supplement 1). We conclude that also in the context of the full TTF cascade model, robustness is improved when progressing through repressor decay rather than activator relay.

A TTF circuit can be positioned in the Decay-Relay timer space based on TTF-deletion phenotypes

The difference in the robustness of the activator-relay and the repressor-decay timer designs motivated us to examine which of the respective interactions dominates in defining the in vivo timer progression. We therefore searched for experiments that could distinguish properties of the in vivo timer.

Experimentally, TTF deletion is an accessible perturbation. As described above, the consequences of such perturbations were previously reported, but at a resolution that was too low to distinguish between the two timer types. Our simulations pointed to one limitation of existing data: for some mutants, the consequence of TTF deletion was defined by measuring the fates of the post-mitotic neurons, and therefore did not provide conclusive data about possible co-expression phases in which two consecutive TTFs are expressed within the NB, but one of them dominates in generating neuronal identity. This significantly limited our ability to precisely deduce the TTF expression timing in either wild-type or mutant embryos, and thereby greatly increased the spectrum of circuits that were scored as consistent with measured phenotypes.

With this in mind, we examined computationally whether the consequences of TTFs deletions, if analyzed at higher resolution, could distinguish between the repressor-decay and activator-relay timers. First, we examined how Pdm induction time changes following deletion of either Hb (its repressor, allowing Pdm induction only after its levels are sufficiently reduced) or Kr (its activator, allowing Pdm induction only after its levels are sufficiently induced). Specifically, for each of the consistent circuits described in Figures 1H and 2E above, we tested how Pdm induction time changes when simulating the removal of Hb and when simulating the removal of Kr (Figure 3A). These two values uniquely position each consistent circuit (Figure 3B). Once positioned, we color each circuit by its robustness score for the WT circuit (same color as in Figure 2E), which allows us to observe robustness of WT circuits as function of their Pdm induction sensitivity to Hb and Kr deletions (Figure 3B). As can be appreciated, high robustness was found exclusively in circuits for which Pdm induction was dependent only on Hb decay. Analogous analysis of Cas induction time shows a similar, although less pronounced bias (Figure 3—figure supplement 1).

Figure 3 with 1 supplement see all
The TTF circuit can be positioned in the Decay-Relay timer space based on TTF deletion phenotypes.

(A–B) TTF deletion phenotypes can distinguish robust circuits: all consistent circuits, as described in Figures 12 above, were considered. Each consistent circuit was scored by measuring the change in Pdm induction times following deletion of Hb (A, left) or deletion of Kr (A, right). These two values define the ‘Hb deletion’ and ‘Kr deletion’ sensitivity of Pdm induction respectively, for each parameter set. We then use these two values to define the Hb-Kr deletion sensitivity space, where we uniquely position each consistent circuit (B). Color-coding circuits based on their robustness score for the WT circuit (as in Figure 2E), allows us to observe robustness of WT circuits as function of their Pdm induction sensitivity to Hb and Kr deletions. This analysis shows that robust circuits are only found in a small region in the Kr-Hb sensitivity space, in which Pdm induction time is much more sensitive to Hb than to Kr deletion. (C–F) Sensitivity to TTF deletion (X axis) correlates with the sensitivity to the specific removal of the respective activator-relay or repressor-decay interactions (Y axis): all consistent circuits, as described in Figures 12 above, were considered. For each consistent circuit, the changes in Pdm or Cas induction times following TTF deletion or removal of regulatory interactions was measured. Correlations between the effects of TTF deletion and removal of the respective regulatory link are shown. Each dot in these correlation figures represent one consistent circuit, color-coded by its robustness score for the WT circuit.

https://doi.org/10.7554/eLife.38631.006

Deletion of the TTF which functions as an activator or repressor abolishes the respective relay or decay interactions. However, it may have additional effects that are not directly related to these interactions. We therefore used our simulations to examine whether TTF deletion phenotypes can predict the consequence of specifically abolishing the respective activator-relay or repressor-decay regulation. To this end, we considered again all consistent circuits. For each consistent circuit, we examined how Pdm induction time changes when specifically removing either the activator-relay (Kr-to-Pdm) or the inhibitor-decay (Hb-to-Pdm) interactions. This allowed us to compare, for each consistent circuit, the change in Pdm induction time when an upstream TTF (e.g. Kr) was deleted, or when the respective interaction (e.g. Kr-to-Pdm) was specifically removed (Figure 3C,D). As can be seen, the consequences of these two perturbations were tightly correlated, in particular when comparing the effect of deleting Kr to the removal of Kr-dependent regulation (Figure 3D). In the case of Hb, the correlation was somewhat lower, reflecting the multiple roles of Hb in this circuit. However, for the robust parameter sets, which we predicted to describe the in-vivo circuit, correlation was higher (Figure 3C). A tight correlation was also observed when comparing the change in Cas induction time following the deletion of its activator (Pdm) or the removal of the Pdm-to-Cas activating link only, and when comparing the consequences of deleting the Cas repressor Kr to the specific removal of the Kr-to-Cas repression link (Figure 3E,F). We conclude that following Pdm and Cas expression timing in mutant embryos has the power to inform us not only about the robustness of the in vivo timer, but also about the relative contributions of the relay and decay regulations to the TTF progression.

Timing of Pdm and Cas expression is highly sensitive to deletion of TTF repressors, but less sensitive to deletion of TTF activators

As described above, our modeling suggests that activator-relay and repressor-decay timers can be distinguished based on the TTF deletion phenotypes, but this would require data on TTF expression levels and timing at a much higher temporal resolution than previously obtained data. To this end, we stained embryos for the TTF of interest, and for the Worniu and Engrailed markers, which allow us to unambiguously identify NB7-1 (Figure 4A). TTF protein intensity levels were quantified using confocal microscopy (Figure 4B). Variability in staining intensities was controlled by normalizing TTF staining to that of Engrailed, which is constantly expressed in NB7-1.

Figure 4 with 1 supplement see all
High temporal resolution analysis of Pdm expression.

(A) Confocal image of the neuroblast layer from ventral nerve cord segments T2 and T3 of an early stage 11 embryo (boxed area in illustrated embryo on the left). The NB7-1 was identified by the pan-NB marker Worniu (Wor) and the NB spatial marker Engrailed (En). NB6-1 is the most anterior medial En +NB, with the En +NB7-1 just posterior and lateral (red arrow), and En +NB1-2 completing the diagonal. Genotype: y1 w1. Scale bar: 20 um. (B) Methodology for obtaining transcription factor levels in G1/G2/S-phase of NB7-1. Confocal section stacks (at a 1 um interval) of individual NB nuclei were obtained, and the area and signal intensity of each section were measured and summed to obtain the total intensity of TTFs. (C) Data from the number of NB7-1 indicated in Supplementary file 3 is summarized by box plots of measured log(Pdm/En) staining intensity as a function of time. The 1.96 SEM (95% confidence interval) is shown as a red rectangle with a horizontal red line for the mean, with a blue rectangle marking the limits of one standard deviation above and below the mean. Time duration of the Pdm phase (approximately 180 min) is indicated in red. We do not yet have an explanation for the moderate transient decrease in Pdm levels around 620 min. (D) Confocal image of a NB7-1 lineage marked with GFP (NB7-1-Gal4, UAS-GFP) in an early stage 11 embryo. Arrowheads indicate three consecutive GMCs (Ase+) which are Kr+Pdm- (green), Kr+Pdm+ (pink), and Kr-Pdm+ (orange). Genotype: ac-VP16AD gsb-Gal4DBD UAS-superfoldGFP. Scale bar: 5 um. (E) Data from the number of NB7-1 indicated in Supplementary file 3 is summarized by box plots of measured log(Pdm/En) staining intensity as a function of the number of progeny GMC. The 1.96 SEM (95% confidence interval) is shows in red rectangle with a horizontal red line for the mean, one standard deviation above and below the mean in blue rectangle. Scheme below the X axis shows which neuronal progeny is hypothesized to be derived from the GMC.

https://doi.org/10.7554/eLife.38631.008

Our data confirmed the sequential expression of Hb, Kr, Pdm, and Cas within the NB7-1 lineage (data not shown). It further revealed that Pdm expression was longer than expected: about 180 min (Figure 4C), a time window that is long enough to generate more than the two previously reported Pdm +GMCs (Isshiki et al., 2001). To determine if there were additional Pdm +GMCs in the lineage, we used the NB7-1-specific Gal4 driver to drive the expression of membrane-tethered superfold GFP and co-stained for Pdm and the GMC marker Asense (Figure 4D). We found that Pdm was upregulated when NB7-1 was producing the 4th GMC and downregulated after the NB generated the 7th GMC (Figure 4E), indicating that four GMCs are produced within the Pdm expression window. Consistent with this finding, we observed a novel Kr+Pdm+ GMC in the lineage, which was not previously reported (Isshiki et al., 2001). The newly discovered GMC may produce an Eve-negative motor neuron, interneuron, or undergo programmed cell death (see Discussion).

The Pdm expression window is therefore significantly longer than the duration inferred from the previous data used to calibrate our model. This did not affect our analysis, however, since in our original analysis we did allow for solutions of similarly long Pdm windows, accounting for the uncertainty of the experimental data (Figure 4—figure supplement 1). We next used the high temporal resolution expression data to determine whether the relay-timer or decay-timer could best account for Pdm and Cas expression timing in TTF mutant backgrounds. We found that Kr mutants did not alter Pdm induction timing, whereas hb mutants advanced Pdm induction by about two cell-cycles (Figure 5A–C), showing that Pdm induction is more sensitive to deletion of the upstream repressor Hb. Similarly, pdm mutants did not have as much effect on Cas induction as did Kr mutants, showing that Casinduction is more sensitive to deletion of the upstream repressor Kr rather than the upstream activator Pdm (Figure 5D–F).

