Abstract: When investigating the development and function of multicellular biological systems it is not enough to only consider the behaviour of individual cells in isolation. For example when studying tissue development, how individual cells interact, both mechanically and biochemically, influences the resulting tissues form and function. Cell based modelling allows you to represent and track the interaction of individual cells in a developing tissue. Existing models including lattice based models (cellular automata and cellular Potts) and off-lattice based models (cell centre and vertex based representations) have given us insight into how tissues maintain homeostasis and how mutations spread. However, when tissues develop they interact biochemically and biomechanically with the environment and in order to capture these interactions, and the effect they have on development, the environment must be considered. We present a framework which allows multiple individual based models to be coupled together, in order to model both the tissue and the surrounding environment. The framework can use different modeling paradigms for each component, and subcellular behaviour (for example the cell cycle) can be considered. In this talk we present two examples of such a coupling, from the fields of developmental biology and vascular remodelling.

Abstract: Continuum partial differential equation models of the movement and growth of large numbers of cells generally involve constitutive assumptions about macro-scale cell population behaviour. It is difficult to know whether these assumptions accurately represent the mechanical and chemical processes that occur at the level of discrete cells. By deriving continuum models from individual-based models (IBMs) we can obtain PDE approximations to IBMs and conditions for their validity. We have developed a hybrid discrete-continuum model of nutrient-dependent growth of a line of discrete cells on a substrate in a nutrient bath. The cells are represented by linear springs connected in series, with resting lengths that evolve according to the local nutrient concentration. In turn, the continuous nutrient field changes as the cells grow due to the change in nutrient uptake with changes in cell density and the length of the cell line. Following Fozard et al. [Math. Med. and Biol., 27(1):39--74, 2010], we have derived a PDE continuum model from the discrete model ODEs for the motion of the cell vertices and cell growth by taking the large cell number limit. We have identified the conditions under which the continuum model accurately approximates the IBM by comparing numerical simulations of the two models. In addition to making the discrete and continuum frameworks more suitable for modelling cell growth by incorporating nutrient transport, our work provides conditions on the cell density to determine whether the IBM or continuum model should be used. This is an important step towards developing a hybrid model of tissue growth that uses both the IBM and its continuum limit in different regions.

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Abstract: Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within mesenchymal tissue that is itself growing. We use an agent-based model to simulate ENC colonisation and obtain agent lineage tracing data, which we analyse using econometric data analysis tools. Biological trials with clonally labelled ENS cells were also performed. In all realisations a small proportion of identical initial agents accounts for a substantial proportion of the total agent population. We term these individuals superstars. Their existence is consistent across individual realisations and is robust to changes in model parameters. However which individual agents will become a superstar is unpredictable. This inequality of outcome is amplified at elevated proliferation rate. Biological trials revealed identical and heretofore unexpected clonal behaviour. The experiments and model suggest that stochastic competition for resources is an important concept when understanding biological processes that feature high levels of cell proliferation. The results have implications for cell fate processes in the ENS and in other situations with invasive proliferative cells, such as invasive cancer.

Abstract: There are over 40 million people currently infected worldwide, and efforts to develop a vaccine would be improved greatly by a better understanding of how HIV survives and evolves. Recent studies discovered the ability of HIV target cells to present viral particles on the surface and trigger immune recognition and suppression by ÒkillerÓ cells of immune system. The effect of ÒkillersÓ remains to be poorly understood, however it plays a key role in control of HIV infection. While traditional vaccine approaches became unsuccessful, the vaccines against early expressed conservative viral parts are promising and would make possible managing the ability of the virus to mutate and avoid immune recognition. To discover the mechanism of ÒkillerÓ cells I developed an agent-based stochastic model of HIV dynamics at the cellular level. While the classic ODE approach is unable to simulate similar dynamics that I observed in the experimental data, the agent-based stochastic model is easily comprehensible and exposes similar kinetics. The complexity of the method increases greatly with the number of agents in the model and may be effectively resolved by using parallel computations on Graphics Processing Units (GPUs). I found that the simulated dynamics almost completely resembles the experimental data and provides answer on the addressed question. Also, the model may be applied in further developments on the design of experiments to distinguish mechanisms more precisely.