Propagation and control of gene expression noise with non-linear translation kinetics

Gene expression is a stochastic process involving small numbers of molecules. As a consequence, cells in a clonal population vary randomly and sometimes substantially from one another in the concentration of mRNA and protein species, a phenomenon known as gene expression noise. Previous theoretical models of gene expression noise assumed that translation is first-order (linear) in mRNA concentration, leading to unfiltered propagation of mRNA noise to the protein level. Here I consider the biological ramifications of relaxing this assumption. Specifically, I solve for the noise statistics of gene expression assuming that translation obeys hyperbolic, Michaelis-Menten kinetics with respect to mRNA concentration. I generalize previous stochastic gene expression models by allowing the kinetic order of translation, denoted here by a, to vary continuously from zero-order (a = 0), where ribosomes are fully saturated with mRNA, to first order (a = 1), where ribosomes are unsaturated and mRNA is limiting for translation. In general, hyperbolic translation acts as a high-amplitude filter of mRNA noise. This hyperbolic filtering greatly attenuates the propagation of transcriptional noise to the protein level and qualitatively changes the selective and synthetic targets of noise control. In principle, natural selection or synthetic biologists could exploit this feature to limit or amplify gene expression noise by tuning mRNA and ribosome levels to control the kinetic order of translation.