Figure 5 with 2 supplements see all
Positioning the in-vivo TTF circuit in the Decay-Relay timer space.

(A–C) Pdm levels in NB7-1. Pdm levels was quantified in wild-type and mutant embryos. Data from the number of NB7-1 indicated in Supplementary file 3 is summarized by a box-plot, with 95% confidence interval shown in red rectangle, mean in red horizontal line and the one SD above and below the mean in blue. Developmental stages are indicated on the X axis. Stages of Pdm induction are indicated by black arrows. Induction stages were determined by calculating a background Pdm level as the mean of Pdm in the second and third stages (S10E and S10), in WT. The stage of induction was defined as the first stage for which the 1.96 SEM (95% confidence interval- red rectangle) was above background (see Materials and methods for details). Early transient inductions are indicated by grey arrows. (D–F) Cas levels in NB7-1 wild type and mutant embryos. Data was plotted as described in (A–C). For both Pdm in WT (A) and Cas in the Kr mutant (E), early transient induction of the TTF was detected at stage 9. We attribute this to basal transcription levels which cause protein production until enough repressor is accumulated. Interestingly, for Cas no such transient early induction appears in WT and Hb mutant (E, Figure 5—figure supplement 1). These results suggest the transient early induction is an Hb-related phenomenon which could stem from slow Hb accumulation, compared to Pdm and Cas. (G) Position of the in vivo timer in the Pdm Hb-Kr sensitivity space: The measured changes in Pdm induction time following Kr and Hb deletions were used to position the in vivo circuit in the Hb-Kr sensitivity space (black diamond), as described for the simulated data Figure 3B. Error bars are based on the experimental temporal resolution (see Materials and methods for details). (H) Estimating the sensitivity of the in vivo timer to removal of delay or relay interactions: The measured changes in Pdm and Cas induction times following TTF deletions were used to position the in vivo circuit on the correlation plots from Figure 3C–F by taking the measured range denoted by 1,2 for ΔHb and 3,4 for ΔKr in Figure 5G and measuring the corresponding ranges for regulation removal. These are denoted by 1’,2’ and 3’, 4’ respectively in Figure 5H upper plots. Similarly, this was done for Cas regulation in Figure 5H lower plots (see Materials and methods for details). (I) The TTF circuit is positioned in the region of repressor-delay timers: data from A-H above defined the positioning of the TTF circuit on the Decay-Relay timer space. The location of the in vivo circuit on the X axis, indicating the significance of the decay network, was defined by the range between points 1’ and 2’: point 1’ is the lower bound on decay significance and point 2’ is the upper bound- based on Pdm. Together with a corresponding analysis for Cas, these points determined the location and error margin for the in vivo circuit on the X axis. Similarly, the location on the Y axis, indicating the significance of the relay network, was defined by points 3’,4’ together with the corresponding points for Cas (see text and Materials and methods). Location of the in vivo circuit is indicated by a black diamond, with error margins indicated by dashed error bars. (J) Our analysis indicates that the progress of TTF expression is dominated by repressor-decay, and not activator-accumulation. The NB TTF timer regulatory network is shown again, with dominant decay regulations in bold.

https://doi.org/10.7554/eLife.38631.010

Cas induction in Kr mutants was moderate compared to its induction in WT embryos. This moderate induction is sufficient to induce the Cas-positive U5 neuron, produced in Kr mutants (Isshiki et al., 2001), and may result from its earlier induction, at a time when Hb, its second repressor, is still highly expressed. Consistent with the contribution of Hb to Cas repression, Cas induction was advanced in Hb mutants to stage 11, similarly to Kr mutants (Figure 5—figure supplement 1).

Our measurements defined the change in Pdm and Cas induction times following the deletion of their activator or repressor TTFs. Both induction times showed higher sensitivity to repressor deletion than to the deletion of their activator, suggesting that the in-vivo timer progresses primarily through the decay of repressors, with the activator relay playing a minor part.

To examine this conclusion more rigorously, we have linked the measurements to our theory, by examining which of the consistent circuits, identified previously, are also consistent with the higher resolution data we obtained. As can be seen in Figure 5—figure supplement 2, our higher resolution data indeed largely restricted the range of possible parameters that remained consistent. This allowed us to more precisely position the in vivo circuit on the Decay-Relay space (Figure 5G–H, Materials and methods). As can be seen, the in vivo circuit is in the region of robust timers that are dominated by repressor-decay interactions (Figure 5I). We therefore conclude that the timing of TTF expression is driven by a repressor-decay mechanism, rather than an activator-accumulation mechanism (Figure 5j).

Discussion

Our study suggests that a repressor-decay timer drives the sequential TTF expression to generate stereotyped temporal fate specification in Drosophila embryonic NB lineages (Figure 5J). This finding may appear surprising, as previously this timer was thought to progress through a relay of activators achieved by feed-forward activation combined with feedback repression. A similar activator-relay mechanism was implicated also in driving the TTF cascade in Drosophila optic lobe NB lineages (Bertet et al., 2014; Li et al., 2013). Still, experimentally established cross-regulations between the TTFs are consistent with both activator-relay and repressor-decay mechanisms, and the parameters defining the relative contributions of repressor decay or activator accumulation to the expression timing of each TTF were unknown.

We provided evidence that the TTF progression is dominated by the repressor-decay interactions by measuring the expression timing of the last two TTFs in the cascade, Pdm and Cas. In both cases, TTF induction time was defined by the reduction in upstream repressor level, but showed little, if any change when upstream activator was deleted. Kr induction was not included in this analysis since we found that Kr was maintained in hb mutant embryos (data not shown (Isshiki et al., 2001)), indicating that Kr is induced by a factor external to the cascade, similarly to Hb. Notably, Kr remained constitutively expressed in embryos which were forced to express constitutive levels of Hb. Therefore, while Hb is an activator of Kr, it affects Kr expression not by determining its induction time but rather by determining shut-off time, allowing Kr decay only when Hb decays below a threshold, again implementing a repressor-decay, rather than an activator-relay timer. Hb is rapidly degraded during early embryogenesis, with an estimated half-life of ~15 min (Okabe-Oho et al., 2009). While this half-life was not measured directly in NBs, it is likely to be similarly short based on the 1:1 relationship between hb transcriptional activity (detected with an intron probe) and Hb protein levels (detected with an antibody) (Grosskortenhaus et al., 2005). Assuming that Hb mRNA is similarly fast degrading, and that Hb is transcribed for only one cell-cycle, we estimate that Pdm starts expressing when Hb levels reduce to about 1–10% of their maximal value.

Our quantification of Pdm levels in wild-type embryos revealed that this phase is longer than previously thought, and led to the identification of a previously unrecognized Kr +Pdm + GMC generated during this phase. Six motor neurons have previously been reported for the NB7-1 lineage (Landgraf et al., 1997; Schmid et al., 1999), yet there are only five Eve + motor neurons in the lineage, raising the possibility that this ‘new’ GMC may produce an Eve-negative motor neuron. Our analysis also revealed that Pdm is expressed in a burst during the Hb window. This was noted by Isshiki et al. (2001) but neither the functional significance nor the mechanism was discussed. Regarding function, we suggest that this early window of Pdm expression may allow it to be inherited in the first-born GMC, where in at least one lineage (NB4-2) it is required to specify first-born GMC identity, together with Hb (Bhat et al., 1995; Bhat and Schedl, 1994; McDonald et al., 2003; Yang et al., 1993; Yeo et al., 1995). Regarding mechanism, early Pdm and Cas expression is likely to be due to independent transcriptional activation of both genes, followed by repression of pdm transcription by Hb protein (Kambadur et al., 1998). The Pdm protein produced from the initial transcriptional burst, prior to Hb-mediated transcriptional repression, may persist into the new-born GMC. Alternatively, there may be a mechanism for blocking Hb repression of pdm transcription specifically in early-forming NBs.

We propose that repressor-decay dominating TTF progression was favored in evolution because it better buffers variation (‘noise’) in molecular parameters. Robust TTF progression is needed to maintain synchrony with the NB division cycles, a prerequisite for generating a reproducible NB lineage. At first sight, repressor degradation and activator accumulation may appear equivalent for measuring time delays. However, closer examination shows that they are in fact very different (Rappaport et al., 2005). First, activator accumulation requires continuous transcription while repressor degradation occurs following transcription shutdown. Second, activator accumulation approaches some steady state, which limits the possible readout thresholds. Furthermore, most of the dynamics is spent close to this threshold, so that small changes in threshold levels are translated into large changes in the measured delay time. By contrast, there is no such (theoretical) restriction on the readout threshold as a repressor decays to zero expression. Together, these properties lead to different buffering capacities, both when considering a single-step timer, and in the context of the full TTF timer model. In all cases, encoding time-delays by repressor decay greatly promotes robustness.

In this study, we did not measure robustness experimentally and did not verify experimentally the predicted difference in the robustness of relay- and decay-based timers. Such a comparison can be done by identifying biological circuits that encode these two timers and are equivalent in all other aspects. Alternatively, the respective timers can be engineered using a synthetic biology approach.

Testing experimentally the proposal that robustness acts as a selection pressure may be more difficult. Defining selective pressures that act during evolution is intrinsically complicated by our limited knowledge of species natural history. The hypothesis that robustness serves as an evolutionary-relevant selection pressure proved useful in defining the evolutionary selected circuit designs in multiple studies from our lab and from others (Alon et al., 1999; Barkai and Leibler, 1997; Eldar et al., 2002; Eldar et al., 2003; Gavish et al., 2016; Hart et al., 2014; Haskel-Ittah et al., 2012), and our current study further supports this notion. Still, experimentally, this notion remained untested.

