Translocation of a β-hairpin-forming peptide through a cylindrical tunnel

Direct Observation of the Mechanical Role of Bacterial Chaperones in Protein Folding

Protein folding under force is an integral source of generating mechanical energy in various cellular processes, ranging from protein translation to degradation. Although chaperones are well known to interact with proteins under mechanical force, how they respond to force and control cellular energetics remains unknown. To address this question, we introduce a real-time magnetic tweezer technology herein to mimic the physiological force environment on client proteins, keeping the chaperones unperturbed. We studied two structurally distinct client proteins--protein L and talin with seven different chaperones─independently and in combination and proposed a novel mechanical activity of chaperones. We found that chaperones behave differently, while these client proteins are under force, than their previously known functions. For instance, tunnel-associated chaperones (DsbA and trigger factor), otherwise working as holdase without force, assist folding under force. This process generates an additional mechanical energy up to ∼147 zJ to facilitate translation or translocation. However, well-known cytoplasmic foldase chaperones (PDI, thioredoxin, or DnaKJE) do not possess the mechanical folding ability under force. Notably, the transferring chaperones (DnaK, DnaJ, and SecB) act as holdase and slow down the folding process, both in the presence and absence of force, to prevent misfolding of the client proteins. This provides an emerging insight of mechanical roles of chaperones: they can generate or consume energy by shifting the energy landscape of the client proteins toward a folded or an unfolded state, suggesting an evolutionary mechanism to minimize energy consumption in various biological processes.

Hydrophobic and electrostatic interactions modulate protein escape at the ribosomal exit tunnel

After translation, nascent proteins must escape the ribosomal exit tunnel to attain complete folding to their native states. This escape process also frees up the ribosome tunnel for a new translation job. In this study, we investigate the impacts of energetic interactions between the ribosomal exit tunnel and nascent proteins on the protein escape process by molecular dynamics simulations using partially coarse-grained models that incorporate hydrophobic and electrostatic interactions of the ribosome tunnel of Haloarcula marismortui with nascent proteins. We find that, in general, attractive interactions slow down the protein escape process, whereas repulsive interactions speed it up. For the small globular proteins considered, the median escape time correlates with both the number of hydrophobic residues, N_h, and the net charge, Q, of a nascent protein. A correlation coefficient exceeding 0.96 is found for the relation between the median escape time and a combined quantity of N_h + 5.9Q, suggesting that it is ∼6 times more efficient to modulate the escape time by changing the total charge than the number of hydrophobic residues. The estimated median escape times are found in the submillisecond-to-millisecond range, indicating that the escape does not delay the ribosome recycling. For various types of the tunnel model, with and without hydrophobic and electrostatic interactions, the escape time distribution always follows a simple diffusion model that describes the escape process as a downhill drift of a Brownian particle, suggesting that nascent proteins escape along barrier-less pathways at the ribosome tunnel.

DsbA is a redox-switchable mechanical chaperone

DsbA is a ubiquitous bacterial oxidoreductase that associates with substrates during and after translocation, yet its involvement in protein folding and translocation remains an open question. Here we demonstrate a redox-controlled chaperone activity of DsbA, on both cysteine-containing and cysteine-free substrates, using magnetic tweezers-based single molecule force spectroscopy that enables independent measurements of oxidoreductase activity and chaperone behavior. Interestingly we found that this chaperone activity is tuned by the oxidation state of DsbA; oxidized DsbA is a strong promoter of folding, but the effect is weakened by the reduction of the catalytic CXXC motif. We further localize the chaperone binding site of DsbA using a seven-residue peptide which effectively blocks the chaperone activity. We found that the DsbA assisted folding of proteins in the periplasm generates enough mechanical work to decrease the ATP consumption needed for periplasmic translocation by up to 33%.

