So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Genetics and analysis of quantitative traits

Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages of ADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.

/pdf/ad-model-builder-using-automatic-differentiation-for-18b5wunetc.pdf

AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

A positive temperature coefficient is the term which has been used to indicate that an increase in solubility occurs as the temperature is raised, whereas a negative coefficient indicates a decrease in solubility with rise in temperature.

Effect of Temperature

Repetitive DNA sequences are abundant in a broad range of species, from bacteria to mammals, and they cover nearly half of the human genome. Repeats have always presented technical challenges for sequence alignment and assembly programs. Next-generation sequencing projects, with their short read lengths and high data volumes, have made these challenges more difficult. From a computational perspective, repeats create ambiguities in alignment and assembly, which, in turn, can produce biases and errors when interpreting results. Simply ignoring repeats is not an option, as this creates problems of its own and may mean that important biological phenomena are missed. We discuss the computational problems surrounding repeats and describe strategies used by current bioinformatics systems to solve them.

https://www.csie.ntu.edu.tw/~kmchao/bioinformatics12spr/presentation/Report_20120604%236.pdf

Repetitive DNA and next-generation sequencing: computational challenges and solutions.

Predicting how a genetic change affects a given character is a major challenge in biology, and being able to tackle this problem relies on our ability to develop realistic models of gene networks. However, such models are rarely tractable mathematically. In this paper, we propose a mathematical analysis of the sigmoid variant of the Wagner gene-network model. By considering the simplest case, that is, one unique self-regulating gene, we show that numerical simulations are not the only tool available to study such models: theoretical studies can be done too, by mathematical analysis of discrete dynamical systems. It is first shown that the particular sigmoid function can be theoretically investigated. Secondly, we provide an illustration of how to apply such investigations in the case of the dynamical system representing the one self-regulating gene. In this context, we focused on the composite function f a ( m . x ) where f a is the parametric sigmoid function and m is a scalar not in { 0 , 1 } and we have proven that the number of fixed-point can be deduced theoretically, according to the values of a and m.

https://hal.archives-ouvertes.fr/hal-02155175/document

Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model

Robustness to genetic or environmental disturbances is often considered as a key property of living systems. Yet, in spite of being discussed since the 1950s, how robustness emerges from the complexity of genetic architectures and how it evolves still remains unclear. In particular, whether or not robustness to various sources of perturbations is independent conditions the range of adaptive scenarios that can be considered. For instance, selection for robustness to heritable mutations is likely to be modest and indirect, and its evolution might result from indirect selection on a pleiotropically-related character (e.g., homeostasis) rather than adaptation. Here, I propose to treat various robustness measurements as quantitative characters, and study theoretically, by individual-based simulations, their propensity to evolve independently. Based on a simple evolutionary model of a gene regulatory network, I showed that different ways to measure the robustness of gene expression to genetic or non-genetic disturbances were substantially correlated. Yet, robustness was evolvable in several dimensions, and robustness components could evolve differentially under direct selection pressure. Therefore, the fact that the sensitivity of gene expression to e.g. mutations and environmental factors rely on the same gene networks does not preclude that robustness components may have distinct evolutionary histories.

Gene network robustness as a multivariate character

Glycolysis and fatty acid (FA) synthesis directs the production of energy-carrying molecules and building blocks necessary to support cell growth, although the absolute requirement of these metabolic pathways must be deeply investigated. Here, we used Drosophila genetics and focus on the TOR (Target of Rapamycin) signaling network that controls cell growth and homeostasis. In mammals, mTOR (mechanistic-TOR) is present in two distinct complexes, mTORC1 and mTORC2; the former directly responds to amino acids and energy levels, whereas the latter sustains insulin-like-peptide (Ilp) response. The TORC1 and Ilp signaling branches can be independently modulated in most Drosophila tissues. We show that TORC1 and Ilp-dependent overgrowth can operate independently in fat cells and that ubiquitous over-activation of TORC1 or Ilp signaling affects basal metabolism, supporting the use of Drosophila as a powerful model to study the link between growth and metabolism. We show that cell-autonomous restriction of glycolysis or FA synthesis in fat cells retrains overgrowth dependent on Ilp signaling but not TORC1 signaling. Additionally, the mutation of FASN (Fatty acid synthase) results in a drop in TORC1 but not Ilp signaling, whereas, at the cell-autonomous level, this mutation affects none of these signals in fat cells. These findings thus reveal differential metabolic sensitivity of TORC1- and Ilp-dependent growth and suggest that cell-autonomous metabolic defects might elicit local compensatory pathways. Conversely, enzyme knockdown in the whole organism results in animal death. Importantly, our study weakens the use of single inhibitors to fight mTOR-related diseases and strengthens the use of drug combination and selective tissue-targeting.

Differential metabolic sensitivity of insulin-like-response- and TORC1-dependent overgrowth in Drosophila fat cells

Robustness to genetic or environmental disturbances is often considered as a key property of living systems. Yet, in spite of being discussed since the 1950s, how robustness emerges from the complexity of genetic architectures and how it evolves still remains unclear. In particular, whether or not robustness to various sources of perturbations is independent conditions the range of adaptive scenarios that can be considered. For instance, selection for robustness to heritable mutations is likely to be modest and indirect, and its evolution might result from indirect selection on a pleiotropically-related character (e.g., homeostasis) rather than adaptation. Here, I propose to treat various robustness measurements as quantitative characters, and study theoretically, by individual-based simulations, their propensity to evolve independently. Based on a simple evolutionary model of a gene regulatory network, I showed that different ways to measure the robustness of gene expression to genetic or non-genetic disturbances were substantially correlated. Yet, robustness was evolvable in several dimensions, and robustness components could evolve differentially under direct selection pressure. Therefore, the fact that the sensitivity of gene expression to e.g. mutations and environmental factors rely on the same gene networks does not preclude that robustness components may have distinct evolutionary histories. 

In many studies, related individuals are phenotyped in order to infer how their genotype contributes to their phenotype, through the estimation of parameters such as breeding values or locus effects. When it is not possible to phenotype all the individuals, it is important to properly sample the population to improve the precision of the statistical analysis. This article studies how to optimize such sampling designs for pedigrees and association studies. Two sampling methods are developed, stratified sampling and D optimality. It is found that it is important to take account of mutation when sampling pedigrees with many generations: as the size of mutation effects increases, optimized designs sample more individuals in late generations. Optimized designs for association studies tend to improve the joint estimation of breeding values and locus effects, all the more as sample size is low and the genetic architecture of the trait is simple. When the trait is determined by few loci, they are reminiscent of classical experimental designs for regression models and tend to select homozygous individuals. When the trait is determined by many loci, locus effects may be difficult to estimate, even if an optimized design is used.

Arnaud Le Rouzic

Papers

Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model

Gene network robustness as a multivariate character

Differential metabolic sensitivity of insulin-like-response- and TORC1-dependent overgrowth in Drosophila fat cells

Gene network robustness as a multivariate character

Optimization of sampling designs for pedigrees and association studies