ABSTRACT
A balance between phenotypic variability and robustness is crucial for populations to adapt to multiple selection pressures. The plasticity of genetic pathways underlies this balance. We investigated this plasticity by studying the regulation of phenotypic mean and variance in a biparental recombinant population of Saccharomyces cerevisiae grown in a variety of environments. We found that the growth of this population was well buffered in most environments, such that majority of alleles regulated the mean value of phenotype, and only a subset of these alleles regulated phenotypic variance. This latter class of alleles allowed the other genetic variants to express a range of phenotypic values around a shifted mean. This shift depends on the population and the environment, i.e. based on the evolutionary history of a strain, buffering can result in either a superior or an inferior phenotype in an environment but never both. Interestingly, intricate coupling of the genetic network regulating mean phenotype and robustness was observed in a few environments, which highlighted the importance of phenotypic buffering in layout of the genetic architecture. For loci regulating variance, show a higher tendency of genetic interactions, which not only establishes a genetic basis of release of variance, but also emphasizes the importance of mapping robustness in understanding the network topology of complex traits. Our study demonstrates differential robustness as one of the central mechanisms regulating variation in populations and underlines its role in identifying missing heritability in complex phenotypes and diseases.
INTRODUCTION
The effect of genetic variation can either remain dormant or manifest itself phenotypically, a phenomenon referred to as phenotypic capacitance (Masel and Siegal 2009; Félix and Barkoulas 2015; Hayden et al. 2015). The process of revelation of phenotypic variability (decanalization) has adaptive potential for populations in novel or stressful environments (Masel 2013). Released mutations, often referred to as cryptic genetic variability (CGV) (Paaby and Rockman 2014) can exhibit high phenotypic variability across multiple environments, which provides adaptive diversity (Chevin et al. 2010; Geiler-Samerotte et al. 2013). Understanding the processes underlying phenotypic capacitance is important for interpreting evolutionary effects of forces acting on populations, which result in missing heritability and incomplete penetrance of complex traits and disease. Such processes may ultimately govern the origin and development of complex genetic and molecular networks (Siegal and Leu 2014).
Recent advances in systems biology have revealed that interpreting molecular mechanisms of evolution is the key in understanding the highly interconnected genetic map (Wagner et al. 2007; Costanzo et al. 2010). Certain genes, called hubs, show higher connectivity than others and thus holding the network together (Vidal et al. 2011). Deciphering the mechanisms, by which these network hubs modulate the effector genes in an environment-and genetic-background dependent manner to influence the phenotype, is the key to understanding how phenotypic capacitance and variability have created the genotype-phenotype (GP) map.
Despite being proposed over half a century ago (Jamniczky et al. 2010), only recently, a few studies have begun to identify possible regulators that buffer this genetic diversity (Félix and Barkoulas 2015). Evidence from various genome-wide deletion, protein-protein and transcriptional network analyses have proposed chromatin regulators as network hubs regulating phenotypic capacitance and variability (Levy and Siegal 2008; Tirosh et al. 2010). However, the molecular mechanisms through which these networks mediate the variability in the effector genes and generate diverse phenotypic responses are largely unknown. To date, the mechanistic bases have been identified only in a few cases, e.g. Hsp90, a highly conserved protein that regulates the phenotypic variance through altered protein folding (Rutherford and Lindquist 1998; Queitsch et al. 2002).
In this study, we have attempted to address the following two questions. How important is regulation of robustness for genetic regulation of the phenotype? And, whether perturbation of this robustness and the subsequent release of CGV are beneficial or detrimental for the population growth?
