Decomposing bulk signals to reveal hidden information in processive enzyme reactions: A case study in mRNA translation

Processive enzymes like polymerases or ribosomes are often studied in bulk experiments by monitoring time-dependent signals, such as fluorescence time traces. However, due to biomolecular process stochasticity, ensemble signals may lack the distinct features of single-molecule signals. Here, we demonstrate that, under certain conditions, bulk signals from processive reactions can be decomposed to unveil hidden information about individual reaction steps. Using mRNA translation as a case study, we show that decomposing a noisy ensemble signal generated by the translation of mRNAs with more than a few codons is an ill-posed problem, addressable through Tikhonov regularization. We apply our method to the fluorescence signatures of in-vitro translated LepB mRNA and determine codon-position dependent translation rates and corresponding state-specific fluorescence intensities. We find a significant change in fluorescence intensity after the fourth and the fifth peptide bond formation, and show that both codon position and encoded amino acid have an effect on the elongation rate. This demonstrates that our approach enhances the information content extracted from bulk experiments, thereby expanding the range of these time- and cost-efficient methods.

Utilizing high-resolution ribosome profiling for the global investigation of gene expression in Chlamydomonas

Ribosome profiling (Ribo-seq) is a powerful method for the deep analysis of translation mechanisms and regulatory circuits during gene expression. Extraction and sequencing of ribosome-protected fragments (RPFs) and parallel RNA-seq yields genome-wide insight into translational dynamics and post-transcriptional control of gene expression. Here, we provide details on the Ribo-seq method and the subsequent analysis with the unicellular model alga Chlamydomonas reinhardtii (Chlamydomonas) for generating high-resolution data covering more than 10 000 different transcripts. Detailed analysis of the ribosomal offsets on transcripts uncovers presumable transition states during translocation of elongating ribosomes within the 5' and 3' sections of transcripts and characteristics of eukaryotic translation termination, which are fundamentally distinct for chloroplast translation. In chloroplasts, a heterogeneous RPF size distribution along the coding sequence indicates specific regulatory phases during protein synthesis. For example, local accumulation of small RPFs correlates with local slowdown of psbA translation, possibly uncovering an uncharacterized regulatory step during PsbA/D1 synthesis. Further analyses of RPF distribution along specific cytosolic transcripts revealed characteristic patterns of translation elongation exemplified for the major light-harvesting complex proteins, LHCs. By providing high-quality datasets for all subcellular genomes and attaching our data to the Chlamydomonas reference genome, we aim to make ribosome profiles easily accessible for the broad research community. The data can be browsed without advanced bioinformatic background knowledge for translation output levels of specific genes and their splice variants and for monitoring genome annotation.

Computational analysis of protein synthesis, diffusion, and binding in compartmental biochips

Protein complex assembly facilitates the combination of individual protein subunits into functional entities, and thus plays a crucial role in biology and biotechnology. Recently, we developed quasi-twodimensional, silicon-based compartmental biochips that are designed to study and administer the synthesis and assembly of protein complexes. At these biochips, individual protein subunits are synthesized from locally confined high-density DNA brushes and are captured on the chip surface by molecular traps. Here, we investigate single-gene versions of our quasi-twodimensional synthesis systems and introduce the trap-binding efficiency to characterize their performance. We show by mathematical and computational modeling how a finite trap density determines the dynamics of protein-trap binding and identify three distinct regimes of the trap-binding efficiency. We systematically study how protein-trap binding is governed by the system's three key parameters, which are the synthesis rate, the diffusion constant and the trap-binding affinity of the expressed protein. In addition, we describe how spatially differential patterns of traps modulate the protein-trap binding dynamics. In this way, we extend the theoretical knowledge base for synthesis, diffusion, and binding in compartmental systems, which helps to achieve better control of directed molecular self-assembly required for the fabrication of nanomachines for synthetic biology applications or nanotechnological purposes.

