Systems Biology Chaste: Multi-scale modelling in systems biology
Introduction and aims
We have recently begun to extend the cell-based simulation component of Chaste into a general framework for the simulation of multi-scale, computationally demanding problems arising in systems biology. This work is part of the Oxford Centre for Integrative Systems Biology (OCISB). More information on the OCISB can be found here.
In collaboration with experimentalists based at the OCISB and elsewhere, we are building integrative models of well-defined biological systems within the Chaste framework, with a view to explaining (quantitatively) how specific functions (motion, cell division, death, particular response to particular stimulus. etc.) arise at the system level.
Modelling approach
We employ a multi-scale modelling framework comprising of up to three interlinked modules: a model of cellular behaviour (for example, progress through the cell cycle); a model of the movement and mechanical interaction between cells; and a model of the transport of key nutrients, signalling molecules or waste products. Models of sub-cellular behaviour may be either deterministic or stochastic, and range from simple rule-based models to highly non-linear ordinary differential equation models. There are a variety of discrete model frameworks that can be used to describe the mechanical behaviour of cell aggregates, ranging from lattice-based models to cell-centre models and the non-point-mass vertex-based models. The Chaste code currently supports the simulation of cell populations using a cell-centre approach (with connectivity defined either by a Voronoi tessellation or 'overlapping spheres') or a vertex approach. The transport of nutrients, signalling molecules or waste products may be modelled using a continuum approach; due to the presence of cell growth and division, such partial differential equation models must be solved on an irregular and evolving domain.
Applications
Bacterial biofilm formationIn a recently initiated collaboration with George Wadhams (OCISB) and Marcus Tindall (University of Reading), we are using mathematical modelling to investigate the early stages of biofilm formation in R. sphaeroides. Biofilm formation is a multi-stage process occurring over multiple time scales. Biofilms are of interest as they are key factors in problems such as human and animal infections, fouling of industrial equipment and water systems, and waste treatment and remediation. Using a cell-based approach, we will explore the role of cell growth, adhesion, chain formation and cell-fluid interactions in biofilm formation. This modelling work will be informed and validated by experiments.
An example of the output of an initial test simulation is given below.
Outside the OCISB, in collaboration with Martin Baron (Biochemistry, University of Manchester), we are using mathematical modelling to investigate how multiple pathways, involving intrinsic factors and extrinsic signals, interact to control stem cell self-renewal, proliferation and differentiation within the Drosophila melanogaster ovary (a model system for stem cell biology). Currently we are building a cell-based model of the ovary to investigate how multiple cell types interact to generate a dynamic equilibrium.