In conclusion, we propose that the need to maintain robust gene expression timing within a noisy biological environment favored evolution of repressor-decay regulatory circuits controlling developmental patterning. This was previously shown for circuits that coordinate spatial patterning through the establishment of morphogen gradients or the control of direct cell-to-cell communication (Barkai and Shilo, 2009; Eldar et al., 2002; Eldar et al., 2003; Gavish et al., 2016; Rahimi et al., 2016). Our study suggests that robustness also played a major role in the design of developmental timers that function in neuronal differentiation.

Materials and methods

Computational methods

Mathematical model and numerical screen

Randomized parameter sets (circuits) were generated by randomly drawing values for model parameters out of the ranges indicated in Supplementary file 4, using a log uniform distribution. Parameters were then substituted into model equations (Supplementary file 1) and solved numerically by a standard MATLAB ODE solver. We selected the ranges for model parameters as follows. First, we chose a ‘reference’ set of parameters, which gave rise to a consistent circuit and are biologically reasonable based on experimental data. The overall time for the simulation was selected based on the duration of the cascade as measured in (Grosskortenhaus et al., 2006; Isshiki et al., 2001), the degradation rates were based on measurements of Hb half-life of ~15 min (Okabe-Oho et al., 2009) which corresponds to a degradation rate of ~0.05 [1/min] – which is the middle of the range we used for degradation rates. While this half-life was not measured directly in NBs, it is likely to be similarly short based on the 1:1 relationship between hb transcriptional activity (detected with an intron probe) and Hb protein levels (detected with an antibody) (Grosskortenhaus et al., 2005). Degradation rates for the other TTFs were selected to be close to this value. Since production rates and thresholds are only significant as a ratio in our model (Supplementary file 1), their units can remain arbitrary as long as biologically reasonable ratios are maintained. Since we estimate that Pdm starts expressing when Hb levels reduce to about 1–10% of their maximal value (Grosskortenhaus et al., 2006) and a threshold of 1% was used in our previous analytical analysis (Rappaport et al., 2005) we restricted ourselves to this range of ratios between maximal levels (ratio between production and degradation) and thresholds. Second, for each model parameter, the range of possible values was selected to be wide going over several orders of magnitude around the value used for the reference set in order to capture the systems behavior in a large part of parameter space. We believe these ranges are wide enough to capture biologically reasonable values. The model we solve numerically always includes all the known interactions between the TTFs (both the repressor decay and activator relay interactions). The values of these randomly drawn parameters determine the relative significance of the interactions in driving the cascade. By repeating this process for millions of such circuits, we examine a wide range of network designs spanning from circuits which are driven mainly by decay to circuits driven mainly by relay and combinations of both.

Consistency

The solutions were tested for consistency: a consistent solution is one in which the temporal sequence of ‘on’ (above threshold) TTFs is according to experimental observations for both WT and all mutants (Figure 1C,D). The durations of phases were not considered here, only their sequence.

Robustness and robustness score

Consistent parameter sets were scored for robustness to TTF production rates. When testing set robustness, we solved model equations for all combinatorial combinations of adding or subtracting 20% to all the TTFs production rates. Since the model contains 6 TTF production rate parameters (TTF regulated production for Hb,Kr,Pdm and Cas and basal production for Pdm and Cas- see Supplementary file 1) this yielded 2^6 = 64 noise combinations. For example, one such noise combination is a parameter set where Hb, Kr,Pdm production rates were each increased by 20% and Cas production and Pdm and Cas basal production were each decreased by 20%. For each noise combination, we compared TTF expression phase durations to those of the original set solution. Only if a noise combination yielded phase durations which are all within 10% distance of the respective original durations, the noise combination was considered ‘close’ to the original. A robustness score was then calculated as the percentage of ‘close’ noise combinations. In the example shown in Figure 2D, the two Pdm temporal dynamics plots for the perturbed systems #1 and #N, show Pdm levels in a consistent parameter set (solid line) and in the noise combination (dashed line). The expression phase of Pdm is ‘close’ to the original in #1 and not ‘close’ in #N. The overall robustness score for this parameter set was calculated using this and all other noise combinations and expression phases not shows in these plots. The expression phases considered for this purpose were expression/co-expression phases leading to different neuronal fates (Supplementary file 2). For example, a phase of Hb only expression followed by co-expression of Hb and Kr was considered a single phase since both lead to the 1 and 2 neuronal fates rendering the timing of Kr induction irrelevant in terms of NB lineage.

Perturbed parameter sets: deletion of TTF and specific regulations in the model

In order to create perturbed parameter sets, parameter values or terms in model equations were changed accordingly: for TTF deletion the respective production rates were set to 0. For constitutive expression of a TTF, all the terms in model equations regulating this TTFs production were set to 1. For specific regulation removal, the regulation term was set to 1 (see Supplementary file 1 for model equations).

Placing parameter sets in Decay-Relay space

For Figure 1H, Figure 2 and Figure 2—figure supplement 1, Figure 2—figure supplement 2 significance scores of decay and relay for each consistent parameter set were first calculated with respect to Pdm and Cas separately (Figure 2—figure supplement 1) and then a combined score based on both TTFs was calculated (Figure 1H, Figure 2, Figure 2—figure supplement 2). The TTF-specific scores for Pdm and Cas were based on change in Pdm/ Cas induction times caused by removing the decay or relay regulations governing these inductions. For example, for Pdm the decay removal perturbation is removal of Hb--|Pdm, and the relay removal perturbation is the removal of Kr-->Pdm. We then measured Pdm/Cas induction times in the perturbed sets. The difference from WT in induction time for each perturbed set was calculated as Δtind=100*tPerturbedind-tWild TypeindtWild Typeind. The combined decay significance score, based on both Pdm and Cas, was calculated by summing Δtind for Pdm (perturbation: removal of Hb--|Pdm) and Δtind for Cas (perturbation: removal of Kr--|Cas). The relay significance score was calculated similarly, only with relay removal perturbations for both Pdm and Cas. The possible range (in absolute value in minutes) of earlier induction or delay is different between Pdm and Cas. For example, Pdm could potentially be up-regulated at t=0 when its repressor Hb is removed. For Cas, upregulation at t=0 is not possible because even when the repressor Kr is absent, another repressor Hb is still active. Due to this difference, when calculating the combined delay and decay scores a normalization was performed: each TTF-specific relay/decay Δtind was taken as percentage out of the maximal Δtind observed for all sets.

Calculating the location of the in vivo system in Decay-Relay space

For Pdm in Figure 5G, the calculation of in vivo system location according to its Δtindfor TTF deletion perturbations was performed by assuming the experimentally observed tWild Typeind and tPerturbedind were the middle of the stage in which induction occurred. The assumed error margin was half that stage duration. These error margins were further increased when translating from Δtind for TTF deletions to Δtind for appropriate regulation removal using the model. This translation was performed by placing the measured Δtind for TTF deletion on the appropriate correlation plot in Figure 5H. This range is shown in Figure 5H upper left plot, by the two points denoted 1,2. Points 1 and 2 represent the upper and lower bound on measured earlier induction of Pdm due to Hb deletion. This range is then translated by the model into the possible range of earlier Pdm induction due to removal of the Hb—| Pdm regulation. This is done using the same correlation plot, by taking the maximal range on the Y axis reached by robust (robustness score>80) sets, within the X axis range of the measured Δtind as defined by points 1,2. This results in the range defined by points 1’ and 2’ which define the range for Δtind caused to Pdm upregulation by Hb--|Pdm removal. Similarly, points 3,4 indicating the lower and upper bound on Pdm Δtind due to Kr deletion were translated to points 3’ and 4’ indicating the lower and upper bound on Pdm Δtind due to the removal of Pdm activation by Kr (Figure 5H upper right plot). A similar analysis was carried out for Cas, in Figure 5H lower plots.

In Figure 5I, experimentally measured values of the decay-relay significance scores were indicated on Figure 2E by a black diamond shaped marker. These experimental, joint Pdm and Cas, decay and relay significance scores were calculated as previously described for simulated parameter sets: by adding the scores for both Pdm and Cas and then normalizing. Normalization of measured Δtind for Pdm was done by dividing by greatest experimentally observable values: Pdm induction at t=0 which corresponds to Δtind=100% in the decay case and the middle of the last stage in the experiment (S12) in the relay case. For Cas, there was no need to normalize Δtind for relay removal since Cas induction in this case occurred during the last stage (S12) in the experiment. Cas decay removal Δtind was normalized by greatest Δtind observed in simulated parameter sets since we cannot expect Cas upregulation at t=0 due to inhibition by Hb.

Experimental methods

Data acquisition

The following flies were used: (1) y1w1 (FBst0001495); (2) hbFB,hbP1/TM3 ftz-lacZ (Isshiki et al., 2001); (3) KrCD,Kr1/CyO wg-lacZ (Isshiki et al., 2001); (4) Df(2L)ED773/CyO wg-lacZ (Grosskortenhaus et al., 2006); (5) ac-VP16AD,gsb-Gal4DBD (Kohwi and Doe, 2013); (6) w1118; 10xUAS-IVS-myr::sfGFP-THS-10xUAS(FRT.stop)myr::smGdP-HA(attP2)(FBst0062127). Embryos were collected and incubated at 25˚C until designated stages, and then fixed and stained with antibodies by following published protocols (Grosskortenhaus et al., 2005; Kohwi and Doe, 2013; Tran and Doe, 2008). The primary antibodies used in the studies were: rabbit anti-Ase (Cheng-Yu Lee, University of Michigan), mouse-anti-beta-galactosidase (Promega), rabbit anti-Cas (Mellerick et al., 1992) (Doe lab), rat anti-Dpn (Abcam, Eugene, OR), mouse anti-En 4D9 (Developmental Studies Hybridoma Bank (DHSB), Iowa City, IA), mouse anti-Hb (Abcam, Eugene, OR), guinea pig anti-Kr (Doe lab), rat anti-Pdm2 (Abcam, Eugene, OR), and rabbit anti-Wor (Doe lab). Fluorophore-conjugated secondary antibodies were from Jackson ImmunoResearch. Confocal images were taken by Zeiss LSM710 and protein quantities were measured with open software FIJI (Schindelin et al., 2012).

