Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Multilevel modelling for inference of genetic regulatory networks

Time-course experiments with microarrays are often used to study dynamic biological systems and genetic regulatory networks (GRNs) that model how genes influence each other in cell-level development of organisms. The inference for GRNs provides important insights into the fundamental biological processes such as growth and is useful in disease diagnosis and genomic drug design. Due to the experimental design, multilevel data hierarchies are often present in time-course gene expression data. Most existing methods, however, ignore the dependency of the expression measurements over time and the correlation among gene expression profiles. Such independence assumptions violate regulatory interactions and can result in overlooking certain important subject effects and lead to spurious inference for regulatory networks or mechanisms. In this paper, a multilevel mixed-effects model is adopted to incorporate data hierarchies in the analysis of time-course data, where temporal and subject effects are both assumed to be random. The method starts with the clustering of genes by fitting the mixture model within the multilevel random-effects model framework using the expectation-maximization (EM) algorithm. The network of regulatory interactions is then determined by searching for regulatory control elements (activators and inhibitors) shared by the clusters of co-expressed genes, based on a time-lagged correlation coefficients measurement. The method is applied to two real time-course datasets from the budding yeast (Saccharomyces cerevisiae) genome. It is shown that the proposed method provides clusters of cell-cycle regulated genes that are supported by existing gene function annotations, and hence enables inference on regulatory interactions for the genetic network.

Steady-state expression of self-regulated genes.

MOTIVATION: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of appropriate behavior. The lack of precise knowledge on the steady-state distribution of gene expression requires the use of Gillespie algorithms and Monte-Carlo approximations. METHODOLOGY: In this study, we provide new exact formulas and efficient numerical algorithms for computing/modeling the steady-state of a class of self-regulated genes, and we use it to model/compute the stochastic expression of a gene of interest in an engineered network introduced in mammalian cells. The behavior of the genetic network is then analyzed experimentally in living cells. RESULTS: Stochastic models often reveal counter-intuitive experimental behaviors, and we find that this genetic architecture displays a unimodal behavior in mammalian cells, which was unexpected given its known bimodal response in unicellular organisms. We provide a molecular rationale for this behavior, and we implement it in the mathematical picture to explain the experimental results obtained from this network.

Measuring the diurnal pattern of leaf hyponasty and growth in Arabidopsis - a novel phenotyping approach using laser scanning

Plants forming a rosette during their juvenile growth phase, such as Arabidopsis thaliana (L.) Heynh., are able to adjust the size, position and orientation of their leaves. These growth responses are under the control of the plants circadian clock and follow a characteristic diurnal rhythm. For instance, increased leaf elongation and hyponasty - defined here as the increase in leaf elevation angle - can be observed when plants are shaded. Shading can either be caused by a decrease in the fluence rate of photosynthetically active radiation (direct shade) or a decrease in the fluence rate of red compared with far-red radiation (neighbour detection). In this paper we report on a phenotyping approach based on laser scanning to measure the diurnal pattern of leaf hyponasty and increase in rosette size. In short days, leaves showed constitutively increased leaf elevation angles compared with long days, but the overall diurnal pattern and the magnitude of up and downward leaf movement was independent of daylength. Shade treatment led to elevated leaf angles during the first day of application, but did not affect the magnitude of up and downward leaf movement in the following day. Using our phenotyping device, individual plants can be non-invasively monitored during several days under different light conditions. Hence, it represents a proper tool to phenotype light- and circadian clock-mediated growth responses in order to better understand the underlying regulatory genetic network.

Les impacts de la dispersion historique sur la variabilité génétique à différentes échelles spatiales : connaître l'histoire pour mieux comprendre le présent.

