Isocost lines in the cellular economy: gene expression is coupled due to competition for shared resources

Andras Gyorgy1,*, Jose I. Jimenez2,*, Hattie Chung3,
Ron Weiss1 and Domitilla Del Vecchio1

1Massachusetts Institute of Technology, Cambridge USA

2University of Surrey, Guildford UK

3Harvard Medical School, Cambridge USA

*equal contribution

Transcriptional and translational resources are available in limited amounts. Since genetic circuits in living cells share these common resources, unexpected couplings can arise among seemingly unconnected genetic modules, yielding poorly predictable circuit behavior. Among the cellular resources required for gene expression, RNAP and ribosomes are key factors. Therefore, characterizing how gene expression becomes coupled due to the limited availability of RNAP and ribosomes is essential both for understanding the behavior of natural circuits and for engineering new ones.
Using a physics-based model together with experiments on synthetic constructs in E. coli, we discover that the expression of two genes without a regulatory link between them is linearly constrained. This linear relationship can be interpreted as an isocost line, introduced in microeconomics to describe what combinations of two products can be purchased with a limited budget. We characterize the extent by which proteins become coupled due to the limited availability of RNAP and ribosomes: it is substantial ranging from 60% when genes are on medium copy number plasmids to
30% when genes are on low copy number plasmids. These effects are therefore significant in the design of synthetic gene circuits even when assembled on low copy number plasmids.
Furthermore, as RBS strength and plasmid copy number are two of the most commonly tuned experimental parameters, we characterize how changing them affects salient features of the isocost line, such as its slope, establishing the extent of coupling. To this end, we construct a system with two fluorescent reporter proteins, one inducible and one constitutive without a regulatory path between them on the same plasmid, for several combinations of plasmid copy number and RBS strength for the inducible gene. In agreement with the mathematical predictions, changing the RBS strength of the inducible gene rotates the isocost line, while changing the plasmid copy number shifts the isocost line.
Our work demonstrates that isocost lines can be employed to reliably predict how the behavior of genetic circuits become coupled when sharing limited cellular resources, and that they provide design guidelines for minimizing the effects of such couplings. For instance, our results reveal, perhaps counter-intuitively, that choosing the strongest RBS for the inducible gene is the best strategy to minimize its effect on the expression of the constitutive gene.

Keywords: gene regulation, context-dependence, cellular economy, modeling