Protein escape at the ribosomal exit tunnel: Effect of the tunnel shape

We study the post-translational escape of nascent proteins at the ribosomal exit tunnel with the consideration of a real shape atomistic tunnel based on the Protein Data Bank structure of the large ribosome subunit of archeon Haloarcula marismortui. Molecular dynamics simulations employing the Go-like model for the proteins show that at intermediate and high temperatures, including a presumable physiological temperature, the protein escape process at the atomistic tunnel is quantitatively similar to that at a cylinder tunnel of length L = 72 Å and diameter d = 16 Å. At low temperatures, the atomistic tunnel, however, yields an increased probability of protein trapping inside the tunnel, while the cylinder tunnel does not cause the trapping. All-β proteins tend to escape faster than all-α proteins, but this difference is blurred on increasing the protein's chain length. A 29-residue zinc-finger domain is shown to be severely trapped inside the tunnel. Most of the single-domain proteins considered, however, can escape efficiently at the physiological temperature with the escape time distribution following the diffusion model proposed in our previous works. An extrapolation of the simulation data to a realistic value of the friction coefficient for amino acids indicates that the escape times of globular proteins are at the sub-millisecond scale. It is argued that this time scale is short enough for the smooth functioning of the ribosome by not allowing nascent proteins to jam the ribosome tunnel.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon

An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) time scales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels.

Large-scale simulations of nucleoprotein complexes: ribosomes, nucleosomes, chromatin, chromosomes and CRISPR

Recent advances in biotechnology such as Hi-C, CRISPR/Cas9 and ribosome display have placed nucleoprotein complexes at center stage. Understanding the structural dynamics of these complexes aids in optimizing protocols and interpreting data for these new technologies. The integration of simulation and experiment has helped advance mechanistic understanding of these systems. Coarse-grained simulations, reduced-description models, and explicit solvent molecular dynamics simulations yield useful complementary perspectives on nucleoprotein complex structural dynamics. When combined with Hi-C, cryo-EM, and single molecule measurements, these simulations integrate disparate forms of experimental data into a coherent mechanism.

Origins of the Mechanochemical Coupling of Peptide Bond Formation to Protein Synthesis

Mechanical forces acting on the ribosome can alter the speed of protein synthesis, indicating that mechanochemistry can contribute to translation control of gene expression. The naturally occurring sources of these mechanical forces, the mechanism by which they are transmitted 10 nm to the ribosome's catalytic core, and how they influence peptide bond formation rates are largely unknown. Here, we identify a new source of mechanical force acting on the ribosome by using in situ experimental measurements of changes in nascent-chain extension in the exit tunnel in conjunction with all-atom and coarse-grained computer simulations. We demonstrate that when the number of residues composing a nascent chain increases, its unstructured segments outside the ribosome exit tunnel generate piconewtons of force that are fully transmitted to the ribosome's P-site. The route of force transmission is shown to be through the nascent polypetide's backbone, not through the wall of the ribosome's exit tunnel. Utilizing quantum mechanical calculations we find that a consequence of such a pulling force is to decrease the transition state free energy barrier to peptide bond formation, indicating that the elongation of a nascent chain can accelerate translation. Since nascent protein segments can start out as largely unfolded structural ensembles, these results suggest a pulling force is present during protein synthesis that can modulate translation speed. The mechanism of force transmission we have identified and its consequences for peptide bond formation should be relevant regardless of the source of the pulling force.

Folding and escape of nascent proteins at ribosomal exit tunnel

We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein.

Insights into Cotranslational Nascent Protein Behavior from Computer Simulations

Regulation of protein stability and function in vivo begins during protein synthesis, when the ribosome translates a messenger RNA into a nascent polypeptide. Cotranslational processes involving a nascent protein include folding, binding to other macromolecules, enzymatic modification, and secretion through membranes. Experiments have shown that the rate at which the ribosome adds amino acids to the elongating nascent chain influences the efficiency of these processes, with alterations to these rates possibly contributing to diseases, including some types of cancer. In this review, we discuss recent insights into cotranslational processes gained from molecular simulations, how different computational approaches have been combined to understand cotranslational processes at multiple scales, and the new scenarios illuminated by these simulations. We conclude by suggesting interesting questions that computational approaches in this research area can address over the next few years.

Unfolding knots by proteasome-like systems: simulations of the behaviour of folded and neurotoxic proteins

Knots in proteins have been proposed to resist proteasomal degradation, thought in turn to be related to neurodegenerative diseases such as Huntington.

