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Deducing the kinetics of protein synthesis in vivo from the transition rates measured in vitro.

Rudorf S, Thommen M, Rodnina MV, Lipowsky R - PLoS Comput. Biol. (2014)

Bottom Line: In all cases, we find good agreement between theory and experiment without adjusting any fit parameter.The deduced in-vivo rates lead to smaller error frequencies than the known in-vitro rates, primarily by an improved initial selection of tRNA.The method introduced here is relatively simple from a computational point of view and can be applied to any biomolecular process, for which we have detailed information about the in-vitro kinetics.

View Article: PubMed Central - PubMed

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

ABSTRACT
The molecular machinery of life relies on complex multistep processes that involve numerous individual transitions, such as molecular association and dissociation steps, chemical reactions, and mechanical movements. The corresponding transition rates can be typically measured in vitro but not in vivo. Here, we develop a general method to deduce the in-vivo rates from their in-vitro values. The method has two basic components. First, we introduce the kinetic distance, a new concept by which we can quantitatively compare the kinetics of a multistep process in different environments. The kinetic distance depends logarithmically on the transition rates and can be interpreted in terms of the underlying free energy barriers. Second, we minimize the kinetic distance between the in-vitro and the in-vivo process, imposing the constraint that the deduced rates reproduce a known global property such as the overall in-vivo speed. In order to demonstrate the predictive power of our method, we apply it to protein synthesis by ribosomes, a key process of gene expression. We describe the latter process by a codon-specific Markov model with three reaction pathways, corresponding to the initial binding of cognate, near-cognate, and non-cognate tRNA, for which we determine all individual transition rates in vitro. We then predict the in-vivo rates by the constrained minimization procedure and validate these rates by three independent sets of in-vivo data, obtained for codon-dependent translation speeds, codon-specific translation dynamics, and missense error frequencies. In all cases, we find good agreement between theory and experiment without adjusting any fit parameter. The deduced in-vivo rates lead to smaller error frequencies than the known in-vitro rates, primarily by an improved initial selection of tRNA. The method introduced here is relatively simple from a computational point of view and can be applied to any biomolecular process, for which we have detailed information about the in-vitro kinetics.

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Comparison with in-vivo experiments of translation elongation.(A) Codon-specific elongation rates  as determined here from the complete set of individual transition rates for E. coli at a growth rate of 2.5 dbl/h, see Eq. 21 and Supporting Figure S3, compared to relative translation rates as measured in Ref. [29] for 29 codons; highlighted symbols indicate the codons CGA, CGC, and CGU (orange) as well as the codons UUU, UUC, UUG, UCC, and CCC (cyan), see text. The Pearson correlation coefficient is 0.56 for all codons and 0.73 when the highlighted codons are excluded (linear fit in gray). (B) For the incorporation of radioactively labeled amino acids as a function of time, we find very good agreement between the experimental data in Ref. [30] and the calculated curve (orange) based on the in-vivo rates  for 0.7 dbl/h in Table 2. For both (A) and (B), our computations do not involve any fit parameter.
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pcbi-1003909-g006: Comparison with in-vivo experiments of translation elongation.(A) Codon-specific elongation rates as determined here from the complete set of individual transition rates for E. coli at a growth rate of 2.5 dbl/h, see Eq. 21 and Supporting Figure S3, compared to relative translation rates as measured in Ref. [29] for 29 codons; highlighted symbols indicate the codons CGA, CGC, and CGU (orange) as well as the codons UUU, UUC, UUG, UCC, and CCC (cyan), see text. The Pearson correlation coefficient is 0.56 for all codons and 0.73 when the highlighted codons are excluded (linear fit in gray). (B) For the incorporation of radioactively labeled amino acids as a function of time, we find very good agreement between the experimental data in Ref. [30] and the calculated curve (orange) based on the in-vivo rates for 0.7 dbl/h in Table 2. For both (A) and (B), our computations do not involve any fit parameter.

Mentions: Starting from the complete set of individual in-vivo rates (Table 2), we computed the codon-specific elongation rates as described in the Methods section (Eq. 21, Supporting Figure S3). We then compared the in-vivo rates calculated for a growth rate of 2.5 dbl/h to relative translation rates as estimated in Ref. [29] based on the frequencies of the measured +1 frameshifting vs. readthrough of different codons. As shown in Fig. 6A, we obtain reasonable overall agreement between both data sets with a Pearson correlation coefficient of 0.56. The deviations reflect both limitations of our model parametrization and uncertainties in the experimental method. First, the calculated elongation rates for CGA, CGC, and CGU appear to be overestimated. These codons are all read by tRNA, which does not form a Watson-Crick base pair with any of its cognate codons because it carries inosine at the wobble position of its anticodon ICG. The corresponding reductions in the transition rates are not included in the parametrization of our model because we use only two different sets of values for these rates, corresponding to an average over all cognate and over all near-cognate ternary complexes, respectively. Second, for the experimental setup in [29], the UUU, UUC, UUG, UCC, and CCC codons, when located between a preceding CUU codon and a subsequent CXX codon, generate potential slippery sequences, which can lead to frameshifting events. The latter events were not considered and, thus, not taken into account by [29], which implies that the frameshifting rates were underestimated and the translation rates were overestimated for the respective codons. When we exclude these two particular sets of codons, we obtain an increased correlation coefficient of 0.73 as shown in Fig. 6A. Thus, the deduced values of the individual transition rates in vivo lead to a reliable description for the majority of codons.


