Quantitative perturbation-phenotype maps reveal nonlinear responses underlying robustness of PAR-dependent asymmetric cell division

Abstract

A key challenge in the development of an organism is to maintain robust phenotypic outcomes in the face of perturbation. Yet, it is often unclear how such robust outcomes are encoded by developmental networks. Here, we use the Caenorhabditis elegans zygote as a model to understand sources of developmental robustness during PAR polarity-dependent asymmetric cell division. By quantitatively linking alterations in protein dosage to phenotype in individual embryos, we show that spatial information in the zygote is read out in a highly nonlinear fashion and, as a result, phenotypes are highly canalized against substantial variation in input signals. Our data point towards robustness of the conserved PAR polarity network that renders polarity axis specification resistant to variations in both the strength of upstream symmetry-breaking cues and PAR protein dosage. Analogously, downstream pathways involved in cell size and fate asymmetry are robust to dosage-dependent changes in the local concentrations of PAR proteins, implying nontrivial complexity in translating PAR concentration profiles into pathway outputs. We propose that these nonlinear signal-response dynamics between symmetry-breaking, PAR polarity, and asymmetric division modules effectively insulate each individual module from variation arising in others. This decoupling helps maintain the embryo along the correct developmental trajectory, thereby ensuring that asymmetric division is robust to perturbation. Such modular organization of developmental networks is likely to be a general mechanism to achieve robust developmental outcomes.

Fig 1. Potential mechanisms for dosage robustness in asymmetric division.

(A) Schematic of the asymmetric division pathway in C. elegans zygotes. A local cue induces asymmetry of PAR proteins which is then reinforced by mutual antagonism between anterior and posterior PAR proteins (aPAR, pPAR) to generate stable domains. PAR proteins then spatially regulate downstream processes to drive division asymmetry. Due to this mutually antagonistic relationship, aPAR and pPAR protein levels/activities must be balanced to achieve proper polarity. (B) While we know that polarity, asymmetric division, and viability rely on PAR proteins and that animals heterozygous for par mutations are generally viable, the quantitative relationships between genotype, protein dosage, polarity, asymmetric division, and viability have not been measured, leaving the root mechanisms underlying robustness of division asymmetry unclear. (C) Mechanisms underlying robustness: (1) compensation—PAR protein levels actively adapt to gene/protein dosage changes to restore balance; (2) network properties—features of the network, such as feedback circuits, compensate for dosage imbalance to maintain stable polarity signals; (3) canalization—downstream asymmetric division pathways that drive size/fate asymmetry are robust to variability in polarity signals.

Fig 2. Minimal compensatory regulation in response to par gene/protein dosage changes.

(A) Schematic for dosage compensation assay. Levels of XFP (GFP or mNG) were measured for embryos of 3 genotypes: homozygous, carrying 2 copies of an XFP::par allele (xfp/xfp); heterozygous, carrying 1 copy of XFP::par allele and 1 untagged allele (xfp/+), which is expected to express XFP at approximately 50% levels of homozygotes; and heterozygous, carrying 1 copy of the XFP::par allele and either a mutant or RNAi-silenced allele (xfp/- or xfp/RNAi). Dosage compensation is quantified as the degree of excess XFP signal in xfp/- or xfp/RNAi embryos, expressed as the fraction of the difference in XFP signal between xfp/xfp and xfp/+ animals. (B, C) Normalized GFP concentrations of PAR-6::GFP (B) or GFP::PAR-2 (C) as measured in embryos with the indicated genotypes: homozygous (gfp/gfp), heterozygous mutant (gfp/-), and heterozygous untagged (gfp/+) genotypes. Unpaired t test. (D) Modest or no dosage compensation exhibited for various par::XFP gene fusions when expressed in a heterozygous condition together with either a mutant (xfp/-) or an RNAi-silenced allele (xfp₁/xfp₂(RNAi)). ***p < 0.0001, *p < 0.05, one-sample t test. Additional details for allele-specific RNAi in S1 Fig. (E) Total PAR-2 concentration is constant as a function of PAR-6 dosage. Embryos expressing both mCh::PAR-2 and PAR-6::mNG from the endogenous loci were subjected to progressive depletion of PAR-6 by RNAi and total concentrations of mNG and mCh measured. Green data points are embryos treated with control RNAi (i.e., showing wild-type protein levels). (F) Total PAR-6 concentration is constant as a function of PAR-2 dosage. Fluorescence tags as in (E), but embryos were subjected to progressive depletion of PAR-2 by RNAi. (G, H) PAR-1 and LGL-1 concentrations are unchanged in par-6(RNAi). (I, J) PKC-3 and PAR-3 concentrations are unchanged in par-2(RNAi). In B–D, G–J, individual embryo values shown with mean indicated. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 3. Division asymmetry is robust to changes in PAR dosage.