Data analysis

Data was processed and plotted in MATLAB. Mean volume and standard deviation (STD) for all wild type NB7-1s were calculated. All NBs whose volume was further than 2 STD from mean volume (above or below) weren’t included in analysis, assuming these are currently dividing or miss identified cells.

Determining TTF induction stage in WT and mutants

In order to determine the stage of Pdm and Cas induction from box plots in Figure 5A–F,a ‘background’ level for both TTFs was defined as the mean of their mean levels (red line in box plots) in the second and third stages (S10E and S10), for WT. The first stage (S9) was not considered for this purpose due to possible early transient induction which occurs for Pdm. The stage of induction was then defined as the first stage for which the 1.96 SEM (95% confidence interval- red rectangle) was above this calculated background.

References

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
    The Drosophila miti-mere gene, a member of the POU family, is required for the specification of the RP2/sibling lineage during neurogenesis
    1. KM Bhat
    2. P Schedl
    (1994)
    Development 120:1483–1501.
  8. 8
  9. 9
    Cellular diversity in the developing nervous system: a temporal view from Drosophila
    1. T Brody
    2. WF Odenwald
    (2002)
    Development 129:3763–3770.
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17
  18. 18
  19. 19
  20. 20
  21. 21
  22. 22
  23. 23
  24. 24
  25. 25
  26. 26
  27. 27
  28. 28
  29. 29
  30. 30
  31. 31
  32. 32
  33. 33
  34. 34
  35. 35
  36. 36
  37. 37
  38. 38
    Clonal analysis of Drosophila embryonic neuroblasts: neural cell types, axon projections and muscle targets
    1. A Schmid
    2. A Chiba
    3. CQ Doe
    (1999)
    Development 126:4653–4689.
  39. 39
  40. 40
  41. 41
  42. 42
  43. 43

Decision letter

  1. Wenying Shou
    Reviewing Editor; Fred Hutchinson Cancer Research Center, United States
  2. Marianne E Bronner
    Senior Editor; California Institute of Technology, United States

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article "A repressor-decay timer for robust temporal patterning in embryonic Drosophila neuroblast lineages" for consideration by eLife. Your article has been reviewed by three peer reviewers, including Wenying Shou as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Aviv Regev as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Lea Goentoro (Reviewer #3).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We thought that the work is interesting. However, major points need to be revised and the paper needs to be decompressed. In particular, the reviewers highlight the need to better understand whether repressor decay is in theory (per Figure 2A,B) more robust than activator accumulation (as per the reviews below). We chose to provide you with the full reviews, as all the reviewers agreed those reflect the key issues to be addressed.

Reviewer #1:

In the Drosophila embryo, neural progenitors produce a sequence of neurons whose identities depend on the sequential expression of temporal transcription factors (TTF). Although this process is thought to be driven by a relay of activators, Averbukh et al. proposed that a repressor-decay timer is the main player. To evaluate the relative contribution of activator-relay and repressor-decay, they mathematically modeled the TTF timer network, and predicted that with repressor-decay, induction timing of a transcription factor was more robust (changed less) when, for example, activator synthesis rate was reduced. They reasoned that the timer had evolved to be robust, and thus, repressor-decay (which supports higher robustness) should be important. They then did more modeling to design experiments and predict experiment results. Experimental tests supported the repressor-decay mechanism in that the induction timing of Pdm and Cas expression was sensitive to the deletion of the respective repressor and much less so to the deletion of activator. The followings are NOT tested experimentally: repressor-decay timer being more robust than activator-relay timer, and robustness being the selective pressure for evolving repressor-decay timer. However, I do like how the authors use modeling in different ways to gain biological insight and to instruct experiment design. Modeling worked rather well!

The biggest problem I have with this paper is the argument of repressor-decay causing less perturbation in induction timing than activator-accumulation (Figure 2A-B). Seems that this assertion is sensitive to the line slope (the less steep a line e.g. Figure 2A, the bigger the timing perturbation). The line slope will in turn depend on parameters, and the two mechanisms can have different parameters. The argument on this point is also rather hand-wavy in the Discussion (second paragraph). This needs to be clarified.

I find Figure 3B difficult to follow. If my understanding is correct, then the lower right dot essentially says that for this particular set of parameters, deleting HB (but not Kr) causes dramatic phenotype, meaning that HB (decay timer) is important. With this set of parameters, the original "wildtype" network is robust. It took me a couple readings to get this. This needs to be explained better.

"Robustness score", a concept key to this article, had no visual aids. Even in the Materials and methods, the explanation of robustness score was not clear (e.g. "phase duration"). I recommend adding conceptual illustrations like Figure 2D.

Reviewer #2:

I find all the exercise of constraining the model with data quite interesting. I also find the experimental results interesting. That said, I am not entirely convinced by the logic of the reasoning presented. For instance, the experimental results presented in the fourth paragraph of “Timing of Pdm and Cas expression is highly sensitive to deletion of TTF repressors, but less sensitive to deletion of TTF activators” validate the idea that the system is not a relay timer. But do we really need the theoretical study on robustness to get there? In fact, to validate the repressor decay vs. the activator relay model, the only solution is to directly perform those experiments (and maybe other ones to really validate the mechanism). The paper tries very hard to argue that an elaborated theory related to robustness is needed to predict the network topology, but I am rather unconvinced. It could be that the activator relay mechanism is impossible for other reasons that have nothing to do with robustness, so such robustness arguments are in my opinion neither very illuminating nor conclusive.

The attempt to "force" the model to predict experimental results also leads to the strange third paragraph in subsection “Timing of Pdm and Cas expression is highly sensitive to deletion of TTF repressors, but less sensitive to deletion of TTF activators”, where we basically learn that, after experimental verification, all the calibration of the model related to Pdm is incorrect, but that does not matter. It seems to me that in such situation, it would be more reasonable to use this information to redo the theoretical study with the new calibration; one could well learn something new.

On top of that, I found the paper at times difficult to follow. The paper seems to have been initially written for a journal with a very compressed format, but I believe it would be much better if some details and more explanations were given in the main text (I give some suggestions below but they are not exhaustive).

Other comments (in no particular order):

1) The authors postulate a dichotomy between activator-relay and repressor decay. This seems a bit arbitrary to me. One could well imagine more complex networks, a mix of the two via genes that are not known to be implicated, etc. I understand there is a limit to what one can do on the theory side, but I feel some discussions should be added. For instance is it known that the genes studied in the model are necessary and sufficient for the entire process?

2) I found the introduction of the parameter exploration a bit too concise. It would be good to explain how the parameters were chosen and constrained. For instance are there experimental data that are constraining them like degradation rates? More generally, are the parameters found after optimization consistent with what is known or reasonable?

3) Obviously there are also predictions on the possible ranges of parameters when theory is combined with experimental data. I found this is a potentially very interesting aspect of the paper that is not explored sufficiently. For instance can we get more information on parameters from the experimental constraints shown on Figure 5 G and I?

4) I find statements in the first paragraph of subsection “A TTF circuit can be positioned in the relay-decay timer space based on TTF-deletion phenotypes” on the connections between robustness and evolution too speculative and in my opinion confusing.

Reviewer #3:

In this paper, the authors combined modeling of interactions between four Temporal Transcription Factors (TTFs) with experiments to understand the architecture of the TTF timer in neuroblasts. The authors developed a computational framework to distinguish between relay and decay timers, identified all possible circuits that can reproduce normal and perturbed neuroblast phenotypes, and then showed how delay timers are more robust to parameter variations than relay timers. Lastly, they collected high-resolution data for TTF induction time in WT and knockout fly lines, and concluded that temporal TTF activation is primarily governed by a decay-timer circuit.

The authors concluded that robustness is not only a feature of spatial patterning, but also temporal patterning in embryos. The work also provides a wonderful insight into the longstanding question of activation vs. repression in biology.

Major comments:

1) It is unclear why only production rates are being varied for the perturbation analysis, especially since the reasoning for robustness in decay timers (subsection “A repressor-decay timer is more robust than an activator-relay timer”) is based on sensitivity to thresholds Tr. Can the authors provide a rationale? What happens if other parameters are varied as well?

2) Figures 2E, 3B, and Figure 2—figure supplement 2 may appear conflicting. Figure 3B clearly demonstrates that decay timers are more robust than relay timers, with robust circuits concentrated in the bottom right of the perturbation-space. In Figure 2E however, robustness seems to be dependent on the decay interaction, while invariant to the relay-interaction. Finally, in Figure 2—figure supplement 2, robustness shows more complicated dependencies.a) It would be helpful to see Figure 2E and 5I split up into two figures, one for Pdm induction, and one for Cas induction – possibly as supplemental figures. Combining the two as they are currently in Figure 2E, raise questions if there are some patterns that are missed, especially since Figure 3B and Figure 2—figure supplement 2 look so distinct. Could it be that Pdm, but not Cas, induction is the sensitive step in the network where robustness analysis can distinguish relay vs decay?b) Additionally, the Materials and methods indicate that when estimating the significance of the decay network for Cas induction, only the Kr-Cas interaction is removed, and the Hb-Cas interaction is left intact. Can the authors discuss why the dual-repression of Cas is not needed?

