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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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Codon-specific Markov process for translation elongation based on 12 ribosomal states for each codon .The elongation cycle starts in state 0 corresponding to a ribosome without any bound ternary complex. Initial binding of a cognate, near-cognate, or non-cognate ternary complex is indicated by the green, orange, and purple arrow, compare the color code in Fig. 4; the corresponding association rates are proportional to the association rate constant  as in Eq. 9. The black arrows represent the individual transitions along the reaction pathways. All ternary complexes dissociate initially with the same dissociation rate . Likewise, cognate and near-cognate ternary complexes are governed by the same recognition rate , conformational rate , and processing rate . The kinetic distinction between the cognate and near-cognate branches arises from initial selection at the states 2 and 7 as well as from proofreading at the states 4 and 9.
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pcbi-1003909-g003: Codon-specific Markov process for translation elongation based on 12 ribosomal states for each codon .The elongation cycle starts in state 0 corresponding to a ribosome without any bound ternary complex. Initial binding of a cognate, near-cognate, or non-cognate ternary complex is indicated by the green, orange, and purple arrow, compare the color code in Fig. 4; the corresponding association rates are proportional to the association rate constant as in Eq. 9. The black arrows represent the individual transitions along the reaction pathways. All ternary complexes dissociate initially with the same dissociation rate . Likewise, cognate and near-cognate ternary complexes are governed by the same recognition rate , conformational rate , and processing rate . The kinetic distinction between the cognate and near-cognate branches arises from initial selection at the states 2 and 7 as well as from proofreading at the states 4 and 9.

Mentions: Aminoacyl-tRNA (small gray, green, purple, or orange sphere) is delivered to the ribosome in a ternary complex with the elongation factor EF-Tu (larger blue sphere) and GTP (not shown). In addition to the initial binding site, the ribosome has three tRNA binding sites, the A, P, and E sites. The elongation cycle of translation starts when the A site of the ribosome has arrived at a new codon (green) of the mRNA. The ribosome then binds a ternary complex with a tRNA that may be cognate, near-cognate, or non-cognate to this codon. As a consequence, the elongation cycle exhibits three different branches corresponding to three different reaction pathways: (left) A non-cognate ternary complex is again released from the initial binding site of the ribosome; (top) A near-cognate ternary complex is usually rejected but is very rarely used to elongate the peptide chain; and (bottom) A cognate ternary complex may also be rejected but is typically used for elongation of the peptide chain. The two dotted arrows correspond to additional intermediate states and transitions as explained in more detail in Fig. 3 below.


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)

Codon-specific Markov process for translation elongation based on 12 ribosomal states for each codon .The elongation cycle starts in state 0 corresponding to a ribosome without any bound ternary complex. Initial binding of a cognate, near-cognate, or non-cognate ternary complex is indicated by the green, orange, and purple arrow, compare the color code in Fig. 4; the corresponding association rates are proportional to the association rate constant  as in Eq. 9. The black arrows represent the individual transitions along the reaction pathways. All ternary complexes dissociate initially with the same dissociation rate . Likewise, cognate and near-cognate ternary complexes are governed by the same recognition rate , conformational rate , and processing rate . The kinetic distinction between the cognate and near-cognate branches arises from initial selection at the states 2 and 7 as well as from proofreading at the states 4 and 9.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214572&req=5

pcbi-1003909-g003: Codon-specific Markov process for translation elongation based on 12 ribosomal states for each codon .The elongation cycle starts in state 0 corresponding to a ribosome without any bound ternary complex. Initial binding of a cognate, near-cognate, or non-cognate ternary complex is indicated by the green, orange, and purple arrow, compare the color code in Fig. 4; the corresponding association rates are proportional to the association rate constant as in Eq. 9. The black arrows represent the individual transitions along the reaction pathways. All ternary complexes dissociate initially with the same dissociation rate . Likewise, cognate and near-cognate ternary complexes are governed by the same recognition rate , conformational rate , and processing rate . The kinetic distinction between the cognate and near-cognate branches arises from initial selection at the states 2 and 7 as well as from proofreading at the states 4 and 9.
Mentions: Aminoacyl-tRNA (small gray, green, purple, or orange sphere) is delivered to the ribosome in a ternary complex with the elongation factor EF-Tu (larger blue sphere) and GTP (not shown). In addition to the initial binding site, the ribosome has three tRNA binding sites, the A, P, and E sites. The elongation cycle of translation starts when the A site of the ribosome has arrived at a new codon (green) of the mRNA. The ribosome then binds a ternary complex with a tRNA that may be cognate, near-cognate, or non-cognate to this codon. As a consequence, the elongation cycle exhibits three different branches corresponding to three different reaction pathways: (left) A non-cognate ternary complex is again released from the initial binding site of the ribosome; (top) A near-cognate ternary complex is usually rejected but is very rarely used to elongate the peptide chain; and (bottom) A cognate ternary complex may also be rejected but is typically used for elongation of the peptide chain. The two dotted arrows correspond to additional intermediate states and transitions as explained in more detail in Fig. 3 below.

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