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  Mathematical models of RNA and protein dynamics and their integration with gene expression data

   School of Biological Sciences

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  Prof Ramon Grima, Dr N Popovic  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

A gene regulatory network involves a set of genes interacting with each other to control cellular functions. For example, in autoregulation, a protein expressed from a gene activates or suppresses its own transcription, thereby regulating the number of proteins through negative or positive feedback [1].

Mathematical models of stochastic gene expression have provided insight into how intrinsic noise (due to transcriptional and translational processes) can be controlled via feedback mechanisms [1]. These models also have shown how noise can generate oscillations and multi-stable states. However, these models ignore important sources of fluctuations such as those due to cell growth, cell division, DNA replication and cell size dependent transcription.

In this project, the student will build on recent advances [2] to construct a detailed stochastic model of gene regulation that includes these noise sources. A first aim is the approximate analytical solution of this stochastic model and its use to precisely quantify how each different source of noise contributes to emergent phenomena observed at the single-cell level. A secondary aim is to obtain a reduced version of this detailed model by the modification of recently proposed AI techniques [3]. A final aim involves the use of the analytical solution within a Bayesian inference framework to estimate the parameters of gene regulatory networks from single cell data.  

The project will give the student a solid foundation in the basic molecular biology of transcription, and its modelling using stochastic simulations, the chemical master equation and techniques from machine learning. No previous background on these topics is assumed, though experience in the analytical and numerical solution of ordinary differential equations and some experience in coding is preferable.

The project is ideal for a student with a mathematics or physics bachelor’s degree who is interested in the quantitative modelling of living systems. The student will be part of the group of Prof. Ramon Grima They will be based in the C. H. Waddington building which houses the Centre for Synthetic and Systems Biology at the University of Edinburgh. The prospective second supervisor, Dr. Nikola Popovic, is based in the School of Mathematics at the University of Edinburgh and will contribute expertise in the qualitative analysis of differential equations to the project.

Interested students should contact Prof. Ramon Grima ([Email Address Removed]) to discuss the project and the application procedure.

The School of Biological Sciences is committed to Equality & Diversity:

Biological Sciences (4) Computer Science (8) Mathematics (25)

Funding Notes

This 4 year PhD project is funded by EPSRC Doctoral Training Partnership.
This opportunity is open to UK and International students and provides funding to cover stipend at UKRI standard rate (£18,622 for 2023-24) and UK level tuition fees. The fee difference will be covered by the University of Edinburgh for successful international applicants, however any Visa or Health Insurance costs are not covered.

UKRI eligibility guidance:
Terms and Conditions:
Closing date for applications: Friday 15th March 2024


[1] R. Grima et al "Steady-state fluctuations of a genetic feedback loop: An exact solution." The Journal of chemical physics 137.3 (2012): 035104; Z. Cao and R. Grima. "Linear mapping approximation of gene regulatory networks with stochastic dynamics." Nature communications 9.1 (2018): 1-15.
[2] C. Jia and R. Grima. "Frequency domain analysis of fluctuations of mRNA and protein copy numbers within a cell lineage: theory and experimental validation." Physical Review X 11.2 (2021): 021032.
[3] J. Qingchao, et al. "Neural network aided approximation and parameter inference of non-Markovian models of gene expression." Nature communications 12.1 (2021): 1-12

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