3) Figure 5A-F clearly demonstrate that removing the immediate activators has no effect on Pdm and Cas induction timing, and removing the repressor clearly affects timing of Pdm induction. But we have the most trouble with Figure 5E.a) First, Cas induction is pretty modest in both at st11 and 12. Then, based on the network, Cas represses Pdm, and we see this borne out in WT, where at st12, high Cas correlates with low Pdm. However, in Kruppel mutant, Pdm remains high, which seems to signify that there isn't much Cas induction? Can the authors discuss how they see these data? Is there an independent way to confirm that Cas is induced, and induced earlier?b) For Figure 5A-F: It would be helpful to draw a line indicating the "background level" of TTFs, to allow readers to see significance more easily. It would also be helpful to immediately see in the legend the way significant induction is determined. Also, the black arrows are not defined in legend.c) Cas is also repressed by Hb. Can the authors justify why they didn't analyze Cas induction in Hb mutant?

4) It would help to have the Materials and methods be better organized. Perhaps with separate sections, so readers can easily find the relevant information. For instance, we had trouble keeping track of the different ways Δtind normalization was performed.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "A repressor-decay timer for robust temporal patterning in embryonic Drosophila neuroblast lineages" for further consideration at eLife. Your revised article has been evaluated by Aviv Regev (Senior Editor), and three reviewers, one of whom is a member of our Board of Reviewing Editors.

The manuscript has been greatly improved but there are some remaining issues that need to be addressed by writing changes before acceptance. In particular, the reviewers requested that certain aspects be written more explicitly and clearly, and in a manner geared toward a general audience. Furthermore, they ask that the evolution aspect should be de-emphasized given the lack of direct data, although raising all such matters in the Discussion section should address this concern.

Because some of the reviewers have been grappling in their consultation specifically around writing and presentation, we highlight below the key areas and items that need to be addressed, and the specific writing revisions we request.

1) One reviewer still found the paper rather hard to read, and was not really convinced by the articulation between theory and experiments as is. The experiments done directly show some repressions from upstream genes, so as pointed out in the first review, one does not really need a very elaborated theory to predict this since it is a direct verification. The understand the authors argument that theory helps better refining what experiments to do, but believe that the authors should explain this more clearly. The actual experiments potentially related to theory are in Figure 5: they are connected to the correlations between times on Figure 3 C-D. I found the explanations there too short and concise, and unclear. There is too much of handwaving ("as seen in") making the arguments difficult to understand. On the one hand there are many mutants, on the other hand each mutant gives essentially one point in parameter space that is then placed in the abstract sensitivity space. There are several layers of reasoning here that could be much better explained (Figure 5H is particularly obscure). The reviewer also felt there could be some intuitive or analytical explanations. The authors allude to some analytical work in their rebuttal letter, is there a simple way to interpret the tight correlations of Figure 3 (it seems the correlation simply comes from the existence of one activation)? Also it seems the only argument for the "decay" part is the point 1', but is this really a strong effect?"

To address this, the reviewers together suggest:

The paper should clarify that it presents two parallel arguments for the decay timer:

1) The robustness from modeling analysis.

2) The experiment.

(i.e. rather than a "linear" model-predicts-experiment paper). A paragraph in the Introduction to better clarify the logic of the paper could help.

2) One of the reviewers has an ongoing concern with the robustness argument presented as the core of the paper, as hypothetically, there could be many ways to have a more "robust" network to noise. The fact that a less complicated network is less robust was not fully convincing in implying that robustness is a good biological criterion to assess the evolutionary origin of the network architecture.

We suggest that the results and interpretation of the paper should stand independent of this conjecture to focus on the repressor decay mechanism as a better explanation of the experimental results (which would roughly correspond to what is done in Figure 5 and associated theory), and reduce overinterpretation of the evolutionary origin of the network structure. Overall, given that the paper does not show that robustness is the selective pressure for evolving repressor-decay timer, we prefer this emphasis be reduced, for example, by moving this point to the Discussion.

3) The Discussion should also include the responses (from the authors' rebuttal) on work that was not done.

4) Another concern from the initial reviews was the issue of predicting parameter values from the simulations, and the authors' response that they could not really see anything. If the parameters are truly completely random in the region compatible with data, we would ask to show it explicitly. It seems a bit paradoxical that, following the authors' line of thought, one could predict so carefully the existence of extra negative interactions from the study, but nothing on the actual parameters corresponding to those interactions. At the very least the negative interactions should have parameters significantly different from a "default" state where they would not contribute. This point should be clarified.

5) While we very much appreciate the extra experiment to address our most important concern about the Cas experiments, we are however, still concerned by the fact that Cas delay-relay space (Figure 2—figure supplement 2B) does not support the robustness argument (third paragraph of subsection “A repressor-decay timer is more robust than an activator-relay timer”). We do see the robustness argument with the Pdm space (Figure 2—figure supplement 2A) and when considering the combined Pdm-Cas space in Figure 2E. This concerns us because it can compromise the overall robustness argument, in several ways:a) Perhaps Figure 2E sets up expectations about the robustness of the decay circuits, only to find out in the supplement that it is more true for Pdm, but not as much for Cas.b) It could also raise doubts on the analysis. E.g., what if Cas is less pronounced because the metric "decay significance" vs. "relay significance" does not capture the effects comprehensively enough for Cas. For instance, Cas is inhibited by Hb and Kr, but one could also view Hb's inhibition of Pdm is an inhibition of Cas (which is not removed in the analysis).

In either case, we ask that this be addressed by some re-writing, e.g., for point a, state earlier the difference between Pdm and Cas analysis, so readers are not led to expect more after seeing Figure 2E.

For point b: Add more explanation to the label "significance of decay", perhaps in parentheses, with what is actually being evaluated, e.g., "removal of Pdm--|Cas interaction".

https://doi.org/10.7554/eLife.38631.020

Author response

We thought that the work is interesting. However, major points need to be revised and the paper needs to decompressed. In particular, the reviewers highlight the need to understand better whether repressor decay is in theory (per Figure 2A,B) more robust than activator accumulation (as per the reviews below). We chose to provide you with the full reviews, as all the reviewers agreed those reflect the key issues to be addressed.

We explain this in some detail below: our theoretical analysis indeed shows that a timer that progresses through decay of repressors is more robust than a timer that progresses by the accumulation of activators. This point is important, and we thank the reviewers for pointing out that our explanation was missing. We now expand on it at length in the revised manuscript

Reviewer #1:

In the Drosophila embryo, neural progenitors produce a sequence of neurons whose identities depend on the sequential expression of temporal transcription factors (TTF). Although this process is thought to be driven by a relay of activators, Averbukh et al. proposed that a repressor-decay timer is the main player. To evaluate the relative contribution of activator-relay and repressor-decay, they mathematically modeled the TTF timer network, and predicted that with repressor-decay, induction timing of a transcription factor was more robust (changed less) when, for example, activator synthesis rate was reduced. They reasoned that the timer had evolved to be robust, and thus, repressor-decay (which supports higher robustness) should be important. They then did more modeling to design experiments and predict experiment results. Experimental tests supported the repressor-decay mechanism in that the induction timing of Pdm and Cas expression was sensitive to the deletion of the respective repressor and much less so to the deletion of activator. The followings are NOT tested experimentally: repressor-decay timer being more robust than activator-relay timer, and robustness being the selective pressure for evolving repressor-decay timer. However, I do like how the authors use modeling in different ways to gain biological insight and to instruct experiment design. Modeling worked rather well!

We thank the reviewer for the support. We agree with the description above of what our study shows and what it does not.

Comparing experimentally the robustness of the two timers: this could be done in two ways, one would require constructing these timers using a synthetic biology approach, namely, engineering cells to express appropriately wired TTFs complying with the two models. Another approach could be conclusively identifying biological circuits that encode the two timers and are equivalent in all other respects. At this time, the former approach is more realistic, and we agree it is a good experiment, which we will contemplate doing. However, it is beyond the scope of the present manuscript.

Showing experimentally that robustness acts as a selection pressure: defining selective pressures that act during evolution is intrinsically difficult, as it is unclear how to simulate the species natural history. Our approach for that is to examine the consequences of evolutionary-plausible hypothesis, and examine whether these hypothesis lead to useful, and experimentally testable predictions about present-day mechanisms. A long-term hypothesis that guides multiple studies in our lab and others is that robustnesspresents an evolutionary-relevant selection pressure that plays a critical role in defining the selected circuit design. Our finding that the computationally identified robust design correctly predicts the in-vivocircuit mechanism supports this hypothesis and approach.

The biggest problem I have with this paper is the argument of repressor-decay causing less perturbation in induction timing than activator-accumulation (Figure 2A-B). Seems that this assertion is sensitive to the line slope (the less steep a line e.g. Figure 2A, the bigger the timing perturbation). The line slope will in turn depend on parameters, and the two mechanisms can have different parameters. The argument on this point is also rather hand-wavy in the Discussions (second paragraph). This needs to be clarified.

We thank the reviewer for this question, which made us realize that we did not explain well enough how we compared the two mechanisms. As stated by the reviewer, the performance of each model depends on the specific kinetic parameters quantifying the respective reactions, and it is therefore not possible to provide one number defining model’s robustness: within each model,

robustnessdepends on the choice of parameters. This raises the fair question of whether it is even possible to compare the robustness of two models.

Our approach for comparing the robustness of different models (e.g. Figure 2A-B) is to control for the quantitative function of the circuit. In our context, we compare two circuits, implementing the respective timer mechanisms, using parameters that result in the same absolute time-delay. This restricts the value of parameters within each model, and allows for a fair and controlled comparison. Specifically, we base our controlled comparison on the following:

1) For some parameters (e.g. protein degradation time), the identity of the factor, as an activator or a repressor, does not matter. We do not change these parameters between the circuits. That is, degradation rates are the same in compared circuits.

