The role of tumour-stromal interactions in progression is generally well accepted but their role in initiation or treatment is less well understood. It is now generally agreed that rather than consisting solely of malignant cells, tumours consist of a complex dynamic mixture of cancer cells, host fibroblasts, endothelial cells, and immune cells that interact with each other and micro-environmental factors to drive tumour progression. We are particularly interested in stromal cells (for example fibroblasts) and stromal factors (for example fibronectin) as important players in tumour progression since they have also been implicated in drug resistance. Here we develop an integrated approach to understand the role of such stromal cells and factors in the growth and maintenance of tumours as well as their potential impact on treatment resistance, specifically in application to melanoma. Using a suite of experimental assays we show that melanoma cells can stimulate the recruitment of fibroblasts and activate them, resulting in melanoma cell growth by providing both structural (extra-cellular matrix proteins) and chemical support (growth factors). Motivated by these experimental results we construct a compartment model and use it to investigate the roles of both stromal activation and tumour aggressiveness in melanoma growth and progression. We utilise this model to investigate the role fibroblasts might play in melanoma treatment resistance and the clinically observed flare phenomena that is seen when a patient, who appears resistant to a targeted drug, is removed from that treatment. Our model makes the unexpected prediction that targeted therapies may actually hasten tumour progression once resistance has occurred. If confirmed experimentally, this provocative prediction may bring important new insights into how drug resistance could be managed clinically.

The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads the pattern outwards from the source. Convection adds instability to the reaction-diffusion system. The result of this instability is a readiness to create a pattern. We choose the Lambda-Omega reaction functions for their simple limit cycle. We carry out a transformation of the dependent variables into polar form. From this we consider the initiation of the pattern to approximate a traveling wave. We carry out numerical experiments to test our analysis. These confirm the premise of the analysis, that the initiation can be modeled by a traveling wave. Furthermore, the analysis produces a good estimate of the numerical results. Most significantly, we confirm that the pattern consists of two different types.

We consider the steady state of an open biochemical pathway, with controlled flow. Previously we have shown that the steady state of open enzyme catalysed reactions may be unstable, which discourages the application of the quasi-steady-state approximation (QSSA) (IEE Proc. Syst. Biol. 153 (2006) 187 (2007) 295), we employ the Gershgorin circle theorem, which elegantly assesses stability. This is the key tool for our analysis. Once we have the linear stability matrix laid out in a suitable form, the application of the method is straightforward. We find that in open biochemical pathways, simple chains, branches and loops always have stable steady states. We conclude that simple open pathways are stable.