Mathias Luidor Heltberg

A thesis for the degree of Doctor of Philosophy defended April 2019.

The PhD School of Science, Faculty of Science, Biocomplexity, Niels Bohr Institute, University of Copenhagen

Supervisor:
Mogens H. Jensen

Complex Dynamics in Cell Signalling

This thesis consists of five results sections, in which biological systems are examined through mathematical modelling. The first section examines how the transcription factor NF-kB is affected by oscillations in the ligand TNF. Since the presence of a constant level of TNF induces oscillations in NF-kB, they create a system of two coupled oscillators that can lead to entrainment depending on the coupling strength between them and the ratio between their original frequencies.For a range of parameters, this led to two stable limit cycles, and in the presence of noise transitions between the two cycles occurred and we termed this modehopping. We measured the distribution of transition times, and found this to be the sum of two exponentials we described by a simple 1D model. Next we considered how this affects downstream genes, and constructed a model that separates genes depending on the affinity and cooperativity of the NF-kB binding to the promoter region of the gene. We found that the transitions in NF-kB oscillations creates multiplexing between different families of genes. Then we increased the amplitude of TNF further and observed chaotic dynamics in NF-kB, with statistical properties similar to the trends found in modehopping. The chaotic dynamics created a variety of different amplitudes, and we realized that this was a mechanism to enhance low affinity genes. We found that this led to a significant raise in protein complex formation and that chaos enhanced both the efficiency and economy of this process.

Finally we found that chaotic dynamics creates a population of heterogeneous cells that individually changes state in time. This was found to increase the survival rate in various toxic environments.