Phase transitions within the isolated polymer molecule: Coupling of the polymer threading a membrane transition to the helix-random coil, the collapse, the adsorption, and the equilibrium polymerization transitions

Pore shapes effects on polymer translocation

We translocated polymers through pores of different shapes and interaction patterns in three dimensions by Langevin molecular dynamics. There were four simple cylindrical pores of the same length but with different diameters. The results showed that even though decreasing the pore diameter would always decrease the translocation velocity, it was strongly dependent on the shape of the increased pore diameter. Although increasing the pore diameter made the translocation faster in simple cylindrical pores, it was complicated in different pore shapes, e.g. increasing the diameter in the middle decreased the translocation velocity. Investigating polymer shapes through the translocation process and comparing the shapes by the cumulative waiting time for different pore structures reveals the non-equilibrium properties of translocation. Moreover, polymer shape parameters such as gyration radius, polymer center of mass, and average aspect ratio help us to distinguish different pore shapes and/or different polymers.

Chaperone-driven polymer translocation through nanopore: Spatial distribution and binding energy

Chaperones are binding proteins working as a driving force in biopolymer translocation. They bind to the biopolymer near the pore and prevent its backsliding. Chaperones may have different spatial distributions. Recently, we showed the importance of their spatial distribution in translocation and its effects on the sequence dependency of the translocation time. Here we focus on homopolymers and exponential distribution. Because of the exponential distribution of chaperones, the energy dependency of the translocation time will change. Here we find a minimum in translocation time versus binding effective energy (EBE) curve. The same trend can be seen in the scaling exponent of time versus polymer length, [Formula: see text] ([Formula: see text]), when plotted against EBE. Interestingly in some special cases, e.g. chaperones of size [Formula: see text] and with an exponential distribution rate of [Formula: see text], the minimum even reaches to an amount of less than 1 ([Formula: see text]). We explain the possibility of this rare result. Moreover, based on a theoretical discussion we show that, by taking into account the velocity dependency of the translocation on polymer length, one can truly predict the value of this minimum.

Placement of oppositely charged aminoacids at a polypeptide termini determines the voltage-controlled braking of polymer transport through nanometer-scale pores

Protein and solid-state nanometer-scale pores are being developed for the detection, analysis, and manipulation of single molecules. In the simplest embodiment, the entry of a molecule into a nanopore causes a reduction in the latter's ionic conductance. The ionic current blockade depth and residence time have been shown to provide detailed information on the size, adsorbed charge, and other properties of molecules. Here we describe the use of the nanopore formed by Staphylococcus aureus α-hemolysin and polypeptides with oppositely charged segments at the N- and C-termini to increase both the polypeptide capture rate and mean residence time of them in the pore, regardless of the polarity of the applied electrostatic potential. The technique provides the means to improve the signal to noise of single molecule nanopore-based measurements.

Anthrax toxin-induced rupture of artificial lipid bilayer membranes

We demonstrate experimentally that anthrax toxin complexes rupture artificial lipid bilayer membranes when isolated from the blood of infected animals. When the solution pH is temporally acidified to mimic that process in endosomes, recombinant anthrax toxin forms an irreversibly bound complex, which also destabilizes membranes. The results suggest an alternative mechanism for the translocation of anthrax toxin into the cytoplasm.

Stochastic nature of series of waiting times

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the "waiting times" series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2<H<1. We also study positive-negative level asymmetry of the waiting time distribution. We find that the logarithmic difference of waiting times series has a short-range correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number turbulence and determine the level dependence of Markov time scales, as well as the drift and diffusion coefficients. We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution with a continuous time random walk.

Escape of polymer chains from an attractive channel under electrical force

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ(0)) on the polymer-channel interaction (ɛ), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both ɛ and E play very important roles in the escaping dynamics. For small ɛ, the polymer chain moves out of the channel continuously and quickly. While for large ɛ, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τ(trap)) when the end segment is near the critical point x(C). These results are consistent with the theoretical results for the free energy profiles at small ɛ and large ɛ, respectively. The dependence of x(C) and τ(trap) on ɛ and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process.

