lag-2 and lin-31 reliably mark the Pn.a and Pn.p cells, respectively
To identify a marker of P-cell polarity, we quantified the mRNA expression of a panel of 26 genes using single-cell transcript counting (Raj et al, 2008
). This panel includes genes that were previously reported to be expressed in P cells and their descendants and also genes from the major signaling pathways (Wnt, Notch, FGF, EGF, and TGF). A set of about 48 single-stranded 20-mer oligonucleotides were designed for visualization of each transcript. These fluorescently labeled oligonucleotides are complementary to the transcript and bind each individual transcript. This becomes visible as a diffraction-limited spot using fluorescence microscopy. Using a custom-written software, we manually segmented the individual cells and computationally determined the transcript number in each cell. The ratio of the expression in the Pn.a versus Pn.p daughters was used to quantify the specificity of the putative markers (Supplementary Table S1
). We identified lag-2
, a transmembrane protein of the Delta/serrate/lag-2 family, as the most promising Pn.a marker having the largest expression ratio (37.3). lin-31
, a gene previously reported as a Pn.p marker (Tan et al, 1998
), was found to be the most promising Pn.p marker with lowest expression ratio (0.08). Using these markers, the anterior and posterior daughters of the P3–P10 cells can be scored with high confidence ( and ; Supplementary Figure 1
Figure 2 Inhibition of Wnt/β-catenin asymmetry pathway. (A) In WT animals, lag-2 transcript (red) and lin-12 transcript (green) are found in the Pn.a and Pn.p respectively. (B) In mom-4; lit-1 worms that have been transferred to 25°C for 9h (more ...)
Although both daughter cells initially inherit lag-2 mRNA from the P cell, lag-2 is rapidly degraded in the Pn.p cells (). We quantified lag-2 and lin-31 expression by counting individual transcripts in the Pn.p and Pn.a cells excluding cells immediately after division. We observed that in wild-type (WT) animals lag-2 and lin-31 expression is mutually exclusive (). In WT animals, the lag-2 count in Pn.a cells is always much larger than the lag-2 count in Pn.p cells ().
Role of the Wnt/β-catenin asymmetry pathway in regulating P cells' divisions
Many asymmetric divisions in C. elegans
are regulated by the Wnt/β-catenin asymmetry pathway through polarization of the mother cell before division (Mizumoto and Sawa, 2007b
). In this pathway, asymmetry localization of many regulatory proteins (including WRM-1 and APR-1) in the mother cell is set up by Wnt ligands and receptors, leading to different nuclear levels of POP-1 and SYS-1 in the daughter cells after division. A high level of POP-1 and low level of SYS-1 in the anterior daughter leads to inhibition of Wnt signaling, whereas a low level of POP-1 and high level of SYS-1 in the posterior daughter leads to transcription of Wnt responsive genes. The amount of nuclear POP-1 in the posterior daughter is regulated by MOM-4 and LIT-1 proteins, which function in exporting POP-1 from the nuclear into the cytoplasm.
To test if the Wnt/β-catenin asymmetry pathway plays a similar role in P cells, we examined the nuclear levels of POP-1 in the daughter cells after division in a POP–GFP translational fusion strain. We found that the anterior daughter has a higher level of nuclear POP-1 than the posterior daughter (). This differential level of POP-1 is also observed in other daughter cells regulated by the Wnt/β-catenin asymmetry pathway (Mizumoto and Sawa, 2007b
). Next, we disrupted the POP-1 branch in the asymmetry pathway by a temperature shift in mom-4
mutant worms (Takeshita and Sawa, 2005
). Similar to WT animals, both Pn.a and Pn.p in mom-4
mutant worms inherited lag-2 mRNA from the P cells. But unlike WT animals, Pn.p cells continue to express lag-2
some time after division ( and ). This lag-2
expression is sustained even after Pn.p cells go on to divide in L1. (). In WT animals, Pn.p cells do not divide until the L3 stage. This suggests that upon inhibition of the Wnt/β-catenin asymmetry pathway, the Pn.p cells have adopted Pn.a-like fates where they expressed lag-2
and divide in L1. This effect is similar to that observed in other cells whereby disruption of the Wnt/β-catenin asymmetry pathway caused the posterior daughter to take on anterior cell fate (Bertrand and Hobert, 2009
; Gleason and Eisenmann, 2010
). These experiments confirm the role of Wnt/β-catenin asymmetry pathway in polarizing P cells and show that lag-2
expression in the daughter cells after division is a good reflection of the polarity of the mother P cell before division.
Figure 3 lag-2 expression in different mutants. Plot of lag-2 mRNA counts in Pn.p versus Pn.a in WT animals. (A) In animals with inhibition of Wnt/β-catenin asymmetry pathway, mom-4; lit-1 (B), multiple-ligand mutant, egl-20; cwn-1; cwn-2, (C) and double-receptor (more ...)
