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Complex degradation processes lead to non-exponential decay patterns and age-dependent decay rates of messenger RNA.

Deneke C, Lipowsky R, Valleriani A - PLoS ONE (2013)

Bottom Line: Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified.Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation.We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs.

View Article: PubMed Central - PubMed

Affiliation: Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany.

ABSTRACT
Experimental studies on mRNA stability have established several, qualitatively distinct decay patterns for the amount of mRNA within the living cell. Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified. The central aim of this paper is to bring together both the experimental evidence about the decay patterns and the biochemical knowledge about the multi-step nature of mRNA degradation in a coherent mathematical theory. We first introduce a mathematical relationship between the mRNA decay pattern and the lifetime distribution of individual mRNA molecules. This relationship reveals that the mRNA decay patterns at steady state expression level must obey a general convexity condition, which applies to any degradation mechanism. Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation. We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs. Thereby, we show how to extract single-molecule properties of an mRNA, such as the age-dependent decay rate and the residual lifetime. Finally, we analyze the decay patterns of the whole translatome of yeast cells and show that yeast mRNAs can be grouped into three broad classes that exhibit three distinct decay patterns. This paper provides both a method to accurately analyze non-exponential mRNA decay patterns and a tool to validate different models of degradation using decay data.

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Related in: MedlinePlus

Comparison of fitting errors.The plot shows the residual sum of squares (RSS) after fitting the exponential model (abscissa) and the multistep model (ordinate) to the experiment data from Ref. [23]. Clearly, the multistep model leads to a considerable improvement of the fitting procedure, resulting in an average error reduction by almost one order of magnitude. Moreover, we also display the errors corresponding to the different categories in Fig. 5 as black, blue and red dots, respectively. The latter two represent the non-exponential patterns and typically imply a strong reduction of the fitting error. Additionally, we have highlighted the two representative cases RPS16B and MGS1 belonging to the two non-exponential categories, as given in Fig. 3A. One may notice that there are some black dots, corresponding to the exponential decay patterns in Fig. 5. For these decay patterns, the fitting with a multi-step model does not provide a significant improvement of the fit compared to the exponential function.
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pone-0055442-g008: Comparison of fitting errors.The plot shows the residual sum of squares (RSS) after fitting the exponential model (abscissa) and the multistep model (ordinate) to the experiment data from Ref. [23]. Clearly, the multistep model leads to a considerable improvement of the fitting procedure, resulting in an average error reduction by almost one order of magnitude. Moreover, we also display the errors corresponding to the different categories in Fig. 5 as black, blue and red dots, respectively. The latter two represent the non-exponential patterns and typically imply a strong reduction of the fitting error. Additionally, we have highlighted the two representative cases RPS16B and MGS1 belonging to the two non-exponential categories, as given in Fig. 3A. One may notice that there are some black dots, corresponding to the exponential decay patterns in Fig. 5. For these decay patterns, the fitting with a multi-step model does not provide a significant improvement of the fit compared to the exponential function.

Mentions: All blue curves in Fig. 5 resulted in the smallest deviation to the experimental data by fitting this equation together with (1) under the constraint . The improvement obtained by fitting the data with a multi-step model is displayed in Fig. 8. When one applies only the exponential model, the fitting error is typically large and less than half of the mRNAs lead to a residual sum of squares smaller than 0.01. In contrast, with a multi-step model more than 95% of the data can be fitted with great accuracy (i.e. RSS ). Nevertheless, some mRNA decay patterns are truly exponential. We have indeed rejected a more complex model, compared to the exponential function, if the more complex model did not improve the RSS by at least 10%. The black dots in Fig. 8 correspond to those decay patterns for which the exponential fit performed already very well and no significant improvement could be obtained with a multi-step fitting. A table with a list of all genes considered in this study and the optimal fit parameters to describe their decay is provided in the supporting information.


Complex degradation processes lead to non-exponential decay patterns and age-dependent decay rates of messenger RNA.

Deneke C, Lipowsky R, Valleriani A - PLoS ONE (2013)

Comparison of fitting errors.The plot shows the residual sum of squares (RSS) after fitting the exponential model (abscissa) and the multistep model (ordinate) to the experiment data from Ref. [23]. Clearly, the multistep model leads to a considerable improvement of the fitting procedure, resulting in an average error reduction by almost one order of magnitude. Moreover, we also display the errors corresponding to the different categories in Fig. 5 as black, blue and red dots, respectively. The latter two represent the non-exponential patterns and typically imply a strong reduction of the fitting error. Additionally, we have highlighted the two representative cases RPS16B and MGS1 belonging to the two non-exponential categories, as given in Fig. 3A. One may notice that there are some black dots, corresponding to the exponential decay patterns in Fig. 5. For these decay patterns, the fitting with a multi-step model does not provide a significant improvement of the fit compared to the exponential function.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3569439&req=5

pone-0055442-g008: Comparison of fitting errors.The plot shows the residual sum of squares (RSS) after fitting the exponential model (abscissa) and the multistep model (ordinate) to the experiment data from Ref. [23]. Clearly, the multistep model leads to a considerable improvement of the fitting procedure, resulting in an average error reduction by almost one order of magnitude. Moreover, we also display the errors corresponding to the different categories in Fig. 5 as black, blue and red dots, respectively. The latter two represent the non-exponential patterns and typically imply a strong reduction of the fitting error. Additionally, we have highlighted the two representative cases RPS16B and MGS1 belonging to the two non-exponential categories, as given in Fig. 3A. One may notice that there are some black dots, corresponding to the exponential decay patterns in Fig. 5. For these decay patterns, the fitting with a multi-step model does not provide a significant improvement of the fit compared to the exponential function.
Mentions: All blue curves in Fig. 5 resulted in the smallest deviation to the experimental data by fitting this equation together with (1) under the constraint . The improvement obtained by fitting the data with a multi-step model is displayed in Fig. 8. When one applies only the exponential model, the fitting error is typically large and less than half of the mRNAs lead to a residual sum of squares smaller than 0.01. In contrast, with a multi-step model more than 95% of the data can be fitted with great accuracy (i.e. RSS ). Nevertheless, some mRNA decay patterns are truly exponential. We have indeed rejected a more complex model, compared to the exponential function, if the more complex model did not improve the RSS by at least 10%. The black dots in Fig. 8 correspond to those decay patterns for which the exponential fit performed already very well and no significant improvement could be obtained with a multi-step fitting. A table with a list of all genes considered in this study and the optimal fit parameters to describe their decay is provided in the supporting information.

Bottom Line: Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified.Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation.We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs.

View Article: PubMed Central - PubMed

Affiliation: Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany.

ABSTRACT
Experimental studies on mRNA stability have established several, qualitatively distinct decay patterns for the amount of mRNA within the living cell. Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified. The central aim of this paper is to bring together both the experimental evidence about the decay patterns and the biochemical knowledge about the multi-step nature of mRNA degradation in a coherent mathematical theory. We first introduce a mathematical relationship between the mRNA decay pattern and the lifetime distribution of individual mRNA molecules. This relationship reveals that the mRNA decay patterns at steady state expression level must obey a general convexity condition, which applies to any degradation mechanism. Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation. We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs. Thereby, we show how to extract single-molecule properties of an mRNA, such as the age-dependent decay rate and the residual lifetime. Finally, we analyze the decay patterns of the whole translatome of yeast cells and show that yeast mRNAs can be grouped into three broad classes that exhibit three distinct decay patterns. This paper provides both a method to accurately analyze non-exponential mRNA decay patterns and a tool to validate different models of degradation using decay data.

Show MeSH
Related in: MedlinePlus