Reducing noise through translational control in an auto-regulatory gene network

Auto-regulatory transcriptional feedback, where the protein expressed from a gene inhibits its own transcription, is known to reduce stochastic fluctuations in protein numbers. Work has demonstrated the existence of negative feedback loops not only at the transcriptional level but also at the translational level. We investigate the noise suppression abilities of feedback loops at the translational level and compare them with transcriptional feedback. In particular, we consider two feedbacks at the translational level: translation blocking feedback, where the protein inhibits the translation of its mRNA, and degradation enhancing feedback, where the protein increases the degradation rate of its mRNA. We derive analytical formulas for the protein noise level corresponding to different feedback mechanisms. These noise levels are then compared with each other for fixed steady- state average number of protein and mRNA molecules. We show that translation blocking feedback always yields smaller levels of protein noise than transcriptional feedback. We further show that the difference between the protein noise levels with translation blocking and transcriptional feedback critically depends on how fast the protein dynamics is compared to the mRNA dynamics. In particular, this difference increases as we make the protein dynamics faster than the mRNA dynamics, while making it slower has an opposite effect. Finally, we show that degradation enhancing feedback provides the same noise level as transcriptional feedback. This result shows that regulation at the translational level may not always be better than regulation at the transcriptional level in terms of reducing noise in the protein population.