Sequence dependence of the binding energy in chaperone-driven polymer translocation through a nanopore

We study the translocation of stiff polymers through a nanopore, driven by the chemical-potential gradient exerted by binding proteins (chaperones) on the trans side of the pore. Bound chaperones prevent backsliding through the pore and, therefore, partially rectify the polymer passage. We show that the sequence of chain monomers with different binding affinity for the chaperones significantly affects the translocation dynamics. In particular, we investigate the effect of the nearest-neighbor adjacency probability of the two monomer types. Depending on the magnitude of the involved binding energies, the translocation speed may either increase or decrease with the adjacency probability. We determine the mean first passage time and show that, by tuning the effective binding energy, the motion changes continuously from purely diffusive to ballistic translocation.

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.

Probing single nanometer-scale pores with polymeric molecular rulers

We previously demonstrated that individual molecules of single-stranded DNA can be driven electrophoretically through a single Staphylococcus aureus alpha-hemolysin ion channel. Polynucleotides thread through the channel as extended chains and the polymer-induced ionic current blockades exhibit stable modes during the interactions. We show here that polynucleotides can be used to probe structural features of the alpha-hemolysin channel itself. Specifically, both the pore length and channel aperture profile can be estimated. The results are consistent with the channel crystal structure and suggest that polymer-based "molecular rulers" may prove useful in deducing the structures of nanometer-scale pores in general.

Molecular simulation of protein dynamics in nanopores. II. Diffusion

A novel combination of discontinuous molecular dynamics and the Langevin equation, together with an intermediate-resolution model of proteins, is used to carry out long (several microsecond) simulations in order to study transport of proteins in nanopores. We simulated single-domain proteins with the alpha-helical native structure. Both attractive and repulsive interaction potentials between the proteins and the pores' walls are considered. The diffusivity D of the proteins is computed not only under the bulk conditions but also as a function of their "length" (the number of the amino-acid groups), temperature T, pore size, and interaction potentials with the walls. Compared with the experimental data, the computed diffusivities under the bulk conditions are of the correct order of magnitude. The diffusivities both in the bulk and in the pores follow a power law in the length [script-l] of the proteins and are larger in pores with repulsive walls. D(+)/D(-), the ratio of the diffusivities in pores with attractive and repulsive walls, exhibits two local maxima in its dependence on the pore size h, which are attributed to the pore sizes and protein configurations that induce long-lasting simultaneous interactions with both walls of the pores. Far from the folding temperature T(f), D increases about linearly with T, but due to the thermal fluctuations and their effect on the proteins' structure near T(f), the dependence of D on T in this region is nonlinear. We propose a novel and general "phase diagram," consisting of four regions, that describes qualitatively the effect of h, T, and interaction potentials with the walls on the diffusivity D of a protein.

Passage times for polymer translocation pulled through a narrow pore

We study the passage times of a translocating polymer of length N in three dimensions, while it is pulled through a narrow pore with a constant force F applied to one end of the polymer. At small to moderate forces, satisfying the condition FN(nu)/k(B)T less, similar 1, where nu approximately 0.588 is the Flory exponent for the polymer, we find that tau(N), the mean time the polymer takes to leave the pore, scales as N(2+nu) independent of F, in agreement with our earlier result for F = 0. At strong forces, i.e., for, FN(nu)/k(B)T >> 1, the behavior of the passage time crosses over to tau(N) approximately N(2)/F. We show here that these behaviors stem from the polymer dynamics at the immediate vicinity of the pore-in particular, the memory effects in the polymer chain tension imbalance across the pore.

Nanoscopic porous sensors

There are thousands of different nanometer-scale pores in biology, many of which act as sensors for specific chemical agents. Recent work suggests that protein and solid-state nanopores have many potential uses in a wide variety of analytical applications. In this review we survey this field of research and discuss the prospects for advances that could be made in the near future.

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.

Translocation and insertion of an amphiphilic polymer

Translocation of amphiphilic polymers (random and block copolymers), consisting of hydrophilic and hydrophobic monomers, threading a pore is studied by using a three-dimensional dynamic Monte Carlo simulation. We find that there is a "translocation-insertion" threshold in the fraction of hydrophobic monomers on an amphiphilic polymer. The translocation time is given by simple scaling laws and increases with increasing the fraction of hydrophobic monomers.

How does the coupling of secondary and tertiary interactions control the folding of helical macromolecules?

