Non-local models for the formation of hepatocyte-stellate cell aggregates |
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Authors: | JEF Green SL Waters JP Whiteley KM Shakesheff |
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Institution: | a Computational Biology Group, School of Computer Science and Software Engineering, Faculty of Engineering, Computing and Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia b Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK c Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK d Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK e Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2 f Tissue Engineering Group, School of Pharmacy, University of Nottingham, Nottingham NG7 2RD, UK |
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Abstract: | Liver cell aggregates may be grown in vitro by co-culturing hepatocytes with stellate cells. This method results in more rapid aggregation than hepatocyte-only culture, and appears to enhance cell viability and the expression of markers of liver-specific functions. We consider the early stages of aggregate formation, and develop a new mathematical model to investigate two alternative hypotheses (based on evidence in the experimental literature) for the role of stellate cells in promoting aggregate formation. Under Hypothesis 1, each population produces a chemical signal which affects the other, and enhanced aggregation is due to chemotaxis. Hypothesis 2 asserts that the interaction between the two cell types is by direct physical contact: the stellates extend long cellular processes which pull the hepatocytes into the aggregates. Under both hypotheses, hepatocytes are attracted to a chemical they themselves produce, and the cells can experience repulsive forces due to overcrowding. We formulate non-local (integro-partial differential) equations to describe the densities of cells, which are coupled to reaction-diffusion equations for the chemical concentrations. The behaviour of the model under each hypothesis is studied using a combination of linear stability analysis and numerical simulations. Our results show how the initial rate of aggregation depends upon the cell seeding ratio, and how the distribution of cells within aggregates depends on the relative strengths of attraction and repulsion between the cell types. Guided by our results, we suggest experiments which could be performed to distinguish between the two hypotheses. |
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Keywords: | Cell aggregation Chemotaxis Tissue engineering Integro-differential equations |
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