Precise temporal control of neuroblast migration through combined regulation and feedback of a Wnt receptor

Many developmental processes depend on precise temporal control of gene expression. We have previously established a theoretical framework for regulatory strategies that can govern such high temporal precision, but experimental validation of these predictions was still lacking. Here, we use the time-dependent expression of a Wnt receptor that controls neuroblast migration in Caenorhabditis elegans as a tractable system to study a robust, cell-intrinsic timing mechanism in vivo. Single-molecule mRNA quantification showed that the expression of the receptor increases non-linearly, a dynamic that is predicted to enhance timing precision over an unregulated, linear increase in timekeeper abundance. We show that this upregulation depends on transcriptional activation, providing in vivo evidence for a model in which the timing of receptor expression is regulated through an accumulating activator that triggers expression when a specific threshold is reached. This timing mechanism acts across a cell division that occurs in the neuroblast lineage and is influenced by the asymmetry of the division. Finally, we show that positive feedback of receptor expression through the canonical Wnt pathway enhances temporal precision. We conclude that robust cell-intrinsic timing can be achieved by combining regulation and feedback of the timekeeper gene.

such high temporal precision, but experimental validation of these predictions was still lacking. 23 Here, we use the time-dependent expression of a Wnt receptor that controls neuroblast 24 migration in C. elegans as a tractable system to study a robust, cell-intrinsic timing mechanism 25 in vivo. Single molecule mRNA quantification showed that the expression of the receptor 26 increases non-linearly, a dynamic that is predicted to enhance timing precision over an 27 unregulated, linear increase in timekeeper abundance. We show that this upregulation 28 depends on transcriptional activation, providing in vivo evidence for a model in which the 29 timing of receptor expression is regulated through an accumulating activator that triggers 30 expression when a specific threshold is reached. This timing mechanism acts across a cell 31 division that occurs in the neuroblast lineage, and is influenced by the asymmetry of the 32 division. Finally, we show that positive feedback of receptor expression through the canonical 33

Introduction 36 37
Timing plays a central role in development, coordinating processes ranging from cell division 38 (Tyson and Novak, 2008) and differentiation (Ray et al., 2022), to the complex segmentation 39 (Dequeant and Pourquie, 2008) and limb development of vertebrate embryos (Pickering et al., 40 2018). To measure time, biological clocks generally utilize a component that increases or 41 decreases in activity or abundance (a timer), or cycles through a high and low state (an 42 oscillator), and triggers a response when a specific threshold is crossed (Gliech and Holland, 43 2020). An example of such a biological clock is the time-dependent expression of Neuropilin-44 1 in retinal ganglion cells (RGCs), which influences the trajectory of the outgrowing RGC axons 45 (Baudet et al., 2011;Campbell et al., 2001). Here, the clock mechanism consists of a 46 transcriptional repressor (CoREST) that gradually decreases in abundance as a result of 47 microRNA dependent inhibition, and releases Neuropilin-1 expression once it reaches a 48 specific threshold. With its dependence on protein production, degradation and molecular 49 interactions between proteins, such a timekeeping mechanism is inherently noisy, raising 50 questions on the regulatory strategies that biological clocks have evolved to increase 51

