By Oliver Clemenston, Swinburne University of Technology

Gene expression is known as the process by which genetic instructions are used to synthesise gene products [1]. This process occurs in a wide range of real-world phenomena, including protein and even cancer networks. The aim of this project was to gain a greater understanding of how introducing a distributed time delay into a system of gene expression would affect the system overall, with the hope that this information could one day be expanded upon and be used in the treatment of cancer cells and networks.

The 6-week project was broken down as follows. Firstly, we identified the mathematical model for a system of gene expression that we would eventually introduce with a time delay and explored some of the main concepts behind the process of gene expression, such as the processes of transcription and translation and the time delays associated with them. The next step of the research project was to investigate the existence of the positive equilibrium of the model identified as well as the linear stability of said equilibrium, which was done analytically. Finally, numerical solutions were produced for the system with distributed time delay in an attempt to determine how inducing the time delay affected the positive equilibrium and linear stability of the system as a whole. This was done by first mathematically inducing a distributed time delay into the system before converting these equations back into a system of ODEs which could be easily modelled using MATLAB’s Matcont software package.

The effect of introducing distributed time delays into the system of gene expression is discussed deeply in the research paper. Future work for the extension of this research may include introducing a discrete time delay and comparing how differently the two types of delay affect the system, as well as varying a range of other free parameters mentioned in the paper. The purpose of this would be to see how changing other factors in the model would affect the positive equilibrium and linear stability, in the hope of one day producing more accurate models of real-life systems of gene expression, such as that of the cancer regulatory network.

[1] Taft, R.J., Pang, K.C., Mercer, T.R., Dinger, M. & Mattick, J.S., 2010. “Non‐coding RNAs: regulators of disease.” The Journal of Pathology, 220; 126-139.

Oliver Clemenston was one of the recipients of a 2016/17 AMSI Vacation Research Scholarship.

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