Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Pareto Local Optima of Multiobjective NK-Landscapes with Correlated Objectives

International audienceIn this paper, we conduct a fitness landscape analysis for multiobjective combinatorial optimization, based on the local optima of multiobjective NK-landscapes with objective correlation. In single-objective optimization, it has become clear that local optima have a strong impact on the performance of metaheuristics. Here, we propose an extension to the multiobjective case, based on the Pareto dominance. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives and the correlation degree between objective functions on the number of Pareto local optima

A new mapping method for quantitative trait loci of silkworm

<p>Abstract</p> <p>Background</p> <p>Silkworm is the basis of sericultural industry and the model organism in insect genetics study. Mapping quantitative trait loci (QTLs) underlying economically important traits of silkworm is of high significance for promoting the silkworm molecular breeding and advancing our knowledge on genetic architecture of the Lepidoptera. Yet, the currently used mapping methods are not well suitable for silkworm, because of ignoring the recombination difference in meiosis between two sexes.</p> <p>Results</p> <p>A mixed linear model including QTL main effects, epistatic effects, and QTL × sex interaction effects was proposed for mapping QTLs in an F₂population of silkworm. The number and positions of QTLs were determined by <it>F</it>-test and model selection. The Markov chain Monte Carlo (MCMC) algorithm was employed to estimate and test genetic effects of QTLs and QTL × sex interaction effects. The effectiveness of the model and statistical method was validated by a series of simulations. The results indicate that when markers are distributed sparsely on chromosomes, our method will substantially improve estimation accuracy as compared to the normal chiasmate F₂model. We also found that a sample size of hundreds was sufficiently large to unbiasedly estimate all the four types of epistases (i.e., additive-additive, additive-dominance, dominance-additive, and dominance-dominance) when the paired QTLs reside on different chromosomes in silkworm.</p> <p>Conclusion</p> <p>The proposed method could accurately estimate not only the additive, dominance and digenic epistatic effects but also their interaction effects with sex, correcting the potential bias and precision loss in the current QTL mapping practice of silkworm and thus representing an important addition to the arsenal of QTL mapping tools.</p

Nonlinear regulation enhances the phenotypic expression of trans-acting genetic polymorphisms

<p>Abstract</p> <p>Background</p> <p>Genetic variation explains a considerable part of observed phenotypic variation in gene expression networks. This variation has been shown to be located both locally (<it>cis</it>) and distally (<it>trans</it>) to the genes being measured. Here we explore to which degree the phenotypic manifestation of local and distant polymorphisms is a dynamic feature of regulatory design.</p> <p>Results</p> <p>By combining mathematical models of gene expression networks with genetic maps and linkage analysis we find that very different network structures and regulatory motifs give similar <it>cis</it>/<it>trans </it>linkage patterns. However, when the shape of the <it>cis-</it>regulatory input functions is more nonlinear or threshold-like, we observe for all networks a dramatic increase in the phenotypic expression of distant compared to local polymorphisms under otherwise equal conditions.</p> <p>Conclusion</p> <p>Our findings indicate that genetic variation affecting the form of <it>cis</it>-regulatory input functions may reshape the genotype-phenotype map by changing the relative importance of <it>cis </it>and <it>trans </it>variation. Our approach combining nonlinear dynamic models with statistical genetics opens up for a systematic investigation of how functional genetic variation is translated into phenotypic variation under various systemic conditions.</p

Combining growth-promoting genes leads to positive epistasis in Arabidopsis thaliana

Several genes have been described to positively influence final leaf size in Arabidopsis when mutated or overexpressed. However, the connections between these growth regulating genes are still poorly understood. Clearly such knowledge would significantly contribute to understand the biological processes driving leaf growth. In this study, we performed a combinatorial screen with thirteen transgenic Arabidopsis lines with an increased leaf size. Surprisingly, we found that from 61 analyzed combinations, 39% showed an additional increase in leaf size and most of these resulted from a positive epistasis on growth. Similar to what is found in other organisms in which such an epistasis assay was performed, only few genes were highly connected in synergistic combinations. We also observed a positive epistasis in the majority of the combinations with samba, BR11(OE) or SAUR19(OE), suggesting that these growth regulators are more prone to lead to synergistic effects in binary combinations. Furthermore, positive epistasis was not only found with combinations of genes with a similar mode of action, but also with genes which affect distinct processes, such as cell proliferation and cell expansion