In order to understand the regulation of phenotypic variability and plasticity, it is necessary to investigate the effect of regulators on diverse mutations, an approach applied so far to only a few genes (Queitsch et al. 2012). For a single species, though not achievable through single gene perturbation studies, recombinant populations analyzed in various environments provide an excellent platform to study such effects (Lempe et al. 2013). The allelic variants that mediate how phenotypes are regulated have two potential outcomes. First, there is an effect on the ‘mean’ value of some readout, such as growth in different environments in the case of yeast. Mapping such an effect on population ‘mean’ values allows the identification of alleles that affect phenotypes independent of the genetic background. In addition, there is a second consequence, i.e. an effect on the ‘variance’ of the readout (Hall et al. 2007; Lee et al. 2014), which is often ignored in many studies. Alleles that cause such differences in population ‘variance’ have a more subtle effect, whereby genetic diversity is retained in the population (Figure 1A). In our study, we used a synthesis of both these mapping approaches to discern patterns of regulation of variation in a recombinant population. We find that the genetic loci, and their networks, regulating robustness are a subset of the conventionally studied loci, which affect phenotypic mean. However, in certain environments, based on the evolutionary history of the parental strains, these two networks are very closely intertwined as demonstrated by complete loss of buffering in the recombinants. Such environments highlight the importance of mechanisms regulating robustness in the genetic architecture. Based on our analysis, we propose differential robustness of alleles as a major contributor to antagonistic pleiotropy. Finally, we provide evidence for genetic basis of loss of robustness and therefore propose variance mapping as a methodology to uncover the genetic interactions regulating complex traits.
RESULTS
High overlap between mean and variance QTL
Using a recombinant population generated from a biparental cross, we carried out linkage mapping to identify genetic loci regulating both phenotypic mean (QTL) and phenotypic robustness (variance QTL or vQTL) of colony size variation across 34 diverse environments ranging from different carbon sources to oxidative and DNA damaging stress (see Methods). To compare the genetic loci identified by QTL and vQTL mapping, the genome was binned into 595 bins (see Methods, Tables S1, S2). The distribution of loci showing a difference in mean only, variance (robustness) only or both, differed across environments (Figure 1B). The majority of all loci identified affected only mean (70%) with 4% affecting only robustness. However, a substantial 27% loci were both QTL + vQTL (Figure 1C). For these loci, pleiotropic hotspots were identified, which regulated mean, robustness or both across multiple environments (Table S2).
Environment dependent regulation of phenotypic mean and robustness
While there was no association between number of QTL and vQTL identified across environments, there was a negative correlation (r2 = −0.4) between the number of QTL and the number of loci which were both QTL + vQTL associated across environments. This indicated that there is a decrease in the number of loci with independent effects as the number of loci regulating variance increase. Based on the overlap between mean and variance loci, we could divide the environments into three categories – (i) No overlap between QTL and vQTL: this indicated that growth was tightly buffered in the recombinants and while the genetic variants affected the mean of the phenotype, robustness was maintained. These environments were enriched in various carbon sources. (ii) Partial overlap between QTL and vQTL: some loci showed difference in robustness but the majority affected only the mean. (iii) Almost complete overlap: in these environments, all loci which affected the phenotypic mean resulted in varying degrees of loss of robustness. In such environments only two states were possible, i.e. either the allele contributed to the buffered state or it resulted in loss of robustness. Growth in such environments emphasized the role of robustness in regulating phenotypic variation.
Release of phenotypic variance is directional
A high overlap of regulation of mean and robustness indicated that the loci regulating phenotypic variability were a subset of the loci that have been implicated to be associated with a shift in the mean upon release of variation. While pleiotropic hotspots regulated the mean and the variance across multiple environments, no discernible pattern was observed in the directionality of this effect, except when considering each environment independently (Figure 2A). In the majority of environments (26/33), we observed a strong correlation between the effect of the allele on the mean and the variance for the significant loci. One half of the environments (13/26) showed a strong positive correlation (r2 > +0.5) indicating that loss of robustness was, on an average, advantageous, and the other half showed a negative correlation (r2 < −0.5), i.e. loss of robustness was detrimental for the population (Figure 2B).
