Summary
During development, cell fate decisions are often highly stochastic, but with the frequency of the different possible fates tightly controlled. To understand how signaling networks control the cell fate frequency of such random decisions, we studied the stochastic differentiation of the C. elegans P3.p cell, using time-lapse microscopy to measure the single-cell dynamics of key regulators of cell fate frequency. Strikingly, we observed pulsatile accumulation dynamics of BAR-1/β-catenin, a key component in Wnt signaling, during the cell fate decision. Combining quantitative analysis and mathematical modeling, we found that the timing of the BAR-1/β-catenin pulse was a key determinant of the outcome of the cell fate decision. Our results highlight that timing of cell signaling dynamics, rather than its average level or amplitude, can play an instructive role in determining cell fate.
Introduction
During development, cells robustly obtain the correct cell fate to give rise to a viable adult organism, despite internal molecular noise and environmental variability. It is commonly assumed that suppressing this variability is essential for successful development. However, stochastic cell fate decisions, where cells randomly assume one cell fate out of a limited repertoire of different fates, is the cornerstone of many developmental processes (Johnston and Desplan 2010). For example, the first cell fate decision in the mouse embryo, between trophectoderm or primitive endoderm fate, is stochastic (Zernicka-Goetz et al. 2009). Similarly, photoreceptor cells in the human retina randomly express either a red, green or blue photoreceptor gene (Roorda and Williams 1999; Smallwood et al. 2002). In these stochastic decision processes, even though each individual outcome is random, the relative frequency of the different cells fates is often tightly controlled.
Currently, stochastic cell fate decisions are best understood in the context of single-celled organisms, where gene expression noise dominates as the key source of variability driving stochastic cell fate decisions (Balaban 2004; Süel et al. 2006; Maamar et al. 2007; Losick and Desplan 2008). However, it remains poorly understood how stochastic cell fate decisions are regulated during animal development, as multicellular organisms pose unique constraints compared to single-celled organisms. Here, stochastic cell fate decisions have to be precisely coordinated with developmental timing, are potentially influenced by neighboring cells and rely on external, long-range signals mediated by a small number of key developmental signaling pathways. How these canonical signaling pathways drive stochastic cell fate decisions with strong control over cell fate frequencies is an open question.
The Wnt pathway is a highly conserved signaling pathway that regulates many developmental events and cell fates (Mucenski et al. 2003; Hirabayashi 2004; Ohyama 2006; Clevers and Nusse 2012; Hudson et al. 2013; Lindström et al. 2014). In the canonical pathway, the presence of Wnt ligands leads to the accumulation of the transcriptional co-activator BAR-1/β–catenin, which co-regulates Wnt pathway target genes (Eisenmann et al. 1998; Korswagen et al. 2000; Korswagen 2002; Sawa and Korswagen 2013). During C. elegans larval development, the Wnt/β-catenin pathway is required for specification of vulval precursor cell (VPC) competence group early in the L2 larval stage (Gleason et al. 2002; Myers and Greenwald 2007). This group consists of six epidermal cells named P3.p-P8.p, which are subsequently patterned to various vulval cell fates by multiple signaling pathways (Sternberg and Horvitz 1986; Hill and Sternberg 1993; Eisenmann et al. 1998; Gleason et al. 2002; Félix 2012; Gupta et al. 2012).
The establishment of the VPC competence group is partly stochastic, as the P3.p cell assumes VPC fate in only ~50% of wild-type hermaphrodites (Fig. 1a). In the other 50%, P3.p assumes hypodermal fate by fusing to a neighboring syncytial hypodermal cell, called hyp7 (Sternberg and Horvitz 1986; Shemer and Podbilewicz 2002). Previous investigations into the P3.p cell fate decision showed that its cell fate frequency is extremely sensitive to the dosage of Wnt ligands, particularly cwn-1, suggesting that variability in the ligand concentration or in the response of the P3.p cell to Wnt ligands could provide the noise source driving the stochastic fate decision (Pénigault and Félix 2011a; b). In addition, mutations in the C. elegans Hox gene lin-39 impact the Pn.p cell fate frequencies, by repression of cell fusion and promoting division of VPC fate cells (Clark et al. 1993; Maloof and Kenyon 1998; Koh et al. 2002; Shemer and Podbilewicz 2002; Roiz et al. 2016). Both Wnt signaling and LIN-39 inhibit hyp7/fusion fate, with loss-of-function mutants exhibiting increased frequency of cell fusion, including in the P4.p-P8.p cells that otherwise never assume hyp7/fusion fate (Gleason et al. 2006; Myers and Greenwald 2007). However, what aspects of Wnt signaling and LIN-39 dynamics control the frequency of hyp7/fusion versus VPC fate in P3.p remains unknown.
Here, we use a novel time-lapse microscopy approach (Gritti et al. 2016) to observe gene expression and signaling dynamics in single Pn.p cells during specification of the VPCs, allowing us to directly connect variability during the decision process to the final cell fate outcome. Using this approach, we found that BAR-1/β–catenin accumulated in a dynamic, pulsatile manner at the time of the hyp7/fusion versus VPC fate decision, with strong variability in pulse slope and timing. Combining quantitative data analysis with mathematical modeling, we found that cell fate outcome depended strongly on the time of the BAR-1/β–catenin pulse onset, identifying the timing of Wnt signaling dynamics as a key control parameter of cell fate.
Results
Time-lapse microscopy of a stochastic cell fate decision
So far, whether P3.p undergoes fusion or assumes VPC fate in wild-type or mutant animals has been assessed only after the process has completed (Eisenmann et al. 1998; Alper and Kenyon 2001, 2002; Chen and Han 2001; Myers and Greenwald 2007; Pénigault and Félix 2011b; a). To correlate early stochastic molecular events to eventual cell fate outcome it is essential to follow these processes directly in time. Here, we utilize a fluorescent time-lapse microscopy approach we developed recently to study single-cell dynamics inside moving and feeding C. elegans larvae for their entire ~40hr development (Gritti et al. 2016). We tested whether we could directly observe the occurrence of P3.p fusion events inside single animals. We initially used two measures of cell fusion: first, imaging the apical junction protein AJM-1, which localizes on the apical edge of Pn.p cells but is degraded upon cell fusion (Brabin et al. 2011). Second, observing the flow of GFP from the hypodermis into the fused Pn.p cell, using animals carrying an extrachromosal array targeting GFP expression to the hyp7 hypodermal syncytium. Initially the AJM-1::mCherry signal expanded along the A-P axis during the early L2 larval stage (Supplementary Movies 1-2, Fig. 1c). In animals with a fusing cell, this was followed by a sudden and pronounced ruffling of the AJM-1:mCherry signal and a rapid retraction of AJM-1::mCherry towards the posterior, with the fluorescent signal fully disappearing from P3.p within 1 hr (Fig. 1c). Inflow of GFP from the hypodermis into P3.p was observed as soon as AJM-1::mCherry retraction commenced (Fig. 1c,d), showing that both are accurate markers of (the time of) fusion. Because AJM-1 was more easily monitored, we used AJM-1 dynamics to establish fate and timing of P3.p fusion for all subsequent experiments
Even though changes to the frequency of P3.p hyp7/fusion versus VPC fate in mutants are well studied (Eisenmann et al. 1998; Alper and Kenyon 2001, 2002; Chen and Han 2001; Myers and Greenwald 2007; Pénigault and Félix 2011b; a), it was not known how such mutants impact the timing of this decision. We quantified the time of P3.p fusion in wild-type animals and found that cell fusion occurred in a relatively narrow time window between 40-60% of the L2 larval stage (Fig. 1f). We then examined mutants in which fusion frequency is increased by removing inhibitory Wnt signaling or LIN-39 (Fig. 1b). We found that in these mutants P3.p fusion occurred within the same time window as wild-type animals, with only small differences between wild-type and mutant animals in average timing (Fig. 1f). Strikingly, even though the exact time of fusion can vary as much as 2 hrs between animals, when multiple VPCs fuse in a single animal, they typically do so at the same time (Fig. 1g). The observation that, in the absence of key repressors of hyp7/fusion fate, cell fusion frequency is increased independently of its timing provides evidence that a yet-unknown signal exists that activates cell fusion at the appropriate time. In contrast, hyp7/fusion inhibitors (Wnt signaling, LIN-39) do not control timing of fusion, but rather modulate hyp7/fusion versus VPC fate frequency.
