ABSTRACT
Most biological traits and common diseases have a strong but complex genetic basis, controlled by large numbers of genetic variants with small contributions to a trait or disease risk. The effect-size of most genetic variants is not absolute, but can depend on a number of factors including the age and genetic background of an organism. In order to understand the mechanisms that cause these changes, we are studying heritable trait differences between two domesticated strains of C. elegans. We previously identified a major effect locus, caused by a mutation in a component of the NURF chromatin remodeling complex, that regulated reproductive output in an age-dependent manner. The effect-size of this locus changes from positive to negative over the course of an animal’s reproductive lifespan. Using a previously published macroscale model of egg-laying rate in C. elegans, we show how time-dependent effect-size can be explained by an unequal use of sperm combined with negative feedback between sperm and ovulation rate. We validate a number of key predictions of this model using controlled mating experiments and quantification of oogenesis and sperm use. By incorporating this model into QTL mapping, we identify and partition new QTLs into specific aspects of the egg-laying process. Finally, we show how epistasis between two genetic variants is predicted by this modeling as a consequence of unequal use of sperm. This work demonstrates how modeling of multicellular communication systems can improve our ability to predict and understand the role of genetic variation on a complex phenotype. Negative autoregulatory feedback loops, common in transcriptional regulation, could play an important role in modifying genetic architecture in other traits.
AUTHOR SUMMARY Complex traits are influenced not only by the individual effects of genetic variants, but also how these variants interact with the environment, age, and each other. While complex genetic architectures seem to be ubiquitous in natural traits, little is known about the mechanisms that cause them. Here we identify an example of age-dependent genetic architecture controlling the rate and timing of reproduction in the hermaphroditic nematode C. elegans. Using computational modeling, we demonstrate how this age-dependent genetic architecture can arise as a consequence of two factors: hormonal feedback on oocytes mediated by major sperm protein (MSP) released by sperm stored in the spermatheca and life history differences in sperm use caused by genetic variants. Our work also suggests how age-dependent epistasis can emerge from multicellular feedback systems.
INTRODUCTION
Most biological traits have a strong heritable, or genetic, component. There is general interest to understand the genetic basis of these traits, often by identifying the quantitative trait nucleotides (QTNs) that underlie heritable variation segregating within a population. Two decades of studies of biological traits in humans and other model organisms has made it clear that the genetic basis controlling most biological traits is incredibly complex – not only are dozens to hundreds genes involved, but non-linear effects are also at play. While the role of statistical epistasis, or the deviation from a linear model in a sampled population, is debated (1), work in model organisms have demonstrated that genetic epistasis (2) (also called biological epistasis (3) or compositional epistasis (4)) between two loci is ubiquitous, observed in fungi (5-7), plants (8-11), insects (12, 13), nematodes (14, 15), birds (16, 17), and mammals (18-21). Environment and age are also relevant covariates, influencing the effect and onset of the QTN on the phenotype. A recent survey of natural variation in gene expression in C. elegans identified > 900 eQTLs with time-dependent dynamics (22). While identification of QTNs remains a worthwhile and necessary goal, development of novel approaches that can integrate and simplify how large numbers of genetic variants modify phenotypic divergence represents a necessary accomplishment for the field.
GWAS and QTL mapping, two common quantitative genetics techniques, are usually unable to identify interacting genetic variants. GWAS, which can narrow down causative genetic variants to small regions, are typically underpowered to identify statistically significant epistatic interactions due to low natural allele frequencies and the large number of statistical tests that must be performed (23). QTL mapping, on the other hand, has increased power to identify interacting QTLs due to equal allele frequencies but identifies large regions in linkage disequilibrium containing thousands of potential variants (24). Due to this inherent difficulty in studying epistasis that occurs between genetic variants that segregate within a population, studies of epistasis have typically focused on laboratory induced loss-of-function mutations through mutagenesis or RNAi. It is unknown whether the mechanisms that cause epistasis in these approaches will apply in natural populations.
