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Effects of promoter leakage on dynamics of gene expression.

Huang L, Yuan Z, Liu P, Zhou T - BMC Syst Biol (2015)

Bottom Line: Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes.We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics.Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

View Article: PubMed Central - PubMed

Affiliation: Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, PR China. hlfang208@163.com.

ABSTRACT

Background: Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear.

Results: In this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts.

Conclusions: Our results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

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Related in: MedlinePlus

Effects of promoter leakage on the time-dependent number of gene product molecules, where the leakage rate is set as either λ0 = 0 (A, B) or λ0 = 10 (D, E).(A and D) no feedback, where the parameter values are the same as those used in Figure 3(A); (B and E) negative feedback, where the parameter values are the same as those used in Figure 3(B); (C and F) positive feedback, where the leakage rate λ1 is set as 10 for (F) or as 0 for (C), and the other parameter values are the same as those used in Figure 3(C).
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Fig5: Effects of promoter leakage on the time-dependent number of gene product molecules, where the leakage rate is set as either λ0 = 0 (A, B) or λ0 = 10 (D, E).(A and D) no feedback, where the parameter values are the same as those used in Figure 3(A); (B and E) negative feedback, where the parameter values are the same as those used in Figure 3(B); (C and F) positive feedback, where the leakage rate λ1 is set as 10 for (F) or as 0 for (C), and the other parameter values are the same as those used in Figure 3(C).

Mentions: Before presenting results, let us simply introduce computation formulae associated with bursting kinetics. Recall that in the case of no feedback, the mean BF and the mean BS are calculated according to the following formulae [42]8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \left\langle BF\right\rangle =\frac{1}{\tau_{OFF}},\left\langle BS\right\rangle ={k}_{transcription}\cdot {\tau}_{ON} $$ \end{document}BF=1τOFF,BS=ktranscription⋅τONwhere τOFF and τON represent the mean time dwelling at OFF and ON states respectively, and ktranscription is the transcription rate when the gene is at ON state. First, consider that our model has no feedback, i.e., f = 0. If λ0 compared to λ1 is so small that it may be ignored (in this case, D1 represents the ON state), then we have τOFF = 1/γ1 [62,63], which implies 〈BF〉 = γ1, and τON = 1/γ0 [62,63], which implies 〈BS〉 = λ1/γ0. Similarly, if λ1 compared to λ0 is so small that it may be ignored (in this case, D0 represents the ON state), then we have τOFF = 1/γ0, which implies 〈BF〉 = γ0, and τON = 1/γ1, which implies 〈BS〉 = λ0/γ1. Thus, for the former case, we see from Eq. (11) that increasing the leakage rate λ0 does not change the mean BF nor change the mean BS, referring to Figure 4(A) and (D), but may make the original low expression amount of the gene product have a rise. Moreover, it can be seen from the time series shown in Figure 5 (more precisely, by comparing Figure 5(A) which corresponds to the case of no leakage with Figure 5(D) which corresponds to the case that the leakage rate is 10) that the number of gene product molecules tends to centralize a certain value. The similar phenomena can take place in the latter case.Figure 4


Effects of promoter leakage on dynamics of gene expression.

Huang L, Yuan Z, Liu P, Zhou T - BMC Syst Biol (2015)

Effects of promoter leakage on the time-dependent number of gene product molecules, where the leakage rate is set as either λ0 = 0 (A, B) or λ0 = 10 (D, E).(A and D) no feedback, where the parameter values are the same as those used in Figure 3(A); (B and E) negative feedback, where the parameter values are the same as those used in Figure 3(B); (C and F) positive feedback, where the leakage rate λ1 is set as 10 for (F) or as 0 for (C), and the other parameter values are the same as those used in Figure 3(C).
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Related In: Results  -  Collection

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Fig5: Effects of promoter leakage on the time-dependent number of gene product molecules, where the leakage rate is set as either λ0 = 0 (A, B) or λ0 = 10 (D, E).(A and D) no feedback, where the parameter values are the same as those used in Figure 3(A); (B and E) negative feedback, where the parameter values are the same as those used in Figure 3(B); (C and F) positive feedback, where the leakage rate λ1 is set as 10 for (F) or as 0 for (C), and the other parameter values are the same as those used in Figure 3(C).
Mentions: Before presenting results, let us simply introduce computation formulae associated with bursting kinetics. Recall that in the case of no feedback, the mean BF and the mean BS are calculated according to the following formulae [42]8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \left\langle BF\right\rangle =\frac{1}{\tau_{OFF}},\left\langle BS\right\rangle ={k}_{transcription}\cdot {\tau}_{ON} $$ \end{document}BF=1τOFF,BS=ktranscription⋅τONwhere τOFF and τON represent the mean time dwelling at OFF and ON states respectively, and ktranscription is the transcription rate when the gene is at ON state. First, consider that our model has no feedback, i.e., f = 0. If λ0 compared to λ1 is so small that it may be ignored (in this case, D1 represents the ON state), then we have τOFF = 1/γ1 [62,63], which implies 〈BF〉 = γ1, and τON = 1/γ0 [62,63], which implies 〈BS〉 = λ1/γ0. Similarly, if λ1 compared to λ0 is so small that it may be ignored (in this case, D0 represents the ON state), then we have τOFF = 1/γ0, which implies 〈BF〉 = γ0, and τON = 1/γ1, which implies 〈BS〉 = λ0/γ1. Thus, for the former case, we see from Eq. (11) that increasing the leakage rate λ0 does not change the mean BF nor change the mean BS, referring to Figure 4(A) and (D), but may make the original low expression amount of the gene product have a rise. Moreover, it can be seen from the time series shown in Figure 5 (more precisely, by comparing Figure 5(A) which corresponds to the case of no leakage with Figure 5(D) which corresponds to the case that the leakage rate is 10) that the number of gene product molecules tends to centralize a certain value. The similar phenomena can take place in the latter case.Figure 4

Bottom Line: Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes.We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics.Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

View Article: PubMed Central - PubMed

Affiliation: Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, PR China. hlfang208@163.com.

ABSTRACT

Background: Quantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear.

Results: In this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts.

Conclusions: Our results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

Show MeSH
Related in: MedlinePlus