Effects of causal networks on the structure and stability of resource allocation trait correlations

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval [Formula: see text] and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.

The Wright stuff: reimagining path analysis reveals novel components of the sex determination hierarchy in Drosophila melanogaster

BACKGROUND

The Drosophila sex determination hierarchy is a classic example of a transcriptional regulatory hierarchy, with sex-specific isoforms regulating morphology and behavior. We use a structural equation modeling approach, leveraging natural genetic variation from two studies on Drosophila female head tissues--DSPR collection (596 F1-hybrids from crosses between DSPR sub-populations) and CEGS population (75 F1-hybrids from crosses between DGRP/Winters lines to a reference strain w1118)--to expand understanding of the sex hierarchy gene regulatory network (GRN). This approach is completely generalizable to any natural population, including humans.

RESULTS

We expanded the sex hierarchy GRN adding novel links among genes, including a link from fruitless (fru) to Sex-lethal (Sxl) identified in both populations. This link is further supported by the presence of fru binding sites in the Sxl locus. 754 candidate genes were added to the pathway, including the splicing factors male-specific lethal 2 and Rm62 as downstream targets of Sxl which are well-supported links in males. Independent studies of doublesex and transformer mutants support many additions, including evidence for a link between the sex hierarchy and metabolism, via Insulin-like receptor.

CONCLUSIONS

The genes added in the CEGS population were enriched for genes with sex-biased splicing and components of the spliceosome. A common goal of molecular biologists is to expand understanding about regulatory interactions among genes. Using natural alleles we can not only identify novel relationships, but using supervised approaches can order genes into a regulatory hierarchy. Combining these results with independent large effect mutation studies, allows clear candidates for detailed molecular follow-up to emerge.

Complex genetic effects on early vegetative development shape resource allocation differences between Arabidopsis lyrata populations

Costs of reproduction due to resource allocation trade-offs have long been recognized as key forces in life history evolution, but little is known about their functional or genetic basis. Arabidopsis lyrata, a perennial relative of the annual model plant A. thaliana with a wide climatic distribution, has populations that are strongly diverged in resource allocation. In this study, we evaluated the genetic and functional basis for variation in resource allocation in a reciprocal transplant experiment, using four A. lyrata populations and F2 progeny from a cross between North Carolina (NC) and Norway parents, which had the most divergent resource allocation patterns. Local alleles at quantitative trait loci (QTL) at a North Carolina field site increased reproductive output while reducing vegetative growth. These QTL had little overlap with flowering date QTL. Structural equation models incorporating QTL genotypes and traits indicated that resource allocation differences result primarily from QTL effects on early vegetative growth patterns, with cascading effects on later vegetative and reproductive development. At a Norway field site, North Carolina alleles at some of the same QTL regions reduced survival and reproductive output components, but these effects were not associated with resource allocation trade-offs in the Norway environment. Our results indicate that resource allocation in perennial plants may involve important adaptive mechanisms largely independent of flowering time. Moreover, the contributions of resource allocation QTL to local adaptation appear to result from their effects on developmental timing and its interaction with environmental constraints, and not from simple models of reproductive costs.

Paths to selection on life history loci in different natural environments across the native range of Arabidopsis thaliana

Selection on quantitative trait loci (QTL) may vary among natural environments due to differences in the genetic architecture of traits, environment-specific allelic effects or changes in the direction and magnitude of selection on specific traits. To dissect the environmental differences in selection on life history QTL across climatic regions, we grew a panel of interconnected recombinant inbred lines (RILs) of Arabidopsis thaliana in four field sites across its native European range. For each environment, we mapped QTL for growth, reproductive timing and development. Several QTL were pleiotropic across environments, three colocalizing with known functional polymorphisms in flowering time genes (CRY2, FRI and MAF2-5), but major QTL differed across field sites, showing conditional neutrality. We used structural equation models to trace selection paths from QTL to lifetime fitness in each environment. Only three QTL directly affected fruit number, measuring fitness. Most QTL had an indirect effect on fitness through their effect on bolting time or leaf length. Influence of life history traits on fitness differed dramatically across sites, resulting in different patterns of selection on reproductive timing and underlying QTL. In two oceanic field sites with high prereproductive mortality, QTL alleles contributing to early reproduction resulted in greater fruit production, conferring selective advantage, whereas alleles contributing to later reproduction resulted in larger size and higher fitness in a continental site. This demonstrates how environmental variation leads to change in both QTL effect sizes and direction of selection on traits, justifying the persistence of allelic polymorphism at life history QTL across the species range.

The many faces of pleiotropy

Pleiotropy is the well-established phenomenon of a single gene affecting multiple traits. It has long played a central role in theoretical, experimental, and clinical research in genetics, development, molecular biology, evolution, and medicine. In recent years, genomic techniques have brought data to bear on fundamental questions about the nature and extent of pleiotropy. However, these efforts are plagued by conceptual difficulties derived from disparate meanings and interpretations of pleiotropy. Here, we describe distinct uses of the pleiotropy concept and explain the pitfalls associated with applying empirical data to them. We conclude that, for any question about the nature or extent of pleiotropy, the appropriate answer is always 'What do you mean?'.