As a more tractable model to understand how genetic variants impact a trait, we are focusing our studies on two C. elegans strains, N2 and LSJ2, derived from an individual hermaphrodite isolated in 1951. Due to a reproductive system that primarily relies on self-fertilization, the population these two strains derived from was genetically identical, at which point they were separated into distinct cultures of either solid or liquid media sometime between 1957 and 1958 (Figure 1A) (25) and allowed to diverge. N2 was cultured for ∼15 years on agar plates while LSJ2 was cultured for ∼50 years in liquid culture. Using next-generation sequencing, we identified 94 new mutations that were fixed in the N2 lineage and 188 new mutations were fixed in the LSJ2 lineage (26). Despite this low-level of genetic diversity, a large number of phenotypic differences distinguish the two strains. A total of five QTNs have been identified in these strains, providing empirical evidence linking variation in a neuropeptide receptor activity to changes in social behavior (27), variation in sensory gene deployment with specific chemosensory responses (25, 26, 28), variation in chromatin remodeling with life history tradeoffs decisions (29), and variation in an actetyltransferase as the source of cryptic genetic variation affecting organ development (30). To date, however, these studies have focused on QTNs for large-effect QTLs and have largely ignored the role of multigenic changes.
To address this deficiency, we studied the genetic basis of reproductive differences between the N2 and LSJ2 strains at five different time points spanning their reproductive lifespan. Our goal for this study was to identify examples of complex genetic architecture and understand their molecular and cellular causes.
RESULTS
A major effect QTL surrounding nurf-1 has an age-dependent effect size
We previously performed QTL mapping on reproductive rate using 94 recombinant inbred strains (RILs) generated between LSJ2 and CX12311 (29). CX12311 is a strain that derives the majority (>99%) of its DNA from N2 with the exception of a small amount of DNA backcrossed from the CB4856 wild strain that surrounds the npr-1 and glb-5 genes (Figure 1B) (26). Novel mutations in these two genes became fixed in the N2 lineage and result in pleiotropic effects on a large number of phenotypes. Use of the CX12311 strain allows us to avoid studying their effects. To study the role age plays on reproduction, we chose five time points that spanned the reproductive lifespan of the CX12311 animals. Egg-laying rate was quantified by counting the number of eggs laid by six animals for six hours on agar plates seeded with E. coli bacteria (Figure 1C). We previously identified a major effect QTL centered over the nurf-1 gene that accounted for ∼50% of the observed phenotypic variation (26). To study how the animal’s age affected the effect-size of this locus, we first segregated the 94 RIL strains based upon their genotype at nurf-1 (Figure 1D – top panel). At the first three time points, RIL strains with the N2 genotype laid more eggs than RIL strains with the LSJ2 genotype, however, at the fourth and fifth time point, this relationship flipped - animals with the LSJ2 allele of nurf-1 laid more eggs than animals with the N2 allele. To visualize this effect more clearly, we also plotted the effect-size of the nurf-1 locus at all five time points (Figure 1D – bottom panel) by subtracting the egg-laying rate of the strains with each genotype. The effect-size of the LSJ2 allele of nurf-1 was negative for the first three time points and positive for the last two time points. This is a clear example of age-dependence, i.e. the prediction of the effect of the nurf-1 locus on the egglaying rate requires knowledge of both the nurf-1 genotype as well as the current animal’s age.
To verify these observations, we next assayed a near isogenic line (NIL) constructed by backcrossing the region surrounding nurf-1 from LSJ2 into the CX12311 strain (Figure 1B) along with the CX12311 and LSJ2 parental strains. The CX12311 strain (containing the N2 allele of the nurf-1 locus) laid more eggs than the NILnurf-1 strain for the first three time points but fewer eggs at the fourth and fifth time points, again resulting in a time-dependent effect size that flips from positive to negative (Figure 1E – top and bottom panel). The effect size of nurf-1 calculated using both the RIL and NIL strains and showed good qualitative agreement (Figure 1D and 1E – bottom panel). Due to additional segregating variants in the RIL strains, we do not expect these two calculations to be identical. In both experimental designs, the crossing of the two lines was due to a decrease in the egg-laying rate in the strain containing N2 nurf-1 as opposed to an increase in egg-laying of the LSJ2 nurf-1 strains. The LSJ2 strain was statistically indistinguishable at the first three time points from the NIL strain. However, at the last two time points, LSJ2 laid additional eggs resulting in a larger effect-size at these two points. These results demonstrate that the nurf-1 locus can have both positive and negative effects on egg-laying in a manner correlated with the animal’s age.
