A percolation-like model for simulating inter-cellular diffusion in the context of bystander signalling in tumour

Despite ongoing active research, the role of the radiation bystander effect in modifying local tissue response to an ionising radiation dose remains unclear. The present study aims to provide new insight by simulating the diffusion-mediated inter-cellular communication processes in 2D and 3D cell-like structures to calculate likely signal ranges in the diffusion limited case. Random walks of individual signalling molecules were tracked between cells with inclusion of molecule-receptor interactions. The resulting diffusion anomaly is a function of cell density, signal uptake probability and the spatial arrangement of cells local to the signal origin. Uptake probability effects dominate percolation effects in disordered media. Diffusion through 2D structures is more conducive to anomalous diffusion than diffusion through 3D structures. Values for time-dependent diffusion constants and permeability are derived for typical simulation parameters. Even at low signal uptake probabilities the communication range is restricted to a mean value of less than 100 μm owing to complete signal uptake by 600 s. This should be considered in light of the potential influence of signal relaying, flow-dynamics or vasculature-mediated signalling.