Stochastic eff-1 induction precedes P3.p fusion
The most downstream regulator of the hyp7/fusion versus VPC fate decision is the gene eff-1, a fusogenic protein whose expression is sufficient to induce cell fusion (Mohler et al. 2002; Shemer et al. 2004). EFF-1 is a transmembrane protein that is required for most cell fusions in C. elegans, and must be present on both the Pn.p and hyp7 plasma membrane to induce fusion (Zeev-Ben-Mordehai et al. 2014; Smurova and Podbilewicz 2016). To understand how cell fate frequency is regulated on the level of eff-1 expression, we counted eff-1 mRNA molecules in Pn.p cells, using single molecule FISH (smFISH) (Raj et al. 2008). In wild-type animals where P3.p had not undergone fusion, based on presence of the AJM-1 signal, we most frequently observed low eff-1 expression in P3.p, <5 molecules (Fig. 2a,c,d), similar to the P4.p cell that always assumes VPC fate in wild-type animals (Fig. 2c,d). However, in the range of body lengths (340-380 μm) corresponding to the measured time of fusion, we observed a subset of wild-type animals expressing much higher eff-1 levels, ~30-50 molecules (Fig. 2b-d). We found that high eff-1 expression was maintained in fused P3.p cells, before disappearing by the end of the L2 stage (Supplemental Fig. 1a,b). We confirmed that high eff-1 expression preceded cell fusion, rather than following it, by examining a temperature-sensitive loss-of-function point mutation in eff-1 (Mohler et al. 2002). Here, we still found high eff-1 mRNA levels in P3.p at the restrictive temperature, even as P3.p cell fusion was fully inhibited (Supplemental Fig. 1c).
When we examined the distribution of eff-1 mRNA levels in P3.p, we found a broad peak of P3.p cells with low eff-1 mRNA levels (<20 molecules) that was similar to that seen in the non-fusing P4.p cell and a much smaller peak at ~40 eff-1 mRNAs that was not observed in P4.p, indicating that such high levels correspond to P3.p cells about to assume hyp7/fusion fate. An interesting result is that the fraction of wild-type animals showing high (>20 molecules) eff-1 mRNA levels in P3.p was significantly smaller than the expected fraction of animals where P3.p assumes hyp7/fusion fate (Fig. 2d). For our analysis, we randomly sampled animals within the time window we expected fusion to occur. Given the observed variability in the time of fusion (Fig. 1f), it is expected that some animals with low eff-1 expression would have ultimately fused at a later point. In particular, the fraction of animals observed with high eff-1 expression in unfused P3.p cells should increase with the average duration the cell expresses high eff-1 before this results in fusion. Hence, our results suggested that induction of high eff-1 expression was quickly followed by cell fusion.
To understand how eff-1 expression impacts cell fate frequency, we quantified eff-1 levels in a strain with a functional LIN-39::GFP insertion (lin-39(++)) that caused low fusion frequency (~2% P3.p fusion frequency). The resulting eff-1 distribution was similar to wild-type for low eff-1 levels, but lacked the highly expressing P3.p cells (Fig. 2e). In contrast, in the cwn-1(0) mutant that lacks the dominant Wnt ligand and exhibited high (>80%) fusion frequency both in P3.p and P4.p, we found that the fraction of cells in the high eff-1 peak had increased substantially, in particular in P4.p, even though the position of this peak itself had not shifted (Fig. 2f). Together, this indicated that Wnt signaling and LIN-39 controlled cell fate frequency mainly by tuning the fraction of cells in which high eff-1 expression is induced.
No bias of cell fate decision by noise in LIN-39 protein level
The Hox transcription factor LIN-39 inhibits Pn.p hyp7/fusion fate by repressing eff-1 expression (Shemer and Podbilewicz 2002), with lin-39 null mutations causing all Pn.p cells to fuse in the L1 larval stage (Clark et al. 1993; Wang et al. 1993). Hence, stochastic variability in LIN-39 protein levels could result in variability in induction of high eff-1 expression. It was shown previously that LIN-39 levels are similar between P3.p and P4.p in early L2 larval stage animals prior to cell fusion (Pénigault and Félix 2011a), even though both cells have a different fate frequency (Fig. 1b). However, individual cells were not followed over time and it is possible that small differences in LIN-39 between P3.p cells in different animals are sufficient to explain the outcome. To connect animal-to-animal variability in LIN-39 level with P3.p cell fate, we performed time-lapse microscopy on animals carrying a lin-39::GFP translational fusion (Sarov et al. 2012) and ajm-1::GFP as a cell fusion marker (Fig. 3a,b). Since lin-39::GFP (lin-39(++)) is present as a multi-copy insertion, it decreased the P3.p fusion rate from ~30% to ~2%, making it challenging to capture sufficient P3.p fusion events for analysis. For that reason, we further crossed these reporters into the cwn-1(0) mutant, increasing the P3.p and P4.p fusion rates to 20% and 14%, respectively.
We observed that LIN-39 was present in the P3.p nucleus at the start of the L2 larval stage and remained there for the entire larval stage when P3.p assumed VPC fate (Fig. 3a,c). However, in P3.p cells that fused, nuclear LIN-39 levels decreased rapidly after fusion commenced and fully disappeared within 90 mins (Fig.3b,c), consistent with past observations of loss of LIN-39 in fused Pn.p cells (Pénigault and Félix 2011a). We compared the distribution of LIN-39 levels, averaged over 3 hrs prior to fusion in P3.p cells that assumed hyp7/fusion fate with the distribution in P3.p cells that assumed VPC fate, averaged over 3hrs prior to the average time of P3.p fusion in this strain (Fig. 3d). We found strong overlap between the two distributions, also when changing the size of the time window (data not shown), making it unlikely that fluctuations LIN-39 levels drive stochastic eff-1 induction and cell fusion.
