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This work presents mathematical and computational approaches to cover various aspects of metabolic network modelling, especially regarding the limited availability of detailed kinetic knowledge on reaction rates. It is shown that precise mathematical formulations of problems are needed i) to find appropriate and, if possible, efficient algorithms to solve them, and ii) to determine the quality of the found approximate solutions. Furthermore, some means are introduced to gain insights on dynamic properties of metabolic networks either directly from the network structure or by additionally incorporating steady-state information. Finally, an approach to identify key reactions in a metabolic networks is introduced, which helps to develop simple yet useful kinetic models. The rise of novel techniques renders genome sequencing increasingly fast and cheap. In the near future, this will allow to analyze biological networks not only for species but also for individuals. Hence, automatic reconstruction of metabolic networks provides itself as a means for evaluating this huge amount of experimental data. A mathematical formulation as an optimization problem is presented, taking into account existing knowledge and experimental data as well as the probabilistic predictions of various bioinformatical methods. The reconstructed networks are optimized for having large connected components of high accuracy, hence avoiding fragmentation into small isolated subnetworks. The usefulness of this formalism is exemplified on the reconstruction of the sucrose biosynthesis pathway in Chlamydomonas reinhardtii. The problem is shown to be computationally demanding and therefore necessitates efficient approximation algorithms. The problem of minimal nutrient requirements for genome-scale metabolic networks is analyzed. Given a metabolic network and a set of target metabolites, the inverse scope problem has as it objective determining a minimal set of metabolites that have to be provided in order to produce the target metabolites. These target metabolites might stem from experimental measurements and therefore are known to be produced by the metabolic network under study, or are given as the desired end-products of a biotechological application. The inverse scope problem is shown to be computationally hard to solve. However, I assume that the complexity strongly depends on the number of directed cycles within the metabolic network. This might guide the development of efficient approximation algorithms. Assuming mass-action kinetics, chemical reaction network theory (CRNT) allows for eliciting conclusions about multistability directly from the structure of metabolic networks. Although CRNT is based on mass-action kinetics originally, it is shown how to incorporate further reaction schemes by emulating molecular enzyme mechanisms. CRNT is used to compare several models of the Calvin cycle, which differ in size and level of abstraction. Definite results are obtained for small models, but the available set of theorems and algorithms provided by CRNT can not be applied to larger models due to the computational limitations of the currently available implementations of the provided algorithms. Given the stoichiometry of a metabolic network together with steady-state fluxes and concentrations, structural kinetic modelling allows to analyze the dynamic behavior of the metabolic network, even if the explicit rate equations are not known. In particular, this sampling approach is used to study the stabilizing effects of allosteric regulation in a model of human erythrocytes. Furthermore, the reactions of that model can be ranked according to their impact on stability of the steady state. The most important reactions in that respect are identified as hexokinase, phosphofructokinase and pyruvate kinase, which are known to be highly regulated and almost irreversible. Kinetic modelling approaches using standard rate equations are compared and evaluated against reference models for erythrocytes and hepatocytes. The results from this simplified kinetic models can simulate acceptably the temporal behavior for small changes around a given steady state, but fail to capture important characteristics for larger changes. The aforementioned approach to rank reactions according to their influence on stability is used to identify a small number of key reactions. These reactions are modelled in detail, including knowledge about allosteric regulation, while all other reactions were still described by simplified reaction rates. These so-called hybrid models can capture the characteristics of the reference models significantly better than the simplified models alone. The resulting hybrid models might serve as a good starting point for kinetic modelling of genome-scale metabolic networks, as they provide reasonable results in the absence of experimental data, regarding, for instance, allosteric regulations, for a vast majority of enzymatic reactions.
Changes in species' distributions are classically projected based on their climate envelopes. For Siberian forests, which have a tremendous significance for vegetation-climate feedbacks, this implies future shifts of each of the forest-forming larch (Larix) species to the north-east. However, in addition to abiotic factors, reliable projections must assess the role of historical biogeography and biotic interactions. Here, we use sedimentary ancient DNA and individual-based modelling to investigate the distribution of larch species and mitochondrial haplotypes through space and time across the treeline ecotone on the southern Taymyr peninsula, which at the same time presents a boundary area of two larch species. We find spatial and temporal patterns, which suggest that forest density is the most influential driver determining the precise distribution of species and mitochondrial haplotypes. This suggests a strong influence of competition on the species' range shifts. These findings imply possible climate change outcomes that are directly opposed to projections based purely on climate envelopes. Investigations of such fine-scale processes of biodiversity change through time are possible using paleoenvironmental DNA, which is available much more readily than visible fossils and can provide information at a level of resolution that is not reached in classical palaeoecology.
Coarse-grained molecular model for the Glycosylphosphatidylinositol anchor with and without protein
(2020)
Glycosylphosphatidylinositol (GPI) anchors are a unique class of complex glycolipids that anchor a great variety of proteins to the extracellular leaflet of plasma membranes of eukaryotic cells. These anchors can exist either with or without an attached protein called GPI-anchored protein (GPI-AP) both in vitro and in vivo. Although GPIs are known to participate in a broad range of cellular functions, it is to a large extent unknown how these are related to GPI structure and composition. Their conformational flexibility and microheterogeneity make it difficult to study them experimentally. Simplified atomistic models are amenable to all-atom computer simulations in small lipid bilayer patches but not suitable for studying their partitioning and trafficking in complex and heterogeneous membranes. Here, we present a coarse-grained model of the GPI anchor constructed with a modified version of the MARTINI force field that is suited for modeling carbohydrates, proteins, and lipids in an aqueous environment using MARTINI's polarizable water. The nonbonded interactions for sugars were reparametrized by calculating their partitioning free energies between polar and apolar phases. In addition, sugar-sugar interactions were optimized by adjusting the second virial coefficients of osmotic pressures for solutions of glucose, sucrose, and trehalose to match with experimental data. With respect to the conformational dynamics of GPI-anchored green fluorescent protein, the accessible time scales are now at least an order of magnitude larger than for the all-atom system. This is particularly important for fine-tuning the mutual interactions of lipids, carbohydrates, and amino acids when comparing to experimental results. We discuss the prospective use of the coarse-grained GPI model for studying protein-sorting and trafficking in membrane models.
Polar nuclear migration is crucial during the development of diverse eukaryotes. In plants, root hair growth requires polar nuclear migration into the outgrowing hair. However, knowledge about the dynamics and the regulatory mechanisms underlying nuclear movements in root epidermal cells remains limited. Here, we show that both auxin and Rho-of-Plant (ROP) signaling modulate polar nuclear position at the inner epidermal plasma membrane domain oriented to the cortical cells during cell elongation as well as subsequent polar nuclear movement to the outer domain into the emerging hair bulge in Arabidopsis (Arabidopsis thaliana). Auxin signaling via the nuclear AUXIN RESPONSE FACTOR7 (ARF7)/ARF19 and INDOLE ACETIC ACID7 pathway ensures correct nuclear placement toward the inner membrane domain. Moreover, precise inner nuclear placement relies on SPIKE1 Rho-GEF, SUPERCENTIPEDE1 Rho-GDI, and ACTIN7 (ACT7) function and to a lesser extent on VTI11 vacuolar SNARE activity. Strikingly, the directionality and/or velocity of outer polar nuclear migration into the hair outgrowth along actin strands also are ACT7 dependent, auxin sensitive, and regulated by ROP signaling. Thus, our findings provide a founding framework revealing auxin and ROP signaling of inner polar nuclear position with some contribution by vacuolar morphology and of actin-dependent outer polar nuclear migration in root epidermal hair cells.