precision. 52
In clocks that act across multiple cells, robustness can be increased through averaging, 53 synchronization through intercellular communication (Dequeant and Pourquie, 2008;Oates, 54 2020) or entrainment using external signals (Aydogan et al., 2020;Bell-Pedersen et al., 2005). 55 The cell intrinsic mechanisms that control the timekeeping mechanism itself are, however, still 56 poorly understood. Mathematical modeling has provided insight into regulatory circuits that 57 can enhance timing precision. One mechanism for temporal regulation is the constant 58 production of a stable timer molecule, which leads to a gradual accumulation and activation of 59 the time-dependent response once a specific abundance threshold is reached. Modeling has 60 shown that such a linear increase is more precise than a strategy where the timer molecule 61 positively regulates its own expression, as such autoregulation also amplifies the noise 62 (Ghusinga et al., 2017). Using a first-passage time approach, we have recently shown that a 63 regulated strategy where the timekeeping molecule increases non-linearly over time can 64 increase precision (Gupta et al., 2018). Such regulation can be mediated through an 65 accumulating transcriptional activator or a gradually decreasing transcriptional repressor that 66 controls the expression of the timekeeper molecule in a threshold-dependent manner, and we 67 showed this to be robust to additional effects such as cell division and bursts in transcription 68 (Gupta et al., 2018). Moreover, in contrast to autoregulation on its own, we found that precision 69 could be further increased when the regulator was combined with autoregulation of the 70 timekeeper (Gupta et al., 2020). It is not known, however, if this predicted regulatory strategy 71 is utilized by biological clocks in vivo.
final QR descendants localize to a more anterior position in mutants with a shorter body size, 109 and at a more posterior position in animals with a longer body size, although it should be noted 110 that some compensation takes place at the level of migration speed (Dubois et al., 2021). 111 Here, we combine mutant analysis and mathematical modeling to examine the 112 timekeeping mechanism that controls mig-1 expression in the QR lineage. We show that the 113 rapid upregulation of mig-1 expression in QR.pa is dependent on transcriptional activation, 114 supporting a model in which the non-linear increase in mig-1 expression is mediated through 115 threshold-crossing of an accumulating transcriptional activator. We find that this timing 116 mechanism acts across the division of QR.p, but is influenced by the asymmetry of the 117 division. Finally, we show that positive feedback of mig-1 expression through the canonical 118 Wnt pathway decreases temporal variability. We conclude that robust timing of gene 119 expression can be achieved by combining an accumulating transcriptional activator with 120 feedback regulation of the timekeeper molecule. During the anterior migration of the QR descendants, mig-1 expression is low in QR.p, but is 126 strongly upregulated in its daughter QR.pa (Mentink et al., 2014) (Figure 1B), where it triggers 127 the canonical Wnt signaling response that is necessary to stop migration (Rella et al., 2021). 128 The presence of a cell division prior to the upregulation of mig-1 expression -the timing of 129 which is tightly controlled as part of the invariant cell lineage of C. elegans development 130 (Sulston and Horvitz, 1977) -raises the question whether the two are mechanistically linked. 131 To investigate whether the upregulation of mig-1 expression is dependent on the division of 132 QR.p (or the subsequent cell cycle reentry in QR.pa), we blocked QR.p mitosis by conditionally 133 depleting the M-phase regulator CDK-1 using the auxin inducible protein degradation system 134 (Zhang et al., 2015). In this system, proteins tagged with an auxin inducible degron sequence 135 (AID) are degraded in the presence of auxin and the F-box protein TIR1 (Zhang et al., 2015). 136 We endogenously tagged cdk-1 with the AID degron sequence (AID::CDK-1) using 137 CRISPR/Cas9 mediated genome editing and specifically expressed TIR1 in the Q neuroblast 138 lineage using the egl-17 promoter (Branda and Stern, 2000). Since continuous exposure to 139 auxin would block all divisions in the QR lineage, auxin was only applied from the stage at 140 which QR has completed its division (300 -345 min after hatching). We found that this 141 efficiently inhibited the subsequent division of QR.p and its sister cell QR.a, as judged by the 142 absence of their descendants (the apoptotic QR.pp and QR.aa cells and the neuronal QR.paa, 143