Protein unfolding by biological unfoldases: insights from modeling

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.

Computation of transit times using the milestoning method with applications to polymer translocation

Milestoning is an efficient approximation for computing long-time kinetics and thermodynamics of large molecular systems, which are inaccessible to brute-force molecular dynamics simulations. A common use of milestoning is to compute the mean first passage time (MFPT) for a conformational transition of interest. However, the MFPT is not always the experimentally observed timescale. In particular, the duration of the transition path, or the mean transit time, can be measured in single-molecule experiments, such as studies of polymers translocating through pores and fluorescence resonance energy transfer studies of protein folding. Here we show how to use milestoning to compute transit times and illustrate our approach by applying it to the translocation of a polymer through a narrow pore.

Watching single proteins using engineered nanopores

Recent studies in the area of single-molecule detection of proteins with nanopores show a great promise in fundamental science, bionanotechnology and proteomics. In this mini-review, I discuss a comprehensive array of examinations of protein detection and characterization using protein and solid-state nanopores. These investigations demonstrate the power of the single-molecule nanopore measurements to reveal a broad range of functional, structural, biochemical and biophysical features of proteins, such as their backbone flexibility, enzymatic activity, binding affinity as well as their concentration, size and folding state. Engineered nanopores in organic materials and in inorganic membranes coupled with surface modification and protein engineering might provide a new generation of sensing devices for molecular biomedical diagnostics.

Slowing down single-molecule trafficking through a protein nanopore reveals intermediates for peptide translocation

The microscopic details of how peptides translocate one at a time through nanopores are crucial determinants for transport through membrane pores and important in developing nano-technologies. To date, the translocation process has been too fast relative to the resolution of the single molecule techniques that sought to detect its milestones. Using pH-tuned single-molecule electrophysiology and molecular dynamics simulations, we demonstrate how peptide passage through the α-hemolysin protein can be sufficiently slowed down to observe intermediate single-peptide sub-states associated to distinct structural milestones along the pore, and how to control residence time, direction and the sequence of spatio-temporal state-to-state dynamics of a single peptide. Molecular dynamics simulations of peptide translocation reveal the time- dependent ordering of intermediate structures of the translocating peptide inside the pore at atomic resolution. Calculations of the expected current ratios of the different pore-blocking microstates and their time sequencing are in accord with the recorded current traces.

Through the eye of the needle: recent advances in understanding biopolymer translocation

In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.

Simulation study of the role of the ribosomal exit tunnel on protein folding

To investigate the role of the ribosomal exit tunnel on protein folding, we simulate the initial-stage folding behavior of the protein villin headpiece subdomain HP35 (PDB id: 1yrf) with and without prefolding in the exit tunnel by using an all-atom model and find that prefolding in the exit tunnel could effectively help the protein form native secondary structures. Furthermore, our results show that, after releasing from the exit tunnel, the prefolded chains may have a tendency to form more native contacts than those only in free space and this reduces the conformational space of sampling. Our results may provide an alternative way to explain the fast folding mechanism of proteins in vivo.

Mechanical anisotropy of ankyrin repeats

Red blood cells are frequently deformed and their cytoskeletal proteins such as spectrin and ankyrin-R are repeatedly subjected to mechanical forces. While the mechanics of spectrin was thoroughly investigated in vitro and in vivo, little is known about the mechanical behavior of ankyrin-R. In this study, we combine coarse-grained steered molecular dynamics simulations and atomic force spectroscopy to examine the mechanical response of ankyrin repeats (ARs) in a model synthetic AR protein NI6C, and in the D34 fragment of native ankyrin-R when these proteins are subjected to various stretching geometry conditions. Our steered molecular dynamics results, supported by AFM measurements, reveal an unusual mechanical anisotropy of ARs: their mechanical stability is greater when their unfolding is forced to propagate from the N-terminus toward the C-terminus (repeats unfold at ~60 pN), as compared to the unfolding in the opposite direction (unfolding force ∼ 30 pN). This anisotropy is also reflected in the complex refolding behavior of ARs. The origin of this unfolding and refolding anisotropy is in the various numbers of native contacts that are broken and formed at the interfaces between neighboring repeats depending on the unfolding/refolding propagation directions. Finally, we discuss how these complex mechanical properties of ARs in D34 may affect its behavior in vivo.