Difference in early egg-laying rate caused by differences in germline stem cell production, oocyte maturation and/or rate of fertilization
The rate that eggs are laid on an agar plate is dependent on a large number of factors: size and rate of mitosis of a germline progenitor pool, speed of meiosis/differentiation of these cells, maturation and growth of oocytes, ovulation and fertilization of the primary oocyte to produce an egg, and finally the rate of active expulsion of an egg through a controlled motor program that results in the opening of the vulva (Figure 2A). To characterize which factor might be affected by nurf-1, we first characterized the number of fertilized eggs in each strain using DIC microscopy. If the rate fertilized eggs were laid was affected in LSJ2 and NILnurf-1 strains but the rate of production of fertilized eggs remained the same, we would expect LSJ2 and NILnurf-1 to contain more eggs in their uterus than the CX12311 strain. We measured the number of fertilized eggs in each of these three strains at 24 and 48 hours after the L4 stage (Figure 2B). In contrast to this prediction, we found that both LSJ2 and NILnurf-1 had significantly less fertilized eggs than the CX12311 strain. We conclude that production of fertilized eggs must be affected in the LSJ2 and NILnurf-1 strain. The lower number of unlaid fertilized eggs in these strains is potentially a consequence of the reduced rate of production of fertilized eggs.
We next measured the number of large oocytes undergoing oogenesis in these three strains (region marked oogenesis in Figure 2A). We hoped to distinguish between two possible mechanisms modifying the rate of production of fertilized eggs: 1) the rate of production of mature oocytes was decreased in LSJ2/NILnurf-1 strains or 2) the rate of fertilization of a mature oocyte was decreased in the LSJ2/NILnurf-1 strains. We reasoned that in the former case, the number of large oocytes undergoing oogenesis would be lower in LSJ2 and NILnurf-1 due to the decrease in production. In the latter case, if oocyte production was unaffected but the rate they were fertilized was lowered, we reasoned that the number of mature, large oocytes would increase over time. However, when we measured the number of large oocytes in each strain at 24 and 48 hours, we found no statistically significant difference between any of the three strains (Figure 2C). We believe this likely indicates the presence of a homeostatic mechanism that keeps the number of oocytes undergoing maturation constant, despite a difference in how often they are created or fertilized.
Finally, we measured the rate that progenitor germline stem produce new cells through mitosis, as these cells provide the source of meiotic cells that later differentiate into oocytes (marked as mitotic zone in Figure 2A). There is not a one-to-one relationship between the rate of mitosis and oocyte production due to cannibalization of a subset of these cells, but it is thought that there is a relationship between the size of the progenitor pool and subsequent rate of reproduction (31). Progenitor cells can be distinguished from cells in the transition zone based upon nuclear morphology. We observed a significant difference between CX12311 and NILnurf-1 at the 24 hour time point in the number of progenitor cells, suggesting that the difference in egg-laying rate could be caused by this difference (Figure 2D). However, the NILnurf-1 strain was also significantly different from LSJ2 at this time point. This difference disappeared at the 48 hour time point, when each strain had a very similar average number of progenitor cells. We also measured the number of cells undergoing mitosis in the progenitor cells, in case there was also a difference in the ratio of cells dividing in the progenitor zone. We used an antibody to Ser10 phosphorylation in histone H3, which is correlated with chromosome condensation in mitosis (Figure 2E) (32, 33). We observed very similar results to the germline progenitor pool suggesting the ratio of progenitor cells undergoing mitosis was the same in all three strains. The NILnurf-1 was different from both parental strains at the 24 hour time point, and all three strains were indistinguishable from each other at the 48 hours. We conclude from these observations that nurf-1 likely has a modulatory role on the rate of early proliferation of the germline and LSJ2 contains additional genetic variations that can suppress this effect. While this difference in proliferation could account for some of the differences in egg-laying rate, we don’t believe it can explain the entire change as this would indicate different mechanisms are at play between LSJ2 and NILnurf-1.