2) Other parameters do change between the models. For example, the threshold for TF repression could be different from the threshold for TF activation in order to maintain the same time delay for both models. In comparing the models, we choose all these parameters in a way that ensures that the two models define the same time-delay.

Our general, theoretical comparison of the one-step timer is done for circuits that comply with conditions 1-2. The results are shown in Figure 2. Of note, in this simple case, we can solve the system analytically and by this show that for any parameter choice complying with conditions 1-2, the repression-decay is more robust than activator relay.

For a longer cascade, we performed a similar comparison computationally. Figure 2E, for example, compares robustness of all circuits that comply with the experimentally-defined dynamics. We do note that in this case, we do not demand a precise pattern of time delays, but do allow some range of possible dynamics, to account for the low precision of the experimental data. Therefore, not all circuits in this comparison show the precise same dynamics, but they all fall within a similar range that is compatible with the experimental data. We present our data in this way for simplicity. Increasing the precision, namely comparing only circuits that show the precise same time delays, does not change the results: decay-based timers are more robust than relay-based ones. Therefore, our statement that the repressor-decay timer is more robust than the activator-relay one is indeed general for all ‘fair’ comparisons that comply with conditions 1-2.

We now explain this in the manuscript, and add further analysis substantiating our claims (Figure 2—figure supplement 1).

1) When explaining the results of the general model:

“Comparing the robustness of two models is convoluted by the choice of parameters: indeed, similar to the absolute time delays, robustness (defined by sensitivity to parameter variations), is a quantitative measure that depends on the kinetic parameters. Still, the two models can be compared by controlling for the absolute time delays. Thus, we compare activator and repressor that (1) have the same decay rate and (2) require the same time transitioning between two given thresholds. As we showed, the repressor-decay timer necessarily shows higher robustness under these conditions (Rappaport et al., 2005).”

2) When explaining the results of our simulations:

“To rigorously distinguish whether robustness correlates with a specific timer type, we considered again the positioning of all circuits in the decay-relay timer space (c.f. Figure 1H). Unlike the simple case of the one step timer, here we did allow some range of possible dynamics, to account for the low precision of the experimental data. This does not affect our ability to compare the consistent circuits since these differences in dynamics are not correlated with location in relay-decay space (Figure 2—figure supplement 1).”

I find Figure 3B difficult to follow. If my understanding is correct, then the lower right dot essentially says that for this particular set of parameters, deleting HB (but not Kr) causes dramatic phenotype, meaning that HB (decay timer) is important. With this set of parameters, the original "wildtype" network is robust. It took me a couple readings to get this. This needs to be explained better.

Yes – this is what the figure shows. We now explain it better in the text:

“With this in mind, we examined computationally whether the consequences of TTFs deletions, if analyzed at higher resolution, could distinguish between the repressor-decay and activator-relay timers. […]Once positioned, we color each circuit by its robustness score for the WT circuit (same color as in Figure 2E) which allows us to observe robustness of WT circuits as function of their Pdm induction sensitivity to Hb and Kr deletions (Figure 3B).”

And in the caption of Figure 3:

“(A-B) TTF deletion phenotypes can distinguish robust circuits: all consistent circuits, as described in Figure 1-2 above, were considered. […] This analysis shows that robust circuits are only found in a small region in the Kr-Hb sensitivity space, in which Pdm induction time is much more sensitive to Hb than to Kr deletion.”

"Robustness score", a concept key to this article, had no visual aids. Even in the Materials and methods, the explanation of robustness score was not clear (e.g. "phase duration"). I recommend adding conceptual illustrations like Figure 2D.

We thank the reviewer for this suggestion. We replaced Figure 2D with a panel which better explains the concept and added a clearer description of what we do to the Materials and methods section:

“Robustness and robustness score

Consistent parameter sets were scored for robustness to TTF production rates. […] For example, a phase of Hb only expression followed by co-expression of Hb and Kr was considered a single phase since both lead to the 1 and 2 neuronal fates rendering the timing of Kr induction irrelevant in terms of NB lineage.”

Reviewer #2:

I find all the exercise of constraining the model with data quite interesting. I also find the experimental results interesting. That said, I am not entirely convinced by the logic of the reasoning presented. For instance, the experimental results presented in the fourth paragraph of “Timing of Pdm and Cas expression is highly sensitive to deletion of TTF repressors, but less sensitive to deletion of TTF activators” validate the idea that the system is not a relay timer. But do we really need the theoretical study on robustness to get there? In fact, to validate the repressor decay vs. the activator relay model, the only solution is to directly perform those experiments (and maybe other ones to really validate the mechanism).

We appreciate this comment and would like to answer it on two levels. First, as we are sure the reviewer acknowledges, the space of possible experiments is large, and defining the experiment that will provide maximal information about the underlying mechanism is difficult. Modeling can therefore direct experimental efforts to the most informative measurements, and define the resolution needed, as was the case in the present study. It is indeed the fact that these experiments were motivated by the theoretical analysis.

Second, theory is instrumental for comparing qualitative properties of different mechanisms. In the present case, one could naively assume that activator-relay and repressor-decay timers are equivalent. Indeed, mechanistically, both can

define proper timing. Our study showed, however, that the two mechanisms are very different in terms of robustness. At least for us, this qualitative difference was the main motivation to experimentally test which of these mechanisms guides the in-vivo timer.

The paper tries very hard to argue that an elaborated theory related to robustness is needed to predict the network topology, but I am rather unconvinced. It could be that the activator relay mechanism is impossible for other reasons that have nothing to do with robustness, so such robustness arguments are in my opinion neither very illuminating nor conclusive.

We appreciate this comment, and of course cannot refute the possibility that an unknown constraint made it impossible to implement the relay-based timer in-vivo. Our computational analysis suggests that activator-relay can define a timer, but that it is limited in robustness. So all we can say is that the mechanism used in-vivoconforms to the robust design. This corroborates our conjecture that the need for robustness restricts the design of biological circuits, but of course does not prove it.

The attempt to "force" the model to predict experimental results also leads to the strange third paragraph in subsection “Timing of Pdm and Cas expression is highly sensitive to deletion of TTF repressors, but less sensitive to deletion of TTF activators”, where we basically learn that, after experimental verification, all the calibration of the model related to Pdm is incorrect, but that does not matter. It seems to me that in such situation, it would be more reasonable to use this information to redo the theoretical study with the new calibration; one could well learn something new.

We thank the reviewer for this comment – perhaps we did not describe this result clearly enough. It is not that the initial calibration was wrong, but it was of an insufficient temporal resolution. This comment therefore relates again to the issue of defining the most informative experiment. As mentioned above, the space of possible experiments is very large. For this reason, experiments that existed when we began our analysis were mostly of low temporal resolution and the data that we had in hand provided only partial restrictions of the possible parameters. The initial calibration therefore was not wrong, but simply less restrictive.

Specifically for Pdm, the experimental data we had in calibrating the model did not allow us to accurately define its expression period; therefore all solutions that showed proper ordering of the respective TTFs were accepted as consistent. Having this information following our focused time-resolved analysis allowed us to further restrict the analysis, but all the results that were consistent with the new, more restrictive data were also deemed as consistent in the original analysis since we quite deliberately allowed a range of possible dynamics to account for the low temporal resolution of the calibration data.

To better explain that, we added Figure 4—figure supplement 1, where we specifically show the number of Pdm neurons that are defined by the set of circuits that were found to be consistent in the original analysis. As can easily be appreciated form this figure, it includes both the solutions that allow 2-3 Pdm neurons, and these that allow smaller, or larger number.

We also revised the text to better explain that:

“The Pdm expression window is therefore significantly longer than the duration inferred from the previous data used to calibrate our model. This did not affect our analysis, however, since in our original analysis we did allow for solutions of similarly long Pdm windows, accounting for the uncertainty of the experimental data (Figure 4—figure supplement 1).”

On top of that, I found the paper at times difficult to follow. The paper seems to have been initially written for a journal with a very compressed format, but I believe it would be much better if some details and more explanations were given in the main text (I give some suggestions below but they are not exhaustive).

Actually, the paper was not submitted elsewhere – eLife is our first choice and the paper was written specifically for this journal. In fact, one of us (CQD) is sending all of the labs “high impact” papers to eLife instead of CSN. We do thank the reviewer for the suggestions to clarify different aspects of the analysis, all of which we tried to implement.

Other comments (in no particular order):

1) The authors postulate a dichotomy between activator-relay and repressor decay. This seems a bit arbitrary to me. One could well imagine more complex networks, a mix of the two via genes that are not known to be implicated, etc. I understand there is a limit to what one can do on the theory side, but I feel some discussions should be added. For instance is it known that the genes studied in the model are necessary and sufficient for the entire process?

All interactions described in our model have experimental support, as described in our series of studies (Isshiki et al., 2001; Cleary and Doe, 2006; Grosskortenhaus et al., 2005; Grosskortenhaus et al., 2006; Cleary and Doe, 2006; Tran and Doe, 2008). Although we cannot rule out additional regulators, it is believed that the four TTFs are the central drivers of the timer, and additional factors, if exist, would play a more peripheral role.

Please also note that we do not postulate a dichotomy between the activator-relay and repressor-decay models, but in fact allow a continuum of circuits that smoothly shift the mechanism between these two extremes. This is what we capture in the decay-relay phase space, displayed in figures 1H, 2E, and 5I. We now describe this more clearly in the text:

“Further, varying parameters qualitatively changes the regulatory network by varying the relative influence of the different interactions on TTF temporal dynamics. This allows us to capture a wide range of networks, ranging from decay dominant ones, through any mixed models to relay dominant networks all the while taking into account all experimentally observed TTFs and cross-regulations (Supplementary File 1).”