β-catenin activation dynamics during the cell fate decision
We next quantified activation of the Wnt pathway by monitoring the accumulation dynamics of BAR-1/β-catenin in a strain carrying a functional bar-1::GFP reporter (bar-1++) (Eisenmann et al. 1998). In the absence of Wnt ligands, β–catenin is continuously degraded by a degradation complex. Upon activation of Wnt receptors by Wnt ligands, activity of the degradation complex is stopped, allowing β–catenin to accumulate in the cell and nucleus (Sawa and Korswagen 2013). In P3.p, the presence of BAR-1 is required to inhibit eff-1 expression and, hence, inhibit hyp7/fusion fate (Eisenmann et al. 1998). In contrast to β–catenins involved in the Wnt asymmetry pathway (Park and Priess 2003; Mila et al. 2015), dynamics of BAR-1 during canonical Wnt signaling is poorly characterized. Because Wnt ligands are expressed continuously during larval development (Coudreuse et al. 2006), we expected BAR-1 to show constant expression and dynamics in P(3-8).p cells, similar to LIN-39. Instead, we found that BAR-1::GFP levels were strikingly dynamic, with no BAR-1::GFP in P(3-8).p at the start of the L2 stage, followed by pulse of BAR-1::GFP in P(3-8).p at the mid-L2 stage that lasted 1-4 hours and was strongly coordinated between cells (Supplemental Movie 3, Fig. 4a-c). BAR-1 was detected both in the nucleus and cytoplasm. We found stochastic variability in the amplitude of the BAR-1 pulse between different Pn.p cells (Fig. 4b,c). It was speculated that P3.p, which is considered most distant to the source of Wnt ligands, receives a lower Wnt signal than P(4-8).p, thereby resulting in its occasional hyp7/fusion fate (Harterink et al. 2011; Pénigault and Félix 2011b). However, the BAR-1::GFP pulse in P3.p was frequently of similar or higher amplitude compared to the other Pn.p cells and, in general, we found no sign of a systematic spatial pattern in Wnt signaling. We also found significant variability in the amplitude and timing of the BAR-1::GFP pulse in the P3.p cell compared between different animals (Fig. 4d).
Since the BAR-1::GFP reporter is integrated as a functional multi-copy transgene, we expected this strain to act as a BAR-1 overexpression mutant and, indeed, observed no P(3-8).p cell fusions (Supplemental Table 1). Hence, we refer to this strain as bar-1(++). To study how BAR-1 dynamics related to cell fate frequency, we used different approaches to increase the frequency of hyp7/fusion fate, First, we decreased the level of the inhibitor LIN-39, using the lin-39(n709) temperature sensitive loss-of-function mutant, leading to 16/70 P3.p cells assuming hyp7/fusion fate in bar-1(++);lin-39(lf) animals (Supplemental Table 1). We found that bar-1(++);lin-39(lf) animals showed similar BAR-1::GFP pulses (Fig. 4e). Cells that fused always did so during the early accumulation phase of the BAR-1 pulse (Fig. 5a). Next, we sought to lower BAR-1 levels in the bar-1(++) background by decreasing activity of the Wnt signaling pathway, using the cwn-1(0) mutant that lacks the CWN-1 Wnt ligand (Fig. 1a). In these animals, BAR-1::GFP pulse amplitude was lower (Fig. 4f). In some bar-1(++);cwn-1(0) animals the L2 stage was significantly lengthened. Moreover, we found that BAR-1::GFP pulses occured at significantly later times, as fraction of larval stage duration, even in animals with similar duration as the other mutants. Finally, BAR-1 pulses also showed considerable variability in timing and amplitude in these mutants.
Variability in β-catenin pulse dynamics
To characterize variability in BAR-1 accumulation dynamics, we used a minimal parameterization of the BAR-1 pulse to fit to the experimental data (Fig. 5a, Eq. 3 in Methods). Briefly, we assume that prior to the BAR-1 pulse, Wnt signaling is inactivated and BAR-1 is degraded. At pulse onset time t0, Wnt signaling is activated, leading to inhibition of BAR-1 degradation and hence linear accumulation of BAR-1 in the cell. Linear BAR-1 accumulation continues for a pulse duration in cells that assume VPC fate or until the time of fusion, tfusion, in cells that assume hyp7/fusion fate. Upon fusion BAR-1 vanishes immediately, as observed experimentally, whereas in cells that assume VPC fate, BAR-1 levels decrease exponentially once the pulse ends. This fitted the experimental data surprisingly well (Fig. 5a,b). Moreover, it allowed us to describe each BAR-1 pulse by three parameters: pulse onset time t0, pulse slope and pulse duration T for VPC cells or fusion time tfusion for hyp7/fusion cells.
First, we compared the distribution of pulse onset time t0 and linear slope s of BAR-1 accumulation pulses between strains. We found that both were highly variable between animals in all strains (Fig. 5c,d). We found that the pulse parameters of bar-1(++) and bar-1(++);lin-39(lf) were similar, consistent with increase in hyp7/fusion fate frequency in this mutant resulting from the absence of the fusion inhibitor LIN-39 rather than changes in Wnt signaling. In contrast, we assumed that the increase in frequency of hyp7/fusion fate in bar-1(++);cwn-1(0) animals was due to a decrease in BAR-1 level. In the context of the observed BAR-1 pulses this could be achieved in two independent ways, either by decreasing the slope s or by delaying the onset time t0 of the BAR-1 pulse relative to the time of fusion (Fig. 6a,b). Given that BAR-1 accumulation is thought to be proportional to the amount of external Wnt ligands, we expected the cwn-1(0) mutant, that lacks the CWN-1 Wnt ligand, to have a decreased rate of BAR-1 accumulation. Surprisingly, we found that the pulse slope distribution was highly similar for bar-1(++) and bar-1(++);cwn-1(0) animals (Fig. 5c) and that the only different pulse characteristic was the delayed pulse onset (Fig. 5d).
We then compared the timing of the onset of BAR-1 accumulation between P3.p and P4.p cells. Both in bar-1(++) and bar-1(++);lin-39(lf) animals, considerable variability existed in t0, the time of the onset of the BAR-1 pulse, between these cells, with BAR-1 accumulation in P3.p preceding that in P4.p as often as the reverse (Fig. 5b,e). At the same time, pulse onset was correlated between P3.p and P4.p, meaning that if BAR-1 accumulation started late in the L2 larval stage in P3.p, it was also likely to start late in P4.p (Fig. 5e). Strikingly, we not only found that in the bar-1(++); cwn-1(0) mutant the onset of the BAR-1 pulse was delayed, but also that the variability in pulse onset time between P3.p and P4.p was almost completely removed, with the onset of BAR-1 accumulation occurring in P3.p and P4.p within 20 min in all animals (Fig. 5e). This result suggests that the Wnt ligand cwn-1 not only controls the average onset of BAR-1 pulses, but also induces variability in pulse onset time between P3.p and P4.p.
We also observed variability in the duration of BAR-1 pulses when comparing pulses in the same cell between animals (Fig. 5b,f). We examined whether the onset and the duration of BAR-1 pulses were correlated. Because the duration of the L2 larval stage varied significantly between strains and animals, we examined the pulse onset time t0/TL2 and duration T/TL2 relative to the duration of the larval stage, TL2. In this case, we found a striking anti-correlation, with late pulse onset resulting in shorter pulses (Fig. 5f). In fact, the data for all strains clustered along the line T/TL2 = 0.66 − t0/TL2, consistent with a model in which the end of the BAR-1 accumulation occurs at 66% of the L2 larval stage independent of the BAR-1 pulse onset time. This correlation also held for the bar-1(++);cwn-1(0) mutant, where not only the onset of BAR-1 pulses was delayed but also the L2 larval stage was much extended. Hence, the BAR-1 pulse ended independent of its onset time t0 in all mutants examined.