The authors study how the simultaneous presence of short-range secondary and long-range tertiary interactions controls the folding and collapse behavior of a helical macromolecule. The secondary interactions stabilize the helical conformation of the chain, while the tertiary interactions govern its overall three-dimensional shape. The authors have carried out Monte Carlo simulations to study the effect of chain length on the folding and collapse behavior of the chain. They have calculated state diagrams for four chain lengths and found that the physics is very rich with a plethora of stable conformational states. In addition to the helix-coil and coil-globule transitions, their model describes the coupling between them which takes place at low temperatures. Under these conditions, their model predicts a cascade of continuous, conformational transitions between states with an increase in the strength of the tertiary interactions. During each transition the chain shrinks, i.e., collapses, in a rapid and specific manner. In addition, the number of the transitions increases with increasing chain length. They have also found that the low-temperature regions of the state diagram between the transition lines cannot be associated with specific structures of the chain, but rather, with ensembles of various configurations of the chain with similar characteristics. Based on these results the authors propose a mechanism for the folding and collapse of helical macromolecules which is further supported by the analysis of configurational, configurational, and thermodynamic properties of the chain.

Nanopore sequencing technology: research trends and applications

Nanopore sequencing is one of the most promising technologies being developed as a cheap and fast alternative to the conventional Sanger sequencing method. Protein or synthetic nanopores have been used to detect DNA or RNA molecules. Although none of the technologies to date has shown single-base resolution for de novo DNA sequencing, there have been several reports of alpha-hemolysin protein nanopores being used for basic DNA analyses, and various synthetic nanopores have been fabricated. This review will examine current nanopore sequencing technologies, including recent developments of new applications.

Translocation of a proteinlike chain through a finite channel

We use the pruned-enriched-Rosenbluth method and the modified orientation-dependent monomer-monomer interaction model to study the translocation of a proteinlike chain through a finite channel. The mean-square radius of gyration per bond <S2>/N and shape factor <delta*> of proteinlike chains with different secondary structures transporting through a finite channel with different channel radii R=1, 2, 3, 4, and 20 are investigated in the translocation. The average Helmholtz free energy per bond A/N and the mechanical force f are also presented. A/N remains unchanged when X(0)<0 and X(0)>1, and decreases monotonously when 0.5<X(0)<0.1. Here X(0)=X/N identical with 2X/L,X is the position of the first monomer, N is chain length, and L is channel length. No free energy barrier is found in our calculation. f is negative and has a plateaulike behavior. The plateau becomes narrow and the value of f increases as R increases. The total energy per bond <U>/N is also calculated in the process of translocation. An energy barrier is shown. The proteinlike chains must cross this energy barrier when they escape from the channel. The position of the maximum of <U>/N depends on the secondary structures and the channel radius. We also discuss the average contact energy per bond <U>c/N, the average alpha-helical energy per bond <U>h/N, and the average beta-sheet energy per bond <U>b/N.

Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate qκ for binding (with a binding strength κ); except for the case of no binding κ = 0 the presence of the chaperones gives rise to an effective force that drives the translocation process. In more detail, we develop a dynamical description of the process in terms of a (2+1)-variable master equation for the probability of having m monomers on the target side of the membrane with n bound chaperones at time t. Emphasis is put on the calculation of the mean first passage time [Formula: see text] as a function of total chain length M. The transfer coefficients in the master equation are determined through detailed balance, and depend on the relative chaperone size λ and binding strength κ, as well as the two rate constants k and q. The ratio γ = q/k between the two rates determines, together with κ and λ, three limiting cases, for which analytic results are derived: (i) for the case of slow binding ([Formula: see text]), the motion is purely diffusive, and [Formula: see text] for large M; (ii) for fast binding ([Formula: see text]) but slow unbinding ([Formula: see text]), the motion is, for small chaperones λ = 1, ratchet-like, and [Formula: see text]; (iii) for the case of fast binding and unbinding dynamics ([Formula: see text] and [Formula: see text]), we perform the adiabatic elimination of the fast variable n, and find that for a very long polymer [Formula: see text], but with a smaller prefactor than for ratchet-like dynamics. We solve the general case numerically as a function of the dimensionless parameters λ, κ and γ, and compare to the three limiting cases.

