Models of Quantitative Variation of Flux in Metabolic Pathways

As a model of variation in a quantitative character, enzyme activity variation segregating in a population is assumed to affect the flux in simple metabolic pathways. The genetic variation of flux is partitioned into additive and nonadditive components. An interaction component of flux variance is present because the effect of an allelic substitution is modified by other substitutions which change the concentrations of shared metabolites. In a haploid population, the the proportion of interaction variance is a function of the gene frequencies at the loci contributing to the flux variation, enzyme activities of mutant and wild type at variable loci and activities at nonvariable loci. The proportion of interaction variance is inversely related to the ratio of mutant to wild-type activities at the loci controlling the enzyme activities. The interaction component as a function of gene frequencies is at a maximum with high mutant allele frequencies. In contrast, the dominance component which would apply to a diploid population is maximal as a proportion of the total when mutant alleles are at low frequencies. Unless there are many loci with large differences in activity between the alleles, the interaction component is a small proportion of the total variance. Data on enzyme activity variation from natural and artificial populations suggest that such variation generates little nonadditive variance despite the highly interactive nature of the underlying biochemical system.     

Mapping determinants of variation in energy metabolism, respiration and flight in Drosophila

We employed quantitative trait locus (QTL) mapping to dissect the genetic architecture of a hierarchy of functionally related physiological traits, including metabolic enzyme activity, metabolite storage, metabolic rate, and free-flight performance in recombinant inbred lines of Drosophila melanogaster. We identified QTL underlying variation in glycogen synthase, hexokinase, phosphoglucomutase, and trehalase activity. In each case variation mapped away from the enzyme-encoding loci, indicating that trans-acting regions of the genome are important sources of variation within the metabolic network. Individual QTL associated with variation in metabolic rate and flight performance explained between 9 and 35% of the phenotypic variance. Bayesian QTL analysis identified epistatic effects underlying variation in flight velocity, metabolic rate, glycogen content, and several metabolic enzyme activities. A region on the third chromosome was associated with expression of the glucose-6-phosphate branchpoint enzymes and with metabolic rate and flight performance. These genomic regions are of special interest as they may coordinately regulate components of energy metabolism with effects on whole-organism physiological performance. The complex biochemical network is encoded by an equally complex network of interacting genetic elements with potentially pleiotropic effects. This has important consequences for the evolution of performance traits that depend upon these metabolic networks.     

Genetic and nongenetic bases for the L-shaped distribution of quantitative trait loci effects

The L-shaped distribution of estimated QTL effects (R(2)) has long been reported. We recently showed that a metabolic mechanism could account for this phenomenon. But other nonexclusive genetic or nongenetic causes may contribute to generate such a distribution. Using analysis and simulations of an additive genetic model, we show that linkage disequilibrium between QTL, low heritability, and small population size may also be involved, regardless of the gene effect distribution. In addition, a comparison of the additive and metabolic genetic models revealed that estimates of the QTL effects for traits proportional to metabolic flux are far less robust than for additive traits. However, in both models the highest R(2)'s repeatedly correspond to the same set of QTL.     

Explaining the heritability of an ecologically significant trait in terms of individual quantitative trait loci

Most natural populations display substantial genetic variation in behaviour, morphology, physiology, life history and the susceptibility to disease. A major challenge is to determine the contributions of individual loci to variation in complex traits. Quantitative trait locus (QTL) mapping has identified genomic regions affecting ecologically significant traits of many species. In nearly all cases, however, the importance of these QTLs to population variation remains unclear. In this paper, we apply a novel experimental method to parse the genetic variance of floral traits of the annual plant Mimulus guttatus into contributions of individual QTLs. We first use QTL-mapping to identify nine loci and then conduct a population-based breeding experiment to estimate V(Q), the genetic variance attributable to each QTL. We find that three QTLs with moderate effects explain up to one-third of the genetic variance in the natural population. Variation at these loci is probably maintained by some form of balancing selection. Notably, the largest effect QTLs were relatively minor in their contribution to heritability.     

Linkage analysis of quantitative traits in an interspecific cross of tomato (lycopersicon esculentum x lycopersicon pimpinellifolium) by means of genetic markers