La variabilité génétique actuelle est influencée par une combinaison complexe de variables historiques et contemporaines. Dès lors, une interprétation juste de l’impact des processus actuels nécessite une compréhension profonde des processus historiques ayant influencé la variabilité génétique. En se basant sur la prémisse que des populations proches devraient partager une histoire commune récente, nombreuses études, effectuées à petite échelle spatiale, ne prennent pas en considération l’effet potentiel des processus historiques. Cette thèse avait pour but de vérifier la validité de cette prémisse en estimant l’effet de la dispersion historique à grande et à petite échelle spatiale. Le premier volet de cette thèse avait pour but d’évaluer l’impact de la dispersion historique sur la répartition des organismes à grande échelle spatiale. Pour ce faire, les moules d’eau douce du genre flotteurs (Pyganodon spp.) ont servies de modèle biologique. Les moules d'eau douce se dispersent principalement au stade larvaire en tant que parasites des poissons. Une série de modèles nuls ont été développés pour évaluer la co-occurrence entre des parasites et leurs hôtes potenitels. Les associations distinctes du flotteur de Terre-Neuve (P. fragilis) avec des espèces de poissons euryhalins permettent d’expliquer sa répartition. Ces associations distinctes ont également pu favoriser la différenciation entre le flotteur de Terre-Neuve et son taxon soeur : le flotteur de l’Est (P. cataracta). Cette étude a démontré les effets des associations biologiques historiques sur les répartitions à grande échelle spatiale. Le second volet de cette thèse avait pour but d’évaluer l’impact de la dispersion historique sur la variabilité génétique, à petite échelle spatiale. Cette fois, différentes populations de crapet de roche (Ambloplites rupestris) et de crapet soleil (Lepomis gibbosus), dans des drainages adjacents ont servies de modèle biologique. Les différences frappantes observées entre les deux espèces suggèrent des patrons de colonisation opposés. La faible diversité génétique observée en amont des drainages et la forte différenciation observée entre les drainages pour les populations de crapet de roche suggèrent que cette espèce aurait colonisé les drainages à partir d'une source en aval. Au contraire, la faible différenciation et la forte diversité génétique observées en amont des drainages pour les populations de crapet soleil suggèrent une colonisation depuis l’amont, induisant du même coup un faux signal de flux génique entre les drainages. La présente étude a démontré que la dispersion historique peut entraver la capacité d'estimer la connectivité actuelle, à petite échelle spatiale, invalidant ainsi la prémisse testée dans cette thèse. Les impacts des processus historiques sur la variabilité génétique ne sont pas faciles à démontrer. Le troisième volet de cette thèse avait pour but de développer une méthode permettant de les détecter. La méthode proposée est très souple et favorise la comparaison entre la variabilité génétique et plusieurs hypothèses de dispersion. La méthode pourrait donc être utilisée pour comparer des hypothèses de dispersion basées sur le paysage historique et sur le paysage actuel et ainsi permettre l’évaluation des impacts historiques et contemporains sur la variabilité génétique. Les performances de la méthode sont présentées pour plusieurs scénarios de simulations, d’une complexité croissante. Malgré un impact de la différentiation globale, du nombre d’individus ou du nombre de loci échantillonné, la méthode apparaît hautement efficace. Afin d’illustrer le potentiel de la méthode, deux jeux de données empiriques très contrastés, publiés précédemment, ont été ré analysés. Cette thèse a démontré les impacts de la dispersion historique sur la variabilité génétique à différentes échelles spatiales. Les effets historiques potentiels doivent être pris en considération avant d’évaluer les impacts des processus écologiques sur la variabilité génétique. Bref, il faut intégrer l’évolution à l’écologie.

Effet du stress prolifératif sur la fonction des cellules souches hématopoïétiques : rôles des gènes Scl, E2A et Heb