Given that we observed strong variability in pulse onset time relative to the time the pulse ceases (Fig. 5f), we asked whether the time of cell fusion was correlated with either the pulse start or end time. However, because cell fusion is immediately followed by rapid degradation of BAR-1, it was not possible to determine the pulse end time in cells that assumed hyp7/fusion fate. At the same time, P4.p cells often assumed hyp7/fusion fate in bar-1(++);lin-39(lf) and bar-1(++); cwn-1(0) animals. Therefore, we selected animals where one Pn.p cell, either P3.p or P4.p, assumed hyp7/fusion fate whereas the other assumed VPC fate. We then compared within the same animal the fusion time tfusion in the hyp7/fusion cell with the pulse onset time t0 (Fig. 5g) or the pulse end time t0 + T (Supplemental Fig. 2) in the VPC. For bar-1(++);lin-39(lf) animals, the time of fusion correlated most strongly with the pulse onset time (R=0.86, P3.p fusing only) rather than pulse end time (R=0.56). Specifically, the data clustered along the line tfusion/TL2 = 0.2 + t0/TL2, i.e. cell fusion occurs at a time 0.2TL2, or on average ~2 hrs, after the onset of the BAR-1 pulse. Because the bar-1(++);cwn-1(0) mutant has the same pulse slope distribution as the bar-1(++) mutant (Fig. 5c), we examined whether the increased hyp7/fusion frequency in the bar-1(++);cwn-1(0) mutant was due to a shorter delay between pulse onset and time of fusion. Indeed, we found that in bar-1(++);cwn-1(0) animals the delay was halved, with cell fusion now occurring at a time 0.1TL2 after onset of the BAR-1 pulse (Fig. 5g). We found before that bar-1(++);cwn-1(0) animals have a similar rate of BAR-1 accumulation as bar-1(++) (Fig. 5c). Delaying the pulse onset relative to the time of fusion would be an alternative mechanism to lower inhibitory BAR-1 levels.
Bias of cell fate decision by variability in β-catenin pulse timing
To elucidate the mechanism by which BAR-1 pulse dynamics might impact eff-1 expression and cell fate frequency, we constructed a mathematical model of the cell fate induction network that takes into account variability in BAR-1 pulse slope and timing (Fig. 6a-c, see Materials and Methods for details). In the model, hyp7/fusion fate requires sufficiently high eff-1 expression. We assumed that an activator controls the timing of cell fusion in the absence of the fusion inhibitors BAR-1 and LIN-39, consistent with our observations in Fig. 1f. In contrast, BAR-1 and LIN-39 then modulate cell fate outcome by inhibiting eff-1 expression. Specifically, eff-1 expression is induced only when the activator, but not BAR-1 and LIN-39 are bound to the eff-1 promoter (Fig. 6a). Here, BAR-1 is expected to control eff-1 expression in a complex with the Wnt effector POP-1 (Korswagen et al. 2000). In the model, we assumed that the activator is only present from time tfusion at a level ca (Fig. 6b). Also, we assumed that the level of the inhibitor Wnt signal, cW(t), followed the observed BAR-1 dynamics, rising from the pulse onset time t0 with linear slope s (Fig. 6b). Finally, we assumed stochastic variability in activator level, pulse slope and time of pulse onset and fusion.
We constrained almost all model parameters by experimental data (See Materials and Methods) as follows: using experimentally measured correlations between i) pulse onset time in different cells and ii) pulse onset time and time of fusion in the same cell, we estimated the relative contributions of global and cell-specific variability in timing of pulse onset and cell fusion. Next, we fitted the observed distribution of pulse slopes by a Gaussian distribution (Supplemental Fig. 3a). Finally, we adjusted the parameters governing the action of LIN-39 and the activator to reproduce the observed hyp7/fusion frequency in the different strains (Supplemental Fig. 3e). For all mutants, the resulting model provided an excellent fit to the observed distributions of pulse onset time t0 and slope s (Supplemental Fig. 3a-d), the joint distribution of t0 in P(3,4).p (Supplemental Fig. 3f) and that of t0 and fusion time tfusion (Supplemental Fig. 3g). In the model, the increased frequency of hyp7/fusion fate in bar-1(++); lin-39(lf) animals was due to absence of LIN-39 increasing the range of activating and inhibitory signals ca and cw for which eff-1 is expressed sufficiently highly, whereas in the bar-1(++);cwn-1(0) mutant, the reduced delay between t0 and the time, tfusion, when the activator becomes available causes lower inhibitory Wnt signals cw at tfusion (Supplemental Fig. 3e). We used the model to examine a hypothetical mutant that achieves the same hyp7/fusion frequency as the bar-1(++);cwn-1(0) mutant, but by changing pulse slope rather than pulse onset time. We found that this mutant was clearly distinguishable from the bar-1(++);cwn-1(0) mutant in terms of pulse slope distribution and delay between pulse onset and time of fusion (Supplemental Fig. 3b,g), providing further evidence that the change in pulse timing is the key reason hyp7/fusion fate is increased in the bar-1(++);cwn-1(0) mutant.
We next used the model to ask whether variability in BAR-1 pulse timing impacts the outcome of individual cell fate decisions, focusing on the bar-1(++);lin39(lf) mutant that produced most hyp7/fusion cells. We examined the difference in pulse slope and onset time in bar-1(++); lin-39(lf) animals, comparing animals where P3.p fused but P4.p assumed VPC fate with animals where both P3.p and P4.p assumed VPC fate. The model predicted that for animals where both cells assume VPC fate, the distributions P(sP4.p-sP3.p), of difference in pulse slope, and P(t0,P4.p-t0,P3.p), of difference in pulse onset time, are symmetrical (Fig. 6d,f, blue line). However, the model predicted a bias towards low pulse slope and late pulse onset time in fusing P3.p cells compared to non-fusing P4.p cells (Fig. 6d,f, red line), because both decrease the amount of inhibitory BAR-1. In agreement with the model, we found that the experimentally obtained distributions of difference in pulse slope and onset time between P3.p and P4.p were symmetrical, both in bar-1(++) animals, where P(3,4).p never fuse, and bar-1(++);lin-39(lf) animals selected so that both cells assumed VPC fate (Fig. 6e,g, black and blue lines). However, in bar-1(++);lin-39(lf) animals where P3.p, but not P4.p, assume hyp7/fusion fate, we found a weak bias towards lower pulse slope in P3.p and a significantly stronger bias towards delayed BAR-1 pulse onset in fusing P3.p cells compared to non-fusing P4.p cells (Fig 6e,g, red line), with only one animal with a fusing P3.p cell showing BAR-1 accumulation in P3.p prior to P4.p. This difference was particularly striking compared to the bar-1(++) strain, which otherwise showed no difference in relative timing of BAR-1 pulse onset between P3.p and P4.p relative to bar-1(++);lin-39(lf) animals (Fig. 5c).
Even though the above results indicated that BAR-1 pulse timing biased the hyp7/fusion versus VPC fate decision, it left open whether variations in pulse timing achieve this by specifically modulating BAR-1 levels at the time the decision to fuse or not is made. The model predicted that at the time of fusion cells assuming hyp7/fusion fate in bar-1(++);cwn-1(0) mutants should have lower BAR-1 levels than fusing cells in bar-1(++);lin-39(lf) mutants, where fusion frequency is instead increased by removing the inhibitor LIN-39 (Fig. 6h). Indeed, when we compared BAR-1::GFP fluorescence at the time of cell fusion in bar-1(++);lin-39(lf) and bar-1(++);cwn-1(0) animals, we found a bias towards lower BAR-1 levels in fusing P3.p and P4.p cells in the cwn-1(0) background (Fig. 6i). To further link BAR-1 levels to inhibition of cell fusion, we quantified eff-1 transcripts in bar-1::gfp animals and indeed found a negative correlation: Pn.p cells with visible BAR-1::GFP had few eff-1 transcripts, while unfused Pn.p cells without BAR-1::GFP often showed high eff-1 levels (Supplemental Figure 4). Together, these results show that changes in the timing of BAR-1 accumulation pulses are a key determinant of the hyp7/fusion versus VPC fate decision, likely by impacting the BAR-1 level at the time of the decision.
