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

Long-lived metastable knots in polyampholyte chains

Knots in proteins and DNA are known to have significant effect on their equilibrium and dynamic properties as well as on their function. While knot dynamics and thermodynamics in electrically neutral and uniformly charged polymer chains are relatively well understood, proteins are generally polyampholytes, with varied charge distributions along their backbones. Here we use simulations of knotted polymer chains to show that variation in the charge distribution on a polyampholyte chain with zero net charge leads to significant variation in the resulting knot dynamics, with some charge distributions resulting in long-lived metastable knots that escape the (open-ended) chain on a timescale that is much longer than that for knots in electrically neutral chains. The knot dynamics in such systems can be described, quantitatively, using a simple one-dimensional model where the knot undergoes biased Brownian motion along a "reaction coordinate", equal to the knot size, in the presence of a potential of mean force. In this picture, long-lived knots result from charge sequences that create large electrostatic barriers to knot escape. This model allows us to predict knot lifetimes even when those times are not directly accessible by simulations.

Factors underlying asymmetric pore dynamics of disaggregase and microtubule-severing AAA+ machines

Disaggregation and microtubule-severing nanomachines from the AAA+ (ATPases associated with various cellular activities) superfamily assemble into ring-shaped hexamers that enable protein remodeling by coupling large-scale conformational changes with application of mechanical forces within a central pore by loops protruding within the pore. We probed the asymmetric pore motions and intraring interactions that support them by performing extensive molecular dynamics simulations of single-ring severing proteins and the double-ring disaggregase ClpB. Simulations reveal that dynamic stability of hexameric pores of severing proteins and of the nucleotide-binding domain 1 (NBD1) ring of ClpB, which belong to the same clade, involves a network of salt bridges that connect conserved motifs of central pore loops. Clustering analysis of ClpB highlights correlated motions of domains of neighboring protomers supporting strong interprotomer collaboration. Severing proteins have weaker interprotomer coupling and stronger intraprotomer stabilization through salt bridges involving pore loops. Distinct mechanisms are identified in the NBD2 ring of ClpB involving weaker interprotomer coupling through salt bridges formed by noncanonical loops and stronger intraprotomer coupling. Analysis of collective motions of PL1 loops indicates that the largest amplitude motions in the spiral complex of spastin and ClpB involve axial excursions of the loops, whereas for katanin they involve opening and closing of the central pore. All three motors execute primarily axial excursions in the ring complex. These results suggest distinct substrate processing mechanisms of remodeling and translocation by ClpB and spastin compared to katanin, thus providing dynamic support for the differential action of the two severing proteins. Relaxation dynamics of the distance between the PL1 loops and the center of mass of protomers reveals observation-time-dependent dynamics, leading to predicted relaxation times of tens to hundreds of microseconds on millisecond experimental timescales. For ClpB, the predicted relaxation time is in excellent agreement with the extracted time from smFRET experiments.

Unfolding and Translocation of Knotted Proteins by Clp Biological Nanomachines: Synergistic Contribution of Primary Sequence and Topology Revealed by Molecular Dynamics Simulations

We use Langevin dynamics simulations to model, at an atomistic resolution, how various natively knotted proteins are unfolded in repeated allosteric translocating cycles of the ClpY ATPase. We consider proteins representative of different topologies, from the simplest knot (trefoil 3₁), to the three-twist 5₂ knot, to the most complex stevedore, 6₁, knot. We harness the atomistic detail of the simulations to address aspects that have so far remained largely unexplored, such as sequence-dependent effects on the ruggedness of the landscape traversed during knot sliding. Our simulations reveal the combined effect on translocation of the knotted protein structure, i.e., backbone topology and geometry, and primary sequence, i.e., side chain size and interactions, and show that the latter can dominate translocation hindrance. In addition, we observe that due to the interplay between the knotted topology and intramolecular contacts the transmission of tension along the polypeptide chain occurs very differently from that of homopolymers. Finally, by considering native and non-native interactions, we examine how the disruption or formation of such contacts can affect the translocation processivity and concomitantly create multiple unfolding pathways with very different activation barriers.

