Simulation and analysis of single-ribosome translation

On the response of elongating ribosomes to forces opposing translocation

The elongation phase of protein synthesis is a cyclic, steady-state process. It follows that its directionality is determined by the thermodynamics of the accompanying chemical reactions, which strongly favor elongation. Its irreversibility is guaranteed by its coupling to those reactions, rather being a consequence of any of the conformational changes that occur as it unfolds. It also follows that, in general, the rate of elongation is not proportional to the forward rate constants of any of its steps, including its final, mechano-chemical step, translocation. Instead, the reciprocal of the rate of elongation should be linearly related to the reciprocal of those rate constants. When the results of experiments done a decade ago to measure the effect that forces opposing translocation have on the rate of elongation are reinterpreted in light of these findings, it becomes clear that translocation was rate limiting under conditions in which those experiments were done, and that it is likely to be a Brownian ratchet process, as was concluded earlier.

A simple geometrical model of the electrostatic environment around the catalytic center of the ribosome and its significance for the elongation cycle kinetics

The central function of the large subunit of the ribosome is to catalyze peptide bond formation. This biochemical reaction is conducted at the peptidyl transferase center (PTC). Experimental evidence shows that the catalytic activity is affected by the electrostatic environment around the peptidyl transferase center. Here, we set up a minimal geometrical model fitting the available x-ray solved structures of the ribonucleic cavity around the catalytic center of the large subunit of the ribosome. The purpose of this phenomenological model is to estimate quantitatively the electrostatic potential and electric field that are experienced during the peptidyl transfer reaction. At least two reasons motivate the need for developing this quantification. First, we inquire whether the electric field in this particular catalytic environment, made only of nucleic acids, is of the same order of magnitude as the one prevailing in catalytic centers of the proteic enzymes counterparts. Second, the protein synthesis rate is dependent on the nature of the amino acid sequentially incorporated in the nascent chain. The activation energy of the catalytic reaction and its detailed kinetics are shown to be dependent on the mechanical work exerted on the amino acids by the electric field, especially when one of the four charged amino acid residues (R, K, E, D) has previously been incorporated at the carboxy-terminal end of the peptidyl-tRNA. Physical values of the electric field provide quantitative knowledge of mechanical work, activation energy and rate of the peptide bond formation catalyzed by the ribosome. We show that our theoretical calculations are consistent with two independent sets of previously published experimental results. Experimental results for E.coli in the minimal case of the dipeptide bond formation when puromycin is used as the final amino acid acceptor strongly support our theoretically derived reaction time courses. Experimental Ribo-Seq results on E. coli and S. cerevisiae comparing the residence time distribution of ribosomes upon specific codons are also well accounted for by our theoretical calculations. The statistical queueing time theory was used to model the ribosome residence time per codon during nascent protein elongation and applied for the interpretation of the Ribo-Seq data. The hypo-exponential distribution fits the residence time observed distribution of the ribosome on a codon. An educated deconvolution of this distribution is used to estimate the rates of each elongation step in a codon specific manner. Our interpretation of all these results sheds light on the functional role of the electrostatic profile around the PTC and its impact on the ribosome elongation cycle.

Computational Methods for the Analysis and Prediction of EGFR-Mutated Lung Cancer Drug Resistance: Recent Advances in Drug Design, Challenges and Future Prospects

