Translocation of a heterogeneous polymer

Langevin Dynamics Study on the Driven Translocation of Polymer Chains with a Hairpin Structure

The hairpin structure is a common and fundamental secondary structure in macromolecules. In this work, the process of the translocation of a model polymer chain with a hairpin structure is studied using Langevin dynamics simulations. The simulation results show that the dynamics of hairpin polymer translocation through a nanopore are influenced by the hairpin structure. Hairpin polymers can be classified into three categories, namely, linear-like, unsteady hairpin, and steady hairpin, according to the interaction with the stem structure. The translocation behavior of linear-like polymers is similar to that of a linear polymer chain. The time taken for the translocation of unsteady hairpin polymers is longer than that for a linear chain because it takes a long time to unfold the hairpin structure, and this time increases with stem interaction and decreases with the driving force. The translocation of steady hairpin polymers is distinct, especially under a weak driving force; the difficulty of unfolding the hairpin structure leads to a low translocation probability and a short translocation time. The translocation behavior of hairpin polymers can be explained by the theory of the free-energy landscape.

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.

Homopolymer and heteropolymer translocation through patterned pores under fluctuating forces

We investigate the translocation of a semiflexible polymer through extended patterned pores using Langevin dynamics simulations, specifically focusing on the influence of a time-dependent driving force. Our findings reveal that, akin to its flexible counterpart, a rigid chain-like molecule translocates faster when subjected to an oscillating force than a constant force of equivalent average magnitude. The enhanced translocation is strongly correlated with the stiffness of the polymer and the stickiness of the pores. The arrangement of the pores plays a pivotal role in translocation dynamics, deeply influenced by the interplay between polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness, the oscillating force introduces significant variations in the translocation time distributions based on segment sizes and orientations. On the basis of these insights, we propose a sequencing approach that harnesses distinct pore surface properties that are capable of accurately predicting sequences in heteropolymers with diverse bending rigidities.

Translocation, Rejection and Trapping of Polyampholytes

Polyampholytes (PA) are a special class of polymers comprising both positive and negative monomers along their sequence. Most proteins have positive and negative residues and are PAs. Proteins have a well-defined sequence while synthetic PAs have a random charge sequence. We investigated the translocation behavior of random polyampholyte chains through a pore under the action of an electric field by means of Monte Carlo simulations. The simulations incorporated a realistic translocation potential profile along an extended asymmetric pore and translocation was studied for both directions of engagement. The study was conducted from the perspective of statistics for disordered systems. The translocation behavior (translocation vs. rejection) was recorded for all 220 sequences comprised of N = 20 charged monomers. The results were compared with those for 107 random sequences of N = 40 to better demonstrate asymptotic laws. At early times, rejection was mainly controlled by the charge sequence of the head part, but late translocation/rejection was governed by the escape from a trapped state over an antagonistic barrier built up along the sequence. The probability distribution of translocation times from all successful attempts revealed a power-law tail. At finite times, there was a population of trapped sequences that relaxed very slowly (logarithmically) with time. If a subensemble of sequences with prescribed net charge was considered the power-law decay was steeper for a more favorable net charge. Our findings were rationalized by theoretical arguments developed for long chains. We also provided operational criteria for the translocation behavior of a sequence, explaining the selection by the translocation process. From the perspective of protein translocation, our findings can help rationalize the behavior of intrinsically disordered proteins (IDPs), which can be modeled as polyampholytes. Most IDP sequences have a strong net charge favoring translocation. Even for sequences with those large net charges, the translocation times remained very dispersed and the translocation was highly sequence-selective.

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.

