Stochastic Modelling of Gene Expression: From Single Molecules to Populations

Gene expression constitutes a vital life process through which pieces of genetic information stored in the nucleotide sequence of DNA are transformed into functional molecules, namely proteins and RNA chains. These molecules and the intricate network of interactions among them are the driving force behind most cellular processes, including gene expression itself. Also, of particular importance is the regulation of gene expression. By modulating the levels of proteins they produce, cells manage to synchronise their internal workings and adapt to various environmental conditions. Moreover, in this manner cells manage to coordinate their genetically prescribed behaviour when present in populations, such as a developing embryo or a bacterial colony. This thesis presents a theoretical study of gene expression within the context of different organisational levels from the molecular to the cell population level. On the single molecule level special emphasis is given on the dynamics of the RNA polymerase, the enzyme that carries out the transcription of DNA into RNA. Recent single molecule experiments have shed light on the dynamical behaviour of this molecule as it transcribes DNA. Of particular importance is the direct observation of transient pauses in the process of transcription, induced by the he backward translocation of the enzyme along the DNA template, a phenomenon dubbed backtracking. Motivated by this finding and the implications transcriptional pausing has for the regulation of DNA transcription, our work aims at providing a quantitative characterisation of backtracking and the effect of such pauses on the temporal dynamics of the process. Our results indicate that the lifetime of such pauses should obey a wide distribution and can have dramatic effects on the temporal statistics of the transcription process. A particularly interesting function of backtracking is transcriptional error correction. Indeed, RNAP does not copy the genetic information accurately; thermal fluctuations introduce errors to the process that must be corrected on the fly. A proposed mechanism of transcriptional error correction involves backtracking of the RNA polymerase and the subsequent cleavage of the the erroneous RNA segment. Based on the picture of DNA transcription provided by singlemolecule experimentswe propose a putativemodel of this editing process. Our work offers a quantitative picture of transcriptional error correction, predicting the error rate in terms of microscopic rates parameters and allowing one to assess the role of backtracking in transcriptional fidelity. Furthermore, our model puts the specific mechanism of error correction into context by linking it to kinetic proofreading, a general principle of biological accuracy. On a different level, the microscopic dynamics of the DNA transcription ought to have direct implications regarding fluctuations in the numbers of RNA species observed within the cell. These fluctuations have on their turn far-reaching implications regarding cell fate, behaviour and function. To study the effect transcriptional pauses have on the statistics of RNA production we propose an integrated model of DNA transcription. A key element of our model is that several RNAP molecules can transcribe DNA at the same time, moving in tandem on the template. Our results indicate that transcriptional pauses and exclusive interactions between the RNAP molecules, lead to bursts of RNA production and therefore make the process appear more random. Interestingly such pattern of mRNA production has been observed experimentally and hence our model provides a possible explanations of the phenomenon. It also demonstrates how interactions between molecules can affect behaviour at cellular level by introducing fluctuations in the process of gene expression. At an even higher level, one should appreciate the fact that cells rarely exist in isolation. At this level of description we are interested in how intra-cellular fluctuations of molecular species affect the behaviour of populations of cells. In particular, motivated by the complex social behaviour observed in certain bacterial species, we propose an insilico paradigm of bacterial communication. In a nutshell, the circuit enables cells to communicate and choose between two antagonistic social behaviours. We find that owing to intra-cellular fluctuations the population can exist in two states: for low values of intra-cellular coupling the population appears mixed (disordered), with approximately one half of the cells adopting each behaviour. As the coupling is increased the population a consensus state starts to appear. We study the transition between the two regimes of behaviour and find that intra-cellular fluctuations as well as the size of the population affect the steepness of this transition