A macroscale model of egg-laying can predict the age-dependent effect of the nurf-1 locus
While age-dependent QTLs have been identified through genetic mapping approaches, few mechanisms have been demonstrated or even proposed to understand how animal’s age could influence the effect of a genetic variant. To explore possible mechanisms that could cause age-dependence for nurf-1, we leveraged the existing literature on genes controlling egg-laying in C. elegans. One recently described mechanism describes how sperm regulates the rate of egg-laying rate. C. elegans hermaphrodites produce a limited number of sperm (∼300) that are stored in an organ known as the spermatheca before oogenesis begins (34). Sperm release a hormone called major sperm protein (MSP) that stimulates maturation and ovulation of the primary oocyte through ephrin-receptor signaling (Figure 3A) on the oocyte and the gonadal sheath cell (35, 36). The effect of MSP is dose-dependent, so that as the number of sperm stored in the spermatheca decreases (through fertilization), ovulation and oocyte maturation also will decrease (35, 36). This suggests a possible mechanism tying an animal’s age to its egg-laying rate. As an animal ages, each egg it creates through fertilization reduces the number of sperm by one. Animals with N2 nurf-1 lay more eggs during the first three time points compared to LSJ2 nurf-1 animals and will consequently have fewer sperm at the fourth and fifth time point. This reduction in sperm will lower sperm hormone present at the primary oocyte, which counterbalances the positive effect of the N2 nurf-1 allele on egg-laying during the transition from between the third and fourth timepoint.
We tested this hypothesis more formally using a previously published macroscale model (37), which stipulates the egg-laying rate is proportional to the product of the number of oocytes with the number of sperm (Figure 3B). This model is defined by four time-independent parameters: ko, which specifies how rapidly oocytes are created, kc, which specifies a carrying capacity of the gonad, kf, which defines the fertilization rate, and S0, which specifies the number of self-sperm created by the animal. In this report, we excluded the kc parameter, as we found that the carrying capacity of all three strains was similar (Figure 2C), and our attempts to fit this parameter resulted in negative, non-physiological values. Also, due to the nature of the equations, the kf and ko parameters end up having a very similar effect on egg-laying rate. To prevent the noise caused by their tight correlation, we fit a single kf value to be used for all of the strains. This ko value does not distinguish between the number of molecular and cellular processes described above that influence how fast mature oocytes are produced. We fit individual ko and S0 parameters to each of the replicates in Figure 1E (Figure 3C). This model could recapitulate the rise and fall of the egg-laying rate - the rate rose as oocytes were generated and fell as number of sperm decreased (Figure 3D – top panel). A significant increase in S0 was observed in the LSJ2 strain compared to the CX12311 and NILnurf-1 strain (Figure 3C – top panel). This is in good qualitative agreement with our previous demonstration that LSJ2 animals lay more eggs over the course of their lifetime than CX12311 (29). However, the quantitative agreement was rather poor for the LSJ2 strain. While the predicted S0 value of CX12311 was in good agreement with our previously measured fecundity (263 vs. 256), the predicted value of S0 was significantly higher than the measured fecundity (434 vs. 319). This is most likely due to the inability of the model to fully account for the genetic changes in the LSJ2 strain. The average residuals for the LSJ2 strain were significantly higher than CX12311 (2.0 vs. 0.72). The fitted ko parameters matched our expectations - CX12311 had a higher ko value than either the LSJ2 or NILnurf-1 strain (Figure 3C - bottom panel). The effect-size calculated from the modeling experiments (Figure 3D – bottom panel) also qualitatively matched the effect size we experimentally measured (Figure 1E – bottom panel).
This analysis showed that a constant change to oocyte generation rate could have a time-dependent effect on egg-laying resulting in sign-switching at later time points. Our model explicitly predicts that the reduction in CX12311 animals in egg-laying rate at later time points is not due to changes in reproductive capacity but rather decreases in sperm number. To test this prediction, we first measured the number of fertilized eggs and large oocytes in CX12311 animals at 66 hours (Figure 4A). In line with our expectations, we observed a reduction in the number of fertilized eggs (∼10) contained in the CX12311 animals compared to earlier time points (Figure 2B). This indicates that the decrease in egg-laying rate cannot be explained by reduction of in the rate of laying fertilized eggs in the uterus. We also observed a large number of large oocytes (∼22) in CX12311 animals, an increase over the previous two time points (Figure 4A and 2C). This suggests that the change in egg-laying rate is not due to changes in oocyte maturation rate, as mature oocytes are available for fertilization. These observations are consistent with our hypothesis that decreased sperm and MSP at later timepoints are responsible for the decreased rates of egg-laying in CX12311.
Our modeling predicts that the CX12311 strain will have fewer sperm later on in life due to their increase rate of fertilization at earlier time points (Figure 4B). We counted the number of sperm cells present in the spermatheca in CX12311 and NILnurf-1 animals using DAPI staining combined with fluorescence microscopy. At both 48 and 66 hours, an increased number of sperm were present in the NILnurf-1 animals compared to CX12311 in a manner consistent with the modeling.