Discussion
Pulsatile BAR-1/β-catenin dynamics
Here, we combined a novel time-lapse microscopy approach with quantitative analysis and mathematical modeling to study, in developing C. elegans larvae, how the outcome of a stochastic cell fate decision is controlled by random variability in the dynamics of the underlying signaling network. Surprisingly, we found that BAR-1/β-catenin, a core component of the Wnt pathway, accumulated in Pn.p cells in a dynamic, pulsatile manner (Fig. 4) that was precisely timed to influence their stochastic choice between vulva precursor or hypodermal fate, with the latter fate inhibited by BAR-1/β-catenin. Moreover, we found that the timing of the BAR-1/β-catenin pulse was a key control parameter influencing the relative frequency of these two cell fates: first, we observed that the increase in hypodermal fate frequency in bar-1(++);cwn-1(0) mutants, compared to that in bar-1(++) mutants, was not due to systematic changes in the slope of the BAR-1/β-catenin pulse, but rather to a systematic decrease in the time delay between the pulse onset and the time of the cell fusion event that defines hypodermal fate (Fig. 5). Second, in the bar-1(++);lin-39 mutant we found that Pn.p cells that assume hypodermal fate have a later pulse onset that those cells in the same animal that assume vulva precursor fate (Fig. 6). Experiments and modeling suggest that pulse timing influences the cell fate decision by changing the level of BAR-1/β-catenin, and hence the amount of inhibition of hypodermal fate, at the time that hypodermal fate and cell fusion are induced (Fig. 6). Overall, these results indicate that for the cell fate decision studied here, it is not the absolute BAR-1/β-catenin level per se, as is generally assumed, but rather the timing of its accumulation dynamics relative to other developmental events, that is a key factor determining cell fate outcome.
Mechanism of BAR-1/β-catenin pulse generation
A striking feature of BAR-1/β-catenin pulse dynamics is their complex timing: despite considerable differences in time of pulse onset, both between mutants (Fig. 5d) and between Pn.p cells within the same mutant (Fig. 5e), pulse dynamics is otherwise synchronized between the multiple adjacent Pn.p cells (Fig. 4), with the time of the end of the pulse highly similar in all mutants (Fig. 5f). It is an important question how the BAR-1/β-catenin pulse is generated. BAR-1/β-catenin accumulation could be controlled by changes in the level of the Wnt ligands outside of the cell or rather by changes in the Wnt pathway components inside the cell, such as changes to Wnt receptor levels or presence/activity of components of the β-catenin destruction complex. We currently favor the latter hypothesis, since neuronal cells close to the Pn.p cells show BAR-1::GFP expression in the late L1/early L2 stage when Pn.p cells do not, with a significantly decreased BAR-1::GFP signal in those cells in a cwn-1(0) background. This suggests that Wnt ligands are already present and able to activate Wnt signaling at this time and position in the body.
Our observations differ significantly from the current model of Wnt signal propagation at a number of points. First, as ligand-activated Wnt receptors sequester and thereby inactivate the destruction complex that induces β-catenin degradation, it was expected that changing Wnt levels would predominantly impact the rate of β-catenin accumulation (Clevers and Nusse 2012; Sawa and Korswagen 2013). However, using the cwn-1(0) mutant we found that removing a Wnt ligand instead changed only the timing of the induced BAR-1/β-catenin pulse (Fig. 4, 5c,d), which is difficult to explain based on our current knowledge of the Wnt pathway. Particularly surprising is that loss of cwn-1 almost completely removed the variability in BAR-1/β-catenin pulse timing between adjacent Pn.p cells in the same animal (Fig. 5e). In absence of CWN-1, other Wnt ligands such as EGL-20 repress hypodermal fate, albeit at reduced efficiency (Pénigault and Félix 2011b). Our results indicate that CWN-1 acts in a significantly more stochastic manner, either on the level of ligand/receptor interaction or the delivery of ligands to the Pn.p cells, than the other Wnt ligands in the body, even though it is the Wnt ligand expressed closest to the Pn.p cells (Eisenmann 2005; Harterink et al. 2011). It was also suggested that cells respond to fold change rather than the absolute level of β-catenin (Goentoro and Kirschner 2009). However, this is inconsistent with our observation that cell fate frequency is impacted by changes in timing of BAR-1/β-catenin pulse onset, which do not impact fold change, rather than changes in pulse slope (Fig. 5c,d). Moreover, we find higher levels of inhibitory BAR-1/β-catenin at the time of cell fusion in mutants that lack the parallel hypodermal/fusion fate inhibitor LIN-39 (Fig. 6i), another indication that absolute BAR-1/β-catenin levels control the frequency of hypodermal fate.
It is an open question how the decay of the BAR-1/β-catenin pulse is controlled. Negative feedback of the Wnt/β-catenin pathway has been shown to occur through the regulator Axin, which could be responsible for shutting off β-catenin accumulation (Jho et al. 2002). However, this negative feedback model implies that the end of the pulse would be tightly linked to the pulse onset, rather than occurring at a fixed point in the larval stage independent of the start of the pulse, as we observed (Fig 5f). We speculate, based on the link between the BAR-1/β-catenin pulse end time and the timing of the larval stage, that this aspect of pulse timing is regulated by the molting cycle. In particular, it has been shown that many genes show body-wide gene expression oscillations, peaking once every larval stage but at different phases (Hendriks et al. 2014). Some of these genes might be responsible for switching of BAR-1/β-catenin accumulation in all Pn.p cells simultaneously. Our data indeed suggested that a Wnt-independent timing mechanism is present, as the time of cell fusion was unperturbed in a bar-1(0) mutant (Fig. 1f). In general, our observations suggest that timing of BAR-1/β-catenin accumulation dynamic can be regulated both by Wnt-dependent signals and Wnt-independent developmental timing cues.
Role of β-catenin pulses in development
It is increasingly clear that many of the canonical metazoan signaling pathways control development using temporal information encoded in their dynamics (Shimojo et al. 2008; Levine et al. 2013) In particular, pulses in the output of signaling pathways have now been identified in vivo in a number of developmental systems. For example, a recent study showed that EGF signaling acts in a pulsatile manner in the VPCs, with signaling strength transmitted in the frequency of pulses instead of a continuous graded signal (de la Cova et al. 2017). Moreover, time-lapse imaging of oscillatory, rather than pulsatile dynamics of Notch and Wnt signaling during segmentation of mouse embryos showed that the relative phase of the two oscillations instructs the segmentation process by an unknown mechanism (Sonnen et al. 2018). In this study Wnt signaling was monitored indirectly, using an Axin rather than a β-catenin reporter. So far, the dynamics of β-catenin accumulation have rarely been studied directly. Pulses of β-catenin have been observed (Murphy et al., 2014, Kafri et al., 2016), although mostly in cell lines following exogenous application of Wnt ligands rather than in the natural context of the body. For all these studies, differences in timing of β-catenin pulses have not been linked to cell fate outcome.