Native-state fingerprint on the ubiquitin translocation across a nanopore

We study the translocation of the ubiquitin molecule (Ubq) across a channel with a double section which constitutes a general feature of several transmembrane nanopores such as the α-hemolysin (αHL). Our purpose is to establish the structure-dependent character of the Ubq translocation pathway. This implies to find the correspondence, if any, between the translocational unfolding steps and the Ubq native state. For this reason, it is convenient to apply a coarse-grained computational approach, where the protein is described only by the backbone and the force field only exploits the information contained in the native state (in the spirit of Gō-like models, or native-centric models). The αHL-like pore is portrayed as two coaxial confining cylinders: a larger one for the vestibule and a narrower one for the barrel (or stem). Such simplified approach allows a large number of translocation events to be collected by limited computational resources. The co-translocational unfolding of Ubq is described via a few collective variables that characterize the translocation progress. We find two translocation intermediates (stalled conformations) that can be associated with specific unfolding stages. In particular, in the earliest step, the strand S5 unfolds and enters the pore. This step splits the native conformation into two structural clusters packing against each other in the Ubq fold. A second stall occurs when the hairpin of the N terminal engages the stem region.

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).

Translocation intermediates of ubiquitin through an α-hemolysin nanopore: implications for detection of post-translational modifications

Nanopore based sensors constitute a promising approach to single molecule protein characterization being able, in principle, to detect sequences, structural elements and folding states of proteins and polypeptide chains. In narrow nanopores, one of the open issues concerns the coupling between unfolding and translocation. Here, we studied the ubiquitin translocation in an α-hemolysin nanopore, the most widely used pore for nanopore sensing, via all-atom molecular dynamics simulations. We completely characterize the co-translocational unfolding pathway finding that robust translocation intermediates are associated with the rearrangement of secondary structural elements, as also confirmed by coarse grained simulations. An interesting recurrent pattern is the clogging of the α-hemolysin constriction by an N-terminal β-hairpin. This region of ubiquitin is the target of several post-translational modifications. We propose a strategy to detect post-translational modifications at the N-terminal using the α-hemolysin nanopore based on the comparison of the co-translocational unfolding signals associated with modified and unmodified proteins.

Protein sequencing via nanopore based devices: a nanofluidics perspective

Proteins perform a huge number of central functions in living organisms, thus all the new techniques allowing their precise, fast and accurate characterization at single-molecule level certainly represent a burst in proteomics with important biomedical impact. In this review, we describe the recent progresses in the developing of nanopore based devices for protein sequencing. We start with a critical analysis of the main technical requirements for nanopore protein sequencing, summarizing some ideas and methodologies that have recently appeared in the literature. In the last sections, we focus on the physical modelling of the transport phenomena occurring in nanopore based devices. The multiscale nature of the problem is discussed and, in this respect, some of the main possible computational approaches are illustrated.

Nanoporous Hydrogels for the Observation of Anthrax Exotoxin Translocation Dynamics

The ability to observe lethal anthrax exotoxins translocating through size-constricting nanopores in vitro, combined with detailed sequence and structural data, has aided in elucidated mechanisms of exotoxin cell entry and toxicity. However, due to limited observations of anthrax exotoxins translocating through protective antigen nanopores in vitro and the instability of protective antigen-functionalized suspended lipid bilayers, questions remain regarding the native mechanisms of cell entry. Nanoporous hydrogel membranes offer a robust tool for studying protein translocation with ensemble measurements that complement conventional single-molecule translocation measurements. Here, we utilize nanoporous hydrogel membranes to assess the translocation of full-length anthrax lethal and edema factors through nanopores similar in diameter to protective antigen translocons. We find that, relative to globular serum and other proteins that do not translocate natively through nanopores, anthrax exotoxins demonstrate significantly reduced barriers to pore entry. Computed free-energy barriers to the unfolding of proteins and the dissociation of macromolecular complexes are generally found to coincide with translocation. Finally, a nanopore-blocking strategy is developed that utilizes nonspecific synthetic peptide constructs and effectively prevents LF translocation within the nanoporous hydrogel.

Sequential protein unfolding through a carbon nanotube pore

An assortment of biological processes, like protein degradation and the transport of proteins across membranes, depend on protein unfolding events mediated by nanopore interfaces. In this work, we exploit fully atomistic simulations of an artificial, CNT-based nanopore to investigate the nature of ubiquitin unfolding. With one end of the protein subjected to an external force, we observe non-canonical unfolding behaviour as ubiquitin is pulled through the pore opening. Secondary structural elements are sequentially detached from the protein and threaded into the nanotube, interestingly, the remaining part maintains native-like characteristics. The constraints of the nanopore interface thus facilitate the formation of stable "unfoldon" motifs above the nanotube aperture that can exist in the absence of specific native contacts with the other secondary structure. Destruction of these unfoldons gives rise to distinct force peaks in our simulations, providing us with a sensitive probe for studying the kinetics of serial unfolding events. Our detailed analysis of nanopore-mediated protein unfolding events not only provides insight into how related processes might proceed in the cell, but also serves to deepen our understanding of structural arrangements which form the basis for protein conformational stability.