Computational studies of molecular machines: the ribosome

The past decade has produced an avalanche of experimental data on the structure and dynamics of the ribosome. Groundbreaking studies in structural biology and kinetics have placed important constraints on ribosome structural dynamics. However, a gulf remains between static structures and time dependent data. In particular, X-ray crystallography and cryo-EM studies produce static models of the ribosome in various states, but lack dynamic information. Single molecule studies produce information on the rates of transitions between these states but do not have high-resolution spatial information. Computational studies have aided in bridging this gap by providing atomic resolution simulations of structural fluctuations and transitions between configurations.

Coarse-grained models to study dynamics of nanoscale biomolecules and their applications to the ribosome

Biopolymers are of dynamic nature and undergo functional motions spanning a large spectrum of timescales. To study the internal dynamics of nano-sized molecular complexes that exceed hundred thousands of atoms with atomic detail is computationally inefficient. Therefore, to achieve both the spatial and temporal scales of biological interest coarse-grained models of macromolecules are often used. By uniting groups of atoms into single interacting centers one decreases the resolution of the system and gets rid of the irrelevant degrees of freedom. This simplification, even though it requires parameterization, makes the studies of biomolecular dynamics computationally tractable and allows us to reach beyond the microsecond time frame. Here, I review the coarse-grained models of macromolecules composed of proteins and nucleic acids. I give examples of one-bead models that were developed to investigate the internal dynamics and focus on their applications to the ribosome--the nanoscale protein synthesis machine.

Facilitated translocation of polypeptides through a single nanopore

The transport of polypeptides through nanopores is a key process in biology and medical biotechnology. Despite its critical importance, the underlying kinetics of polypeptide translocation through protein nanopores is not yet comprehensively understood. Here, we present a simple two-barrier, one-well kinetic model for the translocation of short positively charged polypeptides through a single transmembrane protein nanopore that is equipped with negatively charged rings, simply called traps. We demonstrate that the presence of these traps within the interior of the nanopore dramatically alters the free energy landscape for the partitioning of the polypeptide into the nanopore interior, as revealed by significant modifications in the activation free energies required for the transitions of the polypeptide from one state to the other. Our kinetic model permits the calculation of the relative and absolute exit frequencies of the short cationic polypeptides through either opening of the nanopore. Moreover, this approach enabled quantitative assessment of the kinetics of translocation of the polypeptides through a protein nanopore, which is strongly dependent on several factors, including the nature of the translocating polypeptide, the position of the traps, the strength of the polypeptide-attractive trap interactions and the applied transmembrane voltage.

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.

Simulating activity of the bacterial ribosome

Computational modeling studies that investigate activity of the bacterial ribosome were reviewed. Computational approaches became possible with the availability of three-dimensional atomic resolution structures of the ribosomal subunits. However, due to the enormous size of the system, theoretical efforts to study the ribosome are few and challenging. For example, to extend the simulation timescales to biologically relevant ones, often, reduced models that require tedious parameterizations need to be applied. To that end, modeling of the ribosome focused on its internal dynamics, electrostatic properties, inhibition by antibiotics, polypeptide folding in the ribosome tunnel and assembly mechanisms driving the formation of the small ribosomal subunit.