Le système hématopoïétique est un tissu en constant renouvellement et les cellules souches hématopoïétiques (CSHs) sont indispensables pour soutenir la production des cellules matures du sang. Deux fonctions définissent les CSHs; la propriété d’auto-renouvellement, soit la capacité de préserver l’identité cellulaire suivant une division, et la multipotence, le potentiel de différenciation permettant de générer toutes les lignées hématopoïétiques. Chez l’adulte, la majorité des CSHs sont quiescentes et l’altération de cet état corrèle avec une diminution du potentiel de reconstitution des CSHs, suggérant que la quiescence protège les fonctions des CSHs. La quiescence est un état réversible et dynamique et les réseaux génétiques le contrôlant restent peu connus. Un nombre croissant d’évidences suggère que si à l’état d’homéostasie il y a une certaine redondance entre les gènes impliqués dans ces réseaux de contrôle, leurs rôles spécifiques sont révélés en situation de stress. La famille des bHLHs (basic helix-loop-helix) inclue différentes classes des protéines dont ceux qui sont tissu-spécifiques comme SCL, et les protéines E, comme E12/E47 et HEB. Certains bHLHs sont proposés êtres important pour la fonction des cellules souches, mais cela ne fait pas l’unanimité, car selon le contexte cellulaire, il y a redondance entre ces facteurs. La question reste donc entière, y a-t-il un rôle redondant entre les bHLHs d’une même classe pour la fonction à long-terme des CSHs? Les travaux présentés dans cette thèse visaient dans un premier temps à explorer le lien encore mal compris entre la quiescence et la fonction des CSHs en mesurant leurs facultés suite à un stress prolifératif intense et dans un deuxième temps, investiguer l’importance et la spécificité de trois gènes pour la fonction des CSHs adultes, soit Scl/Tal1, E2a/Tcf3 et Heb/Tcf12. Pour répondre à ces questions, une approche cellulaire (stress prolifératif) a été combinée avec une approche génétique (invalidation génique). Plus précisément, la résistance des CSHs au stress prolifératif a été étudiée en utilisant deux tests fonctionnels quantitatifs optimisés, soit un traitement basé sur le 5-fluorouracil, une drogue de chimiothérapie, et la transplantation sérielle en nombre limite. Dans la mesure où la fonction d’un réseau génique ne peut être révélée que par une perturbation intrinsèque, trois modèles de souris, i.e. Scl+/-, E2a+/- et Heb+/- ont été utilisés. Ceci a permis de révéler que l’adaptation des CSHs au stress prolifératif et le retour à l’équilibre est strictement contrôlé par les niveaux de Scl, lesquels règlent le métabolisme cellulaire des CSHs en maintenant l’expression de gènes ribosomaux à un niveau basal. D’autre part, bien que les composantes du réseau puissent paraître redondants à l’équilibre, mes travaux montrent qu’en situation de stress prolifératif, les niveaux de Heb restreignent la prolifération excessive des CSHs en induisant la sénescence et que cette fonction ne peut pas être compensée par E2a. En conclusion, les résultats présentés dans cette thèse montrent que les CSHs peuvent tolérer un stress prolifératif intense ainsi que des dommages à l’ADN non-réparés, tout en maintenant leur capacité de reconstituer l’hématopoïèse à long-terme. Cela implique cependant que leur métabolisme revienne au niveau de base, soit celui trouvé à l’état d’homéostasie. Par contre, avec l’augmentation du nombre de division cellulaire les CSHs atteignent éventuellement une limite d’expansion et entrent en sénescence.

A Robust Structural PGN Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks

The cell division cycle comprises a sequence of phenomena controlled by a stable and robust genetic network. We applied a probabilistic genetic network (PGN) to construct a hypothetical model with a dynamical behavior displaying the degree of robustness typical of the biological cell cycle. The structure of our PGN model was inspired in well-established biological facts such as the existence of integrator subsystems, negative and positive feedback loops, and redundant signaling pathways. Our model represents genes interactions as stochastic processes and presents strong robustness in the presence of moderate noise and parameters fluctuations. A recently published deterministic yeast cell-cycle model does not perform as well as our PGN model, even upon moderate noise conditions. In addition, self stimulatory mechanisms can give our PGN model the possibility of having a pacemaker activity similar to the observed in the oscillatory embryonic cell cycle.

Diseño y desarrollo de un modelo booleano probabilístico de regulación genética en el simulador de colonias bacterianas GRO

