Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Using process algebra to quantify the radiation induced bystander effect
Rachel Lintott

Last modified: 2014-03-31


Radiotherapy is one of the most effective treatments for cancer, with an estimated 50% of all patients receiving radiotherapy at some point during their treatment. Ionising radiation acts by damaging the DNA of the targeted cells, with the most important, and difficult to repair, damage being the result of DNA double strand breaks. In recent years, several studies have detected indirect effects of irradiation known as radiation induced bystander effects (RIBEs). The mechanisms of RIBE are not well understood, although experiments have shown that irradiated cells can release a signal into the extra-cellular medium which can cause cell death or DNA damage to cells which have never been directly irradiated. It has also been hypothesised that irradiated cells can cause damage to neighbouring cells through gap-junction-mediated effects.  RIBEs are particularly important at low radiation doses where a high proportion of cells may be damaged but not killed directly, thus facilitating the release of a bystander signal, and causing subsequence damage to surrounding tissue.  Understanding the implications of radiation induced bystander effects may allow these responses to be used to enhance tumour cell killing, or to protect healthy tissue from the potentially harmful effects of ionising radiation.

We present a stochastic process algebra model, defined in bio-PEPA, which models the survival response to a given dose of radiation. Our system aims to quantify the cell kill due to bystander effects, and hence consists of a fixed number of cell colonies which may be: healthy (undamaged by radiation), damaged and able to emit the bystander signal, damaged and non-emitting, or dead. This epidemic-type model is able to predict the surviving fraction of cell colonies, showing good agreement with the commonly-used linear quadratic model, as well as predicting the proportion of cell death caused by the bystander effect. The formulation of this model in bio-PEPA enables us to encode the biological processes described above in a simple and easily interpreted way, whilst also allowing the model to be analysed in a number of different ways. The underlying CTMC is easily solvable both deterministically, via conversion to ODEs, or stochastically using Gillespie’s algorithm. The bio-PEPA model also allows us to easily determine probability density functions for particular, abstract properties of the model, in this case allowing us to estimate the probability of observing bystander effect for a given dose.