Lung cancer is a major cause of cancer deaths worldwide, and has a very low survival rate. Non-small cell lung cancer (NSCLC) is the largest subset of lung cancers, which accounts for about 85% of all cases. It has been well established that a mutation in the epidermal growth factor receptor (EGFR) can lead to lung cancer. EGFR Tyrosine Kinase Inhibitors (TKIs) are developed to target the kinase domain of EGFR. These TKIs produce promising results at the initial stage of therapy, but the efficacy becomes limited due to the development of drug resistance. In this paper, we provide a comprehensive overview of computational methods, for understanding drug resistance mechanisms. The important EGFR mutants and the different generations of EGFR-TKIs, with the survival and response rates are discussed. Next, we evaluate the role of important EGFR parameters in drug resistance mechanism, including structural dynamics, hydrogen bonds, stability, dimerization, binding free energies, and signaling pathways. Personalized drug resistance prediction models, drug response curve, drug synergy, and other data-driven methods are also discussed. Recent advancements in deep learning; such as AlphaFold2, deep generative models, big data analytics, and the applications of statistics and permutation are also highlighted. We explore limitations in the current methodologies, and discuss strategies to overcome them. We believe this review will serve as a reference for researchers; to apply computational techniques for precision medicine, analyzing structures of protein-drug complexes, drug discovery, and understanding the drug response and resistance mechanisms in lung cancer patients.

A potential peptide inhibitor of SARS-CoV-2 S and human ACE2 complex

The disease COVID-19 has caused heavy socio-economic burden and there is immediate need to control it. The disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. The viral entry into human cell depends on the attachment of spike (S) protein via its receptor binding domain (RBD) to human cell receptor angiotensin-converting enzyme 2 (hACE2). Thus, blocking the virus attachment to hACE2 could serve as potential therapeutics for viral infection. We have designed a peptide inhibitor (ΔABP-α2) targeting the RBD of S protein using in-silico approach. Docking studies and computed affinities suggested that peptide inhibitor binds at the RBD with ∼95-fold higher affinity than hACE2. Molecular dynamics (MD) simulation confirms the stable binding of inhibitor to hACE2. Immunoinformatics studies suggest non-immunogenic and non-toxic nature of peptide. Thus, the proposed peptide could serve as potential blocker for viral attachment.

Communicated by Ramaswamy H. Sarma

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics

Systems chemistry has been a key component of origin of life research, invoking models of life's inception based on evolving molecular networks. One such model is the graded autocatalysis replication domain (GARD) formalism embodied in a lipid world scenario, which offers rigorous computer simulation based on defined chemical kinetics equations. GARD suggests that the first pre-RNA life-like entities could have been homeostatically-growing assemblies of amphiphiles, undergoing compositional replication and mutations, as well as rudimentary selection and evolution. Recent progress in molecular dynamics has provided an experimental tool to study complex biological phenomena such as protein folding, ligand-receptor interactions, and micellar formation, growth, and fission. The detailed molecular definition of GARD and its inter-molecular catalytic interactions make it highly compatible with molecular dynamics analyses. We present a roadmap for simulating GARD's kinetic and thermodynamic behavior using various molecular dynamics methodologies. We review different approaches for testing the validity of the GARD model by following micellar accretion and fission events and examining compositional changes over time. Near-future computational advances could provide empirical delineation for further system complexification, from simple compositional non-covalent assemblies towards more life-like protocellular entities with covalent chemistry that underlies metabolism and genetic encoding.

Application of molecular dynamics simulation to improve the theoretical prediction for collisional cross section of aromatic compounds with long alkyl chains in crude oils

RATIONALE

Molecular dynamics (MD) simulations with finite temperature were performed to improve the theoretical prediction of collisional cross section (CCS) values, especially for aromatic compounds containing long alkyl chains.

METHODS

In this study, the CCS values of 11 aromatic compounds with long alkyl chains were calculated by MD simulations while considering internal energy at 300, 500, and 700 K, and the results were compared with experimentally determined values.

RESULTS

The CCS values calculated at higher energies showed better agreement with the experimental values. Polycyclic aromatic hydrocarbons (PAHs) such as pentacene and benz[b]anthracene were also investigated, and better agreement between the theoretical and experimental results was observed when higher temperature (or higher internal energy) was considered.

CONCLUSIONS

The data presented in this study show that the internal degrees of freedom of ions must be considered to accurately predict the CCS values of aromatic compounds with a flexible structure measured by ion mobility mass spectrometry.