(A, B) Size asymmetry (A) and asynchrony in cleavage furrow initiation (B) for AB and P1 blastomeres of 2-cell embryos heterozygous for mutations in the par genes indicated. Genotypes: +/+ (wild type), par-6(tm1425/+), par-3(tm2716/+), par-2(ok1723/+), and par-1(tm2524/+). One-way ANOVA (vs. wild type), Dunnett’s correction. (C–H) AB vs. P1 asynchrony (C–E) and size asymmetry (F–H) as a function of total dosage of PAR-6 (C, F), PAR-2 (D, G), and PAR-1 (E, H). Data for individual embryos subject to RNAi shown (black), compared with embryos from wild-type control (green) and in the case of PAR-2 and PAR-6, heterozygous animals (gfp/-, purple). Lines indicate LOWESS smoothing fit with 95% confidence interval determined by bootstrapping to help visualize trends. Phenotypic variance (Var, see Methods) as a function of dosage is indicated above each panel. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 4. Robustness of polarity to PAR-6 dosage changes.

(A, B) Evolution of PAR-2 and PAR-6 profiles as a function of the dosage of PAR-6 (A, B). Embryos expressing PAR-6::mNG and mCh::PAR-2 (NWG0268) were subject to progressive depletion of PAR-6 by RNAi and dosage measured relative to mean control levels. (A) Sample embryos shown with the dosage of the relevant PAR protein indicated. (B) To illustrate changes in concentration profiles, 7 embryos closest to the indicated dosage levels (1.0, 0.75, 0.5, and 0.25) were selected, membrane concentration profiles extracted and averaged. Mean ± SD shown. Dashed lines in 0.75, 0.5, and 0.25 dosage profiles are the mean profiles for dosage = 1.0 for comparison. (C) Membrane concentrations of PAR-6 decline with total PAR-6 dosage. (D) Reduction of PAR-6 allows invasion of PAR-2 at the anterior pole. Note appearance of anterior PAR-2 (closed circles) as PAR-6 dosage approaches 0.5. (E) The relationship between PAR asymmetry (ASI) and PAR-6 dosage is bimodal. For dosage >~0.8 all embryos exhibit normal asymmetry. As PAR-6 levels drop below 0.75, there is a population of embryos that retain normal asymmetry (ASI > 0.9), but a second population appears in which PAR asymmetry is reduced (ASI < 0.75) and varies linearly with PAR-6 dosage, which generally corresponds to embryos with substantial anterior PAR-2 localization. Below dosage of approximately 0.5, the population exhibiting normal asymmetry disappears. Numbers indicate mean division size asymmetry for embryos within the given ASI bins. Green data points in (C–E) are control RNAi. Orange region in (D, E) highlight range of PAR-6 dosages exhibiting bimodal phenotypes. Note that ASI in (E) is a signal-weighted composite of PAR-2 and PAR-6 asymmetry in individual embryos (see Methods). Scale bars, 10 μm. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 5. Robustness of polarity to PAR-2 dosage changes.