Dominance analysis of competing protein assembly pathways

Most proteins form complexes consisting of two or more subunits, where complex assembly can proceed via two competing pathways: co-translational assembly of a mature and a nascent subunit, and post-translational assembly by two mature protein subunits. Assembly pathway dominance, i.e., which of the two pathways is predominant under which conditions, is poorly understood. Here, we introduce a reaction-diffusion system that describes protein complex formation via post- and co-translational assembly and use it to analyze the dominance of both pathways. Special features of this new system are (i) spatially inhomogeneous sources of reacting species, (ii) a combination of diffusing and immobile species, and (iii) an asymmetric binding competition between the species. We study assembly pathway dominance for the spatially homogeneous system and find that the ratio of production rates of the two protein subunits determines the long-term pathway dominance. This result is independent of the binding rate constants for post- and co-translational assembly and implies that a system with an initial post-translational assembly dominance can eventually exhibit co-translational assembly dominance and vice versa. For exactly balanced production of both subunits, the assembly pathway dominance is determined by the steady state concentration of the subunit that can bind both nascent and mature partners. The introduced system of equations can be applied to describe general dynamics of assembly processes involving both diffusing and immobile components.

Tailoring Codon Usage to the Underlying Biology for Protein Expression Optimization

For heterologous gene expression, codon optimization is required to enhance the quality and quantity of the protein product. Recently, we introduced the software tool OCTOPOS. This sequence optimizer combines a detailed mechanistic mathematical modeling of in vivo protein synthesis with a state-of-the-art machine learning algorithm to find the sequence that best serves a user's needs. Here, we briefly describe the algorithm and its implementation as well as its application in practice using OCTOPOS.

Programming multi-protein assembly by gene-brush patterns and two-dimensional compartment geometry

The assembly of protein machines in cells is precise, rapid, and coupled to protein synthesis with regulation in space and time. The assembly of natural and synthetic nanomachines could be similarly controlled by genetic programming outside the cell. Here, we present quasi-two-dimensional (2D) silicon compartments that enable programming of protein assembly lines by local synthesis from surface-immobilized DNA brushes. Using this platform, we studied the autonomous synthesis and assembly of a structural complex from a bacteriophage and a bacterial RNA-synthesizing machine. Local synthesis and surface capture of complexes provided high assembly yield and sensitive detection of spatially resolved assembly intermediates, with the 3D geometry of the compartment and the 2D pattern of brushes dictating the yield and mode of assembly steps. Localized synthesis of proteins in a single gene brush enhances their interactions, and displacement of their genes in separated brushes leads to step-by-step surface assembly. This methodology enables spatial regulation of protein synthesis, and deciphering, reconstruction and design of biological machine assembly lines.

Decomposition of time-dependent fluorescence signals reveals codon-specific kinetics of protein synthesis

During protein synthesis, the nascent peptide chain traverses the peptide exit tunnel of the ribosome. We monitor the co-translational movement of the nascent peptide using a fluorescent probe attached to the N-terminus of the nascent chain. Due to fluorophore quenching, the time-dependent fluorescence signal emitted by an individual peptide is determined by co-translational events, such as secondary structure formation and peptide-tunnel interactions. To obtain information on these individual events, the measured ensemble fluorescence signal has to be decomposed into position-dependent intensities. Here, we describe mRNA translation as a Markov process with specific fluorescence intensities assigned to the different states of the process. Combining the computed stochastic time evolution of the translation process with a sequence of observed ensemble fluorescence time courses, we compute the unknown position-specific intensities and obtain detailed information on the kinetics of the translation process. In particular, we find that translation of poly(U) mRNAs dramatically slows down at the fourth UUU codon. The method presented here detects subtle differences in the position-specific fluorescence intensities and thus provides a novel approach to study translation kinetics in ensemble experiments.

Efficiency of protein synthesis inhibition depends on tRNA and codon compositions

Regulation and maintenance of protein synthesis are vital to all organisms and are thus key targets of attack and defense at the cellular level. Here, we mathematically analyze protein synthesis for its sensitivity to the inhibition of elongation factor EF-Tu and/or ribosomes in dependence of the system’s tRNA and codon compositions. We find that protein synthesis reacts ultrasensitively to a decrease in the elongation factor’s concentration for systems with an imbalance between codon usages and tRNA concentrations. For well-balanced tRNA/codon compositions, protein synthesis is impeded more effectively by the inhibition of ribosomes instead of EF-Tu. Our predictions are supported by re-evaluated experimental data as well as by independent computer simulations. Not only does the described ultrasensitivity render EF-Tu a distinguished target of protein synthesis inhibiting antibiotics. It may also enable persister cell formation mediated by toxin-antitoxin systems. The strong impact of the tRNA/codon composition provides a basis for tissue-specificities of disorders caused by mutations of human mitochondrial EF-Tu as well as for the potential use of EF-Tu targeting drugs for tissue-specific treatments.