As a final method to test this model, we took advantage of C. elegans’ androdioecious mating system to increase the sperm available to the hermaphrodites at later time points by mating CX12311 and NILnurf-1 hermaphroties to CX12311 males, which result in the transfer of ~1000 sperm to the hermaphrotite. After mating young adult animals, we separated the hermaphrodites from males and measured the egg-laying rate at two time points late in life. Consistent with our predictions, increasing sperm number prevented the sign-switching from occurring at both of these times in unmated animals (Figure 4D). This indicates that decreases in sperm number are the primary reason for decreases in egg-laying rate at late time points.
Identification of modifier QTLs that also effect the egg-laying process
We next investigated whether additional QTLs affected egg-laying rate differences between LSJ2 and CX12311. The presence of a major effect QTL (such as the nurf-1 locus) can mask the effects of smaller QTLs so we performed additional scans using the genotype of nurf-1 as an additive or interacting covariate (Figure 5A) (38). We identified five QTLs that were significant at the genome-wide level: one QTL on the center of chromosome I, one QTL on the center of II, one large QTL on the center and right arm of chromosome IV, one QTL on the right arm of V, and one QTL in the center of × (Figure S1 – S5). The identification of the QTL on chromosome I was expected, as it contains a previously described missense mutation in nath-10 that was shown to affect egg-laying (30). However, the other four QTLs do not contain any genetic variants that are known to affect egg-laying.
In order to analyze how these additional five modifier QTLs regulated the egg-laying rate at the five mapping time points, we segregated the 94 RIL lines based upon their nurf-1 and modifier QTL genotype (Figure 5B). By segregating both genotypes, we could visually determine if any non-linear interactions (i.e. epistasis) existed between nurf-1 and the five modifier loci. Additive interactions would result in two lines with identical slopes while non-linear interactions result in lines with different slopes. Visual inspection of these effect-size graphs indicated that both additive and non-linear effects were present. In order to formalize this analysis, we used ANOVA to determine (i) if the modifier QTL had a significant effect at the particular timepoint, (ii) whether there was a significant interaction term between nurf-1 and the modifier variant, and (iii) the total amount of variance that the modifier QTL explained at that particular timepoint (Figure 5B). We considered two types of epistasis, positive and negative. Positive epistasis is defined as when the modifier variant has the same direction of effect in both nurf-1 genotypes (e.g. the slope is positive for both lines but different magnitude). Negative epistasis is defined when the modifier variant has a different direction of effect in the different nurf-1 genotypes (e.g. one slope is positive and the other slope is negative). This analysis indicated that the effect of these modifier QTLs were also complex. Each QTL was age dependent and showed non-linear interactions with the nurf-1 locus. This mapping suggests that the egg-laying differences between N2 and LSJ2 are multigenic, involve extensive epistatic interactions, and are highly age-dependent.
Modeling also predicts age-dependent epistasis at latter timepoints
Further inspection of the age-dependence and epistasis of the modifier QTLs with nurf-1 revealed a number of interesting trends (Figure 5B). Epistasis was most likely to occur at the first and last two time points (7 out of 8 significant effects) and less likely to be observed at the second and third time point (1 out of 7 significant effects). While statistically significant, it is difficult to interpret epistasis and the first and last time point, as the rate of egg-laying converges on zero in some of these genetic backgrounds. We were more intrigued by the negative epistasis observed in three of the modifier QTLs at the 60 - 66 hour time point. This is the time point where we observed effect-size switching for nurf-1 and we wondered whether the two features could be related. We decided to use additional modeling to determine if epistasis could arise through unequal use of sperm. We modeled a modifier QTL by assuming it changed the oocyte generation rate (ko) in an additive fashion (Figure S6A) and calculated the egg-laying rate predicted by this model for the four possible genotype combinations (nurf-1 and the modifier QTL) (Figure S6B). These values were plotted at three time points in a similar manner as Figure 5B (Figure S6C).