(A, B) Evolution of PAR-2 and PAR-6 profiles as a function of the dosage of PAR-2 (A, B). Embryos expressing PAR-6::mNG and mCh::PAR-2 (NWG0268) were subject to progressive depletion of PAR-2 by RNAi and dosage measured relative to mean control levels. (A) Sample embryos shown with the dosage of the relevant PAR protein indicated. (B) To illustrate changes in concentration profiles, 7 embryos closest to the indicated dosage levels (1.0, 0.75, 0.5, and 0.25) were selected, membrane concentration profiles extracted and averaged. Mean ± SD shown. Dashed lines in 0.75, 0.5, and 0.25 dosage profiles are the mean profiles for dosage = 1.0 for comparison. (C) Membrane concentrations of PAR-2 decline linearly with total PAR-2 dosage. (D) PAR-6 domain size (boundary position relative to anterior pole) as a function of PAR-2 dosage for the PAR-2 dosage bins in (B). Individual data points and mean shown. p = 0.0002, ANOVA, test for trend. (E) Overall PAR asymmetry (ASI) is only weakly affected by PAR-2 reductions due to the stability of aPAR domains. Note that ASI in (E) is a signal-weighted composite of PAR-2 and PAR-6 asymmetry in individual embryos (see Methods). Scale bars, 10 μm. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 6. Spindle positioning is highly robust to PAR dosage changes.

(A) Relative position of the anterior and posterior spindle poles along the A-P axis (x) from NEBD through telophase. Mean behavior for wild-type embryos shown as gray lines in par-2(+/-) and par-6(+/-) heterozygote plots. Note nearly identical behavior in wild-type and heterozygous embryos. Mean ± SD shown (n = 6 embryos, all conditions). (B) Comparison of final spindle pole positions taken at telophase from experiments in (A), defined as the time when the cleavage furrow was 50% ingressed and spindle poles exhibited no further outward motion. Individual data points and mean indicated. One-way ANOVA (vs. relevant wild type), Dunnett’s correction. (C) Schematic for quantifying spindle oscillations. Oscillation magnitude (σ) was defined as the standard deviation of measured spindle pole displacement (y) off the central A-P axis (y = 0) from prometaphase to telophase. (D) Sample plots of spindle pole position for wild type and a par-2(+/-) embryos shown alongside oscillation magnitude (σ). (E) Heterozygous par-2 embryos exhibit reduced spindle oscillations relative to wild-type and par-6 heterozygotes; σ was similar for the anterior spindle pole across all 3 conditions. Individual data points and mean indicated. One-way ANOVA (vs. relevant wild type), Dunnett’s correction. (F) Schematic of spindle severing experiments to detect changes in force applied to anterior and posterior spindle poles. (G) Max outward spindle pole velocity following spindle severing. As previously reported, par-6(-/-) leads to symmetric high and par-2(-/-) leads to symmetric low pulling forces. Both heterozygotes show asymmetric pulling forces, similar to wild type. Mean and individual data points shown. Paired t test, Holm–Sidak correction. (H) Difference in max velocity (Posterior—Anterior) shown for samples in (G). Note that this difference is lost in the par null conditions but are not significantly different from wild type in either heterozygous condition. Mean and individual data points shown. One-way ANOVA (vs. wild type), Dunnett’s correction. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 7. Cytoplasmic asymmetry is robust to perturbations of PAR protein concentrations.

