Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

Genetic team composition and level of selection in the evolution of cooperation

In cooperative multiagent systems, agents interac to solve tasks. Global dynamics of multiagent teams result from local agent interactions, and are complex and difficult to predict. Evolutionary computation has proven a promising approach to the design of such teams. The majority of current studies use teams composed of agents with identical control rules ("geneti- cally homogeneous teams") and select behavior at the team level ("team-level selection"). Here we extend current approaches to include four combinations of genetic team composition and level of selection. We compare the performance of genetically homo- geneous teams evolved with individual-level selection, genetically homogeneous teams evolved with team-level selection, genetically heterogeneous teams evolved with individual-level selection, and genetically heterogeneous teams evolved with team-level selection. We use a simulated foraging task to show that the optimal combination depends on the amount of cooperation required by the task. Accordingly, we distinguish between three types of cooperative tasks and suggest guidelines for the optimal choice of genetic team composition and level of selection

Evolving team compositions by agent swapping

Optimizing collective behavior in multiagent systems requires algorithms to find not only appropriate individual behaviors but also a suitable composition of agents within a team. Over the last two decades, evolutionary methods have emerged as a promising approach for the design of agents and their compositions into teams. The choice of a crossover operator that facilitates the evolution of optimal team composition is recognized to be crucial, but so far, it has never been thoroughly quantified. Here, we highlight the limitations of two different crossover operators that exchange entire agents between teams: restricted agent swapping (RAS) that exchanges only corresponding agents between teams and free agent swapping (FAS) that allows an arbitrary exchange of agents. Our results show that RAS suffers from premature convergence, whereas FAS entails insufficient convergence. Consequently, in both cases, the exploration and exploitation aspects of the evolutionary algorithm are not well balanced resulting in the evolution of suboptimal team compositions. To overcome this problem, we propose combining the two methods. Our approach first applies FAS to explore the search space and then RAS to exploit it. This mixed approach is a much more efficient strategy for the evolution of team compositions compared to either strategy on its own. Our results suggest that such a mixed agent-swapping algorithm should always be preferred whenever the optimal composition of individuals in a multiagent system is unknown.

Additive functions in boolean models of gene regulatory network modules.

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in Boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a Boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred Boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate.

Evolutionary origin and functions of retrogene introns.

Retroposed genes (retrogenes) originate via the reverse transcription of mature messenger RNAs from parental source genes and are therefore usually devoid of introns. Here, we characterize a particular set of mammalian retrogenes that acquired introns upon their emergence and thus represent rare cases of intron gain in mammals. We find that although a few retrogenes evolved introns in their coding or 3' untranslated regions (untranslated region, UTR), most introns originated together with untranslated exons in the 5' flanking regions of the retrogene insertion site. They emerged either de novo or through fusions with 5' UTR exons of host genes into which the retrogenes inserted. Generally, retrogenes with introns display high transcription levels and show broader spatial expression patterns than other retrogenes. Our experimental expression analyses of individual intron-containing retrogenes show that 5' UTR introns may indeed promote higher expression levels, at least in part through encoded regulatory elements. By contrast, 3' UTR introns may lead to downregulation of expression levels via nonsense-mediated decay mechanisms. Notably, the majority of retrogenes with introns in their 5' flanks depend on distant, sometimes bidirectional CpG dinucleotide-enriched promoters for their expression that may be recruited from other genes in the genomic vicinity. We thus propose a scenario where the acquisition of new 5' exon-intron structures was directly linked to the recruitment of distant promoters by these retrogenes, a process potentially facilitated by the presence of proto-splice sites in the genomic vicinity of retrogene insertion sites. Thus, the primary role and selective benefit of new 5' introns (and UTR exons) was probably initially to span the often substantial distances to potent CpG promoters driving retrogene transcription. Later in evolution, these introns then obtained additional regulatory roles in fine tuning retrogene expression levels. Our study provides novel insights regarding mechanisms underlying the origin of new introns, the evolutionary relevance of intron gain, and the origin of new gene promoters.

Two's company, three's a crowd: experimental evaluation of the evolutionary maintenance of trioecy in Mercurialis annua (Euphorbiaceae).