Periodic forces trigger knot untying during translocation of knotted proteins

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, F_c. In this numerical study, we show that for deep knots F_c lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character.

Nanomechanics of Protein Unfolding Outside a Generic Nanopore

Protein folding and unfolding have been the subject of active research for decades. Most of previous studies in protein unfolding were focused on temperature, chemical, and/or force (such as in atomic force microscopy (AFM)) induced denaturations. Recent studies on the functional roles of proteasomes (such as ClpXP) revealed a different unfolding process in cell, during which a target protein is mechanically unfolded and pulled into a confined, pore-like geometry for degradation. While the proteasome nanomachine has been extensively studied, the mechanism for unfolding proteins with the proteasome pore is still poorly understood. Here, we investigate the mechanical unfolding process of ubiquitin with (or really outside) a generic nanopore, and compare such process with that in the AFM pulling experiment. Unexpectedly, the required force for protein unfolding through a pore can be much smaller than that by the AFM. Simulation results also unveiled different nanomechanics, tearing fracture vs shearing friction, in these two distinct types of mechanical unfoldings.

Coarse-Grained Simulations of Topology-Dependent Mechanisms of Protein Unfolding and Translocation Mediated by ClpY ATPase Nanomachines

Clp ATPases are powerful ring shaped nanomachines which participate in the degradation pathway of the protein quality control system, coupling the energy from ATP hydrolysis to threading substrate proteins (SP) through their narrow central pore. Repetitive cycles of sequential intra-ring ATP hydrolysis events induce axial excursions of diaphragm-forming central pore loops that effect the application of mechanical forces onto SPs to promote unfolding and translocation. We perform Langevin dynamics simulations of a coarse-grained model of the ClpY ATPase-SP system to elucidate the molecular details of unfolding and translocation of an α/β model protein. We contrast this mechanism with our previous studies which used an all-α SP. We find conserved aspects of unfolding and translocation mechanisms by allosteric ClpY, including unfolding initiated at the tagged C-terminus and translocation via a power stroke mechanism. Topology-specific aspects include the time scales, the rate limiting steps in the degradation pathway, the effect of force directionality, and the translocase efficacy. Mechanisms of ClpY-assisted unfolding and translocation are distinct from those resulting from non-allosteric mechanical pulling. Bulk unfolding simulations, which mimic Atomic Force Microscopy-type pulling, reveal multiple unfolding pathways initiated at the C-terminus, N-terminus, or simultaneously from both termini. In a non-allosteric ClpY ATPase pore, mechanical pulling with constant velocity yields larger effective forces for SP unfolding, while pulling with constant force results in simultaneous unfolding and translocation.

Cell survival is critically dependent on tightly regulated protein quality control, which includes chaperone-mediated folding and degradation. In the degradation pathway, AAA+ nanomachines, such as bacterial Clp proteases, use ATP-driven mechanisms to mechanically unfold, translocate, and destroy excess or defective proteins. Understanding these remodeling mechanisms is of central importance for deciphering the details of essential cellular processes. We perform coarse-grained computer simulations to extensively probe the effect of substrate protein topology on unfolding and translocation actions of the ClpY ATPase nanomachine. We find that, independent of SP topology, unfolding proceeds from the tagged C-terminus, which is engaged by the ATPase, and translocation involves coordinated steps. Topology-specific aspects include more complex unfolding and translocation pathways of the α/β SP compared with the all-α SP due to high stability of β-hairpins and interplay of tertiary contacts. In addition, directionality of the mechanical force applied by the Clp ATPase gives rise to distinct unfolding pathways.

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.

All-Atom Molecular Dynamics Simulation of Protein Translocation through an α-Hemolysin Nanopore

Nanopore sensing is attracting the attention of a large and varied scientific community. One of the main issues in nanopore sensing is how to associate the measured current signals to specific features of the molecule under investigation. This is particularly relevant when the translocating molecule is a protein and the pore is sufficiently narrow to necessarily involve unfolding of the translocating protein. Recent experimental results characterized the cotranslocational unfolding of Thioredoxin (Trx) passing through an α-hemolisin pore, providing evidence for the existence of a multistep process. In this study we report the results of all-atom molecular dynamics simulations of the same system. Our data indicate that Trx translocation involves two main barriers. The first one is an unfolding barrier associated with a translocation intermediate where the N-terminal region of Trx is stuck at the pore entrance in a conformation that strongly resembles the native one. After the abrupt unfolding of the N-terminal region, the Trx enters the α-hemolisin vestibule. During this stage, the constriction is occupied not only by the translocating residue but also by a hairpin-like structure forming a tangle in the constriction. The second barrier is associated with the disentangling of this region.

Dendrimers in Nanoscale Confinement: The Interplay between Conformational Change and Nanopore Entrance

Hyperbranched dendrimers are nanocarriers for drugs, imaging agents, and catalysts. Their nanoscale confinement is of fundamental interest and occurs when dendrimers with bioactive payload block or pass biological nanochannels or when catalysts are entrapped in inorganic nanoporous support scaffolds. The molecular process of confinement and its effect on dendrimer conformations are, however, poorly understood. Here, we use single-molecule nanopore measurements and molecular dynamics simulations to establish an atomically detailed model of pore dendrimer interactions. We discover and explain that electrophoretic migration of polycationic PAMAM dendrimers into confined space is not dictated by the diameter of the branched molecules but by their size and generation-dependent compressibility. Differences in structural flexibility also rationalize the apparent anomaly that the experimental nanopore current read-out depends in nonlinear fashion on dendrimer size. Nanoscale confinement is inferred to reduce the protonation of the polycationic structures. Our model can likely be expanded to other dendrimers and be applied to improve the analysis of biophysical experiments, rationally design functional materials such as nanoporous filtration devices or nanoscale drug carriers that effectively pass biological pores.

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.

Exploring the topography of the stress-modified energy landscapes of mechanosensitive molecules

We propose a method for computing the activation barrier for chemical reactions involving molecules subjected to mechanical stress. The method avoids reactant and transition-state saddle optimizations at every force by, instead, solving the differential equations governing the force dependence of the critical points (i.e., minima and saddles) on the system's potential energy surface (PES). As a result, only zero-force geometry optimization (or, more generally, optimization performed at a single force value) is required by the method. In many cases, minima and transition-state saddles only exist within a range of forces and disappear beyond a certain critical point. Our method identifies such force-induced instabilities as points at which one of the Hessian eigenvalues vanishes. We elucidate the nature of those instabilities as fold and cusp catastrophes, where two or three critical points on the force-modified PES coalesce, and provide a classification of various physically distinct instability scenarios, each illustrated with a concrete chemical example.

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.

Protein co-translocational unfolding depends on the direction of pulling

Protein unfolding and translocation through pores occurs during trafficking between organelles, protein degradation and bacterial toxin delivery. In vivo, co-translocational unfolding can be affected by the end of the polypeptide that is threaded into the pore first. Recently, we have shown that co-translocational unfolding can be followed in a model system at the single-molecule level, thereby unravelling molecular steps and their kinetics. Here, we show that the unfolding kinetics of the model substrate thioredoxin, when pulled through an α-haemolysin pore, differ markedly depending on whether the process is initiated from the C terminus or the N terminus. Further, when thioredoxin is pulled from the N terminus, the unfolding pathway bifurcates: some molecules finish unfolding quickly, while others finish ~100 times slower. Our findings have important implications for the understanding of biological unfolding mechanisms and in the application of nanopore technology for the detection of proteins and their modifications.

Protein unfolding and translocation through membrane pores occurs in several biological processes and has implications in nanopore technologies. Here, the authors show that the kinetics of unfolding differ depending on which end of the chain enters the pore first.

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.

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.

Disentangling steric and electrostatic factors in nanoscale transport through confined space

The voltage-driven passage of biological polymers through nanoscale pores is an analytically, technologically, and biologically relevant process. Despite various studies on homopolymer translocation there are still several open questions on the fundamental aspects of pore transport. One of the most important unresolved issues revolves around the passage of biopolymers which vary in charge and volume along their sequence. Here we exploit an experimentally tunable system to disentangle and quantify electrostatic and steric factors. This new, fundamental framework facilitates the understanding of how complex biopolymers are transported through confined space and indicates how their translocation can be slowed down to enable future sensing methods.

Single-polymer dynamics under constraints: scaling theory and computer experiment

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.

Unfolding and translocation pathway of substrate protein controlled by structure in repetitive allosteric cycles of the ClpY ATPase

Clp ATPases are ring-shaped AAA+ motors in the degradation pathway that perform critical actions of unfolding and translocating substrate proteins (SPs) through narrow pores to deliver them to peptidase components. These actions are effected by conserved diaphragm-forming loops found in the central channel of the Clp ATPase hexamer. Conformational changes, that take place in the course of repetitive ATP-driven cycles, result in mechanical forces applied by the central channel loops onto the SP. We use coarse-grained simulations to elucidate allostery-driven mechanisms of unfolding and translocation of a tagged four-helix bundle protein by the ClpY ATPase. Unfolding is initiated at the tagged C-terminal region via an obligatory intermediate. The resulting nonnative conformation is competent for translocation, which proceeds on a different time scale than unfolding and involves sharp stepped transitions. Completion of the translocation process requires assistance from the ClpQ peptidase. These mechanisms contrast nonallosteric mechanical unfolding of the SP. In atomic force microscopy experiments, multiple unfolding pathways are available and large mechanical forces are required to unravel the SP relative to those exerted by the central channel loops of ClpY. SP threading through a nonallosteric ClpY nanopore involves simultaneous unfolding and translocation effected by strong pulling forces.

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.

Translocation of α-helix chains through a nanopore

The translocation of α-helix chains through a nanopore is studied through Langevin dynamics simulations. The α-helix chains exhibit several different characteristics about their average translocation times and the α-helix structures when they transport through the nanopores under the driving forces. First, the relationship between average translocation times τ and the chain length N satisfies the scaling law, τ∼N(α), and the scaling exponent α depends on the driving force f for the small forces while it is close to the Flory exponent (ν) in the other force regions. For the chains with given chain lengths, it is observed that the dependence of the average translocation times can be expressed as τ∼f(-1/2) for the small forces while can be described as τ∼f in the large force regions. Second, for the large driving force, the average number of α-helix structures N(h) decreases first and then increases in the translocation process. The average waiting time of each bead, especially of the first bead, is also dependent on the driving forces. Furthermore, an elasticity spring model is presented to reasonably explain the change of the α-helix number during the translocation and its elasticity can be locally damaged by the large driving forces. Our results demonstrate the unique behaviors of α-helix chains transporting through the pores, which can enrich our insights into and knowledge on biopolymers transporting through membranes.

A statistical model for translocation of structured polypeptide chains through nanopores

The translocation process of a globular protein (ubiquitin) across a cylindrical nanopore is studied via molecular dynamics simulations. The ubiquitin is described by a native-centric model on a Calpha carbon backbone to investigate the influence of protein-like structural properties on the translocation mechanism. A thermodynamical and kinetic characterization of the process is obtained by studying the statistics of blockage times, the mobility, and the translocation probability as a function of the pulling force F acting in the pore. The transport dynamics occurs when the force exceeds a threshold Fc depending on a free-energy barrier that ubiquitin has to overcome in order to slide along the channel. Such a barrier results from competition of the unfolding energy and the entropy associated with the confinement effects of the pore. We implement appropriate umbrella sampling simulations to compute the free-energy profile as a function of the position of the ubiquitin center of mass inside of the channel (reaction coordinate). This free energy is then used to construct a phenomenological drift-diffusion model in the reaction coordinate which explains and reproduces the behavior of the observables during the translocation.

Interrogating single proteins through nanopores: challenges and opportunities

A single nanopore represents an amazingly versatile single-molecule probe that can be employed to reveal several important features of polypeptides, such as their folding state, backbone flexibility, mechanical stability, binding affinity to other interacting ligands and enzymatic activity. Moreover, groundwork in this area using engineered protein nanopores has demonstrated new opportunities for discovering the biophysical rules that govern the transport of proteins through transmembrane protein pores. In this review, I summarize the current knowledge in the field and discuss how nanopore probe techniques will provide a new generation of research tools in nanomedicine for quantitatively examining the details of complex recognition and, furthermore, will represent a crucial step in designing other pore-based nanostructures and high-throughput devices for molecular biomedical diagnosis.