Deducing the kinetics of protein synthesis in vivo from the transition rates measured in vitro.

Rudorf S, Thommen M, Rodnina MV, Lipowsky R - PLoS Comput. Biol. (2014)

Comparison with in-vivo experiments of translation elongation.(A) Codon-specific elongation rates  as determined here from the complete set of individual transition rates for E. coli at a growth rate of 2.5 dbl/h, see Eq. 21 and Supporting Figure S3, compared to relative translation rates as measured in Ref. [29] for 29 codons; highlighted symbols indicate the codons CGA, CGC, and CGU (orange) as well as the codons UUU, UUC, UUG, UCC, and CCC (cyan), see text. The Pearson correlation coefficient is 0.56 for all codons and 0.73 when the highlighted codons are excluded (linear fit in gray). (B) For the incorporation of radioactively labeled amino acids as a function of time, we find very good agreement between the experimental data in Ref. [30] and the calculated curve (orange) based on the in-vivo rates  for 0.7 dbl/h in Table 2. For both (A) and (B), our computations do not involve any fit parameter.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4214572&req=5

pcbi-1003909-g006: Comparison with in-vivo experiments of translation elongation.(A) Codon-specific elongation rates as determined here from the complete set of individual transition rates for E. coli at a growth rate of 2.5 dbl/h, see Eq. 21 and Supporting Figure S3, compared to relative translation rates as measured in Ref. [29] for 29 codons; highlighted symbols indicate the codons CGA, CGC, and CGU (orange) as well as the codons UUU, UUC, UUG, UCC, and CCC (cyan), see text. The Pearson correlation coefficient is 0.56 for all codons and 0.73 when the highlighted codons are excluded (linear fit in gray). (B) For the incorporation of radioactively labeled amino acids as a function of time, we find very good agreement between the experimental data in Ref. [30] and the calculated curve (orange) based on the in-vivo rates for 0.7 dbl/h in Table 2. For both (A) and (B), our computations do not involve any fit parameter.
Mentions: Starting from the complete set of individual in-vivo rates (Table 2), we computed the codon-specific elongation rates as described in the Methods section (Eq. 21, Supporting Figure S3). We then compared the in-vivo rates calculated for a growth rate of 2.5 dbl/h to relative translation rates as estimated in Ref. [29] based on the frequencies of the measured +1 frameshifting vs. readthrough of different codons. As shown in Fig. 6A, we obtain reasonable overall agreement between both data sets with a Pearson correlation coefficient of 0.56. The deviations reflect both limitations of our model parametrization and uncertainties in the experimental method. First, the calculated elongation rates for CGA, CGC, and CGU appear to be overestimated. These codons are all read by tRNA, which does not form a Watson-Crick base pair with any of its cognate codons because it carries inosine at the wobble position of its anticodon ICG. The corresponding reductions in the transition rates are not included in the parametrization of our model because we use only two different sets of values for these rates, corresponding to an average over all cognate and over all near-cognate ternary complexes, respectively. Second, for the experimental setup in [29], the UUU, UUC, UUG, UCC, and CCC codons, when located between a preceding CUU codon and a subsequent CXX codon, generate potential slippery sequences, which can lead to frameshifting events. The latter events were not considered and, thus, not taken into account by [29], which implies that the frameshifting rates were underestimated and the translation rates were overestimated for the respective codons. When we exclude these two particular sets of codons, we obtain an increased correlation coefficient of 0.73 as shown in Fig. 6A. Thus, the deduced values of the individual transition rates in vivo lead to a reliable description for the majority of codons.

Bottom Line: In all cases, we find good agreement between theory and experiment without adjusting any fit parameter.The deduced in-vivo rates lead to smaller error frequencies than the known in-vitro rates, primarily by an improved initial selection of tRNA.The method introduced here is relatively simple from a computational point of view and can be applied to any biomolecular process, for which we have detailed information about the in-vitro kinetics.

View Article: PubMed Central - PubMed

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

ABSTRACT
The molecular machinery of life relies on complex multistep processes that involve numerous individual transitions, such as molecular association and dissociation steps, chemical reactions, and mechanical movements. The corresponding transition rates can be typically measured in vitro but not in vivo. Here, we develop a general method to deduce the in-vivo rates from their in-vitro values. The method has two basic components. First, we introduce the kinetic distance, a new concept by which we can quantitatively compare the kinetics of a multistep process in different environments. The kinetic distance depends logarithmically on the transition rates and can be interpreted in terms of the underlying free energy barriers. Second, we minimize the kinetic distance between the in-vitro and the in-vivo process, imposing the constraint that the deduced rates reproduce a known global property such as the overall in-vivo speed. In order to demonstrate the predictive power of our method, we apply it to protein synthesis by ribosomes, a key process of gene expression. We describe the latter process by a codon-specific Markov model with three reaction pathways, corresponding to the initial binding of cognate, near-cognate, and non-cognate tRNA, for which we determine all individual transition rates in vitro. We then predict the in-vivo rates by the constrained minimization procedure and validate these rates by three independent sets of in-vivo data, obtained for codon-dependent translation speeds, codon-specific translation dynamics, and missense error frequencies. In all cases, we find good agreement between theory and experiment without adjusting any fit parameter. The deduced in-vivo rates lead to smaller error frequencies than the known in-vitro rates, primarily by an improved initial selection of tRNA. The method introduced here is relatively simple from a computational point of view and can be applied to any biomolecular process, for which we have detailed information about the in-vitro kinetics.

Show MeSH
Related in: MedlinePlus