Thermodynamic stability of polypeptides folding within modeled ribosomal exit tunnel: a density functional study

The mechanism of polypeptide folding, especially for the formation of tertiary structures, within the ribosomal exit tunnel, remains one of the most important unsolved problems in biophysical chemistry and molecular biology. In this work, we use a density functional theory (DFT) to explore the polypeptide folding within a modified nanopore, which mimics the confined environment of ribosomal exit tunnel. Results indicate that too long polypeptides (N>100 cannot fold into a helix state within the nanopore, and the helix polypeptides favor folding into a negative coiled coil rather than a positive one, because the negative coiled coil has a lower grand potential than the positive one, and the polypeptide folding into the negative coiled coil therefore needs less driving force than the positive one. To fold into the positive coiled coil, the helix polypeptides must have a small minor radius or a short chain length, which provides helpful insights into the design of nanodevices for manipulating the positive coiled coil. In the presence of attractive interaction, helices need more driving force to fold into coiled coil. Importantly, we have also proposed a scaling relation to understand the folding behavior. The scaling relation gives a good estimate for the computational results, and provides a reasonable explanation for the folding behavior. In summary, it is expected that the proposed DFT approach and the scaling relation provide alternative means for the investigation of polypeptide folding in confined environment, and these impressive results could give useful insights into nascent polypeptide folding.

Computer simulations and theory of protein translocation

The translocation of proteins through pores is central to many biological phenomena, such as mitochondrial protein import, protein degradation, and delivery of protein toxins to their cytosolic targets. Because proteins typically have to pass through constrictions that are too narrow to accommodate folded structures, translocation must be coupled to protein unfolding. The simplest model that accounts for such co-translocational unfolding assumes that both translocation and unfolding are accomplished by pulling on the end of the polypeptide chain mechanically. In this Account, we describe theoretical studies and computer simulations of this model and discuss how the time scales of translocation depend on the pulling force and on the protein structure. Computationally, this is a difficult problem because biologically or experimentally relevant time scales of translocation are typically orders of magnitude slower than those accessible by fully atomistic simulations. For this reason, we explore one-dimensional free energy landscapes along suitably defined translocation coordinates and discuss various approaches to their computation. We argue that the free energy landscape of translocation is often bumpy because confinement partitions the protein's configuration space into distinct basins of attraction separated by large entropic barriers. Favorable protein-pore interactions and nonnative interactions within the protein further contribute to the complexity. Computer simulations and simple scaling estimates show that forces of just 2-6 pN are often sufficient to ensure transport of unstructured polypeptides, whereas much higher forces are typically needed to translocate folded protein domains. The unfolding mechanisms found from simulations of translocation are different from those observed in the much better understood case of atomic force microscopy (AFM) pulling studies, in which proteins are unraveled by stretching them between their N- and C-termini. In contrast to AFM experiments, single-molecule experimental studies of protein translocation have just started to emerge. We describe one example of a collaborative study, in which dwell times of beta-hairpin-forming peptides inside the alpha-hemolysin pore were both measured experimentally and estimated using computer simulations. Analysis of the simulated trajectories has explained the experimental finding that more stable hairpins take, on the average, longer to traverse the pore. Despite the insight we have gained, the general relationship between the structure of proteins and their resistance to mechanically driven co-translocational unfolding remains poorly understood. Future theoretical progress likely will be made in conjunction with single-molecule experiments and will require realistic models to account for specific protein-pore interactions and for solvent effects.

Statics of the ribosomal exit tunnel: implications for cotranslational peptide folding, elongation regulation, and antibiotics binding

A sophisticated interplay between the static properties of the ribosomal exit tunnel and its functional role in cotranslational processes is revealed by constraint counting on topological network representations of large ribosomal subunits from four different organisms. As for the global flexibility characteristics of the subunit, the results demonstrate a conserved stable structural environment of the tunnel. The findings render unlikely that deformations of the tunnel move peptides down the tunnel in an active manner. Furthermore, the stable environment rules out that the tunnel can adapt widely so as to allow tertiary folding of nascent chains. Nevertheless, there are local zones of flexible nucleotides within the tunnel, between the peptidyl transferase center and the tunnel constriction, and at the tunnel exit. These flexible zones strikingly agree with previously identified folding zones. As for cotranslational elongation regulation, flexible residues in the beta-hairpin of the ribosomal L22 protein were verified, as suggested previously based on structural results. These results support the hypothesis that L22 can undergo conformational changes that regulate the tunnel voyage of nascent polypeptides. Furthermore, rRNA elements, for which conformational changes have been observed upon interaction of the tunnel wall with a nascent SecM peptide, are less strongly coupled to the subunit core. Sequences of coupled rigid clusters are identified between the tunnel and some of these elements, suggesting signal transmission by a domino-like mechanical coupling. Finally, differences in the flexibility of the glycosidic bonds of bases that form antibiotics-binding crevices within the peptidyl transferase center and the tunnel region are revealed for ribosomal structures from different kingdoms. In order to explain antibiotics selectivity, action, and resistance, according to these results, differences in the degrees of freedom of the binding regions may need to be considered.