Resulta interesante comprender como microorganismos sencillos como la bacteria Escherichia coli poseen mecanismos no tan simples para responder al entorno en el que está gestionada por complicadas redes de regulación formadas por genes y proteínas, donde cada elemento de la red genética debe tomar parte en armonía, en el momento justo y la cantidad adecuada para dar lugar a la respuesta celular apropiada. La biología sintética es un nuevo área de la biología y la tecnología que fusiona la biolog ía molecular, la ingeniería genética y las herramientas computacionales, para crear sistemas biológicos con funcionalidades novedosas. Los sistemas creados sintéticamente son ya una realidad, y cada vez se acumulan más trabajos alrededor del mundo que muestran su factibilidad. En este campo no solo se hacen pequeñas modificaciones en la información genética, sino que también se diseñan, manipulan e introducen circuitos genéticos a los organismos. Actualmente, se hace un gran esfuerzo para construir circuitos genéticos formados por numerosos genes y caracterizar la interacción de los mismos con otras moléculas, su regulaci ón, expresión y funcionalidad en diferentes organismos. La mayoría de los proyectos de biología sintética que se han desarrollado hasta ahora, se basan en el conocimiento actual del funcionamiento de los organismos vivos. Sin embargo, la información es numerosa y creciente, por lo que se requiere de herramientas computacionales y matem áticas para integrar y hacer manejable esta gran cantidad de información. El simulador de colonias bacterianas GRO posee la capacidad de representar las dinámicas más simples del comportamiento celular, tales como crecimiento, división y comunicación intercelular mediante conjugación, pero carece de la capacidad de simular el comportamiento de la colonia en presencia de un circuito genético. Para ello, se ha creado un nuevo módulo de regulación genética que maneja las interaciones entre genes y proteínas de cada célula ejecutando respuestas celulares específicas. Dado que en la mayoría de los experimentos intervienen colonias del orden de 105 individuos, es necesario un módulo de regulación genética simplificado que permita representar de la forma más precisa posible este proceso en colonias de tales magnitudes. El módulo genético integrado en GRO se basa en una red booleana, en la que un gen puede transitar entre dos estados, on (expresado) o off (reprimido), y cuya transición viene dada por una serie de reglas lógicas.---ABSTRACT---It is interesting to understand how simple organisms such as Escherichia coli do not have simple mechanisms to respond to the environment in which they find themselves. This response is managed by complicated regulatory networks formed by genes and proteins, where each element of the genetic network should take part in harmony, at the right time and with the right amount to give rise to the appropriate cellular response. Synthetic biology is a new area of biology and technology that combines molecular biology, genetic engineering and computational tools to create biological systems with novel features. The synthetically created systems are already a reality, and increasingly accumulate work around the world showing their feasibility. In this field not only minor changes are made in the genetic information but also genetic circuits designed, manipulated and introduced into the organisms. Currently, it takes great effort to build genetic circuits formed by numerous genes and characterize their interaction with other molecules, their regulation, their expression and their function in different organisms. Most synthetic biology projects that have been developed so far are based on the current knowledge of the functioning of living organisms. However, there is a lot of information and it keeps accumulating, so it requires computational and mathematical tools to integrate and manage this wealth of information. The bacterial colonies simulator, GRO, has the ability to represent the simplest dynamics of cell behavior, such as growth, division and intercellular communication by conjugation, but lacks the ability to simulate the behavior of the colony in the presence of a genetic circuit. To this end, a new genetic regulation module that handles interactions between genes and proteins for each cell running specific cellular responses has been created. Since most experiments involve colonies of about 105 individuals, a simplified genetic module which represent cell dynamics as accurately and simply as possible is needed. The integrated genetic GRO module is based on a Boolean network, in which a gene can be in either of two states, on (expressed) or off (repressed), and whose transition is given by a set of logical rules.

Complete genome sequence of Caulobacter crescentus

The complete genome sequence of Caulobacter crescentus was determined to be 4,016,942 base pairs in a single circular chromosome encoding 3,767 genes. This organism, which grows in a dilute aquatic environment, coordinates the cell division cycle and multiple cell differentiation events. With the annotated genome sequence, a full description of the genetic network that controls bacterial differentiation, cell growth, and cell cycle progression is within reach. Two-component signal transduction proteins are known to play a significant role in cell cycle progression. Genome analysis revealed that the C. crescentus genome encodes a significantly higher number of these signaling proteins (105) than any bacterial genome sequenced thus far. Another regulatory mechanism involved in cell cycle progression is DNA methylation. The occurrence of the recognition sequence for an essential DNA methylating enzyme that is required for cell cycle regulation is severely limited and shows a bias to intergenic regions. The genome contains multiple clusters of genes encoding proteins essential for survival in a nutrient poor habitat. Included are those involved in chemotaxis, outer membrane channel function, degradation of aromatic ring compounds, and the breakdown of plant-derived carbon sources, in addition to many extracytoplasmic function sigma factors, providing the organism with the ability to respond to a wide range of environmental fluctuations. C. crescentus is, to our knowledge, the first free-living α-class proteobacterium to be sequenced and will serve as a foundation for exploring the biology of this group of bacteria, which includes the obligate endosymbiont and human pathogen Rickettsia prowazekii, the plant pathogen Agrobacterium tumefaciens, and the bovine and human pathogen Brucella abortus.

Temporal and spatial transcriptional programs in murine kidney development

We have performed a systematic temporal and spatial expression profiling of the developing mouse kidney using Compugen long-oligonucleotide microarrays. The activity of 18,000 genes was monitored at 24-h intervals from 10.5-day-postcoitum (dpc) metanephric mesenchyme (MM) through to neonatal kidney, and a cohort of 3,600 dynamically expressed genes was identified. Early metanephric development was further surveyed by directly comparing RNA from 10.5 vs. 11.5 vs. 13.5dpc kidneys. These data showed high concordance with the previously published dynamic profile of rat kidney development (Stuart RO, Bush KT, and Nigam SK. Proc Natl Acad Sci USA 98: 5649-5654, 2001) and our own temporal data. Cluster analyses were used to identify gene ontological terms, functional annotations, and pathways associated with temporal expression profiles. Genetic network analysis was also used to identify biological networks that have maximal transcriptional activity during early metanephric development, highlighting the involvement of proliferation and differentiation. Differential gene expression was validated using whole mount and section in situ hybridization of staged embryonic kidneys. Two spatial profiling experiments were also undertaken. MM (10.5dpc) was compared with adjacent intermediate mesenchyme to further define metanephric commitment. To define the genes involved in branching and in the induction of nephrogenesis, expression profiling was performed on ureteric bud (GFP+) FACS sorted from HoxB7-GFP transgenic mice at 15.5dpc vs. the GFP- mesenchymal derivatives. Comparisons between temporal and spatial data enhanced the ability to predict function for genes and networks. This study provides the most comprehensive temporal and spatial survey of kidney development to date, and the compilation of these transcriptional surveys provides important insights into metanephric development that can now be functionally tested.