This analysis demonstrated the potential role for a modifier QTLs to create negative epistasis, specifically at a time when we observe negative epistasis in our QTL mapping data. How does negative epistasis arise? The reason for this can be deduced from our previous observation that the effect size of the modifier QTL will switch signs due to unequal use of sperm in the two genetic backgrounds. However, the exact time this occurs is also dependent on the genetic background of the nurf-1 locus. The period of time in between these two intersections is when negative epistasis is observed as the modifier has a positive effect in one nurf-1 background but has switched to the negative effect in the other nurf-1 background. After the sign-switching occurs for both genotypes, the modifier allele again has the same direction of effect in both nurf-1 backgrounds. We refer to this time window as the sign epistasis zone (Figure S6B).
Segregating the effects of the modifier QTLs onto ko and S0
Finally, we decided to test whether we could use the macroscale modelling of the egg-laying process to improve our QTL mapping. Instead of performing QTL mapping on each of the five time points, we used this data to estimate a ko and S0 for each RIL strain (assuming as before that kc = 0 and kf was the same for all RIL strains). The distribution of these fitted parameters are plotted in Figure 6A and 6B. We next performed QTL mapping to identify genetic regions that influence these rates. As expected, we identified a number of loci that we found from previous analysis. The QTL surrounding nurf-1 was identified as a regulator of both the oocyte generation rate (ko) and the number of self-sperm (S0). The modifier QTLs on II and X regulated the oocyte generation rate but not the number of sperm number, while the QTL on V had an effect on sperm number but not the oocyte generation rate. Interestingly, this analysis also identified a new QTL on chromosome III as a regulator of sperm number (Figure 6B), suggesting that modeling of the egg-laying process not only helps us understand the modifier QTLs effect but also can help identify new QTL loci.
In order to test these results, we utilized a NIL strain surrounding the QTL on V. We crossed the NILV strain to the NILnurf-1 strain to create the double NILnurf-1;V strain (Figure 6D). This combination of strains allowed us to test the effect of the modifier QTL in both nurf-1 genotypes. For each of these strains, we measured the total amount of progeny produced. These NIL strains showed that the QTLV increased the brood size in both nurf-1 backgrounds, but had a larger effect size in the LSJ2 nurf-1 genotype (60 vs. 30) indicating epistasis does exist between these two loci. This qualitatively agrees with the QTL mapping data (Figure 6B – right panel) but discrepancies were observed between the magnitude of the total broodsizes, suggesting additional improvements to the model might be beneficial.
DISCUSSION
Our results identified four new genetic loci that regulate reproductive rate and/or fecundity that arose and fixed following separation of the N2 and LSJ2 lineages. Polygenic traits are common in natural populations, but it was still surprising how rapidly a polygenic trait could evolve in laboratory conditions. Based upon minimum generation time, we estimate a maximum of 3900 generations separate the LSJ2 and N2 strains. We previously identified one of the causative genetic variants as a 60 bp deletion in nurf-1, which encodes a component of the NURF chromatin remodeling factor (29). This deletion arose and fixed in the LSJ2 lineage. Using competition experiments, we demonstrated this genetic variant was advantageous in the LSJ2 growth conditions, suggesting it was fixed by selection. The additional modifier variants could also be advantageous, which could explain their rapid fixation. However, due to the populations small effective population size and limited outcrossing, genetic draft and genetic drift are also relevant evolutionary forces for these strains. Additional work identifying the exact causative genetic variant will be necessary to determine the lineage it arose within and its fitness in the relevant conditions to determine if its fixation was caused by selection vs. genetic drift or draft. Unfortunately, these experiments are not trivial. Despite the inherent advantages to the system as compared to wild strains, each QTL contains a handful to dozens of potential causative genetic variants. The small effect-size of these variants also requires a large number of animals to be tested to obtain the statistical power to distinguish between strains with and without the variant. High-throughput and automated analysis of reproductive output would greatly aid this work.