Single molecule electrophoresis of star polymers through nanopores: Simulations

We study the translocation of charged star polymers through a solid-state nanopore using coarse-grained Langevin dynamics simulations, in the context of using nanopores as high-throughput devices to characterize polymers based on their architecture. The translocation is driven by an externally applied electric field. Our key observation is that translocation kinetics is highly sensitive to the functionality (number of arms) of the star polymer. The mean translocation time is found to vary non-monotonically with polymer functionality, exhibiting a critical value for which translocation is the fastest. The origin of this effect lies in the competition between the higher driving force inside the nanopore and inter-arm electrostatic repulsion in entering the pore, as the functionality is increased. Our simulations also show that the value of the critical functionality can be tuned by varying nanopore dimensions. Moreover, for narrow nanopores, star polymers above a threshold functionality do not translocate at all. These observations suggest the use of nanopores as a high-throughput low-cost analytical tool to characterize and separate star polymers.

Theoretical study on the polymer translocation into an attractive sphere

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R^* has a scaling relation with the polymer length N as R^* ∼ N^β. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

Translocation of polyampholytes and intrinsically disordered proteins⋆

Polyampholytes are polymers carrying electrical charges of both signs along their backbone. We consider synthetic polyampholytes with a quenched random charge sequence and intrinsically disordered proteins, which have a well-defined charge sequence and behave like polyampholytes in the denaturated state. We study their translocation driven by an electric field through a pore. The role of disorder along the charge sequence of synthetic polyampholytes is analyzed. We show how disorder slows down the translocation dynamics. For intrinsically disordered proteins, the translocation vs. rejection rates by the pore depends on which end is engaged in the translocation channel. We discuss the rejection time, the blockade time distributions and the translocation speed for the charge sequence of two specific intrinsically disordered proteins differing in length and structure.

A Bond-Fluctuation Model of Translational Dynamics of Chain-like Particles through Mucosal Scaffolds

Mucus scaffolds represent one of the most common barriers in targeted drug delivery and can remarkably reduce the outcome of pharmacological therapies. An efficient transport of drug particles through a mucus barrier is a precondition for an efficient drug delivery. Understanding the transport mechanism is particularly important for treatment of disorders such as cystic fibrosis. These are characterized by an onset of high-density mucus scaffolds imposing an increased steric filtering. In this study, we employed the bond-fluctuation model to analyze the effect of steric interactions on slowing the translational dynamics of compound chain-like particles traversing through scaffolds of different configurations (regular isotropic and anisotropic versus irregular random). The model, which accounts for both the geometry-imposed steric interaction as well as the intrachain steric interaction between the chain subunits, yields a transient subdiffusive motional pattern persists between the short-time and long-time Gaussian diffusion limits. The motion is analyzed in terms of a mean-squared displacement, diffusion coefficient, and radius of gyration. With higher levels of restriction or larger particles, the subdiffusive motional regime persists longer. The study also demonstrates that an important feature of the motion is also geometry-induced chain accommodation. The presented model is generic and could also be applied to studying the translational dynamics of other particles with more complex architecture such as dendrites or chain-decorated nanoparticles.

Sequencing of semiflexible polymers of varying bending rigidity using patterned pores

We study the translocation of a semiflexible polymer through extended pores with patterned stickiness, using Langevin dynamics simulations. We find that the consequence of pore patterning on the translocation time dynamics is dramatic and depends strongly on the interplay of polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness along their lengths, we find that variation of the block size of the sequences and the orientation results in large variations in the translocation time distributions. We show how this fact may be utilized to develop an effective sequencing strategy. This strategy involving multiple pores with patterned surface energetics can predict heteropolymer sequences having different bending rigidity to a high degree of accuracy.

Influence of the Location of Attractive Polymer-Pore Interactions on Translocation Dynamics

We probe the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. We investigate the effect of the strength and location of the polymer-pore interaction using nanopores that are partially charged either at the entry or the exit or on both sides of the pore. We study the change in the translocation time as a function of the strength of the polymer-pore interaction for a given chain length and under the effect of an externally applied field. Under a moderate driving force and a chain length longer than the length of the pore, the translocation time shows a nonmonotonic increase with an increase in the attractive interaction. Also, an interaction on the cis side of the pore can increase the translocation probability. In the presence of an external field and a strong attractive force, the translocation time for shorter chains is independent of the polymer-pore interaction at the entry side of the pore, whereas an interaction on the trans side dominates the translocation process. Our simulation results are rationalized by a qualitative analysis of the free energy landscape for polymer translocation.

