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Quantitative perturbation-phenotype maps reveal nonlinear responses underlying robustness of PAR-dependent asymmetric cell division [1]
['Nelio T. L. Rodrigues', 'The Francis Crick Institute', 'London', 'United Kingdom', 'Tom Bland', 'Institute For The Physics Of Living Systems', 'University College London', 'Kangbo Ng', 'Nisha Hirani', 'Nathan W. Goehring']
Date: 2024-12
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.
Funding: This work was supported by the Francis Crick Institute (to N.W.G), which receives its core funding from Cancer Research UK (CC2119 to N.W.G.), the UK Medical Research Council (CC2119 to N.W.G.), and the Wellcome Trust (CC2119 to N.W.G.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Copyright: © 2024 Rodrigues et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Thus, there is an apparent disconnect between the predicted reliance of PAR polarity on balancing aPAR and pPAR activity on one hand, and the apparent robustness of asymmetric division to gene/protein dosage variation on the other. This disconnect led us to quantitatively examine the coupling between symmetry-breaking cues, PAR polarity, and asymmetries in size and fate, with a specific focus on understanding the impact of perturbation in PAR protein/gene dosage ( Fig 1B ). By combining established methods for manipulation of protein dosage in C. elegans [ 59 ] with recently developed image quantitation-based workflows [ 50 , 60 ], we directly relate dosage to phenotype in individual embryos. Our data support a model in which pathway responses are canalized against variation in spatial signals at multiple levels, leading to decoupling between symmetry-breaking, polarity, spindle positioning, and fate segregation modules. This decoupling effectively insulates individual modules from variability arising elsewhere in the pathway, helping to ensure reproducible outcomes in both size and fate asymmetry during asymmetric division.
Due to the mutually antagonistic nature of feedback, PAR polarity generally relies on balancing aPARs and pPARs, which act via their respective polarity kinases PKC-3 and PAR-1 (reviewed in [ 29 , 38 , 39 ]). Mathematical models based on mutual antagonism predict sensitivity to dosage changes, which manifest as shifts in membrane concentrations, relative domain sizes, and ultimately collapse of polarity depending on the magnitude of the perturbation, behaviors which have been generally confirmed in vivo, at least at a qualitative level [ 25 , 53 – 55 ]. Mutations in pPAR genes can be genetically suppressed by partial depletion of aPARs and vice versa. Polarity outcomes are also sensitive to ectopic overexpression of individual PAR proteins, particularly in sensitized backgrounds [ 27 , 33 , 55 – 57 ]. At the same time, there is a notable lack of developmental phenotypes in embryos heterozygous for mutations in par genes or indeed in the vast majority of genes essential for early embryogenesis [ 37 , 57 , 58 ].
The core feedback circuits underlying segregation of PAR proteins in the zygote are a set of mutually antagonistic (double negative) interactions. Specifically, anterior PAR proteins (aPARs)—PAR-3, PAR-6, PKC-3, and CDC-42—restrict membrane association of the opposing posterior (pPAR) proteins—PAR-1, PAR-2, LGL-1, and CHIN-1—through their phosphorylation by PKC-3 [ 41 – 44 ]. Conversely, pPAR proteins exclude aPARs through the phosphorylation of PAR-3 by PAR-1 [ 30 , 45 ] and inhibition of active CDC-42 by the CDC-42 GAP CHIN-1 [ 46 – 48 ]. This reciprocal negative feedback is thought to be complemented by within-group positive feedback, e.g., cooperative membrane binding [ 49 – 52 ].
(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.
Asymmetric division of the zygote is under direct control of a set of conserved cell polarity proteins known as the PAR(-titioning defective) proteins [ 37 ]. The PAR proteins consist of 2 antagonistic groups of membrane-associated proteins that segregate into opposing anterior and posterior membrane domains during the first division [ 38 , 39 ]. Segregation is triggered by a set of semi-redundant symmetry-breaking cues that induce initial asymmetries in the distribution of PAR proteins in the zygote. These asymmetries are then reinforced and maintained through a core set of feedback interactions to generate robustly segregated anterior and posterior PAR domains. Once formed, these PAR domains direct the spatial organization of downstream processes that orchestrate the size and fate asymmetry of cell division [ 40 ] (summarized in Fig 1A ).
In Caenorhabditis elegans and related species, the first cell division is nearly always asymmetric in both size and fate, the latter manifest as cell cycle asynchrony between daughter cells and ultimately their divergence into distinct lineages. Although the precise magnitude of these asymmetries can vary between species, both cell size asymmetry and cell cycle asynchrony are highly reproducible within a given species [ 20 – 23 ]. Moreover, at least in C. elegans, asymmetric division is robust to genetic and environmental perturbations, including both temperature variation and physical deformation [ 24 – 33 ]. While embryos can tolerate some variation in cell size asymmetry and cell cycle asynchrony, in part due to compensatory behaviors that occur later in development [ 34 – 36 ], the design principles that underlie this robustness of division asymmetry itself remain largely unknown.
Regardless of its ultimate mechanistic origin in a given system, robustness is typically associated with nonlinear signal-response curves. Such nonlinearities yield threshold-like behaviors that effectively canalize variable input parameters into similar developmental trajectories, thereby allowing them to converge upon similar outcomes [ 18 , 19 ]. In the case of mutational or allelic variation, such mechanisms can yield highly nonlinear genotype-phenotype maps associated with phenotypic canalization [ 5 ].