Trioecy is an uncommon sexual system in which males, females, and hermaphrodites co-occur as three clearly different gender classes. The evolutionary stability of trioecy is unclear, but would depend on factors such as hermaphroditic sex allocation and rates of outcrossing vs. selfing. Here, trioecious populations of Mercurialis annua are described for the first time. We examined the frequencies of females, males and hermaphrodites across ten natural populations and evaluated the association between the frequency of females and plant densities. Previous studies have shown that selfing rates in this species are density-dependent and are reduced in the presence of males, which produce substantially more pollen than hermaphrodites. Accordingly, we examined the evolutionary stability of trioecy using an experiment in which we (a) indirectly manipulated selfing rates by altering plant densities and the frequency of males in a fully factorial manner across 20 experimental plots and (b) examined the effect of these manipulations on the frequency of the three sex phenotypes in the next generation of plants. In the parental generation, we measured the seed and pollen allocations of hermaphrodites and compared them with allocations by unisexual plants. In natural populations, females occurred at higher frequencies in denser patches, a finding consistent with our expectations. Under our experimental conditions, however, no combination of plant densities and male frequencies was associated with increased frequencies of females. Our results suggest that the factors that regulate female frequencies in trioecious populations of M. annua are independent of those regulating male frequencies (density), and that the stable co-existence of all three sex phenotypes within populations is unlikely.

THE USE OF SIMULATIONS IN EVOLUTIONARY POPULATION GENETICS: APPLICATIONS ON HUMANS, OWLS AND VIRTUAL ORGANISMS

Summary (in English) Computer simulations provide a practical way to address scientific questions that would be otherwise intractable. In evolutionary biology, and in population genetics in particular, the investigation of evolutionary processes frequently involves the implementation of complex models, making simulations a particularly valuable tool in the area. In this thesis work, I explored three questions involving the geographical range expansion of populations, taking advantage of spatially explicit simulations coupled with approximate Bayesian computation. First, the neutral evolutionary history of the human spread around the world was investigated, leading to a surprisingly simple model: A straightforward diffusion process of migrations from east Africa throughout a world map with homogeneous landmasses replicated to very large extent the complex patterns observed in real human populations, suggesting a more continuous (as opposed to structured) view of the distribution of modern human genetic diversity, which may play a better role as a base model for further studies. Second, the postglacial evolution of the European barn owl, with the formation of a remarkable coat-color cline, was inspected with two rounds of simulations: (i) determine the demographic background history and (ii) test the probability of a phenotypic cline, like the one observed in the natural populations, to appear without natural selection. We verified that the modern barn owl population originated from a single Iberian refugium and that they formed their color cline, not due to neutral evolution, but with the necessary participation of selection. The third and last part of this thesis refers to a simulation-only study inspired by the barn owl case above. In this chapter, we showed that selection is, indeed, effective during range expansions and that it leaves a distinguished signature, which can then be used to detect and measure natural selection in range-expanding populations. Résumé (en français) Les simulations fournissent un moyen pratique pour répondre à des questions scientifiques qui seraient inabordable autrement. En génétique des populations, l'étude des processus évolutifs implique souvent la mise en oeuvre de modèles complexes, et les simulations sont un outil particulièrement précieux dans ce domaine. Dans cette thèse, j'ai exploré trois questions en utilisant des simulations spatialement explicites dans un cadre de calculs Bayésiens approximés (approximate Bayesian computation : ABC). Tout d'abord, l'histoire de la colonisation humaine mondiale et de l'évolution de parties neutres du génome a été étudiée grâce à un modèle étonnement simple. Un processus de diffusion des migrants de l'Afrique orientale à travers un monde avec des masses terrestres homogènes a reproduit, dans une très large mesure, les signatures génétiques complexes observées dans les populations humaines réelles. Un tel modèle continu (opposé à un modèle structuré en populations) pourrait être très utile comme modèle de base dans l'étude de génétique humaine à l'avenir. Deuxièmement, l'évolution postglaciaire d'un gradient de couleur chez l'Effraie des clocher (Tyto alba) Européenne, a été examiné avec deux séries de simulations pour : (i) déterminer l'histoire démographique de base et (ii) tester la probabilité qu'un gradient phénotypique, tel qu'observé dans les populations naturelles puisse apparaître sans sélection naturelle. Nous avons montré que la population actuelle des chouettes est sortie d'un unique refuge ibérique et que le gradient de couleur ne peux pas s'être formé de manière neutre (sans l'action de la sélection naturelle). La troisième partie de cette thèse se réfère à une étude par simulations inspirée par l'étude de l'Effraie. Dans ce dernier chapitre, nous avons montré que la sélection est, en effet, aussi efficace dans les cas d'expansion d'aire de distribution et qu'elle laisse une signature unique, qui peut être utilisée pour la détecter et estimer sa force.

