Analysis of Biochemical Reaction Networks using Tropical and Polyhedral Geometry Methods

The field of systems biology makes an attempt to realise various biological functions and processes as the emergent properties of the underlying biochemical network model. The area of computational systems biology deals with the computational methods to compute such properties. In this context, the thesis primarily discusses novel computational methods to compute the emergent properties as well as to recognize the essence in complex network models. The computational methods described in the thesis are based on the computer algebra techniques, namely tropical geometry and extreme currents. Tropical geometry is based on ideas of dominance of monomials appearing in a system of differential equations, which are often used to describe the dynamics of the network model. In such differential equation based models, tropical geometry deals with identification of the metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. The application of such properties in model reduction and symbolic dynamics are demonstrated in the network models obtained from a public database namely Biomodels. Extreme currents are limiting edges of the convex polyhedrons describing the admissible fluxes in biochemical networks, which are helpful to decompose a biochemical network into a set of irreducible pathways. The pathways are shown to be associated with given clinical outcomes thereby providing some mechanistic insights associated with the clinical phenotypes. Similar to the tropical geometry, the method based on extreme currents is evaluated on the network models derived from a public database namely KEGG. Therefore, this thesis makes an attempt to explain the emergent properties of the network model by determining extreme currents or metastable regimes. Additionally, their applicability in the real world network models are discussed

Thermodynamic patterns of life: emergent phenomena in reaction networks

Reaction networks are an important tool for the analysis of complex chemical reaction systems. They help us understand systems ranging from specific metabolisms to planetary atmospheres. This thesis develops methods for the analysis of living systems by using reaction networks with a focus on the inclusion of thermodynamic properties. New methods for more realistic artificial chemistries are developed using thermodynamic constraints. A model of evolvable artificial ecosystems is created to understand the effect of evolution and life on the flow of matter and energy through the system. To investigate general thermodynamic properties of large-scale reaction networks, artificial reaction networks are created with a simple scheme for deriving thermodynamically consistent reaction rates. Linear and nonlinear networks using four different complex network models are simulated to their non-equilibrium steady state for various boundary fluxes. Increasing the flow through nonlinear networks shows to increases the number of cycles and leads to a narrower distribution of chemical potentials. In the context of finding signs of life by detecting chemical disequilibrium, a photochemical model of the modern atmosphere and a model of the Archean atmosphere are compared. Calculating the reaction pathways that are most relevant for explaining their reaction network's steady state with a new method allows for the detection of topological differences between the two models. Pathways of the modern Earth atmosphere are simpler (less reactions) and contain fewer cycles than their Archean counterparts. To model the influence of life on reaction pathways, an artificial ecosystem model is developed. Evolution of the reaction networks entails an evolution of reaction pathways towards simplicity, thus indicating that the presence of pronounced, relatively simple pathways in real systems is a consequence of an evolutionary mechanism

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy

The Combustion of Carbon-Tetrachloride in a High Temperature Methane-Air Flame Environment.

Stable species concentration and temperature profiles are provided for a series of five CCl\sb4/CH\sb4/air flames studied on a flat flame burner at atmospheric pressure. A detailed description of the facility used to collect this data is given. This system includes a novel flue gas collection and treatment system. A new gas chromatographic technique used to analyze subatmospheric gas samples is described in detail. This technique utilizes gas syringes for sampling of selected C\sb1 and C\sb2 hydrocarbons and chlorinated hydrocarbons, as well as fixed gases. Stable species are sampled with aerodynamically cooled quartz microprobes. Temperature measurements are taken with uncoated 0.02 cm type R thermocouple beads. The first three flames comprise a study of the variation of equivalence ratio ($\phi$) at constant atomic chlorine to hydrogen ratio (Cl/H), ($\phi$ = 0.76, 1.02, and 1.17 at Cl/H = 0.3). The first, fourth, and fifth flames comprise a study of the variation of the Cl/H ratio at constant equivalence ratio (Cl/H = 0.073, 0.34, and 0.61 at $\phi$ = 1). Net reaction rate profiles were generated for each flame for CH\sb4 and CCl\sb4. A mass destruction and removal efficiency (DRE) of near 99.99% was achieved in all five flames. Two types of stable intermediates were observed in several of the flames. Chloroform was seen as the most likely candidate product of incomplete combustion (PIC). No candidate PICs were observed in a fuel rich flame. The increasing importance of recombination reactions to form C\sb2 molecules is observed as the Cl/H ratio increases. Saturated hydrocarbons are observed to decrease in stability as the Cl/H increases. A correlation is observed between peak net reaction rate and the overall level of destruction for CH\sb4 and CCl\sb4. For a constant Cl/H ratio, the fuel rich flame has the highest peak reaction rate for CCl\sb4. The highest peak reaction rate for CCl\sb4 among the five flames occurs in the flame with the highest Cl/H ratio. An increasing time delay between CO formation and CO\sb2 formation was observed as the Cl/H ratio increased. This was due to the chlorine inhibition of CO oxidation

Estimating biological elementary flux modes that decompose a flux distribution by the minimal branching property

Motivation: Elementary flux mode (EFM) is a useful tool in constraint-based modeling of metabolic networks. The property that every flux distribution can be decomposed as a weighted sum of EFMs allows certain applications of EFMs to studying flux distributions. The existence of biologically infeasible EFMs and the non-uniqueness of the decomposition, however, undermine the applicability of such methods. Efforts have been made to find biologically feasible EFMs by incorporating information from transcriptional regulation and thermodynamics. Yet, no attempt has been made to distinguish biologically feasible EFMs by considering their graphical properties. A previous study on the transcriptional regulation of metabolic genes found that distinct branches at a branch point metabolite usually belong to distinct metabolic pathways. This suggests an intuitive property of biologically feasible EFMs, i.e. minimal branching. Results: We developed the concept of minimal branching EFM and derived the minimal branching decomposition (MBD) to decompose flux distributions. Testing in the core Escherichia coli metabolic network indicated that MBD can distinguish branches at branch points and greatly reduced the solution space in which the decomposition is often unique. An experimental flux distribution from a previous study on mouse cardiomyocyte was decomposed using MBD. Comparison with decomposition by a minimum number of EFMs showed that MBD found EFMs more consistent with established biological knowledge, which facilitates interpretation. Comparison of the methods applied to a complex flux distribution in Lactococcus lactis similarly showed the advantages of MBD. The minimal branching EFM concept underlying MBD should be useful in other applications.Department of Industrial and Systems Engineerin

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance