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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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Maturation and degradation of mRNA viewed as a Markov chain.During its lifetime, each mRNA undergoes biochemical modifications described by transitions from state i to state  with a rate . These alterations may result in a change of the degradation rate  that governs the transition from state i to the absorbing state 0. The probability density of the time to absorption provides the distribution  for the lifetime of the mRNA. Many known degradation pathways can be described in this manner and thus provide the mRNA lifetime distribution if quantitative information about the rates is available. This model can also be used to fit experimental data, as was done in Figure 3, in order to derive the empirical lifetime distribution.
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pone-0055442-g007: Maturation and degradation of mRNA viewed as a Markov chain.During its lifetime, each mRNA undergoes biochemical modifications described by transitions from state i to state with a rate . These alterations may result in a change of the degradation rate that governs the transition from state i to the absorbing state 0. The probability density of the time to absorption provides the distribution for the lifetime of the mRNA. Many known degradation pathways can be described in this manner and thus provide the mRNA lifetime distribution if quantitative information about the rates is available. This model can also be used to fit experimental data, as was done in Figure 3, in order to derive the empirical lifetime distribution.

Mentions: From the prototypical degradation processes illustrated in Fig. 2 we develop a suitable mathematical framework in order to derive the associated lifetime distribution . This can be done by translating the degradation pathways into the theoretical concept of a Markov chain described in Fig. 7. Here, any biochemical state is mapped onto a state of the Markov chain and a biochemical modification of the mRNA is reflected by a transition from one state to the next. In principle, many biochemical pathways of mRNA degradation can be described in this manner, provided one knows the details of the pathway. Markov chains, moreover, provide a well known tool in stochastic modeling with applications in many problems inspired by biology. One of the big advantages of Markov chains is the simplicity of their mathematical treatment. Some applications to single-molecule analysis similar to the one presented here can be found in Refs. [39]–[42].


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)

Maturation and degradation of mRNA viewed as a Markov chain.During its lifetime, each mRNA undergoes biochemical modifications described by transitions from state i to state  with a rate . These alterations may result in a change of the degradation rate  that governs the transition from state i to the absorbing state 0. The probability density of the time to absorption provides the distribution  for the lifetime of the mRNA. Many known degradation pathways can be described in this manner and thus provide the mRNA lifetime distribution if quantitative information about the rates is available. This model can also be used to fit experimental data, as was done in Figure 3, in order to derive the empirical lifetime distribution.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055442-g007: Maturation and degradation of mRNA viewed as a Markov chain.During its lifetime, each mRNA undergoes biochemical modifications described by transitions from state i to state with a rate . These alterations may result in a change of the degradation rate that governs the transition from state i to the absorbing state 0. The probability density of the time to absorption provides the distribution for the lifetime of the mRNA. Many known degradation pathways can be described in this manner and thus provide the mRNA lifetime distribution if quantitative information about the rates is available. This model can also be used to fit experimental data, as was done in Figure 3, in order to derive the empirical lifetime distribution.
Mentions: From the prototypical degradation processes illustrated in Fig. 2 we develop a suitable mathematical framework in order to derive the associated lifetime distribution . This can be done by translating the degradation pathways into the theoretical concept of a Markov chain described in Fig. 7. Here, any biochemical state is mapped onto a state of the Markov chain and a biochemical modification of the mRNA is reflected by a transition from one state to the next. In principle, many biochemical pathways of mRNA degradation can be described in this manner, provided one knows the details of the pathway. Markov chains, moreover, provide a well known tool in stochastic modeling with applications in many problems inspired by biology. One of the big advantages of Markov chains is the simplicity of their mathematical treatment. Some applications to single-molecule analysis similar to the one presented here can be found in Refs. [39]–[42].

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