Two-Stage Two-Locus Models in Genome-Wide Association

Studies in model organisms suggest that epistasis may play an important role in the etiology of complex diseases and traits in humans. With the era of large-scale genome-wide association studies fast approaching, it is important to quantify whether it will be possible to detect interacting loci using realistic sample sizes in humans and to what extent undetected epistasis will adversely affect power to detect association when single-locus approaches are employed. We therefore investigated the power to detect association for an extensive range of two-locus quantitative trait models that incorporated varying degrees of epistasis. We compared the power to detect association using a single-locus model that ignored interaction effects, a full two-locus model that allowed for interactions, and, most important, two two-stage strategies whereby a subset of loci initially identified using single-locus tests were analyzed using the full two-locus model. Despite the penalty introduced by multiple testing, fitting the full two-locus model performed better than single-locus tests for many of the situations considered, particularly when compared with attempts to detect both individual loci. Using a two-stage strategy reduced the computational burden associated with performing an exhaustive two-locus search across the genome but was not as powerful as the exhaustive search when loci interacted. Two-stage approaches also increased the risk of missing interacting loci that contributed little effect at the margins. Based on our extensive simulations, our results suggest that an exhaustive search involving all pairwise combinations of markers across the genome might provide a useful complement to single-locus scans in identifying interacting loci that contribute to moderate proportions of the phenotypic variance

Evidence for Non-additive Influence of Single Nucleotide Polymorphisms within the Apolipoprotein E Gene

We analyzed 13 single nucleotide polymorphisms (SNPs) within the apolipoprotein E ( APOE ) gene, to identify pairs of SNPs that interact in a non-additive manner to influence genotypic mean levels of the ApoE protein in blood. An overparameterized general linear model of two-SNP genotype means was applied to data from 456 female and 398 male unrelated European Americans from Rochester, MN, USA. We found statistically significant evidence for non-additivity between SNPs within the male sample, but not within the female sample. We observed nine pairs of SNPs with evidence of non-additivity at the Α= 0.05 level of statistical significance within the male sample, when approximately three were expected by chance. Five of the nine pairs involved three SNPs (560, 624 and 1163) that did not have a statistically significant influence when considered separately in a single-site analysis. Three of the nine pairs involving four SNPs (832, 1998, 3937 and 4951) showed significant evidence for non-additivity in at least one of two other male samples from Jackson, MS, USA and North Karelia, Finland. Although all four of these SNPs had a statistically significant influence in Rochester when considered separately, only SNP 3937 gave a significant result in the other male samples. The four SNPs are located in the promoter, intronic and exonic regions, and 3' to the polyadenylation signal in the APOE gene. Our study suggests that analyses that only consider SNPs located in exons and ignore contexts such as those indexed by gender and population, and disregard non-additivity of SNP effects, may inappropriately model the contribution of a gene to the genetic architecture of a trait that has a complex multifactorial etiology.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65641/1/j.1529-8817.2003.00112.x.pd

