Schedule of the LMS Workshop "On Mathematical and Computational Modelling of Biological Systems", 23 September 2015, TSU102

Collective movement of animals (e.g., birds, fish, insects, ungulates, etc.) has attracted scientists’ attention for over 2000 years. More recently, researchers started investigating also the collective movement of cells during development or disease (e.g., cancer). In this talk we discuss a class of nonlocal hyperbolic models for interactions between animals and interactions between cells. The models do not only show a large variety of spatial and spatio-temporal patterns, but also display complex transitions between these patterns. To understand the transitions between some of the patterns exhibited by models for self-organised animal movement, in particular patterns occurring near codimension-2 bifurcation points, we use bifurcation and symmetry theory combined with numerical simulations. We conclude by discussing the patterns exhibited by a nonlocal hyperbolic model for the dynamics of cancer cells, as a result of cells’ responses to TGF-beta molecules. 10.30-10.55: Prof Carmen Molina-Paris (University of Leeds) Title: IL-7 in naive T cell homeostasis: modelling at the molecular, cellular and population scales Abstract: In this talk I will introduce a mathematical model of naive T cell homeostasis. The number of naive T cells in the peripheral pool is regulated by IL-7 signalling, and T cell receptor diversity is regulated by peptide-MHC signalling. The development of a mathematical model requires understanding the key molecular, cellular and population processes involved in peripheral naive T cell homeostasis. In order to do so, we make use of state-of-the-art experimental evidence to develop a model of IL-7 binding to its IL-7 receptor (IL-7R), internalisation, recycling, degradation, and synthesis. At the cellular level, we introduce the idea of survival and proliferation thresholds for naive T cells in the presence of IL-7. These elements allow us to define a population model of resting and cycling naive T cells, that includes the dynamics of extra-cellular IL-7. The model is then used to parameterise recent experiments by Hogan et al (2013). 11.00-11.15: Coffee Break 11.15-11.40: Dr. Eun-jin Kim (University of Sheffield) Title: Variability and degradation of self-sustained oscillators Abstract: Homeostasis is known to be absolutely critical to the sustainability of living organisms. At the heart of homeostasis are various feedback loops, which can control and regulate a system to stay in a most favourable stable state upon the influence of various disturbance. While the variability has emerged as a key factor in sustainability, too much variability however could be detrimental. It is thus absolutely crucial to understand the effect of fluctuation in different feedback loops. Modelling technique has achieved a great advancement to understand this issue, too a complicated model however often prevents us from disentangling different many processes. Homeostasis is known to be absolutely critical to the sustainability of living organisms. At the heart of homeostasis are various feedback loops, which can control and regulate a system to stay in a most favourable stable state upon the influence of various disturbance. While the variability has emerged as a key factor in sustainability, too much variability however could be detrimental. It is thus absolutely crucial to understand the effect of fluctuation in different feedback loops. Modelling technique has achieved a great advancement to understand this issue, too a complicated model however often prevents us from disentangling different many processes. Here, we propose a novel model to gain a key insight into important issue by focusing on variability and degradation of self-sustained oscillation. Specifically, we investigate the effect of fluctuations in positive and negative feedback by taking into account fluctuations in model parameters for self-excitation and nonlinear damping, corresponding to positive and negative feedback, respectively. By systematic study, we highlight the important role of fluctuation in positive and negative feedback in self-excitation and self-regulation of oscillators, respectively, and identify sweet spot in variability in model parameter for self-regulation and the limits beyond which the self-regulation breaks down. While results are generic and could be applied to different self-regulating systems (e.g. selfregulation of neuron activity, cell/tumour growth, etc), we present a specific application to heart dynamics. In particular, we show that fluctuation in positive feedback can lead to slow heart by either amplitude death or oscillation death pathway; (ii) fluctuation in negative feedback can lead to fast heart beat. 11.45-12.10: Dr. Nikos Kavallaris (University of Chester) Title: Mathematical Analysis of shadow-systems of an activator-inhibitor reaction-diffusion system Abstract: The understanding of the qualitative behavior of shadow-systems have been proven crucial towards the understanding of the behavior of the corresponding reaction-diffusion system. The understanding of the qualitative behavior of shadow-systems have been proven crucial towards the understanding of the behavior of the corresponding reaction-diffusion system. However, since shadow-systems usually are reduced to non-local single equations the above approach contains some generic difficulties. In this talk we present some recent results on the global-in-time existence and the finite-time blow-up of the shadow system of the Gierer-Meinhardt (activator-inhibitor) system. These results confirm some of the anticipated results (like Turing instability) predicted also by the corresponding reaction-diffusion system.