Polyelectrolyte entry and transport through an asymmetric alpha-hemolysin channel

We study the entry and transport of a polyelectrolyte, dextran sulfate (DS), through an asymmetric alpha-hemolysin protein channel inserted into a planar lipid bilayer. We compare the dynamics of the DS chains as they enter the channel at the opposite stem or vestibule sides. Experiments are performed at the single-molecule level by using an electrical method. The frequency of current blockades varies exponentially as a function of applied voltage. This frequency is smaller for the stem entrance than for the vestibule one, due to a smaller coupling with the electric field and a larger activation energy for entry. The value of the activation energy is quantitatively interpreted as an entropic effect of chain confinement. The translocation time decreases when the applied voltage increases and displays an exponential variation which is independent of the stem or vestibule sides.

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.

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.

Controlling a single protein in a nanopore through electrostatic traps

Protein-protein pore interaction is a fundamental and ubiquitous process in biology and medical biotechnology. Here, we employed high-resolution time-resolved single-channel electrical recording along with protein engineering to examine a protein-protein pore interaction at single-molecule resolution. The pore was formed by Staphylococcus aureus alpha-hemolysin (alphaHL) protein and contained electrostatic traps formed by rings of seven aspartic acid residues placed at two different positions within the pore lumen. The protein analytes were positively charged presequences (pb2) of varying length fused to the small ribonuclease barnase (Ba). The presence of the electrostatic traps greatly enhanced the interaction of the pb2-Ba protein with the alphaHL protein pore. This study demonstrates the high sensitivity of the nanopore technique to an array of factors that govern the protein-protein pore interaction, including the length of the pb2 presequence, the position of the electrostatic traps within the pore lumen, the ionic strength of the aqueous phase, and the transmembrane potential. Alterations in the functional properties of the pb2-Ba protein and the alphaHL protein pore and systematic changes of the experimental parameters revealed the balance between forces driving the pb2-Ba protein into the pore and forces driving it out.

Catalyzing the translocation of polypeptides through attractive interactions

Facilitated translocation of polypeptides through a protein pore is a ubiquitous and fundamental process in biology. Several translocation systems possess various well-defined binding sites within the pore lumen, but a clear mechanistic understanding of how the interaction of the polypeptides with the binding site alters the underlying kinetics is still missing. Here, we employed rational protein design and single-channel electrical recordings to obtain detailed kinetic signatures of polypeptide translocation through the staphylococcal alpha-hemolysin (alphaHL) transmembrane pore, a robust, tractable, and versatile beta-barrel protein. Acidic binding sites composed of rings of negatively charged aspartic acid residues, engineered at strategic positions within the beta barrel, produced dramatic changes in the functional properties of the alphaHL protein, facilitating the transport of cationic polypeptides from one side of the membrane to the other. When two electrostatic binding sites were introduced, at the entry and exit of the beta barrel, both the rate constants of association and dissociation increased substantially, diminishing the free energy barrier for translocation. By contrast, more hydrophobic polypeptides exhibited a considerable decrease in the rate constant of association to the pore lumen, having to overcome a greater energetic barrier because of the hydrophilic nature of the pore interior.

Simulation study on the translocation of polymer chains through nanopores

The translocation of polymer chains through nanopores is simulated by dynamical Monte Carlo method. The free energy landscape for the translocation of polymer is calculated by scanning method. The dependence of the free energy barrier Fb and the chemical difference Deltamu on the concentration of chains can explain the behavior of polymer translocation at low and high concentration limits. The relationship between Deltamu and the escaping time tau(2) is in good agreement with the theoretical conclusions obtained by Muthukumar [J. Chem. Phys. 111, 10371 (1999)]. Our simulation results show that the relaxation time is mainly dominated by Fb, while the escaping time is mainly dominated by Deltamu.

Unfolding of proteins and long transient conformations detected by single nanopore recording

We study the electrophoretic blockades due to entries of partially unfolded proteins into a nanopore as a function of the concentration of the denaturing agent. Short and long pore blockades are observed by electrical detection. Short blockades are due to the passage of completely unfolded proteins, their frequency increases as the concentration of the denaturing agent increases, following a sigmoidal denaturation curve. Long blockades reveal partially folded conformations. Their duration increases as the proteins are more folded. The observation of a Vogel-Fulcher law suggests a glassy behavior.