Epistasis in a Model of Molecular Signal Transduction

Biological functions typically involve complex interacting molecular networks, with numerous feedback and regulation loops. How the properties of the system are affected when one, or several of its parts are modified is a question of fundamental interest, with numerous implications for the way we study and understand biological processes and treat diseases. This question can be rephrased in terms of relating genotypes to phenotypes: to what extent does the effect of a genetic variation at one locus depend on genetic variation at all other loci? Systematic quantitative measurements of epistasis – the deviation from additivity in the effect of alleles at different loci – on a given quantitative trait remain a major challenge. Here, we take a complementary approach of studying theoretically the effect of varying multiple parameters in a validated model of molecular signal transduction. To connect with the genotype/phenotype mapping we interpret parameters of the model as different loci with discrete choices of these parameters as alleles, which allows us to systematically examine the dependence of the signaling output – a quantitative trait – on the set of possible allelic combinations. We show quite generally that quantitative traits behave approximately additively (weak epistasis) when alleles correspond to small changes of parameters; epistasis appears as a result of large differences between alleles. When epistasis is relatively strong, it is concentrated in a sparse subset of loci and in low order (e.g. pair-wise) interactions. We find that focusing on interaction between loci that exhibit strong additive effects is an efficient way of identifying most of the epistasis. Our model study defines a theoretical framework for interpretation of experimental data and provides statistical predictions for the structure of genetic interaction expected for moderately complex biological circuits

Towards higher predictability in enzyme engineering : investigation of protein epistasis in dynamic ß-lactamases and Cal-A lipase

