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Mathematical modeling of biological phenomena has experienced increasing interest since new high-throughput technologies give access to growing amounts of molecular data. These modeling approaches are especially able to test hypotheses which are not yet experimentally accessible or guide an experimental setup. One particular attempt investigates the evolutionary dynamics responsible for today's composition of organisms. Computer simulations either propose an evolutionary mechanism and thus reproduce a recent finding or rebuild an evolutionary process in order to learn about its mechanism. The quest for evolutionary fingerprints in metabolic and gene-coexpression networks is the central topic of this cumulative thesis based on four published articles. An understanding of the actual origin of life will probably remain an insoluble problem. However, one can argue that after a first simple metabolism has evolved, the further evolution of metabolism occurred in parallel with the evolution of the sequences of the catalyzing enzymes. Indications of such a coevolution can be found when correlating the change in sequence between two enzymes with their distance on the metabolic network which is obtained from the KEGG database. We observe that there exists a small but significant correlation primarily on nearest neighbors. This indicates that enzymes catalyzing subsequent reactions tend to be descended from the same precursor. Since this correlation is relatively small one can at least assume that, if new enzymes are no "genetic children" of the previous enzymes, they certainly be descended from any of the already existing ones. Following this hypothesis, we introduce a model of enzyme-pathway coevolution. By iteratively adding enzymes, this model explores the metabolic network in a manner similar to diffusion. With implementation of an Gillespie-like algorithm we are able to introduce a tunable parameter that controls the weight of sequence similarity when choosing a new enzyme. Furthermore, this method also defines a time difference between successive evolutionary innovations in terms of a new enzyme. Overall, these simulations generate putative time-courses of the evolutionary walk on the metabolic network. By a time-series analysis, we find that the acquisition of new enzymes appears in bursts which are pronounced when the influence of the sequence similarity is higher. This behavior strongly resembles punctuated equilibrium which denotes the observation that new species tend to appear in bursts as well rather than in a gradual manner. Thus, our model helps to establish a better understanding of punctuated equilibrium giving a potential description at molecular level. From the time-courses we also extract a tentative order of new enzymes, metabolites, and even organisms. The consistence of this order with previous findings provides evidence for the validity of our approach. While the sequence of a gene is actually subject to mutations, its expression profile might also indirectly change through the evolutionary events in the cellular interplay. Gene coexpression data is simply accessible by microarray experiments and commonly illustrated using coexpression networks where genes are nodes and get linked once they show a significant coexpression. Since the large number of genes makes an illustration of the entire coexpression network difficult, clustering helps to show the network on a metalevel. Various clustering techniques already exist. However, we introduce a novel one which maintains control of the cluster sizes and thus assures proper visual inspection. An application of the method on Arabidopsis thaliana reveals that genes causing a severe phenotype often show a functional uniqueness in their network vicinity. This leads to 20 genes of so far unknown phenotype which are however suggested to be essential for plant growth. Of these, six indeed provoke such a severe phenotype, shown by mutant analysis. By an inspection of the degree distribution of the A.thaliana coexpression network, we identified two characteristics. The distribution deviates from the frequently observed power-law by a sharp truncation which follows after an over-representation of highly connected nodes. For a better understanding, we developed an evolutionary model which mimics the growth of a coexpression network by gene duplication which underlies a strong selection criterion, and slight mutational changes in the expression profile. Despite the simplicity of our assumption, we can reproduce the observed properties in A.thaliana as well as in E.coli and S.cerevisiae. The over-representation of high-degree nodes could be identified with mutually well connected genes of similar functional families: zinc fingers (PF00096), flagella, and ribosomes respectively. In conclusion, these four manuscripts demonstrate the usefulness of mathematical models and statistical tools as a source of new biological insight. While the clustering approach of gene coexpression data leads to the phenotypic characterization of so far unknown genes and thus supports genome annotation, our model approaches offer explanations for observed properties of the coexpression network and furthermore substantiate punctuated equilibrium as an evolutionary process by a deeper understanding of an underlying molecular mechanism.
Perspectives in modelling earthworm dynamics and their feedbacks with abiotic soil properties
(2012)
Effects of earthworms on soil abiotic properties are well documented from several decades of laboratory and mesocosm experiments, and they are supposed to affect large-scale soil ecosystem functioning. The prediction of the spatiotemporal occurrence of earthworms and the related functional effects in the field or at larger scales, however, is constrained by adequate modelling approaches. Correlative, phenomenological methods, such as species distribution models, facilitate the identification of factors that drive species' distributions. However, these methods ignore the ability of earthworms to select and modify their own habitat and therefore may lead to unreliable predictions. Understanding these feedbacks between earthworms and abiotic soil properties is a key requisite to better understand their spatiotemporal distribution as well as to quantify the various functional effects of earthworms in soil ecosystems. Process-based models that investigate either effects or responses of earthworms on soil environmental conditions are mostly applied in ecotoxicological and bioturbation studies. Process-based models that describe feedbacks between earthworms and soil abiotic properties explicitly are rare. In this review, we analysed 18 process-based earthworm dynamic modelling studies pointing out the current gaps and future challenges in feedback modelling. We identify three main challenges: (i) adequate and reliable process identification in model development at and across relevant spatiotemporal scales (individual behaviour and population dynamics of earthworms), (ii) use of information from different data sources in one model (laboratory or field experiments, earthworm species or functional type) and (iii) quantification of uncertainties in data (e.g. spatiotemporal variability of earthworm abundances and soil hydraulic properties) and derived parameters (e.g. population growth rate and hydraulic conductivity) that are used in the model.