Effect of charge distribution on the translocation of an inhomogeneously charged polymer through a nanopore

We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore-polymer interactions is determined by the entropic cost of translocation, with the optimum charge position being at the midpoint of the chain for a rodlike polymer and close to the leading chain end for an ideal chain. The presence of attractive and repulsive pore-charge interactions yields a shift in the optimum charge position toward the trailing end and the leading end of the chain, respectively. Moreover, our results show that strong attractive or repulsive interactions between the charge and the pore lengthen the translocation time relative to translocation through an inert pore. We generalize our results to accommodate the presence of multiple charged sites on the polymer. Our results provide insight into the effect of charge inhomogeneity on protein translocation through biological membranes.

Excursion of a single polypeptide into a protein pore: simple physics, but complicated biology

Despite its fundamental and critical importance in molecular biology and practical medical biotechnology, how a polypeptide interacts with a transmembrane protein pore is not yet comprehensively understood. Here, we employed single-channel electrical recordings to reveal the interactions of short polypeptides and small folded proteins with a robust beta-barrel protein pore. The short polypeptides were approximately 25 residues in length, resembling positively charged targeting presequences involved in protein import. The proteins were consisted of positively charged pre-cytochrome b2 fragments (pb2) fused to the small ribonuclease barnase (approximately 110 residues, Ba). Single-molecule experiments exploring the interaction of a folded pb2-Ba protein with a single beta-barrel pore, which contained negatively charged electrostatic traps, revealed the complexity of a network of intermolecular forces, including driving and electrostatic ones. In addition, the interaction was dependent on other factors, such as the hydrophobic content of the interacting polypeptide, the location of the electrostatic trap, the length of the pb2 presequence and temperature. This single-molecule approach together with protein design of either the interacting polypeptide or the pore lumen opens new opportunities for the exploration of the polypeptide-pore interaction at high temporal resolution. Such future studies are also expected to unravel the advantages and limitations of the nanopore technique for the detection and exploration of individual polypeptides.

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.

Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.

Extracting kinetics from single-molecule force spectroscopy: nanopore unzipping of DNA hairpins

Single-molecule force experiments provide powerful new tools to explore biomolecular interactions. Here, we describe a systematic procedure for extracting kinetic information from force-spectroscopy experiments, and apply it to nanopore unzipping of individual DNA hairpins. Two types of measurements are considered: unzipping at constant voltage, and unzipping at constant voltage-ramp speeds. We perform a global maximum-likelihood analysis of the experimental data at low-to-intermediate ramp speeds. To validate the theoretical models, we compare their predictions with two independent sets of data, collected at high ramp speeds and at constant voltage, by using a quantitative relation between the two types of measurements. Microscopic approaches based on Kramers theory of diffusive barrier crossing allow us to estimate not only intrinsic rates and transition state locations, as in the widely used phenomenological approach based on Bell's formula, but also free energies of activation. The problem of extracting unique and accurate kinetic parameters of a molecular transition is discussed in light of the apparent success of the microscopic theories in reproducing the experimental data.

Single-molecule electrophoresis of beta-hairpin peptides by electrical recordings and Langevin dynamics simulations

We used single-channel electrical recordings and Langevin molecular dynamics simulations to explore the electrophoretic translocation of various beta-hairpin peptides across the staphylococcal alpha-hemolysin (alphaHL) protein pore at single-molecule resolution. The beta-hairpin peptides, which varied in their folding properties, corresponded to the C terminal residues of the B1 domain of protein G. The translocation time was strongly dependent on the electric force and was correlated with the folding features of the beta-hairpin peptides. Highly unfolded peptides entered the pore in an extended conformation, resulting in fast single-file translocation events. In contrast, the translocation of the folded beta-hairpin peptides occurred more slowly. In this case, the beta-hairpin peptides traversed the alphaHL pore in a misfolded or fully folded conformation. This study demonstrates that the interaction between a polypeptide and a beta-barrel protein pore is dependent on the folding features of the polypeptide.

