Dissertation

Hybrid gene expression models
Iryna Zabaikina
PhD thesis advisor: Pavol Bokes

Abstract: Regulation of gene expression is represented by a variety of control motifs, mathematical models of which can provide a theoretical estimate of the process parameters. In this project, we study three particular examples of regulatory networks. The first one is negative feedback when mRNA indirectly inhibits its production. The second one is an incoherent feed-forward loop, which is represented by the interaction between mRNA and antagonistic microRNA. We construct a generalized hybrid model using a Markovian drift-jump framework with random production bursts and continuous degradation. Combined with the Chapman-Kolmogorov equation, it provides the means to determine the probability distribution of mRNA concentration. We derive the mean steady-state concentration of mRNA for both models. Subsequently, we show that it is less sensitive to the production rate in the feed-forward loop than in the negative feedback. In addition, it turns out that in presence of the low noise, FFL maintains the concentration of mRNA at a steady level despite disturbance in production rate, i.e. is perfectly adaptating. Finally, the third one is the positive feedback on dilution when the protein inhibits cell growth. We model a single cell using the drift-jump framework, then develop a population model using a measure-valued Markov process combined with the population balance equation. We show that this type of regulation causes a difference between single-cell and population protein distributions. We also demonstrate that the nature of the division mechanism, whether stochastic or deterministic (sizer), does not affect the protein distribution.

References
[1] Zabaikina, I., Zhang, Z., Nieto, C., Bokes, P. and Singh, A., 2023, May. Amplification of noisy gene expression by protein burden: An analytical approach. In 2023 American Control Conference (ACC) (pp. 2861-2866). IEEE.
[2] Zabaikina, I., Bokes, P. and Singh, A., 2023. Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution. In Computational Methods in Systems Biology: 21st International Conference (CMSB 2023) (pp. 253-268). Cham : Springer Nature.
[3] Zabaikina, I., Bokes, P. and Singh, A., 2020, May. Optimal bang–bang feedback for bursty gene expression. In 2020 European Control Conference (ECC) (pp. 277-282). IEEE.