Notch signaling is not involved in setting up P-cell polarity
Since Pn.a and Pn.p express high levels of lag-2
, respectively (), we tested for the role of Notch signaling in P-cell polarity. To determine if Notch signaling may be required for maintaining different fates in the Pn.a and Pn.p, we inhibited Notch signaling using a lag-1
temperature-sensitive strain (Qiao et al, 1995
). However, we did not observe any aberrant development in the Pn.a and Pn.p cells. We also examined animals with lin-12
loss of function mutation, lin-12
), and semi-dominant mutation, lin-12
), and did not observe any change in cell fates and the expression of lag-2
in Pn.a and Pn.p cells (Greenwald et al, 1983
). These results suggest that notch signaling is not involved in setting up P-cell polarity.
Mutations in Wnt ligands induce polarity reversal, whereas mutations in Wnt receptors induce polarity loss
To explore which Wnt ligands and receptors are involved in P-cell polarity, we examined lag-2
expression in Pn.a and Pn.p cells in ligand and receptor mutants. WT polarity was observed in most single- and double-ligand mutants, consistent with previous observations on the redundant role of the Wnt ligands (Zinovyeva et al, 2008
) (Supplementary Figure S2
). However, in the double-ligand mutant (egl-20
), triple-ligand mutant (egl-20
), and quintuple-ligand mutant (egl-20
), some Pn.p cells expressed lag-2
and their corresponding Pn.a cells expressed lin-31
, suggesting that the P cell had been polarized in the opposite direction (; Supplementary Figure S3
). We found that in the triple-ligand mutant, 47.9% correctly polarized, 44.0% exhibited a polarity reversal, and 8.1% showed similar levels of lag-2
in both daughters indicative of a symmetric P-cell division and therefore loss of P-cell polarity. A very different phenotype was observed in the Wnt receptor mutants (). In the mom-5
was often observed in both daughter cells (53.5%) and a smaller fraction of cells correctly polarized (38.6%) or reverse polarized (7.9%). The different phenotypes observed in the ligand and receptor mutants suggest that they may play different roles in establishing cell polarity. To determine if the different phenotypes observed is due to the different roles of receptors and ligands in sensing and amplification and to further quantify the phenotypes presented in , we constructed a phenomenological model.
Cell–cell signaling has been found to be important in planar cell polarity models (Tree et al, 2002
). Since pairs of P cells (P3/P4, P5/P6, P7/P8, and P9/P10) are in contact before division, cell–cell signaling may play a role in their divisions. If cell–cell signaling occurs between pair of P cells, we would expect the polarity of division between these pairs of P cells to be correlated. In WT animals, all the divisions are correct hence WT animals cannot be used for this analysis. Hence, we calculate correlation in the triple-ligand mutant (egl-20
) where many of the divisions are polarized in the reversed direction. If there is cell–cell signaling, we would expect pairs of P cells to both divide correctly, leading to both Pn.a daughters having high lag-2
levels, or to both divide with reverse polarity, leading to low levels of lag-2
in both Pn.a daughters. When we examined the lag-2
expression levels in the anterior daughters for the anterior P cell versus the posterior P cell in each pair (Supplementary Figure 4
), no significant correlation is found between their expression levels (correlation value=−0.029, P
-value=0.70). This suggests that cell–cell signaling does not play a significant role in P–cell division.
A phenomenological model for cell polarity
The polarization state of the P cell is denoted by the dynamic variable θ(t), which is an angle that ranges between 0° (reverse polarity) and 90° (WT polarity). We assume that the P cell has initially no polarity (θ(t=0)=45°). For subsequent times, until the P cell divides at time T, we describe the dynamic behavior of θ(t) as a one-dimensional random walk. In the simplest model that only involves the sensing of an external gradient, the probability of taking a right step (increasing θ; towards WT polarity) or left step (decreasing θ; towards reverse polarity) is ((1+g)/2)rTΔt and ((1−g)/2)rTΔt, respectively. Here, g reflects the external gradient that ranges from −1 to 1, rT is the total reaction rate that sets the timescale of the dynamics, Δt is the time step of the numerical simulation. To understand the behavior of the model, we ran stochastic simulations to determine the behavior of individual cells. The chemical master equation is also solved to obtain the distribution for a population of cells at time T. In absence of an external gradient (g=0), θ(t) has equal probability of increasing or decreasing at each step of the simulation () and performs an unbiased random walk resulting in an approximately Gaussian distribution (symmetric about 45°) at the time of P-cell division (, green). If g>0 or g<0, the probabilities of taking a left and right step are unequal, resulting in a biased random walk towards 90° (blue) or 0° (red), respectively (). To summarize the information encoded in the histograms of θ(T) for each set of g and rT, we determine the fraction of the cells that undergoes correct, reverse or loss of polarity based on the following classification rules: θ(T)>75° (correct polarity), θ(T)<15° (reverse polarity), and 15°<θ(T)<75° (loss of polarity). A coordinate on the phase diagram corresponding to the particular set of g and rT, will be colored with different intensities of blue, red, and green depending on the fractions of correct, reverse, and loss of polarity, respectively. () As expected for g>0 and high rT, values of most cells are correctly polarized. For values of g close to 0 and low values of rT, most of the cells are unpolarized. However, this simple model is unable to explain the coexistence of correct and reverse polarity observed in the triple-ligand mutant ().
