Translational autoregulation of RF2 protein in E. coli through programmed frameshifting

Ajeet K. Sharma

Phys. Rev. E 103, 062412 – Published 21 June 2021

Abstract

Various feedback mechanisms regulate the expression of different genes to ensure the required protein levels inside a cell. In this paper, we develop a kinetic model for one such mechanism that autoregulates RF2 protein synthesis in E. coli through programmed frameshifting. The model finds that the programmed frameshifting autoregulates RF2 protein synthesis by two independent mechanisms. First, it increases the rate of RF2 synthesis from each mRNA transcript at low RF2 concentration. Second, programmed frameshifting can dramatically increase the lifetime of RF2 transcripts when RF2 protein levels are lower than a threshold. This sharp increase in mRNA lifetime is caused by a first-order phase transition from a low to a high ribosome density on an RF2 transcript. The high ribosome density prevents the transcript's degradation by shielding it from nucleases, which increases its average lifetime and hence RF2 protein levels. Our study identifies this quality control mechanism that regulates the cellular protein levels by breaking the hierarchy of processes involved in gene expression.

Received 6 April 2020
Revised 20 February 2021
Accepted 4 June 2021

DOI:https://doi.org/10.1103/PhysRevE.103.062412

Physics Subject Headings (PhySH)

Biomolecular processes Gene expression

Proteins

Markovian processes Monte Carlo methods

Physics of Living Systems

Authors & Affiliations

Ajeet K. Sharma^*

Department of Physics, Indian Institute of Technology, Jammu 181221, India

^*ajeet.sharma@iitjammu.ac.in

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Vol. 103, Iss. 6 — June 2021

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Figure 1
Schematic of programmed frameshifting and the process of protein synthesis. (a) A limiting concentration of RF2 proteins allows the ribosomes to spend more time on the UGA codon at the 26th position of the RF2 transcript, thus increasing the chances of frameshifting as the combination of CUUUGA nucleotides (25–26 codons) promotes +1 frameshifting. The frameshifting changes the A-site codon from UGA to GAC (shown in bold font). An abundance of RF2 proteins quickly terminates the protein synthesis at the 26th codon position and releases a 25-amino-acid-long short protein. (b) A ribosome initiates the process of protein synthesis with rate $α$ when the first six codon positions of the transcript are not occupied by other ribosomes. Then the ribosome moves stochastically by taking irreversible steps towards the stop codon. The step from codon $j$ to $j + 1$ occurs with rate $ω (j)$ . Note that a ribosome cannot move forward if its passage is occupied by another ribosome on the same transcript. A ribosome terminates protein synthesis with rate $β$ after it reaches the stop codon.
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Figure 2
A higher RF2 concentration decreases its production. The relative production of RF2 protein is plotted against the steady-state RF2 concentration for $k_{frame} = 1, 5, 10, 20, 30$ , and $40 s^{- 1}$ in black, blue, green, cyan, magenta, and orange, respectively. The discrete data points are obtained from the simulations of RF2 protein synthesis whereas the solid lines are plotted using Eq. (3).
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Figure 3
An increase in RF2 concentration decreases the lifetime of the RF2 transcript. (a) and (b) Average mRNA lifetime of the RF2 transcript plotted against the steady-state RF2 concentration in E. coli. The error bars in (a) and (b) represent the standard error in the measurement of mRNA lifetime with 95% confidence interval. (Note that the error bars in (a) and (b) are smaller than the size of the data point.) (c) and (d) Average number of ribosomes on the RF2 transcript plotted against the RF2 concentrating in E. coli. In (a) and (c) we start mRNA degradation in our simulation after the translation system achieves steady-state conditions, whereas in (b) and (d) we start it from $t = 0$ .
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Figure 4
The transition from a long to a short mRNA lifetime remains robust against any changes in the mRNA degradation and translation termination rates. The average lifetime of the RF2 transcript against steady-state RF2 protein concentration is plotted for (a) varying initiation rate $α$ , (b) $k_{d 1} (0)$ and $k_{d 2}$ , (c) maximum termination rate $V_{\max}$ , and (d) Michaelis constant $K_{M}$ . The error bars represent the standard error in the measurement of mRNA lifetime with 95% confidence interval. Note that the error bars in this figure are smaller than the size of the data point.
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Figure 5
Energy expenditure increases the efficiency of switching between a short and a long RF2 lifetime. The average lifetime of the RF2 transcript is plotted against the steady-state RF2 concentration for varying GTP concentration in E. coli. The effect of varying the GTP concentration is captured by increasing the translation time of each codon in a transcript by 0.05, 0.10, 0.20 and 1.00 s. The error bars in this figure represent the standard error in the measurement of mRNA lifetime with 95% confidence interval. (Note that the error bars are smaller than the size of the data points.)
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Figure 6
An increase in RF2 concentration leads to a decrease in the overall production rate of RF2 proteins. The overall RF2 production rate (in number per second) is plotted against the steady-state concentration of RF2 proteins in E. coli for $k_{frame}$ varying from $1 s^{- 1}$ to $40 s^{- 1}$ for (a) the steady-state case and (b) the non-steady-state case. The forbidden and allowed regions of the steady-state RF2 concentrations are shown in yellow and gray, respectively (see the text for details).
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