It remains an open question what the advantage is of pulsatile BAR-1/β-catenin dynamics for the hypodermal versus VPC decision, as opposed to the constant expression level displayed by the parallel hypodermal fate inhibitor LIN-39 (Fig. 3). So far, our limited observations have not revealed BAR-1 pulsatile dynamics for other canonical Wnt signaling processes during larval development. Our mathematical model indicates one potential advantage, namely that BAR-1/β-catenin pulsatile dynamics allows for pulse timing as an additional control parameter, next to BAR-1/β-catenin accumulation rate, to tune cell fate frequency (Fig. 6). Which cells receive Wnt input is tightly controlled in space, e.g. by regulating Wnt receptor expression. In contrast, pulsatile dynamics of signaling pathways could be a powerful mechanism to control precisely when cells respond to ligands in time. This might be particularly important because the same signaling pathways are used many times during development, sometimes even in the same cell, to control different developmental events. Reading out these signaling pathways only at particular time points, using pulsatile dynamics, would allow the reconfiguration of the pathway from executing one developmental decision to another. Interestingly, Wnt signaling is used in VPCs at the mid-L3 stage, ~10 hrs after the hypodermal versus VPC decision, to control the anteroposterior orientation of the asymmetric divisions of the VPCs (Green et al. 2008). Here, EGL-20 plays an important role, whereas BAR-1 and CWN-1 have a smaller contribution. The decay of the BAR-1/β-catenin pulse at the end of the L2 stage might be crucial to avoid temporal crosstalk between the outputs of the Wnt pathway as the VPCs transition from one process to the next.
In conclusion, we have shown here that β-catenin accumulation can be highly dynamic during development, with temporal information instructing development contained in its dynamics. Many (stochastic) cell fate decisions in organism from nematodes to humans are controlled by Wnt signaling and it will be interesting to see whether pulsatile β-catenin plays a similar role in biases cell fate frequencies in those systems. The quantitative approach we employed here, combining in vivo time-lapse imaging of β-catenin dynamics with measurements of key dynamical parameters such as pulse slope and pulse timing, can provide a template for such future studies.
Materials and Methods
CONTACT FOR REAGENT AND RESOURCE SHARING
Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Jeroen van Zon (j.v.zon{at}amolf.nl).
EXPERIMENTAL MODEL DETAILS
Strains
All strains were handled according to the standard protocol on Nematode growth medium (NGM) agar plates with OP50 bacteria (Brenner 1974). Experiments were performed on L2 stage hermaphrodites. Strains were obtained from the CGC unless otherwise indicated.
The following mutations were used in this study:
LGII: cwn-1(ok546) (The C. elegans Deletion Mutant Consortium 2012),
LGIII: lin-39(gk893) (The C. elegans Deletion Mutant Consortium 2012), lin-39(n709) (Clark et al. 1993)
LGX: bar-1(ga80) (Eisenmann et al. 1998)
The following transgenes were used in this study:
ncIs13[ajm-1::GFP], (Liu et al. 2005)
sIs11337[rCesY37A1B.5::GFP + pCeh361)],
ouIs20 [ajm-1::mCherry + unc-119+] (gift from Alison Woollard),
itIs37[pie-1p::mCherry::H2B::pie-1 3′UTR + unc-119(+)] IV,
stIs10116[his-72(promoter)::his-24::mCherry::let-858 3′UTR + unc-119(+)],
stIs10311[lin-39::TGF(3D3)::GFP::TY1::3xFLAG] (Sarov et al. 2012),
gaIs45[pDE218(bar-1::bar-1::GFP)] (gift from David Eisenmann) (Eisenmann et al. 1998), and stIs10226[his-72p::HIS-24::mCherry::let-858 3′ UTR + unc-119(+),(Sarov et al. 2012)].
The presence of the cwn-1(ok546) homozygous deletion was confirmed by nested PCR screening. The following primers were used: outer left (‘5-TCGTTTCTGACATGGCTCAC-3’), outer right (‘5-ACCCATCCTTTCCCAATCTC-3’), inner left (‘5-CGTATCCACGACCACAACAG-3’) and inner right (5’-AGAATCTTCACACCAACGGG-3’).
METHOD DETAILS
Time-lapse imaging
The microchamber size used in the study was 190 μm × 190 μm, with a depth of 10 μm and made as previously described and imaged with a custom time-lapse microscope (Gritti et al. 2016). Using an eyelash attached to a glass pipette, OP50 bacteria was used as “glue” to transfer eggs into the microchambers using M9 solution to keep the microchamber moist. A Nikon Ti-E inverted microscope with a large chip camera (Hamamatsu sCMOS Orca v2) and a 60 × magnification objective (NA=1.4 oil immersion) was used for imaging. Transmission imaging was performed using an LED light source (CoolLED pE-100 615nm), while 488 and 561 nm fluorescence images were acquired using Coherent OBIS LS 488-100 and OBIS LS 561-100 lasers, respectively. Images were acquired in a temperature controlled room at 19° with a sample temperature of 22°. Exposure time was 10 ms and approximately 25 images were taken with a z-distance of 1 μm. Images were taken every 20 min. Images were 2048 × 2048 pixels and saved in 16-bit TIFF format. Fusion times were determined by ajm-1::GFP localization and morphology.
Quantitative Image Analysis
For all experiments, transmitted light images where used to identify molt times. Custom Python scripts and ImageJ were used to quantitatively analyze the acquired images (Schindelin et al. 2012; Schneider et al. 2012). First, images to be used for quantitative analysis were corrected for uneven laser illumination in the following manner: flat field intensity for the particular experiment was obtained by imaging a uniformly fluorescent (488nm) testing slide, and averaging the result of 10 images. We divided each pixel’s intensity value in the experimental images by the corresponding flat field pixel’s intensity, normalized to the median value of the entire flat field image. This normalization procedure corrects for position-dependent variation in light intensity due to the Gaussian profile of the laser beam. The region of interest was cropped at this time. Pn.p cells were manually identified by stereotyped nuclear position location and the domains of ajm-1::gfp/mcherry expression, if present. To measure lin-39::gfp expression, a mask was manually drawn around the nucleus and the mean fluorescence intensity of the pixels within the mask was calculated. The z-slice closest to the center of the nucleus was used. A background fluorescence measurement for each image was obtained by creating a mask of the intranuclear space in a region near P3.p and P4.p along the axis of the ventral nerve cord. The mean background fluorescence value was then subtracted from the mean fluorescence value of the reporter for the same image. To measure bar-1::gfp expression, a mask was manually drawn around the Pn.p cytoplasmic region using ajm-1::mCherry signal as a positional guide, with background corrections performed similarly as described above. For the Supplementary Movies, fluorescence images were computationally straightened and aligned, using the animal’s body shape and position of the Pn.p cells as measured from the fluorescent markers.
Single-molecule fluorescence in situ hybridization (smFISH)
Probe design and smFISH hybridization to visualize eff-1 mRNA transcripts were performed as previously described (Raj et al. 2008; Huelsz-Prince and van Zon 2017). Custom probes were designed against the exons of the eff-1 gene by utilizing the Stellaris® RNA FISH Probe Designer (Biosearch Technologies, Inc., Petaluma, CA). The probes were hybridized with the Cy5 dye (Huelsz-Prince and van Zon 2017). The sequences of the oligonucleotide probes used in this study are listed in Table 1 of the Supplementary Methods. Animals were collected by washing plates with M9 and were fixed in 4% formaldehyde in 1 × PBS for 45 min at room temperature. Fixed animals were permeabilized in 70% ethanol at least one night at 4°C. Subsequently, animals were incubated with the 0.5 μl probes overnight at 30°C in Stellaris® Hybridization Solution containing 10% formamide. The next day, animals were quickly washed two times with 10% formamide and 2 × SSC, followed by an incubation wash for 30 min at 30°C. DAPI was added at 0.01 μg/ml in a final incubation step for 20 min at 30°C. Animals were mounted in Glox Buffer with catalase and glucose oxidase, and images were acquired with a Nikon Ti-E inverted fluorescence microscope, equipped with a 100X plan-apochromat oil-immersion objective and an Andor Ikon-M CCD camera controlled by μManager software (Edelstein et al. 2014). Stacks of each animal were taken with a z-distance of 0.33 μm and approximately 30 images were taken per animal. Cy5 exposure time was 3 s, while DAPI and GFP exposure time were 100 ms and 500 ms, respectively. Animals were then imaged at 40X to determine their body length, which was measured using ImageJ by drawing a spline from the tip of the head to the end of the tail. smFISH images were analyzed with a custom Python script using techniques previously described (Raj et al. 2008). The ajm-1::gfp transgene was used to determine the cell fusion status. To construct eff-1 distributions in P3.p and P4.p cells prior to fusion (Fig. 2d-f), we used the observation that eff-1 is expressed also in P2.p cells, even though they already fused in the L1 larval stage, at a time similar to that observed in P3.p. Specifically, we found that animals with high eff-1 expression in P3.p (>10 mRNA), always showed similar high levels in P2.p (data not shown). However, we also observed animals with high eff-1 expression in P2.p, but low expression in P3.p (<5 mRNAs), which we interpreted as an animal where P3.p instead assumed VPC fate. Because of the observed variability in the time of fusion, body length was not useful to select for animals with P3.p close to fusion. However, when only selecting data for P3.p and P4.p cells in animals with high eff-1 expression in P2.p (>10 mRNAs), we were able to increase the width of the peak, corresponding to high expressing cells in Figs. 2d-f.