Figure 4 Stochastic modeling. Without feedback (A) Schematics showing the dependence of ra and rp on g. For g=0, ra=rp and for 0<g<1, ra>rp. Values of ra and rp do not depend on θa. (B) (Left) Stochastic simulation of θ (more ...)
To expand beyond this simple model, we included a mechanism that reinforces a deviation from the non-polarized state. Biologically, this reinforcement could be established by, for example, positive feedback regulation. To introduce amplification, we let the probability of taking a right step increase with θ and the probability of taking a left step decrease with θ. The simplest way to reinforce deviation is to introduce linear dependencies on θ into the probabilities of taking a right or left step. In this expanded model, the probability of taking a right step (increasing θ; towards WT polarity) or left step (decreasing θ; towards reversed polarity) is ((1+g
, respectively. g
performs the same role here as in the simple model and characterized the gradient. On the other hand, rT
is replaced by two rates rf
. In the absence of a gradient (g
) has equal probability of increasing or decreasing when the cell is unpolarized (θ=45°) similar to the behavior of the simple model. However, if there is any fluctuation that drives the cell away from the unpolarized state, this fluctuation will be reinforced. In other words, the probability that θ will move in the same direction as the fluctuation does, is larger than the probability to move in the opposite direction of the fluctuation (, green traces). The parameter rf
quantifies this reinforcement. A basal rate independent of θ(t
, is included and set to be a constant. The external gradient is superposed on this process and further biases the random walk (, blue, red, and magenta traces). Another way to view the polarization process is that initially when the cell is unpolarized (θ=45°), the contributions of rf
to the probabilities of taking a right or left step are equal. Hence, the sensing process, represented by g
, plays a more important role is setting up polarization. Once sensing has occurred and θ is no longer close to 45°, contributions of amplification represented by rf
will become important and act synergistically with the gradient to further set up the polarization. A model assuming additive effects of gradient sensing and amplification is also unable to produce the coexistence of correct and reverse polarity (Supplementary Figure S5
We repeated the analysis for the expanded model, setting rb as a constant and found a region in parameter space (g versus rf), which allows for the coexistence for correct and reverse polarity (, magenta), which was absent in the simple model (). We then used this model to further quantify the experimental results and explore where the different mutants are located in this parameter space. Note that the present model is a purely phenomenological model (in contrast to a mechanistic molecular model) that allows us to extract parameters, g and rf, from the experimental data.
Loss of Wnt ligands reduces the parameter g, whereas loss of Wnt receptors results in a decreased value of both g and rf
To compare the predictions of the model to the experimental data, we converted the lag-2 transcript count in each pair of daughter P cell to a single angle θlag-2 (). From the earlier experiments, we observed that inhibition of the Wnt/β-catenin asymmetry pathway, which sets up polarity of the P cell, led to expression of lag-2 in both daughter cells. Hence, θlag-2 is a good approximation of the polarization state of the mother P cell at the time of division θ(T) as calculated by the model above.
Figure 5 Fitting of ligands and receptors mutants distributions. (A) Plot of lag-2 mRNA counts in P3.p versus P3.a in egl-20; cwn-1; cwn-2 strain and illustration of how θlag-2 is calculated. (B) Histograms for θlag-2 (blue) and maximum likelihood (more ...)
To determine the value of rb, we examined the distribution of θlag-2 in the mom-4; lit-1 strain and observed a Gaussian distribution (). Although ligands and receptors are functioning properly in the mom-4; lit-1 strain, Pn.a and Pn.p are unable to execute different cell fates as the MOM-4 and LIT-1 proteins, required for the daughter cells to have different amount of POP-1, lost their function. We observed that the distribution for θlag-2 is centered at 60°. The bias of the θlag-2 distribution is likely to be due to the differential amount of SYS-1 in the two daughter cells. Since information determining through sensing and amplification are not conveyed effectively to the daughter cells as the POP-1 branch is inhibited, we can use this mutant to obtain an estimate for rb=0.006 by setting rf=0. This is likely to be an overestimation as the SYS-1 branch is unaffected. Using this estimation for the value of rb, we determined the values of g and rf that yields maximum likelihood fits for the WT and mutants strains' distributions.