QR.pap and QR.ap cells). 144
Studies in yeast and mammalian cells have shown that loss of CDK1 not only inhibits 145 mitosis, but also cell cycle reentry and DNA replication (Coudreuse and Nurse, 2010). To 146 investigate if the cell cycle is similarly blocked in the undivided QR.p cells, we examined DNA 147 content by measuring total DAPI fluorescence at a time point at which the daughter of QR.p 148 (QR.pa) would normally have divided into the final descendants QR.paa and QR.pap (8 -9 149 hours after hatching), and normalizing to total DAPI fluorescence of the Vn.p (seam) cell 150 nuclei, which are 2C at this stage in L1 larval development (Hedgecock and White, 1985) and 151 have a similarly sized nucleus. Under these conditions, the DNA content is expected to be 8C 152 when the cell completes another S-phase, but 4C when the cell cycle is blocked. As shown in 153 Figure 1C, we observed no significant deviation from a DNA content of 4C. These results show 154 that CDK-1 depletion inhibits mitosis as well as cell cycle reentry in the undivided QR.p cells. 155 Next, we measured mig-1 expression in the AID::CDK-1 strain using single molecule 156 mRNA FISH (smFISH) (Ji et al., 2013). In the absence of auxin, mig-1 expression was not 157 significantly different from animals containing wild type CDK-1 ( Figure 1B, D, E). Importantly, however, we found that in the presence of auxin, upregulation of mig-1 expression in undivided 159 QR.p cells occurs at a similar time and range of expression as in the control animals ( Figure  160 1D, E). We conclude that the temporal regulation of mig-1 expression is independent of the 161 cell cycle and QR.p division.   and quantified the number of mig-1 transcripts in QR and its descendants using smFISH. 177 While deletion of motif pair B had no effect on mig-1 expression, deletion of motif pair A 178 strongly reduced the early expression of mig-1 in the QR neuroblast ( Figure 2B, C). The late 179 expression of mig-1 in QR.pa was, however, not affected by deletion of this motif pair. Taking into account that the late phase of mig-1 expression is independent of cell division and 190 the early phase of expression, we developed a dynamical model of a cell-intrinsic timer 191 mechanism driving mig-1 transcription. Since the speed of QR.p migration -which crosses 192 most of the distance covered by the QR descendants -is roughly constant (Mentink et al.,193 2014), we treated distance along the anteroposterior axis as proportional to time. To account 194 for the decrease (QR), followed by the increase (QR.pa), in the mig-1 amount over time, we hypothesized that mig-1 mRNA is continuously degraded and upregulated by a component 196 with its own dynamics: either a transcriptional activator that increases in time or a repressor 197 that decreases in time (Gupta et al., 2018). Thus, the dynamics of mig-1 mRNA number m are 198 described by dm/dt = −νm + F(t), where ν is the degradation rate, and F(t) accounts for the 199 regulation. For the activator model, we set F(t) = a ! /(a ! + K ! ), where the activator molecule 200 number increases with rate k according to a(t) = kt. For the repressor model, we set F(t) = 201 where the repressor molecule number decreases with rate µ from initial value 202 r " according to r(t) = r " e #$% . In both models, H is the Hill coefficient, and K is the half-maximal 203 value of the regulator. Fitting either model to the mig-1 expression data (see Materials and 204 Methods) gave good agreement ( Figure 2D). Consistent with the intron motif pair A deletion 205 data, we found that lowering the initial mig-1 amount (m(0) = 0) does not affect the later 206 upregulation dynamics ( Figure 2D). Therefore, the model captures the observation that early  is rapidly engulfed and degraded by neighboring cells (Sulston and Horvitz, 1977). Although 250 we found that the division per se is not necessary for the late phase of mig-1 expression, the 251 size difference of the daughter cells and potentially unequal inheritance of the mig-1 activator 252 could contribute to the temporal regulation of mig-1 expression. 253 To investigate the role of the asymmetric division of QR.p in mig-1 regulation, we first 254 compared mig-1 expression in the two daughter cells using a null mutation in the essential cell 255 death regulator ced-3 to prevent apoptosis of QR.pp (Ellis and Horvitz, 1986). As expected, 256 loss of ced-3 did not affect the upregulation of mig-1 expression in QR.pa ( Figure 4A). In correlates with the level of cell size asymmetry, we compared the size ratio of QR.pa/QR.pp 272 pairs with mig-1 expression in QR.pa. As shown in Figure 4C, we found a moderate 273 correlation, with QR.pa cells from less asymmetric pairs showing lower mig-1 expression than 274 QR.pa cells from more asymmetric pairs. 275 To understand the effect of division asymmetry on mig-1 expression, we returned to 276 our activator-based mathematical model. First, we incorporated QR.p division into the model 277 at a time inferred from the data (see Materials and Methods). Because no active transcription 278 of mig-1 was observed in QR.pp experimentally, we set the mig-1 production rate to zero in 279 QR.pp. Despite changes in the overall cell size, we experimentally observed that the nuclear 280 size of QR.pa is not significantly different from that of its parent QR.p ( Figure 4D). Since the 281 activator is likely a transcription factor and therefore acts in the nucleus, the nuclear 282 concentration of the activator in QR.pa should thus depend on its molecule number but not 283 the cell size. Therefore, we assumed that the production of mig-1 in QR.pa is dependent on 284 the number of molecules, and not the concentration, of the activator. Finally, because the 285 nuclear envelope breaks down before division, we assumed that at division, both the activator   However, we found that mig-1 is also expressed in the QR founder cell, raising the question 351 whether these early and late phases of mig-1 expression are linked. Examination of 352 evolutionarily conserved cis-regulatory elements that we deleted from the endogenous mig-1 353 locus using CRSPR/Cas9-mediated genome-editing showed that the two phases are 354 independently regulated. Thus, we identified a small region in the first intron that is required 355 for the early expression of mig-1 in QR, but is dispensable for the late phase of expression in 356 QR.pa. Conversely, two partially redundant regions upstream of the mig-1 coding sequence 357 are required for the late phase of expression, but have no detectable role in the early 358 expression. The early phase of mig-1 expression could therefore be disregarded in the 359 analysis of the late phase of expression, which was confirmed using a dynamic model that 360 was fit to the mig-1 expression data. 361 The dynamic model also made predictions on the regulation of mig-1 expression. In an 362 activator-based model, removal of the activator disrupts the upregulation of mig-1 expression 363 in QR.pa, while in the case of a repressor, removal of the repressor results in premature 364 expression of mig-1 in QR.p. We found that mig-1 expression in QR.pa was lost when the 365 presumptive binding sites of the mig-1 regulator were deleted from the mig-1 upstream region, which supports the conclusion that the time-dependent expression of mig-1 depends on 367 transcriptional activation and not on repression. 368 Another prediction from our mathematical modeling is that the timing precision of a 369 our finding that the activator acts transcriptionally in a cell whose nuclear size does not change 393 upon division. However, for regulators that act post-transcriptionally, or for cells whose nuclear 394 volume changes upon division, the model would predict that the upregulation is governed by 395 the cellular or nuclear concentration of the regulator, respectively, and not its molecule 396 number. Second, the model assumes that the activator and mig-1 transcripts are partitioned 397 at division according to cell volume. This assumption is critical, particularly for the activator. If 398 instead the activator were sequestered to QR.pa, for example, the molecule number would 399 not change after division, and the dynamics of mig-1 expression upregulation therefore would 400 not depend on the QR.pa/QR.pp size ratio. Consequently, we predict that the activator is not 401 sequestered at division, and that unequal partitioning of the mig-1 activator between the 402 differently sized daughter cells is necessary for the rapid upregulation of mig-1 expression in 403