(A) Fate asymmetry is specified by a cytoplasmic gradient of MEX-5 that is downstream of PAR polarity. Cell cycle asynchrony is a commonly used proxy of fate asymmetry. Note that the mechanistic relationship and contributions of cortical vs. cytoplasmic PAR-1 asymmetry are not well understood. (B) PAR-1 gradient asymmetry (ASI) is robust in par-2(+/-) and par-6(+/-) heterozygotes. Genotypes indicated. par-6(RNAi) and par-2(-/-) homozygous mutants shown for comparison. (C) The absolute magnitude of the PAR-1 gradient (ΔPAR-1, arbitrary fluorescence units) declines near linearly with PAR-1 dosage. Magnitude of PAR-1 concentration difference between anterior and posterior (C_P-C_A) shown as a function of PAR-1 dosage. Note for (B, C), PAR-1 levels were the mean intensity in a region of interest containing both local membrane and cytoplasm regions—see Inset, Methods. (D–F) MEX-5 asymmetry responds nonlinearly to depletion of PAR proteins. MEX-5 asymmetry (ASI) as a function of dosage of PAR-6(D), PAR-2(E), and PAR-1(F). Fit lines in (D–F) indicate Lowess fit with 95% confidence interval determined by bootstrapping. In (C–F), wild-type data points are indicated in green. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.

Fig 8. PAR dosage reduction renders polarity sensitive to defects in polarity cues.

(A) Scheme for how reduced PAR dosage could sensitize embryos to compromised symmetry-breaking cues. At full strength, PAR feedback is sufficient to amplify signals provided by a weakened cue and thereby rescue normal polarity (i). Conversely, sufficiently strong cues can compensate for reduced PAR feedback to rescue polarity establishment in embryos partially depleted of PAR proteins (ii). However, in the presence of reduced PAR feedback, polarity becomes sensitive to cue strength (iii). (B) Above a threshold cortical flow velocity, PAR-2 domain size is nearly constant. Only upon progressive reduction in peak cortical flow velocity below a threshold value do PAR-2 domains undergo an abrupt shift to being variable sized and mispositioned, consistent with a shift to a flow-independent symmetry-breaking regime. Cortical flow velocities were reduced by mlc-4(RNAi). Individual embryos are indicated and images of select examples shown at right. (C, D) Inhibition of cortical flow sensitizes symmetry-breaking to reduced PAR-2 dosage. GFP::PAR-2 dosage was progressively reduced by RNAi in wild-type and temperature-sensitive nmy-2(ne3409ts) embryos at the restrictive temperature (25°C) and embryos imaged just prior to NEBD. PAR-2 dosage was measured, embryos scored for the presence of GFP::PAR-2 domains, and the results plotted in (C). Example embryos at different PAR-2 dosages and exhibiting different phenotypes shown in (D). (E, F) Disruption of the centrosome cue sensitizes symmetry-breaking to PAR-2 dosage. Performed as in (C, D), but using the temperature-sensitive allele spd-5(or213). Embryos were scored as exhibiting domains if they exhibited clearly defined PAR-2 domains. Note that spd-5(or213) embryos often exhibit bipolar PAR-2 domains, which were scored as having domains for the purposes of this assay (see I, J). (G, H) Heterozygosity for par-2(ok1723) substantially delays symmetry-breaking in mlc-4(RNAi) embryos with reduced flows. Images (G) and quantification of membrane:cytoplasm ratio (H) at pronuclear meeting (PNM), prometaphase, and anaphase for par-2(gfp/+) or par-2(gfp/ok1723) embryos subject to either control or mlc-4(RNAi). Control data shown in light gray in mlc-4(RNAi) panel for comparison. Note par-2(gfp/+) embryos were used as controls so that quantification would not be affected by differing levels of GFP signal. (I, J) Symmetry-breaking is dosage sensitive in centrosome-compromised embryos. spd-5(RNAi) embryos with the indicated par genotypes were scored for the presence or absence of clearly defined GFP::PAR-2 domains and whether 1 (monopolar) or 2 (bipolar) domains were present (J). Columns indicate frequency distributions for each genotype obtained in 3 replicate experiments (par-2(+/-), n = 9, 14, 13; wild type, n = 12, 9, 11; par-6(+/-), n = 9, 5, 7). Note the first replicate was performed at the semi-restrictive temperature of 20°C, while the remaining 2 were performed at the fully restrictive temperature of 25°C. All show a similar trend. Example images of scored phenotypes in (I). Scale bars, 10 μm. The raw data underlying this figure can be found at https://doi.org/10.25418/crick.27153459.