Deducing the Kinetics of Protein Synthesis In Vivo from the Transition Rates Measured In Vitro

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.

Activities of the peptidyl transferase center of ribosomes lacking protein L27

“…To investigate the importance of L27 for the steps of the elongation cycle that are not reflected in our model assays (e.g., translocation, tRNA competition) or for context-dependent effects on peptide-bond formation, we translated a full-length natural mRNA with ΔL27 ribosomes, using the mRNA coding for the E. coli CspA as a model (Rudorf et al 2014). The time courses of translation (Fig.…”

“…Single-round translation of the full-length CspA mRNA (70 aa) was performed according to Doerfel et al (2013) and Rudorf et al (2014). Wt and ΔL27 ICs were prepared as described above using Bodipy-FL-Met-tRNA fMet .…”

Review: Translational GTPases

“…Taken together, these results show that the ribosome accelerates GTP hydrolysis by EF‐Tu by arranging the catalytic site in a productive way. This finding is supported by the large entropic contribution to the overall activation energy of the GTPase reaction in the presence of the ribosome, which may result from the favorable positioning of the reactive groups, electrostatic effects or shielding from the bulk water . In this context, the contribution of L7/12, which accelerates GTP hydrolysis by EF‐Tu by 2 orders of magnitude, remains unknown.…”

“…The intrinsic selectivity each of initial selection and proofreading is not high, but the combination of two subsequent selection steps increases the fidelity to about 1 wrong amino acid incorporated every 400 codons at in vitro conditions . The same set of rate constants, with only small adjustments for the cellular conditions, account for both the rate and fidelity of decoding in vivo …”

“…The maximum stimulation occurs when the aa-tRNA in the EF-Tu-GTP-aa-tRNA complex is cognate (e.g., fully matching) to the codon in the A site, which increases the GTPase rate by about 6 orders of magnitude. [49][50][51] In comparison, when the codon is near-or non-cognate to the aa-tRNA, the extent of the GTPase activation by the ribosome is much smaller, 2 to 4 orders of magnitude. The programmed ribosome thus acts as a GAP for EF-Tu and the question is how the ribosome contributes to catalysis.…”