Differential regulation of robustness as a major contributor to gene-environment interaction
Pleiotropic loci often have antagonistic mean effects across environments (Yadav et al. 2015). While loci regulating robustness show high environment specificity, we asked if it is possible for a locus to result in robustness in one environment and decanalization in the other by comparing covariance of alleles across environmental pairs (Haber and Dworkin 2015). Forty seven bins were identified that had a significant effect in two or more environments. Eighteen hotspots showed significant difference in the covariance with 10 being significant across multiple pairs of environments (Table S3). Unlike mean effects, high consistency was observed in allelic robustness of a single hotspot across environmental pairs, i.e. within a hotspot the same allele showed a low covariance (high buffering or canalized) across multiple environmental pairs and consequently the other allele consistently showed a high covariance (decanalization). This consistency in buffering, when coupled with high environment specificity of directionality (advantageous or deterimental but not both) of release of variance, explains the abundant antagonistic pleiotropy observed in mean effects of these pleiotropic hotspots (Figure S1) (Yadav et al. 2015). As suggested by our previous analysis, the environment would determine whether the accumulated mutations would be beneficial or detrimental to the phenotype. In conclusion, this covariance analysis shows that differential regulation of robustness is a major contributor to gene-environment interactions, especially antagonistic pleiotropy.
Release of variance is genetic in nature
While most of the polymorphisms in this population were neutral, some showed their direct effects and others were hidden showing their effects only under certain environmental and genetic perturbations. To estimate the extent of genetic basis of loss of robustness, two-QTL interaction mapping was performed by considering the effects of only significant QTL and vQTL loci (see Methods). Amongst the loci showing two-QTL interactions, 10% had only single QTL effects, whereas 80% were either vQTL or both (Table S4) indicating that vQTL were involved in a greater fraction of genetic interactions. These interacting loci showed stronger effects in the decanalized allele than the buffered one (Figure 3B, 3C). In addition to showing that there is a genetic basis regulating the increase in variability, this observation also suggests that altered variance is a good predictor of extent of genetic interactions.
In our analysis, two kinds of interaction hubs were identified: within environment interaction hubs, where a locus interacted with multiple loci to regulate phenotypic variation in a given environment; and across environment interaction hubs, where a pleiotropic locus interacted with different loci across several environments to regulate phenotypic variation (Figure 4A). Overall, our observations support a modular structure of regulation of phenotypic robustness. In within environment hubs, some regulators controlled multiple effector genes in a single environment. In the presence of a decanalized allele, this control is disrupted, resulting in a high variance in the same environment. These hubs were identified in the environments where most loci independently regulated both mean and robustness. On the other hand, in across environment hubs, a different set of effectors functionally regulated the phenotype across distinct environments. This suggests that allelic variations in such hubs will cause changes in variability and control growth across environments.
Network of loci regulate phenotypic buffering
Studies showing high interconnectivity and redundancy in the genetic networks argue for a crosstalk among multiple regulators of phenotypic robustness (Kafri et al. 2009; Li et al. 2010; Costanzo et al. 2010). At a population level, this would translate to maintenance of robustness by a network of loci instead of a single locus. To identify such interactions regulating phenotypic variance, we carried out a two-vQTL interaction mapping using candidate loci (Table S4). To our knowledge, this is the first time that such an analysis has been performed. A large number of two-vQTL interactions were identified, many more than would be expected from proportion of single vQTL analysis, emphasizing the functional relevance of co-regulating variance in population dynamics (Figure 4B). Interestingly, in addition to just the differential regulation of variance, this interaction mapping also identified two-locus pairs which had buffered variance in 3 out of their 4 allelic combinations (Figure 3E, 3F). Indeed, in environments showing high overlap between mean and variance QTL, multiple such pairs were identified (Figure 4C, 4D), indicating that there was a highly connected, redundant multi-locus network that maintained phenotypic robustness. We also observed that it is only under very specific allelic combinations that this network was disrupted to reveal phenotypic variance.
DISCUSSION
Populations balance maintaining a robust phenotype unaffected by genetic perturbation and active accumulation of mutations as potential for evolution. Therefore, it is a reasonable assumption that regulation and mediation of phenotypic variability under different selection pressures plays a significant role in determining the networks governing complex traits (Landry and Rifkin 2010; Geiler-Samerotte et al. 2013).