The study of natural traits from a number of phyla has found a number of examples of biological epistasis (7, 12, 14, 39). Age can also act as an important covariate for genetic variation. The presence of epistasis and age-dependence can obscure the mapping between genotype and phenotype as the effect of causative genetic variants can wash out if mapping populations are not segregated appropriately by age or genetic background. Our results provide a framework to understand how age-dependence can also arise through emergent properties of a cellular network, which we believe to be the major scientific contribution of this work. Our work indicates that the complex seesaw of effects that nurf-1 has on reproductive output can be explained using two major considerations: (1) a hormonally-mediated negative feedback loop linking sperm with oocyte maturation, and (2) the effect nurf-1 has on the rate of oogenesis. Consequently, the molecular details of how nurf-1 modifies protein and cellular function are unnecessary to explain its age-dependence. Our modeling experiments also demonstrated how sign epistasis could arise in an age-dependent manner strictly through age-independent changes in the oocyte production rate. The origin of genetic epistasis is often thought of in terms of biochemical properties of proteins, through physical interactions between two proteins, or through multiple changes to a parallel or linear signaling pathway (40-42). However, these mechanisms were typically identified through analysis of mutations or genetic perturbations generated in the laboratory that have a strong negative effect on fitness. It is interesting to us that such mechanisms don’t seem to be at play here. This is the second example we have identified in C. elegans of what we refer to as cellular epistasis (43) – i.e. the non-linear interactions are an emergent property of the functions of cellular networks as opposed to properties of molecular or biophysical interactions between proteins. It will be interesting to see how often cellular epistasis is responsible for genetic epistasis in natural traits.
While the C. elegans reproductive system is a special case, any negative feedback loops acting on a measurable trait could cause similar age-dependent changes. For example, negative autoregulatory feedback loops are common in transcription factors networks. Any genetic variants (either cis or trans) that increase the rate of transcription of one of these transcription factors will initially appear to have a positive effect-size on the mRNA levels of that gene. However, as the amount of protein product increases, the transcription factor will turn off the expression of its own mRNA. Since the amount of protein product will be higher in the strain with the higher initial expression, the transcription will turn off sooner in that strain, and the genetic variant will soon appear to have a negative effect on expression.
Our work provides an example of how multidisciplinary studies can be used tackle the genetic basis of complex traits – we leveraged quantitative genetics, detailed knowledge of the egg-laying process in C. elegans, and an existing macroscale model of egg-laying to make our conclusions.
Author Contributions
E. E. L. and P.T.M. designed and interpreted experiments and wrote the paper. E. E. L. performed all egg-laying experiments and generated all NILs. E.E.L., R.P. and P.T.M. performed all QTL mapping. R.P and P.T.M. performed all modeling experiments. K.L.W performed all fertilized egg counts, large oocyte counts and sperm counts. K.L.W. and R.F.C. performed all mitotic cell counts. W.X. created nurf-1 CRISPR-Cas9 strains. R.A.B. provided synthetic ascarosides.
Competing Financial Interests
The authors declare no competing financial interests.
METHODS
Strains
Strains were cultivated on agar plates seeded with E. coli strain OP50 at 20°C (44).
Strains used in this study are: N2, LSJ2, CX12311 kyIR1(V, CB4856>N2); qgIR1(X, CB4856>N2).
NIL strains used for this study are: PTM66 (NILnurf-1) kyIR87(II, LSJ2>N2); kyIR1(V, CB4856>N2); qgIR1(X, CB4856>N2), PTM75 (NILV) kahIR2 (V,LSJ2>N2), kyIR1 (V, CB4856>N2); qgIR1(X, CB4856>N2), PTM84 (NILnurf-1, V) kahIR6(IV,LSJ2>N2); kyIR87(II, LSJ2>N2); kyIR1(V, CB4856>N2); qgIR1(X, CB4856>N2)
RIL strains used in this study are sequentially: CX12312 - CX12327, CX12346 - CX12377, CX12381 - CX12388, CX12414 - CX12437, and CX12495-CX12510
Egg-laying assays
Egg-laying assays were performed as previously described (24).
For mating experiments in figure 2E, twelve N2 or CX12311 males were placed on experimental plates with six L4 hermaphrodites of interest for the first time point and mated hermaphrodites were then transferred to experimental plates without males. Successful mating events were validated via the observation of males in the F1 generation of mating plates.
Immunofluorescence and Microscopy
Gonad immunofluorescence was performed on adult animals from each strain 24 and 48 hours after the L4 larval stage. Gonads were dissected in M9 containing 1% Tween and 1 mM levamisole and fixed in 2% paraformaldehyde via freeze cracking. Fixed gonads were stained with a 1:50 conjugated H3KS10p Alexa Fluor 488 antibody (Millipore Cat. 06-570-AF488) specific to mitotically dividing cells and 1.5 mg/mL of DAPI in Vectashield mounting medium (Vector Laboratories Cat. H-1200) (32, 33). Mitotic germline cells and germline stem cells were imaged and scored between the transition zone and the distal tip on an Olympus IX73 inverted microscope with 100×/1.40 UPlanSApo objective (Olympus) and a Hamamatsu Orca-flash4.0 digital camera. The distal tip cell (Figure 2A) is located at the tip of the gonad and releases a factor that promotes mitosis. The transition zone represents the location in the gonad where cells are beginning to undergo meiosis.
