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

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.

interactions -positioned each consistent circuits within the relay-decay timer space (Figure 1H), defining the significance of two respective timers in the circuit. 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 122 progress the TTF timer through an activator-relay or a repressor-decay timer.

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

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To obtain better resolution, we next added robustness criteria to our model. In support of this, 126 we had previously shown that time delays measured by protein decay are more robust than 127 time delays measured by protein accumulation (Rappaport et al., 2005). The reason for this 128 differential robustness is easily appreciated: the time at which a protein decays between two 129 thresholds is only moderately (logarithmically) sensitive to the values of these thresholds ( Figure   130 2A-C). By contrast, the time to increase protein levels between two thresholds depends at least 131 linearly, and typically significantly stronger, on thresholds values (Figure 2A-C).

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We added the robustness criteria to our numerical screen, assigning each consisted circuit a 133 robustness score based on its ability to buffer the temporal durations at which each TTF is 134 expressed against moderate (~20%) variations in TTF production rates (see Methods) Examining 135 the parameter sets that showed high robustness, we noted that they typically gave larger 136 weights to the repressor-decay interactions compared to the activator-relay ones, suggesting 137 that the more robust circuits progress the TTF timer through the repressor decay, rather than 138 activator accumulation (data not shown).

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To more rigorously distinguish whether robustness correlates with a specific timer type, we 140 considered again the positioning of all circuits in the decay-relay timer space (c.f. Figure 1H), 141 and color-coded the circuits by their robustness score ( Figure 2D,E). High robustness scores 142 were found in the region of repressor-decay timers, while activator-relay timers were 143 significantly less robust. We conclude that also in the context of the full model, robustness is 144 improved when progressing through repressor decay rather than activator relay. We hypothesized that robust circuits, with improved ability to buffer variations in parameters,

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were favored in evolution. We therefore predicted that the in-vivo TTF timer is robust, and is 150 thereby driven by a decay timer. To test this hypothesis, we searched for experiments that could 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 157 co-expression phases in which two consecutive TTFs are expressed within the NB, but one of 158 them dominates in generating neuronal identity. This significantly limited our ability to precisely 159 deduce the TTF expression timing in either wild-type or mutant embryos, and thereby greatly 160 increased the spectrum of circuits that were scored as consistent with measured phenotypes.

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With this in mind, we examined computationally whether the consequences of TTFs deletions, if 162 analyzed at higher resolution, could distinguish between the repressor-decay and activator-relay 163 timers. First, we examined how Pdm induction time changes following deletion of either Hb (its 164 repressor) or Kr (its activator). Specifically, for each consistent circuit, as described in Figure 1H     to the specific removal of the Kr-to-Cas repression link (Figure 3E,F). We conclude that following about the robustness of the in-vivo timer, but also about the relative contributions of the relay 190 and decay reactions 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
Engrailed markers, which allow us to unambiguously identify NB7-1 ( Figure 4A). TTF protein 200 intensity levels were quantified using confocal microscopy ( Figure 4B). Variability in staining 201 intensities was controlled by normalizing TTF staining to that of Engrailed, which is constantly 202 expressed in NB7-1.

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Our data confirmed the sequential expression of Hb, Kr, Pdm, and Cas within the NB7-1 lineage 204 (data not shown). It further revealed that Pdm expression was longer than expected: about 180 205 minutes ( Figure 4C). This is long enough to generate more than the two previously reported 206 Pdm+ GMCs (Isshiki et al., 2001). To determine if there were additional Pdm+ GMCs in the 207 lineage, we used the NB7-1-specific Gal4 driver to drive the expression of membrane-tethered 208 superfold GFP and co-stained for Pdm and the GMC marker Asense ( Figure 4D). We found that

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Pdm was upregulated when NB7-1 was producing the 4th GMC and downregulated after the NB

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The Pdm expression window is therefore significantly longer than the duration inferred from the 216 previous data used to calibrate our model. This difference in the timing of Pdm expression in 217 wild-type embryos has no substantial effect on our model. Indeed, apart from minor 218 quantitative differences, our main qualitative results, including the ability to distinguish 219 consistent circuits and the differences between the robustness of decay and relay times, 220 remained the same.

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We next used the high temporal resolution expression data to determine whether the relay-222 timer or decay-timer could best account for Pdm and Cas expression timing in TTF mutant 223 backgrounds. We found that Kr mutants did not alter Pdm expression, whereas hb mutants   Figure 1H). First, to estimate the robustness of the Kr sensitivity space ( Figure 3B) using the measured changes in Pdm induction time following deletion of Hb and of Kr. As can be seen, the in-vivo circuit was positioned in the narrow region 235 in which robust circuits are found, strongly supporting the notion that the in-vivo circuit is 236 indeed robust.
Second, we used our data of TTF deletion phenotypes to estimate the consequences of 238 specifically removing the activator-relay or repressor-decay link. To this end, we used the tight 239 correlations between the respective phenotypes observed in our simulations, as described in 240 Figure 3C-F. Using these values to position the in-vivo circuit on the relay-decay space, clearly 241 identified this circuit as a decay timer as was predicted by the robustness hypothesis. We 242 therefore conclude that the timing of TTF expression is driven by a repressor-decay mechanism, 243 rather than an activator-accumulation mechanism (Figure 5G-I).

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Our study suggests that a repressor-decay timer drives the sequential TTF expression to       Table S3. Parameters sere then substituted into model equations (See SI) and solved numerically by a standard MATLAB ODE solver. The and all mutants (Figure 1C,D). Consistent parameter sets were scored for robustness to TTF

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For Figure 5G and Figure S1, the calculation of in-vivo system location according to its for 346 TTF deletion perturbations was performed by assuming the experimentally observed and were the middle of the stage in which induction occurred, with an overall error 348 margin of half that stage duration. These error margins were further increased when translating from for TTF deletions to for appropriate regulation removal. This translation was performed by placing the measured for TTF deletion on the correlation plots in Figure 5H and defining the range for regulation removal as the maximal range on the Y axis reached 352 by robust (robustness score>80) sets within the X axis range of measured and its error 353 margins. For Figure 5I,

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Experimental Methods

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Similarly, this was done for Cas regulation in Figure 5H lower plots (based on measured ranges 541 in Figure S1, see Methods for details).    Figure 1D. For every combination, the resulting fate is specified along with the genotypes from Figure 1D from

Model equations and Parameters
The molecular interactions driving the embryonic NB timer have been well described  Notations and additional parameters: ( − 0 ) it a temporal step function which allows the production of hb only at t<t 0 .
For the TTF i, is i's production rate, is i's degradation rate, is i's basal production rate in the absence of any activators. , is a hill function representing transcriptional activation by the TTF i of gene j. With , , the K D for i activity on j, and , i's hill coefficient.
, is a hill function representing transcriptional repression by the TTF i.
With , the K D for i activity, and , i's hill coefficient. Additional model parameters are the , which are the thresholds. Only when the concentration of i, [i], is above , i is considered to be "on".
is the duration of the simulation. We solve this full set of ODEs numerically using a standard MATLAB ODE solver. The model equations insure the dominance of the repressors: a gene will not be expressed in the presence of its repressor even if an activator is also present. This property which stems from the multiplication of the production rates by the   Table S 3 -Parameter ranges used when searching for consistent sets. Drawing was done from a log-uniform distribution on indicated ranges. When no specific TTF is indicated for the parameter, it is the same for all four TTFs.