MODEL DETAILS
Parameterization and fitting of BAR-1::GFP dynamics
To fit the experimentally measured BAR-1::GFP dynamics, we assume the following minimal model of BAR-1 production and degradation: where cBAR-1 is the BAR-1 level and kp is the BAR-1 production rate. In the absence of Wnt signaling, S(t)=0, the degradation complex degrades BAR-1 at a basal rate kd. However, in the presence of Wnt signaling, S(t), the degradation complex is inhibited (Eisenmann 2005) and degradation occurs at a reduced rate , with α > 1. In the model, we assume the BAR-1 pulse is generated by changes in Wnt signaling level S(t). In particular, we assume Wnt signaling is activated at a constant level S(t)=1 starting at time t0 and ending at time t0+T, where T is the pulse duration. For other times, Wnt signaling is not activated, S(t)=0. These assumptions yield the following expression for the BAR-1 dynamics:
For sufficiently long pulse duration T, the BAR-1 level will reach a steady state . However, in the experimentally obtained data we never observed BAR-1::GFP levels reaching a steady state before the end of the pulse. Instead, we found that BAR-1::GFP accumulation remained approximately linear throughout the full duration of the pulse. Indeed, when the pulse duration is sufficiently short or the Wnt-mediated inhibition of BAR-1 degradation is sufficiently strong, i.e. (1 + α) ≫ kdT, the exponential term in cBAR-1(t) for t0≤t≤t0+T reduces to an expression that linearly with time in linear fashion, giving rise to the following expression used to fit the experimental data:
We fitted this expression to the experimental BAR-1::GFP data by least-square fitting, using the implementation of the Levenberg-Marquardt algorithm, as implemented in the Python function scipy.optimize.curve_fit (Eric Jones et al. 2001) and using kp, kd, α, t0 and T as fit parameters. We obtained these fit parameters for each Pn.p cell by independent fitting. For fusing cells, we fitted cBAR-1(t) to the experimental data only for time points until the experimentally determined time of fusion, tfusion. We found that cell fusion always occurred before the end of the pulse, i.e. t0+T>tfusion and, hence, T was not defined for fusing cells. In general, this fitting procedure provides good fits for most BAR-1::GFP trajectories, but fails to converge to a correct fit for trajectories with very low pulse amplitude or no apparent pulse. In that case, we assume cBAR-1(t) = 0, with t0 and T not defined. To characterize pulse dynamics for non-fusing cell, we compare pulse onset time t0, pulse duration T and pulse slope . For fusing cells, pulse duration is not defined and instead we compare the time of fusion.
Mathematical model of stochastic Pn.p cell fate decision
Wnt signaling and eff-1 expression. The model is briefly summarized in Fig. 6A,B of the main text. We assume that Wnt signaling (through BAR-1) and LIN-39 inhibit eff-1 expression, whereas an activator A, whose identity is currently not known, induce eff-1 expression. BAR-1 likely controls eff-1 expression as a complex with the TCF/LEF transcription factor POP-1 (Korswagen et al. 2000). However, it is not known whether POP-1 and LIN-39 control eff-1 expression in Pn.p cells by binding directly to the eff-1 promoter, or whether they regulate the expression of other transcription factors that do. For simplicity, here we assume that these transcription factors bind directly and independently of each other to specific binding sites in the eff-1 promoter and control eff-1 expression in a combinatorial manner, with eff-1 production only occurring when the activator A, but not LIN-39 and the BAR-1/POP-1 complex, are bound (Fig. 6A in the main text). Assuming that transcription factor (un)binding is rapid compared to eff-1 expression dynamics, we have the following expression for eff-1 level e in time: where cBAR-1,i, cLIN-39,i and cA are the level of BAR-1, LIN-39 and the activator A in cell i, n is a Hill coefficient and KB, KL and KA are the dissociation constants for the inhibition (BAR-1, LIN-39) and activation (A) of eff-1 expression, respectively. Here, we assume that BAR-1 and activator levels vary in time but LIN-39 levels remain constant (based on Fig. 3 in the main text). Moreover, we assume that the level of the BAR-1/POP-1 complex scales linearly with cBAR-1. To determine whether cell i assumes hyp7/fusion or VPC fate, we calculate the eff-1 level ei(t) as function of cBAR-1,i(t) and cA(t) using Eq. 4. If ei(t) is larger than a threshold value eth for any given time t, cell i assumes hyp7/fusion rather than VPC fate. Based on the observed BAR-1 dynamics (Figs. 4 and 5 in the main text), we assume that the BAR-1 level increases linearly with slope si from the BAR-1 pulse onset time, , onwards, with the level at time of fusion, given by:
For the dynamics of the activator, we assume cA,i(t)=0 for and a positive constant value cA,i for . We observe significant variability in the slope of the BAR-1 accumulation pulse (Fig. 5 in the main text). For that reason, we allow the pulse slope si in cell i to vary stochastically as: where 〈s〉 is the average slope and is a white noise term that is intrinsic to cell i, i.e. and where δi,j is the Kronecker delta and σs is the standard deviation of the noise. Similarly, we assume variability in the level of the activator A: where 〈cA〉 is the average activator level at the time of fusion and is a white noise source with and .
Pulse and fusion timing
We experimentally observed variability in pulse onset time and fusion time that can impact the inhibitory BAR-1 level at the time of fusion and, hence, control the frequency of hyp7/fusion versus VPC fate. We assume that the pulse onset time in cell i is given by: where 〈t0〉 is the average observed pulse onset time, is a white noise term common to all cells in an individual animal and is a white noise term that is intrinsic to each cell i, i.e. and , with and the standard deviation of the common and intrinsic noise, respectively. For the cell fusion time, we assume: where 〈Δtf〉 is the delay between the average pulse onset time and the average time of fusion and is a cell-intrinsic white noise term with standard deviation σf. Equations 8 and 9 correspond to a picture where a common signal impacts the Pn.p cells at time to trigger both the start of the BAR-1 pulse and, after a delay 〈Δtf〉, activation of cell fusion, but with added cell-intrinsic variability in the timing of both events.
