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.
Highlights
Life is based on the continuous synthesis, modification, and degradation of proteins and other macromolecules
In order to demonstrate the predictive power of our method, we apply it to the elongation cycle of protein synthesis, a key process of gene expression
If we looked into any living cell with molecular resolution, we would observe a large variety of highly dynamic processes
Summary
Life is based on the continuous synthesis, modification, and degradation of proteins and other macromolecules These processes are performed by complex biomolecular machines that bind their ligands and transform them into product molecules. Examples are provided by the transcription of DNA by RNA polymerases, the translation of mRNA by ribosomes, or the degradation of proteins by proteasomes. Each of these processes involves several steps: the binding of the ligand molecules, chemical reactions catalyzed at the active sites, as well as specific conformational changes and directed mechanical movements of parts of the molecular machinery. Because the cytosol represents a rather complex buffer, it is difficult to assess whether a certain in-vitro assay provides a reliable description of the process in vivo. One important tool that is missing for such an assessment is a simple measure by which we can quantitatively compare the kinetics of a multistep process in different environments
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