Linkage relationships between loci affecting quantitative traits (QTL) and marker loci were examined in an interspecific cross between Lycopersicon esculentum and Lycopersicon pimpinellifolium. Parental lines differed for six morphological markers and for four electrophoretic markers. Almost 1700 F-2 plants were scored with respect to the genetic markers and also with respect to 18 quantitative traits. Major genes affecting the quantitative traits were not found, but out of 180 possible marker x trait combinations, 85 showed significant quantitative effects associated with the genetic markers. The average marker-associated main effect was on the order of 6% of the mean value of the trait. Most of the main effects were apparently due to linkage of QTL to the marker loci rather than to pleiotropy. Fourteen of the traits showed at least one highly significant effect of opposite sign to the overall difference between the parental lines, demonstrating the ability of this design to uncover cryptic genetic variation. Significant variance and skewness effects on the quantitative traits were found to be associated with the genetic markers, suggesting the possible presence of loci affecting the variance and shape of quantitative trait distribution in a population. Most marker-associated quantitative effects showed some degree of dominance, generally in the direction of the L. pimpinellifolium parent. When the significant marker-associated effects were examined in pairs, 12% showed significant interaction effects. The results of this study illustrate the potential usefulness of this type of analysis for the detailed genetic investigation of quantitative trait variation in suitably marked populations.     

An epistatic genetic basis for physical activity traits in mice

We recently identified several (4-8) quantitative trait loci (QTL) for 3 physical activity traits (daily distance, duration, and speed voluntarily run) in an F(2) population of mice derived from an original intercross of 2 strains that exhibited large differences in activity. These QTL cumulatively explained from 11% to 34% of the variation in these traits, but this was considerably less than their total genetic variability estimated from differences among inbred strains. We therefore decided to test whether epistatic interactions might account for additional genetic variation in these traits in this same population of mice. We conducted a full genome epistasis scan for all possible interactions of QTL between each pair of 20 chromosomes. The results of this scan revealed an abundance of epistasis, with QTL throughout the genome being involved in significant interactions. Overall, epistatic effects contributed an average of 26% of the total variation among the 3 activity traits. These results suggest that epistatic interactions of genes may play as important a role in the genetic architecture of physical activity traits as single-locus effects and need to be considered in future candidate gene identification studies.     

Quantitative trait loci analysis of nitrogen use efficiency in Arabidopsis

Improving plant nitrogen (N) use efficiency or controlling soil N requires a better knowledge of the regulation of plant N metabolism. This could be achieved using Arabidopsis as a model genetic system, taking advantage of the natural variation available among ecotypes. Here, we describe an extensive study of N metabolism variation in the Bay-0 x Shahdara recombinant inbred line population, using quantitative trait locus (QTL) mapping. We mapped QTL for traits such as shoot growth, total N, nitrate, and free-amino acid contents, measured in two contrasting N environments (contrasting nitrate availability in the soil), in controlled conditions. Genetic variation and transgression were observed for all traits, and most of the genetic variation was identified through QTL and QTL x QTL epistatic interactions. The 48 significant QTL represent at least 18 loci that are polymorphic between parents; some may correspond to known genes from the N metabolic pathway, but others represent new genes controlling or interacting with N physiology. The correlations between traits are dissected through QTL colocalizations: The identification of the individual factors contributing to the regulation of different traits sheds new light on the relations among these characters. We also point out that the regulation of our traits is mostly specific to the N environment (N availability). Finally, we describe four interesting loci at which positional cloning is feasible.     

Comparative analysis of genetic architectures for nine developmental traits of rye

Genetic architectures of plant height, stem thickness, spike length, awn length, heading date, thousand-kernel weight, kernel length, leaf area and chlorophyll content were aligned on the DArT-based high-density map of the 541 × Ot1–3 RILs population of rye using the genes interaction assorting by divergent selection (GIABDS) method. Complex sets of QTL for particular traits contained 1–5 loci of the epistatic D class and 10–28 loci of the hypostatic, mostly R and E classes controlling traits variation through D–E or D–R types of two-loci interactions. QTL were distributed on each of the seven rye chromosomes in unique positions or as a coinciding loci for 2–8 traits. Detection of considerable numbers of the reversed (D′, E′ and R′) classes of QTL might be attributed to the transgression effects observed for most of the studied traits. First examples of E* and F QTL classes, defined in the model, are reported for awn length, leaf area, thousand-kernel weight and kernel length. The results of this study extend experimental data to 11 quantitative traits (together with pre-harvest sprouting and alpha-amylase activity) for which genetic architectures fit the model of mechanism underlying alleles distribution within tails of bi-parental populations. They are also a valuable starting point for map-based search of genes underlying detected QTL and for planning advanced marker-assisted multi-trait breeding strategies.     