Network Similarity Measures and Automatic Construction of Graph Models using Genetic Programming

A complex network is an abstract representation of an intricate system of interrelated elements where the patterns of connection hold significant meaning. One particular complex network is a social network whereby the vertices represent people and edges denote their daily interactions. Understanding social network dynamics can be vital to the mitigation of disease spread as these networks model the interactions, and thus avenues of spread, between individuals. To better understand complex networks, algorithms which generate graphs exhibiting observed properties of real-world networks, known as graph models, are often constructed. While various efforts to aid with the construction of graph models have been proposed using statistical and probabilistic methods, genetic programming (GP) has only recently been considered. However, determining that a graph model of a complex network accurately describes the target network(s) is not a trivial task as the graph models are often stochastic in nature and the notion of similarity is dependent upon the expected behavior of the network. This thesis examines a number of well-known network properties to determine which measures best allowed networks generated by different graph models, and thus the models themselves, to be distinguished. A proposed meta-analysis procedure was used to demonstrate how these network measures interact when used together as classifiers to determine network, and thus model, (dis)similarity. The analytical results form the basis of the fitness evaluation for a GP system used to automatically construct graph models for complex networks. The GP-based automatic inference system was used to reproduce existing, well-known graph models as well as a real-world network. Results indicated that the automatically inferred models exemplified functional similarity when compared to their respective target networks. This approach also showed promise when used to infer a model for a mammalian brain network.

Multi-Objective Pipe Smoothing Genetic Algorithm For Water Distribution Network Design

This paper describes the formulation of a Multi-objective Pipe Smoothing Genetic Algorithm (MOPSGA) and its application to the least cost water distribution network design problem. Evolutionary Algorithms have been widely utilised for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we present a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm whilst promoting engineering feasibility within the population of solutions. MOPSGA is based upon the standard Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and incorporates a modified population initialiser and mutation operator which directly targets elements of a network with the aim to increase network smoothness (in terms of progression from one diameter to the next) using network element awareness and an elementary heuristic. The pipe smoothing heuristic used in this algorithm is based upon a fundamental principle employed by water system engineers when designing water distribution pipe networks where the diameter of any pipe is never greater than the sum of the diameters of the pipes directly upstream resulting in the transition from large to small diameters from source to the extremities of the network. MOPSGA is assessed on a number of water distribution network benchmarks from the literature including some real-world based, large scale systems. The performance of MOPSGA is directly compared to that of NSGA-II with regard to solution quality, engineering feasibility (network smoothness) and computational efficiency. MOPSGA is shown to promote both engineering and hydraulic feasibility whilst attaining good infrastructure costs compared to NSGA-II.

A specialized genetic algorithm to solve the short term transmission network expansion planning

In this paper, the short term transmission network expansion planning (STTNEP) is solved through a specialized genetic algorithm (SGA). A complete AC model of the transmission network is used, which permits the formulation of an integrated power system transmission network expansion planning problem (real and reactive power planning). The characteristics of the proposed SGA to solve the STTNEP problem are detailed and an interior point method is employed to solve nonlinear programming problems during the solution steps of the SGA. Results of tests carried out with two electrical energy systems show the capabilities of the SGA and also the viability of using the AC model to solve the STTNEP problem. © 2009 IEEE.

Specialized genetic algorithm for transmission network expansion planning considering reliability

This paper presents a methodology to solve the transmission network expansion planning problem (TNEP) considering reliability and uncertainty in the demand. The proposed methodology provides an optimal expansion plan that allows the power system to operate adequately with an acceptable level of reliability and in an enviroment with uncertainness. The reliability criterion limits the expected value of the reliability index (LOLE - Loss Of Load Expectation) of the expanded system. The reliability is evaluated for the transmission system using an analytical technique based in enumeration. The mathematical model is solved, in a efficient way, using a specialized genetic algorithm of Chu-Beasley modified. Detailed results from an illustrative example are presented and discussed. © 2009 IEEE.