The role of the backbone torsion in protein folding

BACKGROUND

The set of forces and sequence of events that govern the transition from an unfolded polypeptide chain to a functional protein with correct spatial structure remain incompletely known, despite the importance of the problem and decades of theory development, computer simulations, and laboratory experiments. Information about the correctly folded state of most proteins is likely to be present in their sequences, and yet many proteins fail to attain native structure after overexpression in a non-native environment or upon experimental denaturation and refolding.

PRESENTATION OF THE HYPOTHESIS

We hypothesize that correct protein folding in vivo is an active, energy-dependent process that most likely applies torque force co-translationally to all proteins and possibly also post-translationally to many proteins in every cell. When a site on an unfolded polypeptide is rotationally constrained, torsion applied at another site would induce twisting of the main chain, which would initiate the formation of a local secondary structure, such as an alpha-helical turn or a beta-turn/beta-hairpin. The nucleation of structural elements is a rate-limiting, energetically unfavorable step in the process of protein folding, and energy-dependent chain torsion is likely to help overcome this barrier in vivo. Several molecular machines in a cell, primarily ribosomes, but also possibly signal recognition particles and chaperone systems, may play a role in applying torque to an unfolded protein chain, using the energy of GTP or ATP hydrolysis. Lack of such force in the in vitro systems may be the main reason of the failure of many longer proteins to attain the correct functional conformation.

TESTING THE HYPOTHESIS

The hypothesis can be tested using single-molecule approaches, by measuring directly the forces applied to polypeptide chains under controlled conditions in vitro, and in bulk, by assessing folding rates and extent of misfolding in proteins that are engineered to experience transient spatial constraint during their synthesis.

IMPLICATIONS OF THE HYPOTHESIS

Learning about the role of main chain torsion in protein folding will improve our understanding of folding mechanisms and may lead to bioengineering solutions that would enhance the yields of correctly folded proteins in heterologous expression systems.

REVIEWERS

This article was reviewed by Frank Eisenhaber, Igor Berezovsky and Michael Gromiha.

Accurate prediction of cellular co-translational folding indicates proteins can switch from post- to co-translational folding

The rates at which domains fold and codons are translated are important factors in determining whether a nascent protein will co-translationally fold and function or misfold and malfunction. Here we develop a chemical kinetic model that calculates a protein domain's co-translational folding curve during synthesis using only the domain's bulk folding and unfolding rates and codon translation rates. We show that this model accurately predicts the course of co-translational folding measured in vivo for four different protein molecules. We then make predictions for a number of different proteins in yeast and find that synonymous codon substitutions, which change translation-elongation rates, can switch some protein domains from folding post-translationally to folding co-translationally--a result consistent with previous experimental studies. Our approach explains essential features of co-translational folding curves and predicts how varying the translation rate at different codon positions along a transcript's coding sequence affects this self-assembly process.

Molecular dynamics simulations: advances and applications

Molecular dynamics simulations have evolved into a mature technique that can be used effectively to understand macromolecular structure-to-function relationships. Present simulation times are close to biologically relevant ones. Information gathered about the dynamic properties of macromolecules is rich enough to shift the usual paradigm of structural bioinformatics from studying single structures to analyze conformational ensembles. Here, we describe the foundations of molecular dynamics and the improvements made in the direction of getting such ensemble. Specific application of the technique to three main issues (allosteric regulation, docking, and structure refinement) is discussed.

Dwell-Time Distribution, Long Pausing and Arrest of Single-Ribosome Translation through the mRNA Duplex

Proteins in the cell are synthesized by a ribosome translating the genetic information encoded on the single-stranded messenger RNA (mRNA). It has been shown that the ribosome can also translate through the duplex region of the mRNA by unwinding the duplex. Here, based on our proposed model of the ribosome translation through the mRNA duplex we study theoretically the distribution of dwell times of the ribosome translation through the mRNA duplex under the effect of a pulling force externally applied to the ends of the mRNA to unzip the duplex. We provide quantitative explanations of the available single molecule experimental data on the distribution of dwell times with both short and long durations, on rescuing of the long paused ribosomes by raising the pulling force to unzip the duplex, on translational arrests induced by the mRNA duplex and Shine-Dalgarno(SD)-like sequence in the mRNA. The functional consequences of the pauses or arrests caused by the mRNA duplex and the SD sequence are discussed and compared with those obtained from other types of pausing, such as those induced by "hungry" codons or interactions of specific sequences in the nascent chain with the ribosomal exit tunnel.

Quantitative Connection between Ensemble Thermodynamics and Single-Molecule Kinetics: A Case Study Using Cryogenic Electron Microscopy and Single-Molecule Fluorescence Resonance Energy Transfer Investigations of the Ribosome

At equilibrium, thermodynamic and kinetic information can be extracted from biomolecular energy landscapes by many techniques. However, while static, ensemble techniques yield thermodynamic data, often only dynamic, single-molecule techniques can yield the kinetic data that describe transition-state energy barriers. Here we present a generalized framework based upon dwell-time distributions that can be used to connect such static, ensemble techniques with dynamic, single-molecule techniques, and thus characterize energy landscapes to greater resolutions. We demonstrate the utility of this framework by applying it to cryogenic electron microscopy (cryo-EM) and single-molecule fluorescence resonance energy transfer (smFRET) studies of the bacterial ribosomal pre-translocation complex. Among other benefits, application of this framework to these data explains why two transient, intermediate conformations of the pre-translocation complex, which are observed in a cryo-EM study, may not be observed in several smFRET studies.

Decoding mechanisms by which silent codon changes influence protein biogenesis and function

SCOPE

Synonymous codon usage has been a focus of investigation since the discovery of the genetic code and its redundancy. The occurrences of synonymous codons vary between species and within genes of the same genome, known as codon usage bias. Today, bioinformatics and experimental data allow us to compose a global view of the mechanisms by which the redundancy of the genetic code contributes to the complexity of biological systems from affecting survival in prokaryotes, to fine tuning the structure and function of proteins in higher eukaryotes. Studies analyzing the consequences of synonymous codon changes in different organisms have revealed that they impact nucleic acid stability, protein levels, structure and function without altering amino acid sequence. As such, synonymous mutations inevitably contribute to the pathogenesis of complex human diseases. Yet, fundamental questions remain unresolved regarding the impact of silent mutations in human disorders. In the present review we describe developments in this area concentrating on mechanisms by which synonymous mutations may affect protein function and human health.

PURPOSE

This synopsis illustrates the significance of synonymous mutations in disease pathogenesis. We review the different steps of gene expression affected by silent mutations, and assess the benefits and possible harmful effects of codon optimization applied in the development of therapeutic biologics.

PHYSIOLOGICAL AND MEDICAL RELEVANCE

Understanding mechanisms by which synonymous mutations contribute to complex diseases such as cancer, neurodegeneration and genetic disorders, including the limitations of codon-optimized biologics, provides insight concerning interpretation of silent variants and future molecular therapies.

Biphasic character of ribosomal translocation and non-Michaelis-Menten kinetics of translation

We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small 30S and large 50S subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G-GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.

Nonequilibrium stochastic model for tRNA binding time statistics

Protein translation is one of the most important processes in cell life, but despite being well-understood biochemically, the implications of its intrinsic stochastic nature have not been fully elucidated. In this paper we develop a microscopic and stochastic model which describes a crucial step in protein translation, namely the binding of the tRNA to the ribosome. Our model explicitly takes into consideration tRNA recharging dynamics, spatial inhomogeneity, and stochastic fluctuations in the number of charged tRNAs around the ribosome. By analyzing this nonequilibrium system we are able to derive the statistical distribution of the times needed by the tRNAs to bind to the ribosome, and to show that it deviates from an exponential due to the coupling between the fluctuations of charged and uncharged populations of tRNA.

Extracting signal from noise: kinetic mechanisms from a Michaelis-Menten-like expression for enzymatic fluctuations

Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models.

TEMPLATE-DIRECTED BIOPOLYMERIZATION: TAPE-COPYING TURING MACHINES

DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Intermediate states during mRNA-tRNA translocation

Recent studies support the notion that the pre-translocation (PRE) ribosomal complex functions, at least in part, as a Brownian machine, stochastically fluctuating among multiple conformations and transfer RNA (tRNA) binding configurations. Apart from the relatively more energetically stable conformational states of the PRE complex, termed macrostate I (MS I) and macrostate II (MS II), several additional intermediate states have been recently discovered. Structural and kinetic analyses of these states, made possible by cryogenic-electron microscopy (cryo-EM), X-ray crystallography, and single-molecule fluorescence resonance energy transfer (smFRET), have provided important insights into the translocation process, which is now understood to proceed, at least in the first step of the process, as a Brownian machine that is transiently stabilized in the 'productive' MS II conformation by the binding of the translocase elongation factor G (EF-G).

The ribosome uses two active mechanisms to unwind messenger RNA during translation

The ribosome translates the genetic information encoded in messenger RNA into protein. Folded structures in the coding region of an mRNA represent a kinetic barrier that slows the peptide elongation rate, as the ribosome must disrupt structures it encounters in the mRNA at its entry site to enable translocation to the next codon. Such structures are exploited by the cell to create diverse strategies for translation regulation, such as programmed frameshifting^1,2, protein expression levels^3,4, ribosome localization⁵, and cotranslational protein folding⁶. Although strand separation activity is inherent to the ribosome, requiring no exogenous helicases⁷, its mechanism is still unknown. Here, using a single-molecule optical tweezers assay on mRNA hairpins, we find that the translation rate of identical codons at the decoding center is greatly influenced by the G•C content of folded structures at the mRNA entry site. Furthermore, force applied to the ends of the hairpin to favor its unfolding significantly speeds translation. Quantitative analysis of the force dependence of its helicase activity reveals that the ribosome, unlike previously studied helicases, uses two distinct active mechanisms to unwind mRNA structure: (i) it destabilizes the helical junction at the mRNA entry site by biasing its thermal fluctuations toward the open state, increasing the probability for the ribosome to translocate unhindered; and (ii) it also mechanically pulls apart the mRNA single-strands of the closed junction during the conformational changes that accompany ribosome translocation. Our results establish a quantitative mechanical basis for understanding the mechanism of regulation of the elongation rate of translation by structured mRNAs.

Biological mechanisms, one molecule at a time

The last 15 years have witnessed the development of tools that allow the observation and manipulation of single molecules. The rapidly expanding application of these technologies for investigating biological systems of ever-increasing complexity is revolutionizing our ability to probe the mechanisms of biological reactions. Here, we compare the mechanistic information available from single-molecule experiments with the information typically obtained from ensemble studies and show how these two experimental approaches interface with each other. We next present a basic overview of the toolkit for observing and manipulating biology one molecule at a time. We close by presenting a case study demonstrating the impact that single-molecule approaches have had on our understanding of one of life's most fundamental biochemical reactions: the translation of a messenger RNA into its encoded protein by the ribosome.

Converting structural information into an allosteric-energy-based picture for elongation factor Tu activation by the ribosome

The crucial process of aminoacyl-tRNA delivery to the ribosome is energized by the GTPase reaction of the elongation factor Tu (EF-Tu). Advances in the elucidation of the structure of the EF-Tu/ribosome complex provide the rare opportunity of gaining a detailed understanding of the activation process of this system. Here, we use quantitative simulation approaches and reproduce the energetics of the GTPase reaction of EF-Tu with and without the ribosome and with several key mutants. Our study provides a novel insight into the activation process. It is found that the critical H84 residue is not likely to behave as a general base but rather contributes to an allosteric effect, which includes a major transition state stabilization by the electrostatic effect of the P loop and other regions of the protein. Our findings have general relevance to GTPase activation, including the processes that control signal transduction.

Distribution of dwell times of a ribosome: effects of infidelity, kinetic proofreading and ribosome crowding

Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechanochemical cycle of a ribosome. The stochastic movement of the ribosome consists of an alternating sequence of pause and translocation; the sum of the durations of a pause and the following translocation is the time of dwell of the ribosome at the corresponding codon. We derive the analytical expression for the distribution of the dwell times of a ribosome in our model. Wherever experimental data are available, our theoretical predictions are consistent with those results. We suggest appropriate experiments to test the new predictions of our model, particularly the effects of the quality control mechanism of the ribosome and that of their crowding on the mRNA track.

Full reconstruction of a vectorial protein folding pathway by atomic force microscopy and molecular dynamics simulations

During co-translational folding, the nascent polypeptide chain is extruded sequentially from the ribosome exit tunnel and is [corrected] under severe conformational constraints [corrected] dictated by the one-dimensional geometry of the tunnel. [corrected] How do such vectorial constraints impact the folding pathway? Here, we combine single-molecule atomic force spectroscopy and steered molecular dynamics simulations to examine protein folding in the presence of one-dimensional constraints that are similar to those imposed on the nascent polypeptide chain. The simulations exquisitely reproduced the experimental unfolding and refolding force extension relationships and led to the full reconstruction of the vectorial folding pathway of a large polypeptide, the 253-residue consensus ankyrin repeat protein, NI6C. We show that fully stretched and then relaxed NI6C starts folding by the formation of local secondary structures, followed by the nucleation of three N-terminal repeats. This rate-limiting step is then followed by the vectorial and sequential folding of the remaining repeats. However, after partial unfolding, when allowed to refold, the C-terminal repeats successively regain structures without any nucleation step by using the intact N-terminal repeats as a template. These results suggest a pathway for the co-translational folding of repeat proteins and have implications for mechanotransduction.

Mechanistic constraints from the substrate concentration dependence of enzymatic fluctuations

The time it takes an enzyme to complete its reaction is a stochastic quantity governed by thermal fluctuations. With the advent of high-resolution methods of single-molecule manipulation and detection, it is now possible to observe directly this natural variation in the enzymatic cycle completion time and extract kinetic information from the statistics of its fluctuations. To this end, the inverse of the squared coefficient of variation, which we term n(min), is a useful measure of fluctuations because it places a strict lower limit on the number of kinetic states in the enzymatic mechanism. Here we show that there is a single general expression for the substrate dependence of n(min) for a wide range of kinetic models. This expression is governed by three kinetic parameters, which we term N(L), N(S), and alpha. These parameters have simple geometric interpretations and provide clear constraints on possible kinetic mechanisms. As a demonstration of this analysis, we fit the fluctuations in the dwell times of the packaging motor of the bacteriophage varphi29, revealing additional features of the nucleotide loading process in this motor. Because a diverse set of kinetic models display the same substrate dependence for their fluctuations, the expression for this general dependence may prove of use in the characterization and study of the dynamics of a wide range of enzymes.

Revealing the base pair stepping dynamics of nucleic acid motor proteins with optical traps

Nearly all aspects of nucleic acid metabolism involve motor proteins. This diverse group of enzymes, which includes DNA and RNA polymerases, the ribosome, helicases, and other translocases, converts chemical energy in the form of bond hydrolysis into concerted motion along nucleic acid filaments. The direct observation of this motion at its fundamental distance scale of one base pair has required the development of new ultrasensitive techniques. Recent advances in optical traps have now made these length scales, once the exclusive realm of crystallographic techniques, accessible. Several new studies using optical traps have revealed for the first time how motor proteins translocate along their substrates in a stepwise fashion. Though these techniques have only begun to be applied to biological problems, the unprecedented access into nucleic acid motor protein movement has already provided important insights into their mechanism. In this perspective, we review these advances and offer our view on the future of this exciting development.