Modeling the cost and benefit of proteome regulation in a growing bacterial cell

Escherichia coli cells differentially regulate the production of metabolic and ribosomal proteins in order to stay close to an optimal growth rate in different environments, and exhibit the bacterial growth laws as a consequence. We present a simple mathematical model of a growing-dividing cell in which an internal dynamical mechanism regulates the allocation of proteomic resources between different protein sectors. The model allows an endogenous determination of the growth rate of the cell as a function of cellular and environmental parameters, and reproduces the bacterial growth laws. We use the model and its variants to study the balance between the cost and benefit of regulation. A cost is incurred because cellular resources are diverted to produce the regulatory apparatus. We show that there is a window of environments or a 'niche' in which the unregulated cell has a higher fitness than the regulated cell. Outside this niche there is a large space of constant and time varying environments in which regulation is an advantage. A knowledge of the 'niche boundaries' allows one to gain an intuitive understanding of the class of environments in which regulation is an advantage for the organism and which would therefore favour the evolution of regulation. The model allows us to determine the 'niche boundaries' as a function of cellular parameters such as the size of the burden of the regulatory apparatus. This class of models may be useful in elucidating various tradeoffs in cells and in making in-silico predictions relevant for synthetic biology.