Intracellular network attractor selection and the problem of cell fate decision

This project aims at understanding how cell fate decision emerges from the overall intracellular network connectivity and dynamics. To achieve this goal both small paradigmatic signalling-gene regulatory networks and their generalization to highdimensional space were tested. Particularly, we drew special attention to the importance of the effects of time varying parameters in the decision genetic switch with external stimulation. The most striking feature of our findings is the clear and crucial impact of the rate with which the time-dependent parameters are changed. In the presence of small asymmetries and fluctuations, slow passage through the critical region increases substantially specific attractor selection by external transient perturbations. This has strong implications for the cell fate decision problem since cell phenotype in stem cell differentiation, cell cycle progression, or apoptosis studies, has been successfully identified as attractors of a whole network expression process induced by signalling events. Moreover, asymmetry and noise naturally exist in any integrative intracellular decision network. To further clarify the importance of the rate of parameter sweeping, we also studied models from non-equilibrium systems theory. These are traditional in the study of phase transitions in statistical physics and stood as a fundamental tool to extrapolate key results to intracellular network dynamics. Specifically, we analysed the effects of a time-dependent asymmetry in the canonical supercritical pitchfork bifurcation model, both by numerical simulations and analytical solutions. We complemented the discussion of cell fate decision with a study of the effects of non-specific targets of drugs on the Epidermal Growth Factor Receptor pathway. Pathway output has long been correlated with qualitative cell phenotype. Cancer network multitargeting therapies were assessed in the context of whole network attractor phenotypes and the importance of parameter sweeping speed

Kinetic Intersections as a Source of Information on Rate Coefficients

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Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion

Mathematical modelling and systems analysis of intracellular signalling networks and the budding yeast cell cycle

Cellular signalling networks are responsible for coordinating a cell’s response to internal and external perturbations. In order to do this, these networks make use of a wide variety of molecular mechanisms, including allostery, gene regulation, and post-translational modifications. Mathematical modelling and systems approaches have been useful in understanding the signal processing capabilities and potential behaviours of such networks. In this thesis, a series of mathematical modelling and systems investigations are presented into the potential regulation of a variety of cellular systems. These systems range from ubiquitously seen mechanisms and motifs, common to a wide variety of signalling pathways across many organisms, to the study of a particular process in a particular cell type - the cell cycle in Saccharomyces cerevisiae. The first part of the thesis involves the analysis of ubiquitous signalling mechanisms and behaviours. The potential behaviours of these systems are examined, with particular attention paid to properties such as adaptive and switch-like signalling. This series of investigations is followed by a study of the dynamic regulation of cell cycle oscillators by external signalling pathways. A methodology is developed for the study of mathematical models of the cell cycle, based on linear sensitivity analysis, and this methodology is then applied to a range of models of the cell cycle in Saccharomyces cerevisiae. This allows the description of some interesting generic behaviours, such as nonmonotonic approach of cell cycle characteristics to their eventual values, as well as allowing identification of potential principles of dynamic regulation of the cell cycle