Modelling and Reverse-Engineering of Biological Phenomena by means of Metabolic P Systems

Biological networks have a crucial role in each process of life, including gene regulatory mechanisms, cell differentiation, metabolism, the cell cycle, and signal transduction. Advances in experimental methods have enabled large-scale studies of these networks and can reveal the logic that underlies them. Consequently, biologists must integrate great quantities of experimental data and analyze complex networks. Mathematical models are essential tools to link the behaviours of a system to the interaction between its components. Models of biochemical networks are expected to benefit several fields. In medicine, mechanisms of diseases which are characterized by dysfunctions of regulatory processes can be elucidated. Pharmaceutics could take advantage in the search of new treatments and drugs. Biotechnological projects can benefit from predictive models that will replace some tedious and costly experiments in laboratory. And, computational analysis may contribute to basic biological research. Therefore, the success of Systems Biology will certainly require new modelling, simulation tools, and reverse-engineering approaches. In the last years, many tools and computational models have been developed for biological systems analysis. Nonetheless, our current picture of how regulations are carried out is probably still missing several significant pieces. More experimental work is needed, and these experimental results must be incorporated in improved models. This is linked with the necessity to improve reverse-engineering approaches which use time-series data. We emphasize that integration of different types of biological networks will be a fundamental step to the goal of Systems Biology. This would benefit from the creation of a common modelling framework which takes into account different entities, such as genes, proteins, metabolites, etc..., and relationships, like metabolic reactions, interactions, regulations, transports, etc... This represents a field where novel modelling formalisms and simulation tools will have great added value. Several problems and requirements arise toward this advance, such as how to deal with incomplete information, how to manipulate large models, how to extract valuable information about the regulative mechanisms, how to analyse these models, and how to infer suitable models from experimental data. However, the existing frameworks can hardly fulfill such demands, which reflects the need to search for suitable computational models. Moreover, one of the most important features for handling the high complexity of biological phenomena seems to be the possibility to observe these systems from an adequate abstraction level. Along this direction, the Metabolic P systems (MP systems) have been introduced. They are a new computational model which provides a macroscopic, global and time-discrete perspective on metabolic processes and related dynamics. Advantages of this approach are a i) natural mapping between real elements and model elements, ii) the possibility to adapt the model perspective to the temporal grain of observed data, and iii) the Log-Gain theory. According with this theory, the MP modelling process of a biochemical systems can be reduced to a reverse-engineering problem. However, crucial tasks and open problems remained to be performed for a complete discovery of the underlying MP system which explains an observed dynamics. In this Thesis, we propose solutions for these problems and tasks. It starts from the standpoint of biological information and its processing in living organisms. Then, after an overview about modelling and tools in computational biosystems, the Thesis is focused on the main theme: modelling and reverse-engineering of biological phenomena by means of MP systems. The first results prove the usefulness of MP systems to model several classes of phenomena. In fact, i) we modelled the upper part of the glycolysis in Saccharomyces cerevisiae and a synthetic oscillatory genetic network, ii) we developed a work-flow for the estimation of MP systems describing the dynamics of bistable/multistable phenomena. Others results concern MetaPlab, a Java software implemented to automatize modelling, reverse-engineering, and analysis of biochemical phenomena by means of MP systems. The author contributes to develop a flux discovery plugin and to realize a MetaPlab user guide and plugin tutorials. The remaining results represent the core of this work and are related to the Log-Gain theory, which represents the first step to obtain an MP system starting from experimental data. We performed the crucial tasks and solved the open problems of this theory, in order to have a framework useful for a complete discovery of the underlying MP system explaining an observed dynamics. In particular, i) we proved that the Log-Gain theory can be applied even with a lack of information about the regulative mechanisms; ii) we reported results regarding the efficient computations of reaction fluxes; iii) we proposed a heuristic algorithm to compute initial reaction fluxes, which are needed for the application of the Log-Gain theory; iv) we developed a complete pipeline for data analysis which addresses the entire process of flux regulation function synthesis and regulators discovery from data preparation to model validation. Moreover, this Thesis provides the first MP model deduced by means of the Log-Gain theory from experimental data. In fact, we defined an MP model of an important photosynthetic phenomenon called Non Photochemical Quenching, which determines the plant accommodation to the environmental light. Since no previous mathematical models of this phenomenon were available, this result shows the advantage of the Log-Gain theory for deducing mathematical models describing complex systems. In this manner the theory of MP systems can be seen as a new tool for constructing models, where the difficulty of kinetic rate constants evaluation is solved by the log-gain procedure, avoiding analysis at microscopic level. We also recall the models that we obtained for the mitotic oscillator in early amphibian embryos and the metabolic insulin signaling pathway. The results achieved for the first model prove that our framework is able to capture the salient characteristics of a system, also when it is observed from a macroscopic point of view. Differently, the results of the second model present investigations on the use of Graphic Processing Units (GPU) in the context of flux estimation by means of Log-Gain theory. These results are relevant in the framework of fluxes estimation since they highlight the potentialities of MP systems to infer biological fluxes when the size of a phenomenon increases. Simulation studies and a comparison with MatLab clearly shows that the (GPU) implementation outperforms pure sequential counterparts. Finally, we point out that in the search of solutions for the open problems of the Log-Gain theory, a variety of methods naturally occurred, going from vector algebra and vector optimization to artificial neural networks.