The role of gene duplication in the origin and evolution of new biological functions

Abstract : Gene duplication is an essential source of material for the origin of genetic novelty and the evolution of lineage- or species-specific phenotypic traits. The reverse transcription of source gene mRNA followed by the genomic insertion of the resulting cDNA - retroposition - has provided the human genome with a significant number of gene copies during the last ~63 million years (MYA) of primate evolution. We estimated that at least 1 new functional gene (retrogene) per MYA emerged by retroposition in the primate lineage leading to humans. Using a combination of comparative sequencing and evolutionary simulations, we obtained strong evidence of functionality for 7 primate specific retrogenes. Most of these genes are specifically expressed in testis suggesting that retroposition has contributed with genetic raw material necessary for the evolution ofmale-specific functions in primates. We characterized CDC14Bretro (identified in the previous survey) that originated from the retroposition of a cell cycle gene - CDC14B - in the common ancestor of humans and apes. We demonstrate that CDC14Bretro experienced a period of intense positive selection in the African ape ancestor. By virtue of the amino acid substitutions that occurred during this period CDC 14Bretro adapted to a new subcellular compartment in African apes. Further analyses indicate that this subcellular shift reflects the evolution of anew functional role of CDC 14Bretro. Prompted by this result, we used yeast (Saccharomyces cerevisiae) to investigate on a global scale the extent of functional diversification of duplicate genes through the subcellular adaptation of their encoded proteins. We found that duplicate proteins frequently evolved new cellular localization patterns, either by partitioning of ancestral localizations ("sublocalization"), or more frequently by relocalization to previously unoccupied compartments ("neolocalization"). Interestingly, proteins involved in processes with a wider subcellular distribution more frequently evolved new localization patterns suggesting that subcellular localization changes are dependent on progenitor gene functions. Relocated proteins adapted to their new subcellular environments and evolved new functional roles through changes of their physio-chemical properties, expression levels, and interaction partners. Our work suggests an important role of subcellular adaptation for the emergence of new gene functions.

On circuit functionality in boolean networks.

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates." Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.

RNA-based gene duplication: mechanistic and evolutionary insights.

Gene copies that stem from the mRNAs of parental source genes have long been viewed as evolutionary dead-ends with little biological relevance. Here we review a range of recent studies that have unveiled a significant number of functional retroposed gene copies in both mammalian and some non-mammalian genomes. These studies have not only revealed previously unknown mechanisms for the emergence of new genes and their functions but have also provided fascinating general insights into molecular and evolutionary processes that have shaped genomes. For example, analyses of chromosomal gene movement patterns via RNA-based gene duplication have shed fresh light on the evolutionary origin and biology of our sex chromosomes.

A cnidarian homologue of an insect gustatory receptor functions in developmental body patterning.

Insect gustatory and odorant receptors (GRs and ORs) form a superfamily of novel transmembrane proteins, which are expressed in chemosensory neurons that detect environmental stimuli. Here we identify homologues of GRs (Gustatory receptor-like (Grl) genes) in genomes across Protostomia, Deuterostomia and non-Bilateria. Surprisingly, two Grls in the cnidarian Nematostella vectensis, NvecGrl1 and NvecGrl2, are expressed early in development, in the blastula and gastrula, but not at later stages when a putative chemosensory organ forms. NvecGrl1 transcripts are detected around the aboral pole, considered the equivalent to the head-forming region of Bilateria. Morpholino-mediated knockdown of NvecGrl1 causes developmental patterning defects of this region, leading to animals lacking the apical sensory organ. A deuterostome Grl from the sea urchin Strongylocentrotus purpuratus displays similar patterns of developmental expression. These results reveal an early evolutionary origin of the insect chemosensory receptor family and raise the possibility that their ancestral role was in embryonic development.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.