L'ingénierie enzymatique est un outil très avantageux dans l'industrie biotechnologique. Elle permet d'adapter les enzymes à une activité ou à une condition de réaction spécifique. En outre, elle peut permettre de déchiffrer les éléments clés qui ont facilité leur modification. Bien que l'ingénierie enzymatique soit largement pratiquée, elle comporte encore plusieurs goulets d'étranglement. Certains de ces goulets d'étranglement sont techniques, comme le développement de méthodologies pour la création de banques de mutations ciblées ou la réalisation de criblages à haut débit, et d'autres sont conceptuels, comme le déchiffrage des caractéristiques clés pertinentes d'une protéine cible pour la réussite d'un projet d'ingénierie. Parmi ces défis, l'épistasie intra-génique, ou la non-additivité des effets phénotypiques des mutations, est une caractéristique qui entrave grandement la prévisibilité. L'amélioration de l'ingénierie enzymatique nécessite une approche multidisciplinaire qui inclut une meilleure compréhension des relations structure-fonction-évolution. Cette thèse vise à contribuer à l'avancement de l'ingénierie enzymatique en étudiant deux systèmes modèles. Premièrement, des variantes dynamiques de la ß-lactamase TEM-1 ont été choisies pour étudier le lien entre la dynamique des protéines et l'évolution. La ß-lactamase TEM-1 a été largement caractérisée dans la littérature, ce qui s'est traduit par des connaissances approfondies sur son mécanisme de réaction, ses caractéristiques structurelles et son évolution. Les variantes de la ß-lactamase TEM-1 utilisées comme système modèle dans cette thèse ont été largement caractérisées, montrant une dynamique accrue à l'échelle temporelle pertinente pour la catalyse (µs à ms) mais maintenant la reconnaissance du substrat. Dans cette thèse, l'évolution in vitro de ces variantes dynamiques a été réalisée par des cycles itératifs de mutagenèse et de sélection aléatoires pour permettre une exploration impartiale du paysage de ‘fitness’. Nous démontrons que la présence de ces mouvements particuliers au début de l'évolution a permis d'accéder à des voies de mutations connues. De plus, des interactions épistatiques connues ont été introduites dans les variantes dynamiques. Leur caractérisation in silico et cinétique a révélé que les mouvements supplémentaires sur l'échelle de temps de la catalyse ont permis d'accéder à des conformations conduisant à une fonction améliorée, comme dans le TEM-1 natif. Dans l'ensemble, nous démontrons que l'évolution de la b-lactamase TEM-1 vers une nouvelle fonction est compatible avec divers mouvements à l'échelle de temps µs à ms. Il reste à savoir si cela peut se traduire par d'autres enzymes ayant un potentiel biotechnologique. Deuxièmement, la lipase Cal-A, pertinente sur le plan industriel, a été choisie pour identifier les caractéristiques qui pourraient faciliter son ingénierie. La lipase Cal-A présente des caractéristiques telles que la polyvalence du substrat et une grande stabilité thermique et réactivité qui la rendent attrayante pour la modification des triglycérides ou la synthèse de molécules pertinentes dans les industries alimentaire et pharmaceutique. Contrairement à TEM-1, la plupart des études d'évolution in vitro de la lipase Cal-A ont été réalisées dans un but industriel, avec une exploration limitée de l'espace de mutation. Par conséquent, les caractéristiques qui définissent la fonction de la lipase Cal-A restent insaisissables. Dans cette thèse, nous faisons état de la mutagenèse ciblée de la lipase Cal-A, confirmant l'existence d'une région clé pour la reconnaissance du substrat. Cela a été fait en combinant une nouvelle méthodologie de création de bibliothèque basée sur l'assemblage Golden-gate avec une visualisation structurelle basée sur des scripts pour identifier et cartographier les mutations sélectionnées dans la structure 3D. La caractérisation et la déconvolution de deux des plus aptes ont révélé l'existence d'une épistasie dans l'évolution de la lipase Cal-A vers une nouvelle fonction. Dans l'ensemble, nous démontrons que l’identification d'une variété de propriétés suite à la mutagenèse ciblée peut grandement améliorer la connaissance d'une enzyme. Cette information peut être appliquée pour améliorer l'efficacité de l'ingénierie dirigée.Enzyme engineering is a tool with great utility in the biotechnological industry. It allows to tailor enzymes to a specific activity or reaction condition. In addition, it can allow to decipher key elements that facilitated their modification. While enzyme engineering is extensively practised, it still entails several bottlenecks. Some of these bottlenecks are technical such as the development of methodologies for creating targeted mutational libraries or performing high-throughput screening and some are conceptual such as deciphering the key relevant features in a target protein for a successful engineering project. Among these challenges, intragenic epistasis, or the non-additivity of the phenotypic effects of mutations, is a feature that greatly hinders predictability. Improving enzyme engineering needs a multidisciplinary approach that includes gaining a better understanding of structure-function-evolution relations. This thesis seeks to contribute in the advancement of enzyme engineering by investigating two model systems. First, dynamic variants of TEM-1 ß-lactamase were chosen to investigate the link between protein dynamics and evolution. TEM-1 ß-lactamase has been extensively characterized in the literature, which has translated into extensive knowledge on its reaction mechanism, structural features and evolution. The variants of TEM-1 ß-lactamase used as model system in this thesis had been extensively characterized, showing increased dynamics at the timescale relevant to catalysis (µs to ms) but maintaining substrate recognition. In this thesis, in vitro evolution of these dynamic variants was done by iterative rounds of random mutagenesis and selection to allow an unbiased exploration of the fitness landscape. We demonstrate that the presence of these particular motions at the outset of evolution allowed access to known mutational pathways. In addition, known epistatic interactions were introduced in the dynamic variants. Their in silico and kinetic characterization revealed that the additional motions on the timescale of catalysis allowed access to conformations leading to enhanced function, as in native TEM-1. Overall, we demonstrate that the evolution of TEM-1 b-lactamase toward new function is compatible with diverse motions at the µs to ms timescale. Whether this can be translated to other enzymes with biotechnological potential remains to be explored. Secondly, the industrially relevant Cal-A lipase was chosen to identify features that could facilitate its engineering. Cal-A lipase presents characteristics such as substrate versatility and high thermal stability and reactivity that make it attractive for modification of triglycerides or synthesis of relevant molecules in the food and pharmaceutical industries. Contrary to TEM-1, most in vitro evolution studies of Cal-A lipase have been done towards an industrially-specified goal, with limited exploration of mutational space. As a result, features that define function in Cal-A lipase remain elusive. In this thesis, we report on focused mutagenesis of Cal-A lipase, confirming the existence of a key region for substrate recognition. This was done by combining a novel library creation methodology based on Golden-gate assembly with script-based structural visualization to identify and map the selected mutations into the 3D structure. The characterization and deconvolution of two of the fittest revealed the existence of epistasis in the evolution of Cal-A lipase towards new function. Overall, we demonstrate that mapping a variety of properties following mutagenesis targeted to specific regions can greatly improve knowledge of an enzyme that can be applied to improve the efficiency of directed engineering