Abstract
We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.
Highlights
Cancer is a complex disease, triggered by multiple mutations in various genes and exacerbated by a number of different behavioural and environmental factors
In order to gain some first insights into the role of transcriptional and translational delays on the dynamics of gene regulatory networks (GRNs), we focus on the behaviour of the delayed simplified nonlinear model (DSNM) (6)
By reducing the model to the one with a single time delay, we have considered possible behaviour in the quasi-steady state approximation of very fast mRNA dynamics, which has resulted in a lower-dimensional system of DDEs
Summary
Cancer is a complex disease, triggered by multiple mutations in various genes and exacerbated by a number of different behavioural and environmental factors. Many studies have focussed on identifying efficient genetic cancer biomarkers, such as specific genes and groups of genes associated with significant number of cases of breast cancer [3] and prostate [4] and pancreatic cancer [5]. Depending on a particular biological regime in which a given GRN is operating, it is often possible to encounter a situation where there is a significant separation of time scales due to, for instance, very fast mRNA dynamics compared to other characteristic time scales. In such a case it is possible to perform dimensional reduction and concentrate on the dynamics of a smaller number of variables.
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