Translation in the cell under fierce competition for shared resources: a mathematical model
During the process of translation the mRNAs in the cell "compete" for shared resources like tRNA molecules and ribosomes. This creates an indirect and intricate coupling between the mRNAs. For example, if ribosomal "traffic jams" evolve on some mRNA then the abundance of free ribosomes may decrease leading to lower initiation rates in the other mRNAs. When the shared resources are abundant the coupling between mRNAs due to this competition is weak. However, when the resources are scarce, e.g., when the pool of free ribosomes is starved, the competition may have a dramatic effect on the dynamics of translation in the cell. This scenario may be relevant for example under stress conditions or during a high yield viral infection, where the viral mRNAs "hijack" components of the translation machinery. Fierce competition for shared resources may also take place in synthetic or engineered systems such as cell free systems or in the case of high-throughput heteroglougs gene expression. We study this scenario using a mathematical model that includes a network of m ribosome flow models (RFMs) interconnected via a pool of free ribosomes. Each RFM is a non-linear dynamical model for ribosome flow along a single mRNA molecule, and the interconnection via the pool encapsulates the competition for shared resources. We analyze the case where m is large, i.e., a there is a large number of mRNAs. This implies that many ribosomes are attached to the mRNAs and thus the pool is starved. Our model allows quantitative and qualitative analysis of the network steady state when the pool is starved. Our analysis results show that adding an mRNA to the network always decreases the steady state pool density. This makes sense, as every new mRNA "consumes" ribosomes. We also show that adding an mRNA has an intricate effect on the total protein production in the network: on the one-hand, the new mRNA produces new proteins. On the other-hand, the other mRNAs produce less proteins, as the pool that feeds these mRNAs now has a smaller abundance of ribosomes. Our analysis yields an explicit bound for the total production rate of the network when the number of RFMIOs is very large. In particular, we analyze how the total density of ribosomes in the network bounds the total production rate. This bound demonstrates that when the number of mRNAs increases, the marginal utility of adding another mRNA diminishes, and the total protein production rate saturates to a limiting value. We demonstrate our analysis approach using an example of producing insulin in a cell free system.