Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Not the outside but the inside matters : functional analysis of Capricious and Tartan during Drosophila tracheal morphogenesis

The tubular structures, which transport essential gases, liquids, or cells from one site to another, are shared among various divergent organisms. These highly organized tubular networks include lung, kidney, vasculature and mammary gland in mammals as well as trachea and salivary gland in Drosophila melanogaster. Many questions regarding the tubular morphogenesis cannot be addressed sufficiently by investigating the mammalian organs because their structures are extremely complex and therefore, systematic analyses of genetic and cellular programs guiding the development is not possible. In contrast, the Drosophila tracheal development provides an excellent model system since many molecular markers and powerful tools for genetic manipulations are available. Two mechanisms were shown to be important for the outgrowth of tracheal cells: the FGF signaling pathway and the interaction between the tracheal cells and the surrounding mesodermal cells. The Drosophila FGF ligand encoded by branchless (bnl) is localized in groups of cells near tracheal metameres. The tracheal cells expressing the FGF receptor breathless (btl) respond to these sources of FGF ligand and extend towards them. However, this FGF signaling pathway is not sufficient for the formation of continuous dorsal trunk, the only muticellular tube in tracheal system. Recently, it was found out that single mesodermal cells called bridge-cells are essential for the formation of continuous dorsal trunk as they direct the outgrowth of dorsal trunk cells towards the correct targets. The results in this PhD thesis demonstrate that a cell adhesion molecule Capricious (Caps), which is specifically localized on the surface of bridge-cells, plays an essential role in guiding the outgrowing dorsal trunk cells towards their correct targets. When caps is lacking, some bridge-cells cannot stretch properly towards the adjacent posterior tracheal metameres and thus fail to interconnect the juxtaposing dorsal trunk cells. Consequently, discontinuous dorsal trunks containing interruptions at several positions are formed. On the other hand, when caps is ectopically expressed in the mesodermal cells through a twi-GAL4 driver, these mesodermal cells acquire a guidance function through ectopic caps and misguide the outgrowing dorsal trunk cells in abnormal directions. As a result, disconnected dorsal trunks are formed. These loss- and gain-of-function studies suggest that Caps presumably establishes the cell-to-cell contact between the bridge-cells and the tracheal cells and thereby mediates directly the guidance function of bridge-cells. The most similar protein known to Caps is another cell adhesion molecule called Tartan (Trn). Interestingly, trn is expressed in the mesodermal cells but not in the bridge-cells. When trn is lacking, the outgrowth of not only the dorsal trunks but also the lateral trunks are disrupted. However, in contrast to the ectopic expression of caps, the misexpression of trn does not affect tracheal development. Whereas Trn requires only its extracellular domain to mediate the matrix function, Caps requires both its extracellular and intracellular domains to function as a guidance molecule in the bridge-cells. These observations suggest that Trn functions differently from Caps during tracheal morphogenesis. Presumably, Trn mediates a matrix function of mesodermal cells, which support the tracheal cells to extend efficiently through the surrounding mesodermal tissue. In order to determine which domains dictate the functional specificity of Caps, two hybrid proteins CapsEdTrnId, which contains the Caps extracellular domain and the Trn intracellular domain, and TrnEdCapsId, which consists of the Trn extracellular domain and the Caps intracellular domain, were constructed. Gain of function and rescue experiments with these hybrid proteins suggest on one hand that the extracellular domains of Caps and Trn are functionally redundant and on the other hand that the intracellular domain dictates the functional specificity of Caps. In order to identify putative interactors of Caps, yeast two-hybrid screening was performed. An in vivo interaction assay in yeast suggests that Ras64B interacts specifically with the Caps intracellular domain. In addition, an in vitro binding assay reveals a direct interaction between an inactive form of Ras64B and the Caps intracellular domain. ras64B, which encodes a small GTPase, is expressed in the mesodermal cells concurrently as caps. Finally, a gain-of-function study with the constitutively active Ras64B suggests that Ras64B presumably functions downstream of Caps. All these results suggest consistently that the small GTPase Ras64B binds specifically to the Caps intracellular domain and may thereby mediate the guidance function of Caps.

Semantic network analysis of ontologies

A key argument for modeling knowledge in ontologies is the easy re-use and re-engineering of the knowledge. However, beside consistency checking, current ontology engineering tools provide only basic functionalities for analyzing ontologies. Since ontologies can be considered as (labeled, directed) graphs, graph analysis techniques are a suitable answer for this need. Graph analysis has been performed by sociologists for over 60 years, and resulted in the vivid research area of Social Network Analysis (SNA). While social network structures in general currently receive high attention in the Semantic Web community, there are only very few SNA applications up to now, and virtually none for analyzing the structure of ontologies. We illustrate in this paper the benefits of applying SNA to ontologies and the Semantic Web, and discuss which research topics arise on the edge between the two areas. In particular, we discuss how different notions of centrality describe the core content and structure of an ontology. From the rather simple notion of degree centrality over betweenness centrality to the more complex eigenvector centrality based on Hermitian matrices, we illustrate the insights these measures provide on two ontologies, which are different in purpose, scope, and size.

