Cell-to-cell variability and its consequences for cellular communities

The study of genetically identical cells frequently reveals that substantial variation exists between the expression levels of molecules, such as mRNAs and proteins, with respect to time in individual cells and across a population. This is due to intrinsic noise arising from the random timing of biochemical reactions in the gene regulatory network. An additional source of noise in biological systems comes from interactions of unknown molecular components with the network, which are collectively termed extrinsic noise. Mathematical modelling has been used to understand the factors that contribute to the resulting stochasticity in the gene expression dynamics of cells. As many molecular species are present in small numbers, we require a stochastic description of these biochemical systems. Chapter 1 gives a general introduction into the sources of gene expression noise and non-genetic cell-to-cell variability. Throughout Chapters 2-5, we investigate cell-to-cell variability in a wide range of biological systems through the integration of experimental approaches and mathematical modelling.In Chapter 2, we derive a novel approximate method to obtain closed-form expressions for the means, variances, and power spectra of the molecular species within a chemical reaction network with intrinsic and slowly changing extrinsic noise. We do this by extending the conventional linear-noise approximation (LNA) to include systems where extrinsic noise manifests itself as fluctuations in the reaction rates. These extrinsic fluctuations are characterised by a longer timescale compared to the typically fast intrinsic reaction processes. We verify the accuracy of the theory by its application to different models of gene regulatory networks and comparing the analytical predictions to the more computationally costly results produced through stochastic simulations.In Chapter 3, we study the bacterial adaptive immune system CRISPR-Cas in a growing population of Escherichia coli. To survive infection, bacteria are forced to obtain an immunological memory of past infections through a process termed priming, to enable recognition of previously encountered threats. In addition, the cell contains an operon of CRISPR-associated (Cas) proteins which are responsible for finding and eliminating these invaders through a process called interference. We use time-lapse microscopy in combination with microfluidics to obtain single-cell lineage data throughout the entire duration of CRISPR defence. For the first time, we quantify the variation that exists between cells in how fast they can respond to foreign mobile genetic elements. Clearance of previously encountered invaders through CRISPR interference is fast with a narrow distribution. However, invaders can accumulate mutations in the PAM region which allows them to escape direct interference, resulting in large cell-to-cell variability of clearance times. Further analysis of the experimental data, together with a specially developed agent-based stochastic framework which simulates the behaviour of the bacterial population, allow us to identify the acquisition of a new immunological memory (adaptation) as the source of the increased variation in priming. Statistical analysis of cell lineage features reveals that faster growth and cell division, as well as higher levels of the CRISPR surveillance complex Cascade, increase the probability of plasmid clearance by interference. In contrast, slower growth is associated with a higher rate of adaptation. Through mathematical modelling we estimate the influence of target and Cascade copy numbers, as well as Cascade binding affinity of the rate of priming. Our results show that the ability to adapt to an invading threat by primed CRISPR adaptation is highly stochastic, implying that only subpopulations of bacteria can respond to foreign invaders in a timely manner.It has been shown that mutations in the protospacer adjacent motif (PAM), which flanks the DNA sequence targeted by the surveillance complex, affect target recognition by Cascade. In Chapter 3, we found that this reduced binding affinity of Cascade to targets with escaping PAM mutations can explain the observed wide distribution of plasmid loss times. However, the exact mechanism by which Cascade initiates primed adaptation, the acquisition of a new immunological memory, is largely unknown. In Chapter 4, we investigate the primed adaptation mechanism further by characterising the dynamics of CRISPR-mediated target clearance for three different PAM variants. We compare experimental single-cell lineages to simulated trajectories from two mechanisms of primed adaptation proposed in the literature by adapting the agent-based framework developed in the previous chapter. We show that features of the data are consistent with the interference-independent model for adaptation, in which a primed adaptation complex is responsible for the acquisition of new immunological memories. Our results indicate that the CRISPR-response of E. coli depends strongly on the PAM variant, which suggests these bacteria might employ a strategy to balance the relative rates of interference and the acquisition of new memories.While for bacteria the notion of cell-to-cell variability to enable bet-hedging strategies is sensible, for multicellular organisms reproducible and coordinated development might seem more important. Plants have evolved regulatory mechanisms to achieve specialised cell types and robust tissue growth. In Chapter 5 we quantify the noisiness of stochastic gene expression in Arabidopsis thaliana at the cellular level. To this end, we employ a combination of experimental and modelling approaches. First, we use the photoconvertible KikGR marker to show that the protein expressions of individual cells fluctuate over time. A dual reporter system is then used to study extrinsic and intrinsic noise. This reveals that extrinsic noise is the main source of protein variability in both young and old rosette leaves, and that extrinsic noise in stomata is clearly lower in comparison to several other cell types. Finally, through spatial analysis we show that cells are coupled with respect to stochastic protein expression in young leaves, hypocotyls and roots but not in mature leaves. Through theoretical analysis we find that the observed spatial correlation between cells can only partially be explained by the inheritance of mRNA and protein from a shared ancestor, which suggests other extrinsic noise sources affect the cellular dynamics.The results from Chapters 2-5 are discussed in a broader context in Chapter 6. In this general discussion, experimental and computational challenges relating to the study of gene expression noise are reviewed. Furthermore, I discuss possible implications of stochastic gene expression for phenotypic variability