Side reactions do not completely disrupt linear self-replicating chemical reaction systems

A crucial question within the fields of origins of life and metabolic networks is whether or not a self-replicating chemical reaction system is able to persist in the presence of side reactions. Due to the strong nonlinear effects involved in such systems, they are often difficult to study analytically. There are however certain conditions that allow for a wide range of these reaction systems to be well described by a set of linear ordinary differential equations. In this article, we elucidate these conditions and present a method to construct and solve such equations. For those linear self-replicating systems, we quantitatively find that the growth rate of the system is simply proportional to the sum of all the rate constants of the reactions that constitute the system (but is nontrivially determined by the relative values). We also give quantitative descriptions of how strongly side reactions need to be coupled with the system in order to completely disrupt the system

Characterisation of Dynamic Process Systems by Use of Recurrence Texture Analysis

This thesis proposes a method to analyse the dynamic behaviour of process systems using sets of textural features extracted from distance matrices obtained from time series data. Algorithms based on the use of grey level co-occurrence matrices, wavelet transforms, local binary patterns, textons, and the pretrained convolutional neural networks (AlexNet and VGG16) were used to extract features. The method was demonstrated to effectively capture the dynamics of mineral process systems and could outperform competing approaches

Analysis of Generative Chemistries

For the modelling of chemistry we use undirected, labelled graphs as explicit models of molecules and graph transformation rules for modelling generalised chemical reactions. This is used to define artificial chemistries on the level of individual bonds and atoms, where formal graph grammars implicitly represent large spaces of chemical compounds. We use a graph rewriting formalism, rooted in category theory, called the Double Pushout approach, which directly expresses the transition state of chemical reactions. Using concurrency theory for transformation rules, we define algorithms for the composition of rewrite rules in a chemically intuitive manner that enable automatic abstraction of the level of detail in chemical pathways. Based on this rule composition we define an algorithmic framework for generation of vast reaction networks for specific spaces of a given chemistry, while still maintaining the level of detail of the model down to the atomic level. The framework also allows for computation with graphs and graph grammars, which is utilised to model non-trivial chemical systems. The graph generation relies on graph isomorphism testing, and we review the general individualisation-refinement paradigm used in the state-of-the-art algorithms for graph canonicalisation, isomorphism testing, and automorphism discovery. We present a model for chemical pathways based on a generalisation of network flows from ordinary directed graphs to directed hypergraphs. The model allows for reasoning about the flow of individual molecules in general pathways, and the introduction of chemically motivated routing constraints. It further provides the foundation for defining specialised pathway motifs, which is illustrated by defining necessary topological constraints for both catalytic and autocatalytic pathways. We also prove that central types of pathway questions are NP-complete, even for restricted classes of reaction networks. The complete pathway model, including constraints for catalytic and autocatalytic pathways, is implemented using integer linear programming. This implementation is used in a tree search method to enumerate both optimal and near-optimal pathway solutions. The formal methods are applied to multiple chemical systems: the enzyme catalysed beta-lactamase reaction, variations of the glycolysis pathway, and the formose process. In each of these systems we use rule composition to abstract pathways and calculate traces for isotope labelled carbon atoms. The pathway model is used to automatically enumerate alternative non-oxidative glycolysis pathways, and enumerate thousands of candidates for autocatalytic pathways in the formose process

Systematic Analysis of Stability Patterns in Plant Primary Metabolism

Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM) is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models

Development of Machine Learning Models to Detect Dynamic Disturbances in Human Gait

Machine learning has transformed the medical field by automating tasks and achieving objectives that are closer to human cognitive capabilities. Gait is a series of intricate interactions for humans, and identifying impaired gait is critical for effective decision-making in clinical practice. However, analysing the complex biological system that governs gait can be challenging. This research proposes a novel Criticality Analysis (CA) methodology to extract dynamic interactions in human gait and represent multivariate data in a nonlinear space. The proposed methodology characterises each data sample with a unique orbit, resulting from perturbations of a critical system composed of nonlinear controlled oscillators. The scale-free network of orbits is a quantitative measure of non-scale-free interacting sets of patterns, which reveal organised features of the structure of dynamic properties interconnected with human gait. This thesis focuses on implementing robust machine learning algorithms for effective detection and classification of complex dynamic patterns in human gait. The CA method maps gait features into a nonlinear representation, which is then used for training and testing categorisation algorithms. The proposed models utilise the Kernel property of the Support Vector Machines (SVM) classifier to identify high-order interactions between multiple gait data variables that may be challenging for traditional statistics. The algorithm was applied to three real datasets, and the SVM models designed using the CA method achieved an accuracy of 88.27% on average, compared to the K-Nearest Neighbours (KNN) approach's accuracy of 67.7%. The proposed SVM models use the receiver operating characteristics (ROC) and the area under the ROC metrics to evaluate their overall performance. The results of this research suggest that the proposed SVM models, with the support of the CA method, can perform as a robust and reliable classification tool for detecting dynamic disturbances of biological data patterns. This provides tremendous opportunities for clinical diagnosis and rehabilitation