Structuring process models
(2012)
One can fairly adopt the ideas of Donald E. Knuth to conclude that process modeling is both a science and an art. Process modeling does have an aesthetic sense. Similar to composing an opera or writing a novel, process modeling is carried out by humans who undergo creative practices when engineering a process model. Therefore, the very same process can be modeled in a myriad number of ways. Once modeled, processes can be analyzed by employing scientific methods. Usually, process models are formalized as directed graphs, with nodes representing tasks and decisions, and directed arcs describing temporal constraints between the nodes. Common process definition languages, such as Business Process Model and Notation (BPMN) and Event-driven Process Chain (EPC) allow process analysts to define models with arbitrary complex topologies. The absence of structural constraints supports creativity and productivity, as there is no need to force ideas into a limited amount of available structural patterns. Nevertheless, it is often preferable that models follow certain structural rules. A well-known structural property of process models is (well-)structuredness. A process model is (well-)structured if and only if every node with multiple outgoing arcs (a split) has a corresponding node with multiple incoming arcs (a join), and vice versa, such that the set of nodes between the split and the join induces a single-entry-single-exit (SESE) region; otherwise the process model is unstructured. The motivations for well-structured process models are manifold: (i) Well-structured process models are easier to layout for visual representation as their formalizations are planar graphs. (ii) Well-structured process models are easier to comprehend by humans. (iii) Well-structured process models tend to have fewer errors than unstructured ones and it is less probable to introduce new errors when modifying a well-structured process model. (iv) Well-structured process models are better suited for analysis with many existing formal techniques applicable only for well-structured process models. (v) Well-structured process models are better suited for efficient execution and optimization, e.g., when discovering independent regions of a process model that can be executed concurrently. Consequently, there are process modeling languages that encourage well-structured modeling, e.g., Business Process Execution Language (BPEL) and ADEPT. However, the well-structured process modeling implies some limitations: (i) There exist processes that cannot be formalized as well-structured process models. (ii) There exist processes that when formalized as well-structured process models require a considerable duplication of modeling constructs. Rather than expecting well-structured modeling from start, we advocate for the absence of structural constraints when modeling. Afterwards, automated methods can suggest, upon request and whenever possible, alternative formalizations that are "better" structured, preferably well-structured. In this thesis, we study the problem of automatically transforming process models into equivalent well-structured models. The developed transformations are performed under a strong notion of behavioral equivalence which preserves concurrency. The findings are implemented in a tool, which is publicly available.
TURBO2 - a MATLAB simulation to study the effects of bioturbation on paleoceanographic time series
(2013)
Bioturbation (or benthic mixing) causes significant distortions in marine stable isotope signals and other palaeoceanographic records. Although the influence of bioturbation on these records is well known it has rarely been dealt systematically. The MATLAB program called TURBO2 can be used to simulate the effect of bioturbation on individual sediment particles. It can therefore be used to model the distortion of all physical, chemical, and biological signals in deep-sea sediments, such as Mg/Ca ratios and UK37-based sea-surface temperature (SST) variations. In particular, it can be used to study the distortions in paleoceanographic records that are based on individual sediment particles, such as SST records based on foraminifera assemblages. Furthermore. TURBO2 provides a tool to study the effect of benthic mixing of isotope signals such as C-14, delta O-18, and delta C-13, measured in a stratigraphic carrier such as foraminifera shells.
The service-oriented architecture supports the dynamic assembly and runtime reconfiguration of complex open IT landscapes by means of runtime binding of service contracts, launching of new components and termination of outdated ones. Furthermore, the evolution of these IT landscapes is not restricted to exchanging components with other ones using the same service contracts, as new services contracts can be added as well. However, current approaches for modeling and verification of service-oriented architectures do not support these important capabilities to their full extend.In this report we present an extension of the current OMG proposal for service modeling with UML - SoaML - which overcomes these limitations. It permits modeling services and their service contracts at different levels of abstraction, provides a formal semantics for all modeling concepts, and enables verifying critical properties. Our compositional and incremental verification approach allows for complex properties including communication parameters and time and covers besides the dynamic binding of service contracts and the replacement of components also the evolution of the systems by means of new service contracts. The modeling as well as verification capabilities of the presented approach are demonstrated by means of a supply chain example and the verification results of a first prototype are shown.
The development of self-adaptive software requires the engineering of an adaptation engine that controls and adapts the underlying adaptable software by means of feedback loops. The adaptation engine often describes the adaptation by using runtime models representing relevant aspects of the adaptable software and particular activities such as analysis and planning that operate on these runtime models. To systematically address the interplay between runtime models and adaptation activities in adaptation engines, runtime megamodels have been proposed for self-adaptive software. A runtime megamodel is a specific runtime model whose elements are runtime models and adaptation activities. Thus, a megamodel captures the interplay between multiple models and between models and activities as well as the activation of the activities. In this article, we go one step further and present a modeling language for ExecUtable RuntimE MegAmodels (EUREMA) that considerably eases the development of adaptation engines by following a model-driven engineering approach. We provide a domain-specific modeling language and a runtime interpreter for adaptation engines, in particular for feedback loops. Megamodels are kept explicit and alive at runtime and by interpreting them, they are directly executed to run feedback loops. Additionally, they can be dynamically adjusted to adapt feedback loops. Thus, EUREMA supports development by making feedback loops, their runtime models, and adaptation activities explicit at a higher level of abstraction. Moreover, it enables complex solutions where multiple feedback loops interact or even operate on top of each other. Finally, it leverages the co-existence of self-adaptation and off-line adaptation for evolution.
A challenge for eco-evolutionary research is to better understand the effect of climate and landscape changes on species and their distribution. Populations of species can respond to changes in their environment through local genetic adaptation or plasticity, dispersal, or local extinction. The individual-based modeling (IBM) approach has been repeatedly applied to assess organismic responses to environmental changes. IBMs simulate emerging adaptive behaviors from the basic entities upon which both ecological and evolutionary mechanisms act. The objective of this review is to summarize the state of the art of eco-evolutionary IBMs and to explore to what degree they already address the key responses of organisms to environmental change. In this, we identify promising approaches and potential knowledge gaps in the implementation of eco-evolutionary mechanisms to motivate future research. Using mainly the ISI Web of Science, we reveal that most of the progress in eco-evolutionary IBMs in the last decades was achieved for genetic adaptation to novel local environmental conditions. There is, however, not a single eco-evolutionary IBM addressing the three potential adaptive responses simultaneously. Additionally, IBMs implementing adaptive phenotypic plasticity are rare. Most commonly, plasticity was implemented as random noise or reaction norms. Our review further identifies a current lack of models where plasticity is an evolving trait. Future eco-evolutionary models should consider dispersal and plasticity as evolving traits with their associated costs and benefits. Such an integrated approach could help to identify conditions promoting population persistence depending on the life history strategy of organisms and the environment they experience.
The soft error rate (SER) due to heavy-ion irradiation of a clock tree is investigated in this paper. A method for clock tree SER prediction is developed, which employs a dedicated soft error analysis tool to characterize the single-event transient (SET) sensitivities of clock inverters and other commercial tools to calculate the SER through fault-injection simulations. A test circuit including a flip-flop chain and clock tree in a 65 nm CMOS technology is developed through the automatic ASIC design flow. This circuit is analyzed with the developed method to calculate its clock tree SER. In addition, this circuit is implemented in a 65 nm test chip and irradiated by heavy ions to measure its SER resulting from the SETs in the clock tree. The experimental and calculation results of this case study present good correlation, which verifies the effectiveness of the developed method.
Bridging metabolomics with plant phenotypic responses is challenging. Multivariate analyses account for the existing dependencies among metabolites, and regression models in particular capture such dependencies in search for association with a given trait. However, special care should be undertaken with metabolomics data. Here we propose a modeling workflow that considers all caveats imposed by such large data sets.
In near-surface geophysics, small portable loop-loop electro-magnetic induction (EMI) sensors using harmonic sources with a constant and rather small frequency are increasingly used to investigate the electrical properties of the subsurface. For such sensors, the influence of electrical conductivity and magnetic permeability on the EMI response is well-understood. Typically, data analysis focuses on reconstructing an electrical conductivity model by inverting the out-of-phase response. However, in a variety of near-surface applications, magnetic permeability (or susceptibility) models derived from the in-phase (IP) response may provide important additional information. In view of developing a fast 3D inversion procedure of the IP response for a dense grid of measurement points, we first analyze the 3D sensitivity functions associated with a homogeneous permeable half-space. Then, we compare synthetic data computed using a linear forward-modeling method based on these sensitivity functions with synthetic data computed using full nonlinear forward-modeling methods. The results indicate the correctness and applicability of our linear forward-modeling approach. Furthermore, we determine the advantages of converting IP data into apparent permeability, which, for example, allows us to extend the applicability of the linear forward-modeling method to high-magnetic environments. Finally, we compute synthetic data with the linear theory for a model consisting of a controlled magnetic target and compare the results with field data collected with a four-configuration loop-loop EMI sensor. With this field-scale experiment, we determine that our linear forward-modeling approach can reproduce measured data with sufficiently small error, and, thus, it represents the basis for developing efficient inversion approaches.