We predict and analyze the response of differently composed protein synthesis systems to the inhibition of elongation factor EF-Tu and/or ribosomes. The study reveals a strong interdependency of a protein synthesis system’s composition and its susceptibility to inhibition. This interdependency defines a generic mechanism that provides a common basis for a variety of seemingly unrelated phenomena including, for example, persister cell formation and tissue-specificity of certain mitochondrial diseases. The described mechanism applies to simple artificial translation systems as well as to complex protein synthesis in vivo.

Protein Synthesis in E. coli: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

To synthesize a protein, a ribosome moves along a messenger RNA (mRNA), reads it codon by codon, and takes up the corresponding ternary complexes which consist of aminoacylated transfer RNAs (aa-tRNAs), elongation factor Tu (EF-Tu), and GTP. During this process of translation elongation, the ribosome proceeds with a codon-specific rate. Here, we present a general theoretical framework to calculate codon-specific elongation rates and error frequencies based on tRNA concentrations and codon usages. Our theory takes three important aspects of in-vivo translation elongation into account. First, non-cognate, near-cognate and cognate ternary complexes compete for the binding sites on the ribosomes. Second, the corresponding binding rates are determined by the concentrations of free ternary complexes, which must be distinguished from the total tRNA concentrations as measured in vivo. Third, for each tRNA species, the difference between total tRNA and ternary complex concentration depends on the codon usages of the corresponding cognate and near-cognate codons. Furthermore, we apply our theory to two alternative pathways for tRNA release from the ribosomal E site and show how the mechanism of tRNA release influences the concentrations of free ternary complexes and thus the codon-specific elongation rates. Using a recently introduced method to determine kinetic rates of in-vivo translation from in-vitro data, we compute elongation rates for all codons in Escherichia coli. We show that for some tRNA species only a few tRNA molecules are part of ternary complexes and, thus, available for the translating ribosomes. In addition, we find that codon-specific elongation rates strongly depend on the overall codon usage in the cell, which could be altered experimentally by overexpression of individual genes.

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.

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.

Self-assembly of stable monomolecular nucleic acid lipid particles with a size of 30 nm

The design of efficient nucleic acid complexes is key to progress in genetic research and therapies based on RNA interference. For optimal transport within tissue and across extracellular barriers, nucleic acid carriers need to be small and stable. In this Article, we prepare and characterize mono-nucleic acid lipid particles (mono-NALPs). The particles consist of single short double-stranded oligonucleotides or single siRNA molecules each encapsulated within a closed shell of a cationic-zwitterionic lipid bilayer, furnished with an outer polyethylene glycol (PEG) shield. The particles self-assemble by solvent exchange from a solution containing nucleic acid mixed with the four lipid components DOTAP, DOPE, DOPC, and DSPE-PEG(2000). Using fluorescence correlation spectroscopy, we monitor the formation of mono-NALPs from short double-stranded oligonucleotides or siRNA and lipids into monodisperse particles of approximately 30 nm in diameter. Small angle neutron and X-ray scattering and transmission electron microscopy experiments substantiate a micelle-like core-shell structure of the particles. The PEGylated lipid shell protects the nucleic acid core against degradation by nucleases, sterically stabilizes the mono-NALPs against disassembly in collagen networks, and prevents nonspecific binding to cells. Hence, PEG-lipid shielded mono-NALPs are the smallest stable siRNA lipid system possible and may provide a structural design to be built upon for the development of novel nucleic acid delivery systems with enhanced biodistribution in vivo.

Transient phenomena in gene expression after induction of transcription

When transcription of a gene is induced by a stimulus, the number of its mRNA molecules changes with time. Here we discuss how this time evolution depends on the shape of the mRNA lifetime distribution. Analysis of the statistical properties of this change reveals transient effects on polysomes, ribosomal profiles, and rate of protein synthesis. Our studies reveal that transient phenomena in gene expression strongly depend on the specific form of the mRNA lifetime distribution.