And further elaborate in a new Supplementary File 1 section:

“In this model, the relative significance of specific interactions in determining the temporal dynamics, depends on the choice of parameters. […] For example: when βpdmbasal >> 𝛽𝑝𝑑m, induction by Kr will be negligible and downregulation of Hb would be dominant. For βpdmbasal << 𝛽𝑝𝑑m, the opposite is true: Kr-dependent transcription of Pdm is much more substantial.”

2) I found the introduction of the parameter exploration a bit too concise. It would be good to explain how the parameters were chosen and constrained. For instance are there experimental data that are constraining them like degradation rates? More generally, are the parameters found after optimization consistent with what is known or reasonable?

We selected the range of analyzed parameters as follows. First, we chose a ‘reference’ set of parameters, which are biologically reasonable based on experimental data. Second, our screen used parameters that are present within three orders of magnitudes of these reference parameters. This is now explained in the Materials and methods section:

“Mathematical model and Numerical screen

Randomized parameter sets (circuits) were generated by randomly drawing values for model parameters out of the ranges indicated in Supplementary File 4, using a log uniform distribution. […] We believe these ranges are wide enough to capture biologically reasonable values.”

3) Obviously there are also predictions on the possible ranges of parameters when theory is combined with experimental data. I found this is a potentially very interesting aspect of the paper that is not explored sufficiently. For instance can we get more information on parameters from the experimental constraints shown on Figure 5 G and I?

Unfortunately, the range of possible parameter combinations that are consistent with the experiments is still too large to predict reliably the value of any specific quantitative parameters.

4) I find statements in the first paragraph of subsection “A TTF circuit can be positioned in the relay-decay timer space based on TTF-deletion phenotypes” on the connections between robustness and evolution too speculative and in my opinion confusing.

We respectfully disagree. Our working hypothesis, used here and in previous studies is that the need for robustness restricts the design of biological circuits. In the lines the reviewer refers to we clearly state this is a hypothesis. In this study, this hypothesis was indeed useful and helped us correctly predict circuit design.

Reviewer #3:

1) It is unclear why only production rates are being varied for the perturbation analysis, especially since the reasoning for robustness in decay timers (subsection “A repressor-decay timer is more robust than an activator-relay timer”) is based on sensitivity to thresholds Tr. Can the authors provide a rationale? What happens if other parameters are varied as well?

In our formulation, perturbing the thresholds (Kd) is equivalent to perturbing TTF production rate. This is because the relevant quantity defining state-transitions is Kd/[TTF], [TTF] being the TTF concentration. Therefore, randomly varying production rates captures also the consequences of randomly varying the thresholds.

As we write, we do not include the degradation rates in the robustness analysis. This is because degradation rates define the time-scale of timer dynamics, and therefore equally affect both mechanisms. For example, in the case of a one-step cascade, we showed analytically that the delay time is linearly proportion to the degradation rate in both models. Similarly, our numerical analysis confirmed this dependency also in the case of a multi-step cascade.

We explain these points in the manuscript:

“In our model, introducing fluctuations in TTF production rate captures also fluctuations in thresholds values, as circuit function depends on the ratio of TTF levels to their activation thresholds. Finally, degradation rates were kept constant, as they define the time scale of timer dynamics and equally affect all circuits ((Rappaport et al., 2005) and data not shown).”

2) Figures 2E, 3B, and Figure 2—figure supplement 2 may appear conflicting. Figure 3B clearly demonstrates that decay timers are more robust than relay timers, with robust circuits concentrated in the bottom right of the perturbation-space. In Figure 2E however, robustness seems to be dependent on the decay interaction, while invariant to the relay-interaction. Finally, in Figure 2—figure supplement 2, robustness shows more complicated dependencies.

We thank the reviewer for this comment. There are two differences between these figures: first in the type of perturbation used to probe the circuit, and second in how the consequences of these perturbations are measured.

Perturbation type: In Figure 2E, Figure 2—figure supplement 2, we simulate the removal of a specific interaction (for example, the ability of Hb to repress Pdm). By contrast, Figure 3B and Figure 3—figure supplement 1 simulate deletion of the respective TTF (for example, deleting Hb). As is shown in Figure 3C-F, these perturbations lead to similar, but not identical, effects on the Pdm and Cas induction times.

Perturbation consequences: In Figure 2E, we considered the dynamics of both Pdm and Cas, the two steps in the cascade that are completely circuit-autonomous (not sensitive to external signals). The positioning of each circuit in the decay-relay space is therefore defined by the sensitivities of Pdm and Cas induction times to the deletion of the respective interactions. By contrast, in Figure 3B, Figure 2—figure supplement 2 and Figure 3—figure supplement 1, we consider the two TTFs separately. Thus, in Figure 3B we only measure the timing of Pdm induction, whereas in Figure 3—figure supplement 1 we measure the timing of Cas induction.

Therefore, the three figures present the same set of (consistent) circuits, having the same robustness scores (color-coded, based on the WT circuit), yet these circuits are positioned differently, depending on how the decay-relay space is defined: which perturbation are introduced (removing interaction or deleting a factor), and whether we consider both Pdm and Cas (Figure 2E), only Pdm (Figure 3B, Figure 2—figure supplement 2A) or only Cas (Figure 2—figure supplement 2B, Figure 3—figure supplement 1).

a) It would be helpful to see Figure 2E and 5I split up into two figures, one for Pdm induction, and one for Cas induction – possibly as supplemental figures. Combining the two as they are currently in Figure 2E, raise questions if there are some patterns that are missed, especially since Figure 3B and Figure 2—figure supplement 2 look so distinct. Could it be that Pdm, but not Cas, induction is the sensitive step in the network where robustness analysis can distinguish relay vs. decay?

We thank the reviewer for this suggestion. We added a new supplementary figure (Figure 2—figure supplement 2) showing the two separately. As can be appreciated, the increased robustness of the decay timer holds both steps of the cascade also when analyzed separately.

b) Additionally, the Materials and methods indicate that when estimating the significance of the decay network for Cas induction, only the Kr-Cas interaction is removed, and the Hb-Cas interaction is left intact. Can the authors discuss why the dual-repression of Cas is not needed?

We thank the reviewer for this comment, which pointed us to an inaccurate assumption made in our analysis. When performing our simulation, we assumed that, at the time relevant for Cas induction, Kr is present at much higher concentrations compared to Hb, making it the dominant factor repressing Cas. We therefore only considered sensitivity to Kr repression. Following the reviewer comment, we re-examined this assumption. This showed us that the induction time of Cas is indeed sensitive to the Hb-dependent repression in some of the consistent circuits, as is shown in Author response image 1.

Analysis of Cas induction time sensitivity to the removal of Cas repression by Hb. All consistent circuits, as described in Figures 1-2, were considered. Each consistent circuit was scored by measuring the change in Cas induction times following removal of the decay Hb-|Cas (X-axis) or relay Pdm->Cas (Y-axis) regulations. These values were used to uniquely position each circuit in the Hb-Pdm sensitivity space (Materials and methods). Parameter sets are Color-coded based on their robustness score for the WT circuit, as in Figure 2E </Author response image 1 title/legend>

However, this interaction did not appear to provide additional information about the robustness of consistent circuits since robust circuits are found all along the X-axis. This indicates sensitivity to the removal of Cas repression by Hb does not correlate with robustness or location in decay-relay space. We therefore did not include it in the analysis.

3) Figure 5A-F clearly demonstrate that removing the immediate activators has no effect on Pdm and Cas induction timing, and removing the repressor clearly affects timing of Pdm induction. But we have the most trouble with Figure 5E.a) First, Cas induction is pretty modest in both at st11 and 12. Then, based on the network, Cas represses Pdm, and we see this borne out in WT, where at st12, high Cas correlates with low Pdm. However, in Kruppel mutant, Pdm remains high, which seems to signify that there isn't much Cas induction? Can the authors discuss how they see these data? Is there an independent way to confirm that Cas is induced, and induced earlier?

We agree with the reviewer that the induction of Cas in Kr mutant is lower than that of wild-type. Thus, although significant induction is observed earlier than wild-type (at stage 11 Cas is significantly higher in Kr mutants comparted to wild-type), it remains moderate, so that at stage 12, wild-type embryos express significantly higher levels of Cas compared to Kr-mutant embryos.

Still, these moderate levels of Cas, observed in the Kr-mutants in both stages 11-12, are biologically significant, as they are sufficient to induce the Cas-positive U5 neuron generated at this stage (see data in Figure 1D based on Isshiki 2001)

Further, the moderate levels of Cas likely explain why Pdm is not repressed. The simplest explanation of our Kr-mutant data is that Cas is induced earlier than in wild-type, but to moderate levels that are sufficient for generating the Cas-positive neurons, but are too low for repressing Pdm.

In principle, Cas can be independently verified by directly monitoring the activity of cas locus with MS2 coat protein fused GFP (Garcia et al., 2013) or directly observe the synthesis of Cas protein with LlamaTag (Bohmer et al., 2018). Due to the limited time-frame of the revision, we could not perform these experiments, but plan to pursue both of these experiments in the future. Please note that our main conclusion is supported by the clear observation that removal of the relay reaction (Pdm) has no effect on Cas induction time.

We refer to this point in the manuscript.

Cas induction in Kr mutants was moderate compared to its induction in WT embryos. This moderate induction is sufficient to induce the Cas-positive U5 neuron, produced in Kr mutants (Isshiki et al., 2001), and may result from its earlier induction, at a time when Hb, its second repressor, is still highly expressed. Consistent with the contribution of Hb to Cas repression, Cas induction was advanced in Hb mutants to stage 11, similarly to Kr mutants (Figure 5—figure supplement 1).”

b) For Figure 5A-F: It would be helpful to draw a line indicating the "background level" of TTFs, to allow readers to see significance more easily. It would also be helpful to immediately see in the legend the way significant induction is determined. Also, the black arrows are not defined in legend.