Once a population adapts to a particular environment, stabilizing selection acts to maintain the mean at a specific fitness value. While phenotypically uniform, the population needs to maintain genetic diversity to maintain adaptive potential in the face of a change in selection pressure (Hartman et al. 2001; Gibson and Dworkin 2004). This requires the presence of genetic hubs that may sense environmental or genetic perturbations, transducing their responses to the downstream effectors, and therefore, regulate the release of phenotypic capacitance (Figure 5) (Carlborg et al. 2006; Le Rouzic and Carlborg 2008; Hayden et al. 2015). This release of phenotypic diversity can be a result of encountering a novel or a stress environment as well as a result of a change in a regulator (Figure 5) (McGuigan and Sgrò 2009).
Our study showed that high-resolution QTL mapping could be used to distinguish between genetic loci which have a ‘mean’ effect on the phenotype and those which regulate phenotypic robustness. While various studies have compared loci regulating mean and variance in different organisms in the past they were limited either by sample size or range of phenotypes considered, thus showing varying degrees of overlap between loci regulating mean and variance (Hall et al. 2007; Sangster et al. 2008; Lee et al. 2014). Our study shows empirical evidence that regulation of robustness forms the basis of genetic networks regulating a phenotype. Growth in an environment can be regulated in two ways: either most of the loci affect the mean with only a subset affecting robustness, or almost all loci affect both robustness and the mean. In addition to the nature of the environment, this categorization would depend on the evolutionary history of the parental strains.
In our study, presence of majority of alleles differentially affected the phenotype mean without perturbing the buffered state, indicates that the network maintaining robustness is extensive and the genetic variation in the population is not sufficient to perturb it. Alternatively, for the environments which parental strains would have encountered during evolution and were similarly adapted to, viz., various carbon sources, diverse parental alleles maintain similar robust state. On the other hand, in a few environments, all alleles that affected mean also affected robustness. This high coupling indicated that robustness was perturbed in the segregating population such that every allele that affected the phenotype also perturbed its robustness. This could be possible if either one of the strains was not exposed to the environment during its evolution or the strains were buffered through incompatible independent mechanisms. In such environments, the network topology and role of robustness in their layout becomes apparent.
Independent of the kind of environment, strong directionality was observed in the release of cryptic genetic variation. This directionality is likely the frozen-in result of the evolutionary history of the strains or the phenotype (Taute et al. 2014). For a stabilized population in a stressful or a novel environment, the population has an evolutionary imperative to release phenotypic variability, resulting in a positive association between the mean and the variance (Le Rouzic and Carlborg 2008; McGuigan and Sgrò 2009). On the other hand, in an adapted environment, release of variability will be detrimental and would be visible as a negative association between the mean and the variance (see Figure 2A). We observed that while genetic loci showed antagonism in their mean effects across environments, they showed high consistency in directionality of their buffering abilities. Environment-dependent effect of release of variance as well as high consistency in buffering indicates that a locus that buffers the phenotypic capacitance will, as a result, have an antagonistic effect on the population mean in an environment-dependent manner. Additionally, this consistency of effect on robustness is in accordance with the known molecular mechanisms. An allele that perturbs protein folding or chromatin silencing (Taylor and Ehrenreich 2015) will show similar molecular behaviour across environments, whether the release will be beneficial or detrimental will be determined by the phenotype. In summary, our study indicates that altered buffering is a potential cause of antagonistic pleiotropy. While we cannot comment on the genes mediating this phenotypic buffering, our study shows that in different environments, different genetic loci or their hubs regulate robustness. This along with identification of environments with high overlap between regulation of mean and robustness support a scenario where multiple genes are involved in buffering the phenotype and may possibly play a crucial role in layout of genetic networks.
Our variance mapping using biparental recombinant populations adds to the understanding of fundamental questions like missing heritability (Manolio et al. 2009; Eichler et al. 2010). High population dependence and incomplete penetrance impede the identification of disease-causing alleles (Zuk et al. 2012; Mackay 2014). We propose altered phenotypic buffering as a possible causative mechanism behind missing heritability (Queitsch et al. 2012). Effect of a disease-causing locus will be neutralized in the presence of an allele that buffers the phenotypic variance, whereas it will be causative in the decanalized allele (Figure 5). While genome-wide association studies suffer from a lack of power to identify such epistatic interactions, analyzing the variance of a population along with the mean can act as a robust refinement to narrow down the possible interactors of disease-causing alleles.
