Increasing protein production rates can decrease the rate at which functional protein is produced

The rate at which soluble, functional protein is produced by the ribosome has recently been found to vary in complex and unexplained ways as various translation-associated rates are altered through synonymous codon substitutions. We combine a well-established ribosome-traffic model with a master-equation model of co-translational domain folding to explore the scenarios that are possible for the protein production rate, \textbf{\textit{J}}, and the functional-nascent protein production rate, \textbf{\textit{F}}, as the rates associated with translation are altered. We find that while \textbf{\textit{J}} \quad monotonically increases as the rates of translation-initiation, -elongation and -termination increase, \textbf{\textit{F}} can either increase or decrease. \textbf{\textit{F}} exhibits non-monotonic behavior because increasing these rates can cause a protein to be synthesized more rapidly but provide less time for nascent-protein domains to co-translationally fold thereby producing less functional nascent protein immediately after synthesis. We further demonstrate that these non-monotonic changes in \textbf{\textit{F}}\textbf{ }affect the post-translational, steady-state levels of functional protein in a similar manner. Our results provide a possible explanation for recent experimental observations that the specific activity of enzymatic proteins can decrease with increased synthesis rates and can in principle be used to rationally-design transcripts to maximize the production of functional nascent protein.