Physiological analysis of central and peripheral insect circadian pacemaker neurons

Alle bisher untersuchten Lebewesen besitzen (circadiane) innere Uhren, die eine endogene Perioden-länge von ungefähr 24 Stunden generieren. Eine innere Uhr kann über Zeitgeber mit der Umwelt synchronisiert werden und ermöglicht dem Organismus, rhythmische Umweltveränderungen vorweg zu nehmen. Neben einem zentralen Schrittmacher, der Physiologie und Verhalten des Organismus steuert, gibt es in unterschiedlichen Organen auch periphere Uhren, die die zeitlichen Abläufe in der spezifischen Funktion dieser Organe steuern. In dieser Arbeit sollten zentrale und periphere Schrittmacherneurone von Insekten physiologisch untersucht und verglichen werden. Die Neurone der akzessorischen Medulla (AME) von Rhyparobia maderae dienten als Modellsystem für zentrale Schrittmacher, während olfaktorische Rezeptorneurone (ORNs) von Manduca sexta als Modellsystem für periphere Schrittmacher dienten. Die zentralen Schrittmacherneurone wurden in extrazellulären Ableitungen an der isolierten AME (Netzwerkebene) und in Patch-Clamp Experimenten an primären AME Zellkulturen (Einzelzellebene) untersucht. Auf Netzwerkebene zeigten sich zwei charakteristische Aktivitätsmuster: regelmäßige Aktivität und Wechsel zwischen hoher und niedriger Aktivität (Oszillationen). Es wurde gezeigt, dass Glutamat ein Neurotransmitter der weitverbreiteten inhibitorischen Synapsen der AME ist, und dass in geringem Maße auch exzitatorische Synapsen vorkommen. Das Neuropeptid pigment-dispersing factor (PDF), das von nur wenigen AME Neuronen exprimiert wird und ein wichtiger Kopplungsfaktor im circadianen System ist, führte zu Hemmungen, Aktivierungen oder Oszillationen. Die Effekte waren transient oder langanhaltend und wurden wahrscheinlich durch den sekundären Botenstoff cAMP vermittelt. Ein Zielmolekül von cAMP war vermutlich exchange protein directly activated by cAMP (EPAC). Auf Einzelzellebene wurde gezeigt, dass die meisten AME Neurone depolarisiert waren und deshalb nicht feuerten. Die Analyse von Strom-Spannungs-Kennlinien und pharmakologische Experimente ergaben, dass unterschiedliche Ionenkanäle vorhanden waren (Ca2+, Cl-, K+, Na+ Kanäle sowie nicht-spezifische Kationenkanäle). Starke, bei hohen Spannungen aktivierende Ca2+ Ströme (ICa) könnten eine wichtige Rolle bei Ca2+-abhängiger Neurotransmitter-Ausschüttung, Oszillationen, und Aktionspotentialen spielen. PDF hemmte unterschiedliche Ströme (ICa, IK und INa) und aktivierte nicht-spezifische Kationenströme (Ih). Es wurde angenommen, dass simultane PDF-abhängige Hyper- und Depolarisationen rhythmische Membranpotential-Oszillationen verursachen. Dieser Mechanismus könnte eine Rolle bei PDF-abhängigen Synchronisationen spielen. Die Analyse peripherer Schrittmacherneurone konzentrierte sich auf die Charakterisierung des olfaktorischen Corezeptors von M. sexta (MsexORCO). In anderen Insekten ist ORCO für die Membran-Insertion von olfaktorischen Rezeptoren (ORs) erforderlich. ORCO bildet Komplexe mit den ORs, die in heterologen Expressionssystemen als Ionenkanäle fungieren und Duft-Antworten vermitteln. Es wurde die Hypothese aufgestellt, dass MsexORCO in pheromonsensitiven ORNs in vivo nicht als Teil eines ionotropen Rezeptors sondern als Schrittmacherkanal fungiert, der unterschwellige Membranpotential-Oszillationen generiert. MsexORCO wurde mit vermeintlichen Pheromonrezeptoren in human embryonic kidney (HEK 293) Zellen coexprimiert. Immuncytochemie und Ca2+ Imaging Experimente zeigten sehr schwache Expressionsraten. Trotzdem war es möglich zu zeigen, dass MsexORCO wahrscheinlich ein spontan-aktiver, Ca2+-permeabler Ionenkanal ist, der durch den ORCO-Agonisten VUAA1 und cyclische Nucleotide aktiviert wird. Außerdem wiesen die Experimente darauf hin, dass MsexOR-1 offensichtlich der Bombykal-Rezeptor ist. Eine weitere Charakterisierung von MsexORCO in primären M. sexta ORN Zellkulturen konnte nicht vollendet werden, weil die ORNs nicht signifikant auf ORCO-Agonisten oder -Antagonisten reagierten.