Connecting thermal performance curve variation to the genotype: a multivariate QTL approach

Thermal performance curves (TPCs) are continuous reaction norms that describe the relationship between organismal performance and temperature and are useful for understanding trade‐offs involved in thermal adaptation. Although thermal trade‐offs such as those between generalists and specialists or between hot‐ and cold‐adapted phenotypes are known to be genetically variable and evolve during thermal adaptation, little is known of the genetic basis to TPCs – specifically, the loci involved and the directionality of their effects across different temperatures. To address this, we took a multivariate approach, mapping quantitative trait loci (QTL) for locomotor activity TPCs in the fly, Drosophila serrata, using a panel of 76 recombinant inbred lines. The distribution of additive genetic (co)variance in the mapping population was remarkably similar to the distribution of mutational (co)variance for these traits. We detected 11 TPC QTL in females and 4 in males. Multivariate QTL effects were closely aligned with the major axes genetic (co)variation between temperatures; most QTL effects corresponded to variation for either overall increases or decreases in activity with a smaller number indicating possible trade‐offs between activity at high and low temperatures. QTL representing changes in curve shape such as the ‘generalist–specialist’ trade‐off, thought key to thermal adaptation, were poorly represented in the data. We discuss these results in the light of genetic constraints on thermal adaptation.     

Genetic determinants of obesity-related lipid traits

In our ongoing effort to identify genes influencing the biological pathways that underlie the metabolic disturbances associated with obesity, we performed genome-wide scanning in 2,209 individuals distributed over 507 Caucasian families to localize quantitative trait loci (QTLs), which affect variation of plasma lipids. Pedigree-based analysis using a quantitative trait variance component linkage method that localized a QTL on chromosome 7q35-q36, which linked to variation in levels of plasma triglyceride [TG, logarithm of odds (LOD) score = 3.7] and was suggestive of linkage to LDL-cholesterol (LDL-C, LOD = 2.2). Covariates of the TG linkage included waist circumference, fasting insulin, and insulin:glucose, but not body mass index or hip circumference. Plasma HDL-cholesterol (HDL-C) levels were suggestively linked to a second QTL on chromosome 12p12.3 (LOD = 2.6). Five other QTLs with lower LOD scores were identified for plasma levels of LDL-C, HDL-C, and total cholesterol. These newly identified loci likely harbor genetic elements that influence traits underlying lipid adversities associated with obesity.     

Mutation-Selection Balance and Metabolic Control Theory

The evolution of metabolic control is examined with models that unify approaches of classical quantitative genetics and metabolic control theory. The quantitative traits considered are the activities of enzymes embedded within metabolic pathways. In the models, polygenic mutation alters the enzyme activities (Vmax/Km) according to prescribed distributions, and the population evolves following classical haploid viability selection. Stabilizing selection operates on global properties of the metabolic pathway, including either flux or metabolite pool concentration. Analytical results and numerical simulations demonstrate several important properties of these characters, including skewed, non-Gaussian equilibrium distributions, and an expected positive correlation between activities of enzymes flanking a substrate pool undergoing stabilizing selection. The house-of-cards approximation proved to be accurate in predicting the equilibrium distribution of allelic effects for a biologically reasonable segment of the parameter space. Further experimental and theoretical work is needed before a clear assessment can be made whether the observed variance in enzyme activities is explicable by a mutation-selection balance, and this system provides an excellent opportunity for such a test.     

植物数量性状变异的分子基础与QTL克隆研究进展

探讨数量性状变异规律以便对其进行遗传操纵一直是植物遗传学的一个重要领域。DNA分子标记和QTL作图技术的发展以及拟南芥和水稻全基因组测序的完成极大地促进了植物数量性状分子基础的研究。现已克隆了拟南芥ED1、水稻Hdl、玉米Tb1、番茄fw2．2和Brii9-2-5等控制目标数量性状的基因。数量性状表型变异不仅源于多个数量性状基因（QTL）的分离．而且还受到内外环境的修饰。QTL等位基因变异与孟德尔基因变异具有类似的分子基础,即基因表达或蛋白质功能发生改变。通过分析已克隆的植物QTL的变异特征及分子基础,讨论了植物QTL克隆技术策略,并对QTL研究所面临的挑战和应用前景进行了展望。     

Identification of quantitative trait loci controlling winter hardiness in an annual × perennial ryegrass interspecific hybrid population

Winter hardiness is a quantitative trait and the lack of it limits geographic distribution of ryegrass. Improving winter hardiness is an important breeding goal in ryegrass breeding programs. An understanding of the genetic basis for the component traits of winter hardiness would allow more efficient selection. A three-generation interspecific population of an annual × perennial ryegrass consisting of 152 progenies was used to map quantitative trait loci (QTL) that control winter hardiness-related traits including fall growth (FG), freezing tolerance (FT), and winter survival (WS) over 2 years. A total of 39 QTL were identified for the three traits from both the female parental (MFA) and the male parental (MFB) maps, of which 13 were for FG, 6 for FT, and 20 for WS. The proportion of phenotypic variation explained by individual QTL ranged from 10.4 to 22.1%. Both FG and FT were positively correlated with WS. Common QTL were detected between FG, FT, and WS. The QTL associated with WS on linkage groups (LGs) 4 and 5, and the QTL for FT on LG 5 were consistently identified over years and maps. These consistent QTL might serve as potential tools for marker-assisted selection to improve ryegrass winter hardiness.     