METHODS
Dataset
The raw growth data analysed in this study was derived from a study by Bloom et al. (2013), in which the experimental procedures are described in detail. The data we used was generated for 1,008 segregants derived from a cross between S. cerevisiae strains BY (a laboratory strain) and RM11–1a (a wine isolate, indicated as RM). These segregants were grown in 46 different conditions. Of these, we studied 34 conditions (see Table S2, see File S1 for more information).
QTL and vQTL mapping
The single environment QTL and two-QTL mapping was carried out as described previously (Bhatia et al. 2014).
To estimate the difference in phenotypic variance between the two genotypic groups, i.e. to identify vQTL in each environment, the standard Brown-Forsythe (BF) statistic (Lee et al. 2014) and the corresponding LOD score were calculated for each genetic marker in each environment (see File S1). The BF test is equivalent to an F-test performed on the deviations of the phenotypic values from their respective genotypic medians (or the means). Hence, under the alternative hypothesis, the phenotypes of the two alleles reveal a difference in the variance. As a result, the corresponding LOD scores indicate markers responsible for genetic canalization defined as variance-QTL (vQTL).
At a particular marker, let zij be the absolute deviation of segregant i’s phenotypic value yij from its genotypic mean where j can take two values (j = 1: BY allele and j = 2: RM allele).
Then BF statistic for that marker can be computed as follows:
Here, N is the total number of segregants, n1 and n2 are the number of segregants having the BY and RM allele respectively (p = 2). In order to estimate the effects of vQTL in the same order as in QTL, LOD scores were computed as described previously (Broman and Sen 2009).
To establish the statistical significance of the putative QTL and vQTL, P-values were computed using a genome-wide permutation test of 1,000 permutations, where the null distribution consisted of the highest genome-wide LOD score obtained from each permutation. A LOD cut off of 3.0 and a P-value cut off of 0.01 was considered.
To estimate pleiotropy, we divided the genome into 20kb non-overlapping bins (Table S1). Bins containing two or more QTL or vQTL significant (P-value < 0.01) in different environments were considered as pleiotropic bins. The first markers of each of these pleiotropic bins, used as representative of the bins were collated to represent the set of pleiotropic markers (Table S1, S2).
Apart from the standard two-QTL mapping described previously (Bhatia et al. 2014), we mapped variance-controlled interactions, i.e. a two-vQTL interaction, which occurs when the phenotypic variance at one locus depends on the genotype at another locus. To increase power to identify two-QTL and two-vQTL interactions, for environment specific, targeted multi-QTL mapping, genetic loci significant in either QTL or vQTL or both mappings were collated for each environment (Table S2). Additionally the size of the bin was increased from 20kb to 50kb for the same. This collated set of environment-specific loci was tested for both, two-QTL and two-vQTL interactions in their respective environments. A total of 47 two-QTL interactions each significant (P-value < 0.001) in at least one of the 34 environments were obtained. The P-values were computed using a permutation test of 10,000 permutations with the phenotype data shuffled relative to the genotype data.
Covariance across environmental pairs
To assess the differential covariance of a locus across multiple environments, we considered the collated set of pleiotropic markers for our study (Table S3). To quantify the differential covariance across a pair of environments, a Deming regression was calculated between the phenotype values of the chosen pair of environments for each allele, using R package ‘mcr’. Deming regression, which minimizes errors in multiple dimensions simultaneously, served as a suitable measurement error model for assessing buffering across two or more environments. For every possible environment pair, a t-test was performed between the deviations of the phenotypic values from the Deming fit of the BY and RM allele (P-value < 0.05).
AUTHOR CONTRIBUTIONS
Conceived and designed analysis: AY HS. Analysed data: KD AY HS. Wrote the paper: AY HS.
SUPPORTING INFORMATION
File S1: Scripts and datasets for QTL, vQTL, and two-QTL, two-vQTL interaction mapping.
ACKNOWLEDGEMENTS
We thank Gyan Bhanot for critical reading of the manuscript. This research was supported by Tata Institute of Fundamental Research intramural funds (HS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.