Added

c) Cas is also repressed by Hb. Can the authors justify why they didn't analyze Cas induction in Hb mutant?

We now performed this experiment (Figure 5—figure supplement 1) and discuss this in main text:

“Consistent with the contribution of Hb to Cas repression, Cas induction was advanced in Hb mutants to stage 11, similarly to Kr mutants (Figure 5—figure supplement 1).”

4) It would help to have the Materials and methods be better organized. Perhaps with separate sections, so readers can easily find the relevant information. For instance, we had trouble keeping track of the different ways Δtind normalization was performed.

We revised the Materials and methods section as suggested.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

[…] To address this, the reviewers together suggest:

The paper should clarify that it presents two parallel arguments for the decay timer:

1) The robustness from modeling analysis

2) The experiment.

(i.e. rather than a "linear" model-predicts-experiment paper). A paragraph in the Introduction to better clarify the logic of the paper could help.

We added a paragraph to the Discussion and changed the logic of presentation, as suggested. Specifically, we now present our story as follows:

1) Modeling shows that the molecular circuit defined by interactions between the TTF composing the NB timer, can support two, qualitatively different ‘core’ mechanisms: one that progress the TTF cascade by a relay of activator, and one that progresses the TTF cascade by a decay of repressors.

2) Within the actual circuit, both ‘core’ mechanisms can contribute to timer progression. The relative contribution of each mechanism depends on quantitative values of the kinetic parameters.

3) Theory shows that a timer, which progresses by decay of repressors, buffers parameters variations better than a timer that progresses by a relay of activators. (That is, this timer is more robust).

4) This difference between the robustness of the two timers made it interesting to examine which of these two ‘core’ mechanisms dominates timer progression in-vivo.

5) Theory suggests experiments that can best distinguish the relative contribution of these two core mechanisms to the progression of the in-vivo timer.

6) Experiments show that the repressor-decay mechanism dominates the progression of the in-vivo timer. Therefore, the more robust mechanism dominates the in-vivo function.

7) In the Discussion, we raise the possibility that evolution favors the selection of robust mechanisms.

In addition to these changes in presenting our logic, we also tried to simplify the explanations of Figure 5, both in the text and in the figure caption.

2) One of the reviewers has an ongoing concern with the robustness argument presented as the core of the paper, as hypothetically, there could be many ways to have a more "robust" network to noise. The fact that a less complicated network is less robust was not fully convincing in implying that robustness is a good biological criterion to assess the evolutionary origin of the network architecture.

We suggest that the results and interpretation of the paper should stand independent of this conjecture to focus on the repressor decay mechanism as a better explanation of the experimental results (which would roughly correspond to what is done in Figure 5 and associated theory), and reduce overinterpretation of the evolutionary origin of the network structure. Overall, given that the paper does not show that robustness is the selective pressure for evolving repressor-decay timer, we prefer this emphasis be reduced, for example, by moving this point to the Discussion.

We account for that by changing our presentation, as detailed in our reply to comment 1 above. We move our discussion of the possible evolutionary connection between robustness and the mechanism of choice to the discussion. Robustness is now presented as a property that differs between qualitatively different ‘core’ models; a difference that motivated experiments to distinguish which of these ‘core’ models dominates timer progression in-vivo.

We note that the robust model (repressor decay) is not more complicated than the non-robust one (activator relay). In fact, they can be encoded by the same number of components and interactions.

3) The Discussion should also include the responses (from the authors' rebuttal) on work that was not done.

Added

4) Another concern from the initial reviews was the issue of predicting parameter values from the simulations, and the authors' response that they could not really see anything. If the parameters are truly completely random in the region compatible with data, we would ask to show it explicitly. It seems a bit paradoxical that, following the authors' line of thought, one could predict so carefully the existence of extra negative interactions from the study, but nothing on the actual parameters corresponding to those interactions. At the very least the negative interactions should have parameters significantly different from a "default" state where they would not contribute. This point should be clarified.

We agree. The only point we tried to make is that other predictions do not correspond to qualitatively different mechanisms, and therefore we found them less informative. But the reviewer is of course correct that our analysis distinguishes the range of possible values that complies with the theory.

We now added a supplementary figure 5—figure supplement 2 in which we present the range of parameters that are compatible with all experimental observations. In this figure, we show the range of parameters tested in our simulation, the subset which were proven consistent with existing experiments, available prior to our study, and then the restricted subset of parameters that remained consistent also following the experiments we performed.

Please also note that our analysis does not predict the existence of extra negative interactions, only the dominance of known negative interactions over the known positive ones.

5) While we very much appreciate the extra experiment to address our most important concern about the Cas experiments, we are however, still concerned by the fact that Cas delay-relay space (Figure 2—figure supplement 2B) does not support the robustness argument (third paragraph of subsection “A repressor-decay timer is more robust than an activator-relay timer”). We do see the robustness argument with the Pdm space (Figure 2—figure supplement 2A) and when considering the combined Pdm-Cas space in Figure 2E. This concerns us because it can compromise the overall robustness argument, in several ways:a) Perhaps Figure 2E sets up expectations about the robustness of the decay circuits, only to find out in the supplement that it is more true for Pdm, but not as much for Cas.b) It could also raise doubts on the analysis. E.g., what if Cas is less pronounced because the metric "decay significance" vs. "relay significance" does not capture the effects comprehensively enough for Cas.

The argument of robustness is in fact valid also for Cas. We agree that this was not properly presented in our previous sup Figure 2A, and we apologize for that. The reason for this suboptimal presentation is that, overall, Cas induction time is less sensitive to noise compared to Pdm induction time (it is controlled by two repressors: Hb and Kr). However, in previous revision, when we added sup Figure 2A, we chose to show it with the same level of noise (20%) used for generating Figure 2E of Pdm robustness.

We now show the same plots, but for increasing noise levels (20%, 30% and 40%). This is shown for both Pdm and Cas (Figure 2—figure supplement 1). As can be appreciated, when examined at higher noise levels, the robustness benefit of the decay timers becomes evident also for Cas.

For instance, Cas is inhibited by Hb and Kr, but one could also view Hb's inhibition of Pdm is an inhibition of Cas (which is not removed in the analysis).

This is not in fact the case in our simulations. The inhibition of Pdm by Hb does not affect Cas directly since by the time Cas is induced, Pdm is already upregulated. Therefore the Hb inhibition of Pdm is removed much before Cas is being induced.

Either case, we ask that this be addressed by some re-writing, e.g., for point a, state earlier the difference between Pdm and Cas analysis, so readers are not led to expect more after seeing Figure 2E.

We now refer to the different noise sensitivity of Cas and Pdm in main text. With respect to robustness, we believe that the new sup figure we show verifies that robustness favors a decay timer also in the case of Cas.

For point b: Add more explanation to the label "significance of decay", perhaps in parentheses, with what is actually being evaluated, e.g., "removal of Pdm--|Cas interaction".

Done, see new Figure 2—figure supplement 1 axis labels.

https://doi.org/10.7554/eLife.38631.021

Article and author information

Author details

  1. Inna Averbukh

    Department of Molecular Genetics, Weizmann institute of science, Rehovot, Israel
    Contribution
    Conceptualization, Data curation, Software, Investigation, Writing—original draft, Writing—review and editing, Modeling, data analysis
    Contributed equally with
    Sen-Lin Lai
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1863-205X
  2. Sen-Lin Lai

    Institute of Neuroscience, Institute of Molecular Biology, Howard Hughes Medical Institute, University of Oregon, Eugene, United States
    Contribution
    Investigation, Writing—original draft, Writing—review and editing, animal experiments, data analysis
    Contributed equally with
    Inna Averbukh
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-7531-283X
  3. Chris Q Doe

    Institute of Neuroscience, Institute of Molecular Biology, Howard Hughes Medical Institute, University of Oregon, Eugene, United States
    Contribution
    Supervision, Writing—original draft, Writing—review and editing, helped design experiments
    For correspondence
    cdoe@uoneuro.uoregon.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5980-8029
  4. Naama Barkai

    Department of Molecular Genetics, Weizmann institute of science, Rehovot, Israel
    Contribution
    Supervision, Writing—original draft, Writing—review and editing, helped design experiments
    For correspondence
    naama.barkai@weizmann.ac.il
    Competing interests
    Reviewing editor, eLife
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-2444-6061

Funding

Howard Hughes Medical Institute

  • Chris Q Doe

National Institutes of Health (R01-HD27056)

  • Chris Q Doe

European Research Council

  • Naama Barkai

United States - Israel Binational Science Foundation (2017055)

  • Chris Q Doe
  • Naama Barkai

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Benny Shilo, Eyal Schejter, Danny Ben-Zvi and Gat Krieger for comments on the manuscript; Cheng-Yu Lee, Ward Odenwald and DHSB for antibodies. S-LL and CQD were funded by the Howard Hughes Medical Institute, NIH R01-HD27056, and BSF 2017055. NB was supported by a grant from the ERC and BSF 2017055.

Senior Editor

  1. Marianne E Bronner, California Institute of Technology, United States

Reviewing Editor

  1. Wenying Shou, Fred Hutchinson Cancer Research Center, United States

Publication history

  1. Received: May 28, 2018
  2. Accepted: December 10, 2018
  3. Accepted Manuscript published: December 10, 2018 (version 1)
  4. Version of Record published: December 21, 2018 (version 2)

Copyright

© 2018, Averbukh et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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