Empirical model and in vivo characterization of the bacterial response to synthetic gene expression show that ribosome allocation limits growth rate

Synthetic biology uses modeling to facilitate the design of new genetic constructions. In particular, it is of utmost importance to model the reaction of the cellular chassis when expressing heterologous systems. We constructed a mathematical model for the response of a bacterial cell chassis under heterologous expression. For this, we relied on previous characterization of the growth-rate dependence on cellular resource availability (in this case, DNA and RNA polymerases and ribosomes). Accordingly, we estimated the maximum capacities of the cell for heterologous expression to be 46% of the total RNA and the 33% of the total protein. To experimentally validate our model, we engineered two genetic constructions that involved the constitutive expression of a fluorescent reporter in a vector with a tunable origin of replication. We performed fluorescent measurements using population and single-cell fluorescent measurements. Our model predicted cell growth for several heterologous constructions under five different culture conditions and various plasmid copy numbers with significant accuracy, and confirmed that ribosomes act as the limiting resource. Our study also confirmed that the bacterial response to synthetic gene expression could be understood in terms of the requirement for cellular resources and could be predicted from relevant cellular parameters.