Defining the Field of Sequence-Controlled Polymers

Over the last ten years, the development of synthetic polymers containing controlled monomer sequences has become a prominent topic in fundamental and applied polymer science. This emerging area is particularly broad and combines classical polymer chemistry tools with techniques imported from other domains such as biology, biochemistry, organic synthesis, engineering, and bioanalytics. Consequently, it also generates new structures, terminologies, and applications that are not within the traditional scope of polymer science. The term "sequence-controlled polymers" (SCPs) was recently proposed as a generic name to describe all these recent trends. However, since the field of SCPs has been growing very rapidly in recent literature, it is urgent to accurately define its scientific frontiers. In this important context, this review is an attempt to define, rationalize, and classify the field of SCPs. In particular, all synthetic approaches that have been reported for the synthesis of SCPs are discussed and categorized. In addition, the characterization tools, properties, and potential applications of these new polymers are described herein. Overall, this review serves as a reference guide for understanding the burgeoning field of SCPs.

Stochastic resonance during a polymer translocation process

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Effect of charge patterns along a solid-state nanopore on polyelectrolyte translocation

We investigate the effectiveness of charge patterns along a nanopore on translocation dynamics of a flexible polyelectrolyte. We perform a three dimensional Langevin dynamics simulation of a uniformly charged flexible polyelectrolyte translocating under uniform external electric field through a solid-state nanopore. We maintain the total charge along the pore to be constant, while varying its distribution by placing alternate charged and uncharged sections of different lengths along the pore length. Longest average translocation time is observed for a pattern corresponding to an optimum section length, with a major delay in the translocation time during the pore ejection stage. This optimum section length is independent of lengths of polyelectrolyte and pore within the range studied. A theory based on the Fokker-Planck formalism is found to successfully describe the observed trends with reasonable quantitative agreement.

Alpha-synuclein lipid-dependent membrane binding and translocation through the α-hemolysin channel

Gauging the interactions of a natively unfolded Parkinson disease-related protein, alpha-synuclein (α-syn) with membranes and its pathways between and within cells is important for understanding its pathogenesis. Here, to address these questions, we use a robust β-barrel channel, α-hemolysin, reconstituted into planar lipid bilayers. Transient, ~95% blockage of the channel current by α-syn was observed when 1), α-syn was added from the membrane side where the shorter (stem) part of the channel is exposed; and 2), the applied potential was lower on the side of α-syn addition. While the on-rate of α-syn binding to the channel strongly increased with the applied field, the off-rate displayed a turnover behavior. Statistical analysis suggests that at voltages >50 mV, a significant fraction of the α-syn molecules bound to the channel undergoes subsequent translocation. The observed on-rate varied by >100 times depending on the bilayer lipid composition. Removal of the last 25 amino acids from the highly negatively charged C-terminal of α-syn resulted in a significant decrease in the binding rates. Taken together, these results demonstrate that β-barrel channels may serve as sensitive probes of α-syn interactions with membranes as well as model systems for studies of channel-assisted protein transport.

Polymer translocation dynamics in the quasi-static limit

Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.

Translocation dynamics of freely jointed Lennard-Jones chains into adsorbing pores

Polymer translocation into adsorbing nanopores is studied by using the Fokker-Planck equation of chain diffusion along the energy landscape calculated with Monte Carlo simulations using the incremental gauge cell method. The free energy profile of a translocating chain was found by combining two independent sub-chains, one free but tethered to a hard wall, and the other tethered inside an adsorbing pore. Translocation dynamics were revealed by application of the Fokker-Planck equation for normal diffusion. Adsorption of polymer chains into nanopores involves a competition of attractive adsorption and repulsive steric hindrance contributions to the free energy. Translocation times fell into two regimes depending on the strength of the adsorbing pore. In addition, we found a non-monotonic dependence of translocation times with increasing adsorption strength, with sharp peak associated with local free energy minima along the translocation coordinate.