Quantitative trait loci variation for growth and obesity between and within lines of pigs (Sus scrofa)

The hypothesis that quantitative trait loci (QTL) that explain variation between divergent populations also account for genetic variation within populations was tested using pig populations. Two regions of the porcine genome that had previously been reported to harbor QTL with allelic effects that differed between the modern pig and its wild-type ancestor and between the modern pig and a more distantly related population of Asian pigs were studied. QTL for growth and obesity traits were mapped using selectively genotyped half-sib families from five domesticated modern populations. Strong support was found for at least one QTL segregating in each population. For all five populations there was evidence of a segregating QTL affecting fatness in a region on chromosome 7. These findings confirm that QTL can be detected in highly selected commercial populations and are consistent with the hypothesis that the same chromosome locations that account for variation between populations also explain genetic variation within populations.     

Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory.

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance-covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t - 1 implies the generation of episodes of new genetic variation arising during the interval t - 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Optimisation of Enzyme Concentrations for Unbranched Reaction Chains: The Concept of Combined Response Coefficient

In the metabolic control theory, the control coefficient is a key parameter in quantifying the sensitivity of the flux towards an infinitesimal variation of enzyme activity. This concept does not apply just as it is for variations of enzyme concentrations whenever there is spatial, energy or resources limitations in the cell. Due to constraint on total enzyme concentration, the variation of concentration of any given enzyme may affect the concentrations of other enzymes. To take into account these correlations between enzyme concentrations, we propose the concept of "combined response coefficient". Its definition is similar to that of the control coefficient, but its mathematical expression is different. Its range of variation is from – + 1, the null value corresponding to optimum enzyme concentration, i.e. to concentrations that maximise the flux, and the negative values to concentrations beyond the optimum value. A summation property could be derived using a simple weighting of the combined response coefficients, the sum of the weighed coefficient being 0.     

Fine quantitative trait loci mapping of carbon and nitrogen metabolism enzyme activities and seedling biomass in the maize IBM mapping population

Understanding the genetic basis of nitrogen and carbon metabolism will accelerate the development of plant varieties with high yield and improved nitrogen use efficiency. A robotized platform was used to measure the activities of 10 enzymes from carbon and nitrogen metabolism in the maize (Zea mays) intermated B73 × Mo17 mapping population, which provides almost a 4-fold increase in genetic map distance compared with conventional mapping populations. Seedling/juvenile biomass was included to identify its genetic factors and relationships with enzyme activities. All 10 enzymes showed heritable variation in activity. There were strong positive correlations between activities of different enzymes, indicating that they are coregulated. Negative correlations were detected between biomass and the activity of six enzymes. In total, 73 significant quantitative trait loci (QTL) were found that influence the activity of these 10 enzymes and eight QTL that influence biomass. While some QTL were shared by different enzymes or biomass, we critically evaluated the probability that this may be fortuitous. All enzyme activity QTL were in trans to the known genomic locations of structural genes, except for single cis-QTL for nitrate reductase, Glu dehydrogenase, and shikimate dehydrogenase; the low frequency and low additive magnitude compared with trans-QTL indicate that cis-regulation is relatively unimportant versus trans-regulation. Two-gene epistatic interactions were identified for eight enzymes and for biomass, with three epistatic QTL being shared by two other traits; however, epistasis explained on average only 2.8% of the genetic variance. Overall, this study identifies more QTL at a higher resolution than previous studies of genetic variation in metabolism.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Matrix method for determining steps most rate-limiting to metabolic fluxes in biotechnological processes

The metabolic control theory developed by Kacser, Burns, Heinrich, and Rapoport is briefly outlined, extended, and transformed so as optimally to address some biotechnological questions. The extensions include (i) a new theorem that relates the control of metabolite concentrations by enzyme activities to flux ratios at branches in metabolic pathways; (ii) a new theorem that does the same for the control of the distribution of the flux over two branches; (iii) a method that expresses these controls into properties (the so-called elasticity coefficients) of the enzymes in the pathway; and (iv) a theorem that relates the effects of changes in metabolite concentrations on reaction rates to the effects of changes in enzyme properties on the same rates. Matrix equations relating the flux control and concentration control coefficients to the elasticity coefficients of enzymes in simple linear and branched pathways incorporating feedback are given, together with their general solutions and a numerical example. These equations allow one to develop rigorous criteria by which to decide the optimal strategy for the improvement of a microbial process. We show how this could be used in deciding which property of which enzyme should be changed in order to obtain the maximal concentration of a metabolite or the maximal metabolic flux.