Models of noise propagation in growing and regulating bacterial cells

Abstract

At the single cell level, bacterial gene expression is a highly stochastic process. Protein concentrations fluctuate over time, also at timescales shorter than the cell cycle. Especially for metabolic proteins, such fluctuations are expected to affect metabolic fluxes, and therewith transfer to downstream processes such as the instantaneous cellular growth rate. Earlier experiments in Escherichia coli confirmed that temporal fluctuations in the concentration of a particular metabolic protein to some extent correlate with fluctuations observed in the growth rate. Stochastic fluctuations, so-called ‘noise’, thus propagates through the metabolic network.

To understand and describe noise propagation in bacterial cells, mathematical models can be a great asset. Models can be used to test fundamental assumptions, determine routes by which noise reverberates through the cell, and dissect the contribution of different sources of noise to an observed stochastic signal. Conceptually, models concerning noise propagation quickly become complicated. First, growth itself feeds back on fluctuations due to dilution associated with volume growth. Second, although experiments can generally trace a single protein species over time, the concentrations of all proteins species continuously fluctuate, all adding to the cell’s stochasticity. Third, bacteria are known to regulate the (average) expression of most protein species when faced with different external environments. Such regulatory networks are likely to affect noise propagation.

In this thesis we therefore set out to create mathematical models to study noise propagation. We broadly focus on two questions: (1) how are the stochasticity of the growth rate and of a particular protein’s concentration influenced by the stochastic expression of other proteins, and (2) how do regulatory networks influence the propagation of noise? First, we show that single-cell experiments regarding noise propagation can be explained by solely including noise in the production of all protein species, i.e. without the need to include other noise sources such as intrinsic noise in metabolic fluxes, cell division or the environment. In later chapters, we mathematically pinpoint the exact contribution to cellular stochasticity of the cAMP-CRP regulatory network. This regulatory network is commonly known for its role in the cell’s response to changes in the external growth condition. Backed up by experimental data, we show that this regulatory network additionally reacts to internal stochasticity, highlighting a fundamental link between regulation and noise propagation: the cell’s (internal, regulatory) networks that govern the dynamical changes in response to a changing external condition, also shape noise propagation properties in a fixed environment.