Constraining model by experiments
We can constrain many of the model parameters using our experimental observations. For each mutant, we obtain the average pulse slope 〈s〉 and standard deviation σs from the experimentally observed values, allowing us to approximate the experimental observation with a Gaussian distribution with mean 〈s〉 and standard deviation σs (Supplemental Fig. 3a,b). We calculate mean pulse onset time as the average of the mean onset time in P3.p and P4.p, , i.e. the average of the mean pulse onset times observed in non-fusing P3.p and P4.p cells. For the variability in pulse onset time, we obtain estimates for the standard deviations and using the correlation function . In particular, we calculated the standard deviation of the common noise from the cross-correlation between the pulse onset in P3.p and P4.p, . Next, using Eq. 8, we calculated the standard deviation of the cell-intrinsic noise as . Using the estimated parameters, we obtained a good fit with the experimentally observed distribution of pulse onset time in P3.p (Supplemental Fig. 3c,d) and were able to reproduce the experimentally measured joint distribution of pulse onset time in P3.p and P4.p in Fig. 5e in the main text (Supplementary Fig. 3f). Fusing P3.p cells in the bar-1(++);lin-39(lf) mutant often exhibit a pulse with very low amplitude, making it challenging to determine the exact time of pulse onset. However, pulse onset is often strongly correlated between cells in the same animal. To measure the time between pulse onset and time of fusion, we therefore calculate the delay between the pulse onset in P4.p and time of fusion in P3.p, as . To estimate the standard deviation we followed different strategies for the two mutant strains that exhibited Pn.p fusions, bar-1(++);lin-39(0) and bar-1(++);cwn-1(0). For the bar-1(++);lin-39(0) strain, P3.p had a much higher fusion frequency that P4.p (Supplementary Table 1) and we only considered animals where P3.p assumed hyp7/fusion fate and P4.p assumed VPC fate. Here, using Eq. 9, we estimated the standard deviation in fusion time as (σf)2 = Cff − Cf0 where and . For the bar-1(++);cwn-1(0) strain, P3.p and P4.p have similar, but low hyp7/fusion frequencies. Hence, we considered all animals where one cell, either P3.p or P4.p, assumed hyp7/fusion fate and the other assumed VPC fate. We estimated the standard deviation in fusion time as , where Cff = 〈(tf − 〈tf〉)2〉, C00 = 〈(t0 − 〈t0〉)2〉 and Cf0= 〈(tf − 〈tf〉) (t0 − 〈t0〉)Ⱥ. Here, is the standard deviation of the cell-intrinsic pulse onset noise as estimated from the pulse onset timing data. Using the estimated parameter values, the model reproduced the experimentally observed correlation between cell fusion time and BAR-1 pulse onset time (Supplemental Fig. 3g).
Parameter values
Even though we could estimate many model parameters directly from the experiments, this was not possible for all parameters. Because we did not observe cell fusions in the bar-1(++) strain, we were unable to measure the parameters 〈Δtf〉 and σf that dictate the timing of expression of the activator A. For that reason, we assumed that the value of these two parameters was the same as for the bar-1(++);lin-39(0) strain. For the threshold eff-1 level above which cell fusion occurs, we chose and we assumed that eff-1 induction occurred with Hill coefficient n= 3 for both inhibitors and the activator. The remaining parameters CA, σA, KA, cLIN-39 and KL were chosen so that the resulting frequency of hyp7/fusion fate matched the experimentally observed frequencies (Supplemental Table 1, Supplementary Fig. 3e), with the constraint that cLIN-39=0 for the bar-1(++);lin-39(0) strain. In addition to the simulations for the experimentally examined strains, we also simulated a hypothetical mutant that has the same hyp7/fusion frequency as the bar-1(++);cwn-1(0) mutant, but achieves this by reducing the BAR-1 pulse slope rather than the pulse onset time. For this hypothetical mutant, we used the same parameters as for the bar-1(++) strain, but lowered the average pulse slope 〈s〉 until the desired hyp7/fusion frequency was found. For the bar-1(++) mutant, we were unable to find parameter combinations for which the hyp7/fusion frequency in the simulations was close to zero, as observed experimentally. This is likely because the fitted distribution of pulse slopes overestimates the number of cells with low pulse slope (Supplemental Fig. 3a) and, hence, low levels of inhibitory BAR-1. A complete list of all parameters is given in the table below:
Simulation
For all simulations, we generated data for two cells, P3.p and P4.p, in 1 · 1.04 animals. For each cell i, we generated stochastic values for si, cA,i, and according to Eqs. 6–9, where we discarded pulse slope values si<0 as they are an artifact of fitting the experimental distribution by a Gaussian. Based on the values for pulse onset time and pulse slope, we calculated for each cell the inhibitory BAR-1 level cBAR-1 according to Eq. 5, the resulting eff-1 level according to Eq. 4 and marked each cell as hyp7/fusion rather than VPC fate if the eff-1 level exceeded the threshold value eth. In the above table, all times are expressed as fraction of larval stage duration. However, to facilitate comparison with the experimental distribution, the average pulse slope 〈s〉 and its standard deviation σf are in units of fluorescence increase per hour. For that reason, when used the pulse slope to calculate the BAR-1 level cBAR-1 in the experimental units of fluorescence (Fig. 6h), we first converted the time between pulse onset and fusion from dimensionless units to hours, by multiplying the dimensionless time with the average L2 larval stage duration 〈TL2〉;.
Author Contributions
Conceptualization, J.S.v.Z.; Methodology, J.R.K. and J.S.v.Z.; Formal Analysis: J.R.K., J.T, and J.S.v.Z.; Investigation, J.R.K., and J.T.; Writing – Original Draft, J.R.K. and J.S.v.Z.; Writing – Review & Editing, J.R.K. and J.S.v.Z.; Funding Acquisition, J.S.v.Z.; Supervision, J.S.v.Z.
Declaration of Interests
The authors declare no competing interests.
Supplemental Methods Table 1
Supplemental Movies
Movie S1: (Top panel) Apical junction marker AJM-1::mCherry and (bottom panel) GFP expressed in the hypodermal syncytium hyp7 for a P3.p cell assuming hyp7/fusion fate. At the time of fusion with hyp7, 6h20m after the start of the L2 larval stage, pronounced ruffling of AJM-1 is followed by its removal from P3.p. Concomitantly, GFP flows from the hyp7 syncytium into P3.p, as indicated by the yellow arrow. A dpy-7p::mCherry nuclear marker was used for cell identification (top panel).
Movie S2: (Top panel) Apical junction marker AJM-1::mCherry and (bottom panel) GFP expressed in the hypodermal syncytium hyp7 for a P3.p cell that assumes vulva precursor cell fate. AJM-1 is present in P3.p throughout the entire L2 larval stage and no inflow of GFP into P3.p is observed. A dpy-7p::mCherry nuclear marker was used for cell identification (top panel).
Movie S3: Pulsatile BAR-1 dynamics in P(3-5).p cells in a single animal. Time is relative to the start of the L2 larval stage. Each panel corresponds to a single cell. Shown are the apical junction marker AJM-1 (magenta) and BAR-1::GFP (green). The animal examined corresponds to that shown in Fig. 4a,b.
Acknowledgements
We thank Yvonne Goos and Joleen Traets for coupling eff-1 primers to Cy5, and Yvonne Goos for minor technical assistance. We thank Renée van Amerongen, Rik Korswagen, Pieter Rein ten Wolde, and Tom Shimizu for helpful discussions on the manuscript. This work is part of the research program of the Netherlands Organisation for Scientific Research (NWO) and was performed at the research institute AMOLF. Some C. elegans strains were provided by the CGC, which is funded by NIH Office of Research Infrastructure Programs (P40 OD010440). The work was supported by a European Research Council Starting Grant (338200-STOCHCELLFATE) awarded to J.S.v.Z.