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

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.Author Summary: The proverb ‘life is motion’ also applies to the molecular scale. Indeed, if we looked into any living cell with molecular resolution, we would observe a large variety of highly dynamic processes. One particularly striking aspect of these dynamics is that all macromolecules within the cell are continuously synthesized, modified, and degraded by complex biomolecular machines. These ‘nanorobots’ follow intricate reaction pathways that form networks of molecular transitions or transformation steps. Each of these steps is stochastic and takes, on average, a certain amount of time. A fundamentally important question is how these individual step times or the corresponding transition rates determine the overall speed of the process in the cell. This question is difficult to answer, however, because the step times can only be measured in vitro but not in vivo. Here, we develop a general computational method by which one can deduce the individual step times in vivo from their in-vitro values. In order to demonstrate the predictive power of our method, we apply it to protein synthesis by ribosomes, a key process of gene expression, and validate the deduced step times by three independent sets of in-vivo data.