QR.pa. 404
Examination of conserved cis-regulatory elements upstream of mig-1 showed that two  Table S1. 424

Fitting of mathematical model to data 508
We find the parameters of either the increasing activator model or the decreasing repressor 509 model ( Figure 2D) using a least-squares fit to the control data ( Figure 2B). Specifically, to find 510 m(0) and ν, we perform a linear fit to the log of the mig-1 mRNA number for the QR data only, 511 corresponding to exponential decay; we find m(0) = 31 mRNAs and ν #& = 0.65 (in the 512 arbitrary time units of Figure 2D). Then, to find the remaining parameters, we fit the numerical 513 14. For the repressor model we find α = 130, µH = 6.7, and H ln(r " /K) = 18. Although these 517 parameter combinations are sufficient to specify the mig-1 dynamics, for illustrative purposes 518 we plot example activator and repressor dynamics consistent with these values in Figure 2D  4E. The QR.pa dynamics from the model with division, using the wild type mean size ratio ρ = 527 3.5, are fit to the control data using the same procedure as above, yielding the parameters 528 α = 240, K/k = 2.6, and H = 17. This fit is shown for QR.p, QR.pa, and QR.pp in Figure 4E  529 (dark colors). To illustrate the effect of decreasing size ratio ρ, we also plot these dynamics 530 with ρ = [2.7, 1.8, 1] in Figure 4E (light colors). To illustrate the dependence of the QR.pa mig-531 1 molecule number m(t) on the size ratio ρ, we plot m(t) vs. ρ at times between t = 3 and t = 532 3.3 (gray region) and at the midpoint time t = 3.15 (black line) in Figure 4F.