When we fit the WT distributions, we obtained large uncertainties in the fit parameters. This is expected because the parameter range over which WT polarity is observed is large. Although the WT distribution cannot be fitted uniquely, we know that the parameters lie in the parameter space where 100% correct divisions are observed which is bounded by the dashed line in . Next, the experimental distribution of θlag-2 for the different P cells in the ligand and receptor mutants (, blue histograms) were fit to the model (, red lines). The distributions for each of the individual P cells are significantly different; hence, the fit parameters g and rf were determined for each P cell in the ligand mutants and receptor mutants independently. The model is able to reproduce the main features of the experimental distributions. Interestingly, these two parameters segregated out in parameter space (). We found that the gradient parameter g was always lower compared with WT (), suggesting that both Wnt ligands and receptors are important for the sensing of the gradient. However, the feedback parameter rf was significantly smaller when receptors were mutated compared with ligand mutations, suggesting that the receptors might be involved in amplifying the signal.
Decreasing ligand results in symmetric divisions at low rf
From the above analysis, we inferred that Wnt ligands are primarily involved in sensing whereas Wnt receptors function in both sensing and amplification. Mutations in Wnt ligands primarily lead to polarity reversals whereas mutations in Wnt receptors cause loss of polarity. Very similar results have been reported for many tail blast cells in C. elegans
, including the T cell, suggesting that our model maybe generally applicable (Sternberg and Horvitz, 1988
; Herman and Horvitz, 1994
). However, in contrast, it has been reported for the EMS cell in C. elegans
that loss of ligands causes loss of polarity apparently inconsistent with our interpretation (Thorpe et al, 1997
). However, upon closer inspection of the polarity phase diagram (), we hypothesized that in the EMS cell, the WT parameters are likely to be different. For example, the EMS cell might experience a different gradient or has reduced amplification potential compared with the P cells.
The parameter range over which WT polarity is observed is large and is bounded by the dashed line in . If we would reduce rf slightly so that most P cells still correctly polarize (moving from WT to C in ) and subsequently remove ligand (moving from C to U in ) it should be possible to induce loss of polarity upon loss of Wnt ligand. To test this prediction and access the parameter space of low rf, we looked for mutants for which rf is lower than WT but sufficiently high to yield correct divisions. We chose the mom-5 single receptor mutant as our candidate as there are many P cells with correct divisions in this mutant. In the mom-5 mutant, divisions of the P3 and P4 cells are symmetric whereas the divisions of the P5–P10 cells are correct (). Reducing ligand levels in the mom-5; cwn-1 strain led to symmetric divisions in the P5 and P6 cells () confirming our prediction. This behavior was also reproduced in the mom-5; egl-20 and mom-5; egl-20; cwn-1 mutants, where divisions in all P3–P10 cells were affected ().
Figure 6 Effects of reducing ligand in mom-5 background and correlation between receptor level and rf. (A) Histograms of θlag-2 (blue) and maximum likelihood fits (red) for P3–P10 in mom-5 single receptor mutant and mom-5; cwn-1, mom-5; egl-20 (more ...)
Positive correlation between receptor levels and rf
In the mom-5; egl-20 and mom-5; egl-20; cwn-1 strains, where divisions in all P3–P10 cells were affected, we observed a high fraction of symmetric divisions in the P3–P6 cells, lower fractions of symmetric divisions in the P7–P8 cells and coexistence of correct and reverse polarity in the P9 and P10 cells (). It is intriguing that all these different phenotypes were observed in the same mutant strain and even in the same mutant animal, suggesting that the values of rf may vary significantly among P cells in the same animal. We hypothesized that the differences in rf are due to the different expression levels of the receptors. We measured transcriptional levels of the receptors genes, mom-5 and lin-17, using single molecule FISH in the P cells and found that anterior P cells expressed higher levels of mom-5 whereas posterior cells expressed higher levels of lin-17 (). We found a positive correlation between the lin-17 count and the parameter rf () for both the mom-5; egl-20 and mom-5; egl-20; cwn-1 strains. Similarly, a positive correlation was observed between the mom-5 mRNA level and rf in the lin-17; egl-20; cwn-1 strain (). These positive correlations obtained between receptor levels and rf provide quantitative support for our earlier conclusion that receptors may play an important role in amplification. Furthermore, since differences in receptors level could explain most of the differences in rf, it also demonstrates that the ligands' contribution to amplification is less significant.