Embryo/oocytes/sperm/germline stem cells were quantified by fixing whole animals in 95% ethanol and staining nuclei with 1.5 mg/mL DAPI contained in Vectashield mounting medium. Embryos were scored using DIC on a 10x/0.30 UPlanFL N objective (Olympus). DAPI stained oocytes were imaged and scored between the spermatheca and posterior gonadal arm with a 40×/1.3 PlanApo objective (Olympus). Sperm and germline stem cells were identified using z-stack to capture multiple planes within each spermatheca or progenitor zone respectively. The transition zone was identified using morphological criteria based upon the crescent shape of the nucleus. All images and scoring were processed in ImageJ.
Statistics
Significant differences between means were determined using a Mann-Whitney U test, a nonparametric test of the null hypothesis. For simplicity, a Bonferroni correction was used to modify the type I error rate to account for multiple testing. For each figure, we have listed the uncorrected p-value and the number of comparisons used for the Bonferroni correction in Supplemental Table 1. Both the non-parametric test and the Bonferroni correction should be conservative approximations of the true p-value. For the analysis of epistasis in Figure 5, we used ANOVA to calculate a F value and associated p-value using the fitqtl function in R/qtl. We calculated a single position for each of the five modifier QTLs to use for all five time points. All significant QTLs were simultaneously fit together for each of the five timepoints considering both their linear effect and their interaction with the nurf-1 genoypte (i.e. y = QI +QII + Qnurf + QIV + QV + QX + QI*Qnurf + QII*Qnurf + QIV*Qnurf + QV*Qnurf + QX*Qnurf). The F value was calculated by dropping a single QTL at a time. Since most of the parameters were significant before multiple comparison testing, we used the Benjamini-Hochberg procedure to control for the false discovery rate.
QTL Mapping
R/qtl was used to perform a one-dimensional scan using marker regression on the 192 markers (38). The significance threshold (p = 0.05) was determined using 1000 permutation tests. To identify modifier QTLs, the nurf-1 marker was used as an additive and interactive covariate for additional one-dimensional scans, assuming a normal model. The significance threshold (p =0.05) for these two tests was determined using 1000 permutation tests.
Egg-laying model
We adapted a previously published model (37), which simulates the egg-laying rate using the following set of equations: where E is fertilized eggs, O is oocytes, S is sperm, kf is the rate of oocyte fertilization, ko is the rate of ovulation, and kc is the carrying capacity of the uterus. A dot indicates a time-derivative. We solved these ODEs numerically using a Dormand-Prince explicit solver or using an analytical solution (below). To calculate best fits, we assumed that the LSJ2, CX12311, RILs and NILnurf-1 strains had unique values of ko, but shared the kf parameters. These parameters were estimated using a Levenberg-Marquardt non-linear least squares algorithm. To calculate effect-size, we subtracted the two fits.
We used Mathematica to analytically solve the ODE equations:
We used these equations to estimate the parameters using a Levenberg-Marquardt non-linear least squares algorithm.
NIL strains
NILs were generated from previously existing RILs by backcrossing the chromosomal region of interest into a balancer strain containing a CX12311 background along with a fluorescent miniMos insertion near the QTL of interest. For ten generations, males that were heterozygous for the fluorescent marker (as determined by fluorescence intensity) were crossed to hermaphrodites of the balancer strain. On the 11th generation, animals without the fluorescent marker were isolated. Genotyping of one to three markers within the candidate regions was used to confirm the successful introgression of LSJ2 DNA into CX12311. For each NIL strain, the starting RIL strain and the minMos balancer are listed in the table below:
Acknowledgements
We thank the Caenorhabditis Genetics Center, Christian Frokjaer-Jensen, and Erik Jorgensen for strains; Erik Andersen, Joshua Weitz, and Greg Gibson for discussions; and Cori Bargmann, Greg Gibson, Todd Streelman, Hang Lu, and Andres Bendesky for helpful comments on the manuscript. This work was supported by NIH grants R21AG050304, R01GM114170, and the Ellison Medical Foundation (to P.T.M.).