Protein translocation through a tunnel induces changes in folding kinetics: a lattice model study

Compaction of a nascent polypeptide chain inside the ribosomal exit tunnel, before it leaves the ribosome, has been proposed to accelerate the folding of newly synthesized proteins following their release from the ribosome. Thus, we used Kinetic Monte Carlo simulations of a minimalist on-lattice model to explore the effect that polypeptide translocation through a variety of channels has on protein folding kinetics. Our results demonstrate that tunnel confinement promotes faster folding of a well-designed protein relative to its folding in free space by displacing the unfolded state towards more compact structures that are closer to the transition state. Since the tunnel only forbids rarely visited, extended configurations, it has little effect on a "poorly designed" protein whose unfolded state is largely composed of low-energy, compact, misfolded configurations. The beneficial effect of the tunnel depends on its width; for example, a too-narrow tunnel enforces unfolded states with limited or no access to the transition state, while a too-wide tunnel has no effect on the unfolded state entropy. We speculate that such effects are likely to play an important role in the folding of some proteins or protein domains in the cellular environment and might dictate whether a protein folds co-translationally or post-translationally.

Nanotube Confinement Denatures Protein Helices

In striking contrast to simple polymer physics theory, which does not account for solvent effects, we find that physical confinement of solvated biopolymers decreases solvent entropy, which in turn leads to a reduction in the organized structural content of the polymer. Since our theory is based on a fundamental property of water-protein statistical mechanics, we expect it to have broad implications in many biological and material science contexts.

Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.

Asymmetric bridging of interconnected pores by encased semiflexible macromolecules

An increase of chain rigidity of macromolecule encased in interconnected cavities leads to bridging conformational transition in which polymer molecule at certain conditions spans the cavities. This is a similar phenomenon to that described for flexible chains on increase of confinement. Chain stiffness introduces, however, a delicate effect of interplay between confinement, chain stiffness, and concentration that leads to a breakup of symmetric bridging conformation to a striking asymmetric conformation even in the symmetric system of cavities. We provide the first data on this transition with complex translocation landscape and offer a tentative explanation.

Interactions of peptides with a protein pore

The partitioning of polypeptides into nanoscale transmembrane pores is of fundamental importance in biology. Examples include protein translocation in the endoplasmic reticulum and the passage of proteins through the nuclear pore complex. Here we examine the exchange of cationic alpha-helical peptides between the bulk aqueous phase and the transmembrane beta-barrel of the alpha-hemolysin (alphaHL) protein pore at the single-molecule level. The experimental kinetic data suggest a two-barrier, single-well free energy profile for peptide transit through the alphaHL pore. This free energy profile is strongly voltage- and peptide-length-dependent. We used the Woodhull-Eyring formalism to rationalize the values measured for the association and dissociation rate constants k(on) and k(off), and to separate k(off) into individual rate constants for exit through each of the openings of the protein pore. The rate constants k(on), k(off)(cis), and k(off)(trans) decreased with the length of the peptide. At high transmembrane potentials, the alanine-based peptides, which include bulky lysine side chains, bind more strongly (formation constants K(f) approximately tens of M(-1)) than highly flexible polyethylene glycols (K(f) approximately M(-1)) to the lumen of the alphaHL protein pore. In contrast, at zero transmembrane potential, the peptides bind weakly to the lumen of the pore, and the affinity decreases with the peptide length, similar to the case of the polyethylene glycols. The binding is enhanced at increased transmembrane potentials, because the free energy contribution DeltaG = -zetadeltaFV/RT predominates with the peptides. We suggest that the alphaHL protein may serve as a robust and versatile model for examining the interactions between positively charged signal peptides and a beta-barrel pore.