Coupling between helix-coil and coil-globule transitions in helical polymers

We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which could be a helix, a random coil, an amorphous globule, or one of various other globular states which carry residual helical strands. We study the boundaries between states and provide further insight into the physics of the system with a detailed analysis of the order parameter and other properties.

Computer simulation of polypeptide translocation through a nanopore

A simplified model of polypeptide chains was designed and studied by means of computer simulations. Chains were represented by a sequence of united atoms located at the positions of the alpha-carbons. A further assumption was the lattice approximation for the chains. We used a (310) lattice, which was found useful for studying properties of proteins. The force field used consisted of a long-range contact potential between amino-acid residues and a local preference for forming alpha-helical states. The chain consisted of two kinds of residues: hydrophilic (P) and hydrophobic (H) ones forming model helical septets--HHPPHPP--in a sequence. The chains were placed near an impenetrable surface with a square hole in it. The size of the hole was comparable or smaller than the size of a chain. The properties of these model chains were determined using the Monte-Carlo simulation method. During the simulations, translocation of the chain through the hole in the wall was observed. The influence of the chain length, the temperature differences on both sides of the wall and the force field on the chain properties were investigated. It was shown that the translocation time scales as N(2.2) and it was found that the presence of the local helical potential significantly slows down the process of translocation. [Figure: see text]. The snapshots of typical chain's conformation obtained during the simulation for chain consisted of N = 60. The values of the local potential epsilon(loc) = -8.

Purified Bacillus anthracis lethal toxin complex formed in vitro and during infection exhibits functional and biological activity

Anthrax protective antigen (PA, 83 kDa), a pore-forming protein, upon protease activation to 63 kDa (PA(63)), translocates lethal factor (LF) and edema factor (EF) from endosomes into the cytosol of the cell. The relatively small size of the heptameric PA(63) pore (approximately 12 angstroms) raises questions as to how large molecules such as LF and EF can move through the pore. In addition, the reported high binding affinity between PA and EF/LF suggests that EF/LF may not dissociate but remain complexed with activated PA(63). In this study, we found that purified (PA(63))(7)-LF complex exhibited biological and functional activities similar to the free LF. Purified LF complexed with PA(63) heptamer was able to cleave both a synthetic peptide substrate and endogenous mitogen-activated protein kinase kinase substrates and kill susceptible macrophage cells. Electrophysiological studies of the complex showed strong rectification of the ionic current at positive voltages, an effect similar to that observed if LF is added to the channels formed by heptameric PA(63) pore. Complexes of (PA(63))(7)-LF found in the plasma of infected animals showed functional activity. Identifying active complex in the blood of infected animals has important implications for therapeutic design, especially those directed against PA and LF. Our studies suggest that the individual toxin components and the complex must be considered as critical targets for anthrax therapeutics.

Chaperone-assisted translocation

We investigate the translocation of a stiff polymer through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind reversibly to the polymer on both sides of the membrane. A bound chaperone covers one (univalent binding) or many (multivalent binding) binding sites. Assuming that the diffusion of the chaperones is fast compared to the rate of translocation we describe the process by a one-dimensional master equation. We expand previous models by a detailed study of the effective force in the master equation, which is obtained by the appropriate statistical mechanical average over the chaperone states. The dependence of the force on the degree of valency (the number of binding sites occupied by a chaperone) is studied in detail. We obtain finite size corrections (to the thermodynamical expression for the force), which, for univalent binding, can be expressed analytically. We finally investigate the mean velocity for translocation as a function of chaperone binding strength and size. For both univalent and multivalent binding simple results are obtained for the case of a sufficiently long translocating polymer.

Phase transitions of a polymer threading a membrane coupled to coil-globule transitions

We theoretically study phase transitions of a polymer threading through a pore imbedded in a membrane. We focus on the coupling between a partition of the polymer segments through the membrane and a coil-globule transition of the single polymer chain. Based on the Flory model for collapse transitions of a polymer chain, we calculate the fraction of polymer segments and the expansion factor of a polymer coil on each side of the membrane. We predict a first-order phase transition of a polymer threading a membrane; polymer segments in one side are discontinuously translocated into the other side, depending on solvent conditions and molecular weight of the polymer. We also discuss the equilibrium conformation of the polymer chain on each side of the membrane.

Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1) proportional to t(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t) proportional to 1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1) proportional to t(5/8) and tau(t) proportional to n(8/5).