| Abstract | Problems in systems biology are intrinsically multi-scale, with processes occuring on many disparate spatial and temporal scales. We present a multi-scale framework for mathematical modelling in systems biology. Utilising the natural structural unit of the cell, the framework consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level (micro-scale). Cells are modelled as discrete interacting entities using either an off-lattice tessellation, or a vertex based model. The behaviour at the tissue level is currently represented by field equations for nutrient or messenger diffusion, with cells functioning as sinks and sources. However, the versatility of the framework facilitates the implementation of more biologically realistic models, for example dynamic vascular networks. The sub-cellular level concerns numerous metabolic processes and is represented by interaction networks rendered into ODEs. The modular approach of the framework enables much more complicated sub-cellular behaviour to be considered. Interactions occur between all spatial scales. The multi-scale framework is implemented in an open source software library known as Chaste (http://web.comlab.ox.ac.uk/chaste). This software library consists of object orientated C++, developed using an agile development approach. All software is tested, robust, reliable and extensible. In this talk we introduce the Chaste computational framework and discuss both its functionality and development. This framework is illustrated by presenting possible applications in tissue growth, looking at colorectal cancer (within the geometry of the intestinal crypt) and the growth of tumour spheroids, developmental biology (with applications in cell sorting) and bacterial biofilms. An important consideration for any multi-scale framework is the propagation of error in the system: how coarse graining models at lower scales affects behaviour at the cell and tissue level. We use a pedagogical example to illustrate the behaviour of the overall system for varying sub-cellular models, identifying when such simplifications are possible and what levels of error are introduced. |
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