The robustness of phenotypic outcomes has many origins and includes mechanisms that act at multiple scales of organization [ 3 – 5 ]. Molecular buffering or dosage compensation mechanisms can directly compensate for variance in network components [ 6 – 9 ]. Network features, such as activity-dependent feedback, saturation, or kinetic linkage, can also ensure that input–output functions of the network remain robust to variation in particular components [ 10 – 14 ]. Finally, the organism may have network-extrinsic mechanisms that allow systems to correct for variability in network outputs [ 15 – 17 ].
Developmental systems possess a remarkable ability to maintain stable phenotypes in the face of perturbations including variable gene expression, noise, environmental conditions, physical insult or constraints, or even mutational load. This has led to the notion that systems have evolved to minimize variance in outputs, i.e., phenotypic traits, in the face of perturbations or variation in input signals, rendering them robust [ 1 , 2 ].
Results
We reasoned that robustness of asymmetric division in the C. elegans zygote to changes in par gene or PAR protein dosage could arise from a variety of mechanisms known to contribute to the robustness of developmental processes: (1) Dosage compensation: animals harboring a loss of function par allele could up-regulate expression of the remaining functional allele, ensuring normal concentrations. Alternatively, compensatory changes to levels of other PAR proteins within the network could act to restore normal function, as in [6]. (2) PAR network properties: features of the PAR network, such as feedback circuit design, render its outputs insensitive to modest changes in dosage of any given component, as in [13,14]. (3) Canalization: the downstream asymmetric division machinery is insensitive to dosage-dependent variation in PAR concentration profiles/domain size, as in [19]. In other words, PAR distributions may be dosage sensitive, but downstream pathways are robust to these changes (Fig 1C).
Compensatory dosage regulation cannot explain robustness to heterozygosity in par genes We first asked whether embryos exhibited dosage compensation. Chromosome-wide dosage compensation is well known in the context of sex chromosomes: Gene expression is systematically up- or down-regulated to account for differences in sex chromosome number in males and females [61]. However, dosage compensation of individual autosomal genes is less well understood. Systematic transcriptional analysis suggests that the degree of compensation can vary substantially at the level of individual genes, though the vast majority show no or only partial compensation [62,63]. We initially looked for evidence of dosage compensation in animals heterozygous for mutant alleles of 2 polarity genes par-6 and par-2, as representatives of aPAR and pPAR genes, respectively. Due to maternal provision to oocytes, the mRNA and protein composition is primarily determined by the mother’s genotype. Thus, for simplicity, hereafter we refer to embryos by the genotype of the mother, i.e., heterozygous embryos = embryos from heterozygous mothers. To test whether compensation occurs, we applied spectral autofluorescence correction using SAIBR [60] to accurately quantify and compare GFP levels in embryos of 3 genotypes: (1) homozygous for endogenously gfp-tagged alleles (gfp/gfp) in which all protein is GFP-tagged; (2) heterozygous embryos carrying a single tagged allele together with an untagged wild-type allele (gfp/+), in which we expect GFP-labeled protein to constitute roughly half of total protein; and (3) heterozygous embryos carrying a single tagged allele over either a null allele or an allele that can be selectively depleted by RNAi (gfp/-). For perfect dosage compensation, we would expect levels of GFP in gfp/gfp and gfp/- to be similar (Fig 2A). However, we find that embryos from gfp/- worms expressed levels of GFP that were only modestly increased relative to gfp/+, and well below those of gfp/gfp embryos, suggesting only partial up-regulation (Figs 2B–2D and S1). Similar results were obtained for other par genes examined, including par-1, par-3, and pkc-3, which showed modest to no compensation in heterozygotes (Figs 2D and S1). PPT PowerPoint slide
PNG larger image
TIFF original image Download: 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 (xfp 1 /xfp 2 (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.
https://doi.org/10.1371/journal.pbio.3002437.g002 Because of the requirement for balanced activity of aPAR and pPAR proteins [38,39], we also asked whether down-regulation of other components in the PAR network could help explain the robustness of embryos to dosage changes in individual PAR proteins. In other words, would depletion of a given PAR protein lead to reduction in the concentration of opposing PAR proteins? We therefore performed progressive depletion of either PAR-2 or PAR-6 by RNAi and monitored the dosage of the other. We found that dosage of PAR-2 remained constant across the full range of PAR-6 depletion conditions and that PAR-6 dosage was similarly constant across the full range of PAR-2 depletion (Fig 2E and 2F). Consistent with these results, we found that the other posterior PAR proteins PAR-1 and LGL-1 were unchanged in PAR-6-depleted animals (Fig 2G and 2H), while the levels of anterior PAR proteins PKC-3 and PAR-3 were unchanged in PAR-2-depleted animals (Fig 2I and 2J). Thus, there do not appear to be coordinated alterations in protein amounts to compensate for changes in the dosage of a given PAR protein. We conclude that C. elegans embryos do not exert homeostatic regulation of PAR concentrations in response to dosage changes. It is possible that modest up-regulation of protein amounts for some par genes (par-1, par-2, par-6) could partially contribute to stable phenotypes in heterozygotes. However, embryos heterozygous for par-3 and pkc-3 did not exhibit such increases (Fig 2D), suggesting that partial up-regulation is neither a general adaptation of par genes nor a requirement for the reported viability of par heterozygotes. Moreover, the limited degree of up-regulation where it exists means that heterozygotes are viable despite harboring 30% to 50% less PAR protein than wild type, raising the question of how dosage variation impacts signaling activity, polarity, and ultimately asymmetric division.
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