Driven translocation of a polymer: role of pore friction and crowding.

Force-driven translocation of a macromolecule through a nanopore is investigated systematically by taking into account the monomer-pore friction as well as the "crowding" of monomers on the trans-side of the membrane which counterbalance the driving force acting in the pore. The problem is treated self-consistently, so that the resulting force in the pore and the dynamics on the cis and trans sides mutually influence each other. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent α in the translocation time-vs.-chain length scaling law, τ ∝ N(α), becomes smaller for relatively small chain lengths as the monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings show that the variety of values for α reported in experiments and computer simulations, may be attributed to different pore frictions, whereas crowding effects can generally be neglected.

Structure and dynamics of a polymer melt at an attractive surface.

We study the structural and dynamic properties of a polymer melt in the vicinity of an adhesive solid substrate by means of Molecular Dynamics simulation at various degrees of surface adhesion. The properties of the individual polymer chains are examined as a function of the distance to the interface and found to agree favorably with theoretical predictions. Thus, the adsorbed amount at the adhesive surface is found to scale with the macromolecule length as Γ is proportional to √N, regardless of the adsorption strength. For chains within the range of adsorption we analyze in detail the probability size distributions of the various building blocks: loops, tails and trains, and find that loops and tails sizes follow power laws while train lengths decay exponentially thus confirming some recent theoretical results. The chain dynamics as well as the monomer mobility are also investigated and found to depend significantly on the proximity of a given layer to the solid adhesive surface with onset of vitrification for sufficiently strong adsorption.

Thermal decomposition of a honeycomb-network sheet: a molecular dynamics simulation study.

The thermal degradation of a graphene-like two-dimensional honeycomb membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that at lower temperature the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet whereas at higher temperature bonds break at random everywhere in the hexagonal flake. The mean breakage time τ is found to decrease with the total number of network nodes N by a power law τ ∝ N(-0.5) and reveals an Arrhenian dependence on temperature T. Scission times are themselves exponentially distributed. The fragmentation kinetics of the average number of clusters can be described by first-order chemical reactions between network nodes n(i) of different coordination. The distribution of fragments sizes evolves with time elapsed from initially a δ-function through a bimodal one into a single-peaked again at late times. Our simulation results are complemented by a set of 1st-order kinetic differential equations for n(i) which can be solved exactly and compared to data derived from the computer experiment, providing deeper insight into the thermolysis mechanism.

Thermal degradation of unstrained single polymer chain: non-linear effects at work.

We examine the thermally induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of molecular dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped dynamics are investigated, and a comparison with recent studies of bond scission in model polymers with harmonic interactions is performed. We find that the polymer degradation changes qualitatively between the inertial regime and that of heavily damped dynamics. The role of bond healing (recombination) is also studied and probability distributions for the recombination times and overstretched bond lengths are obtained. Our extensive simulations reveal many properties of the scission dynamics in agreement with the notion of random breakdown of independent bonds, e.g., the mean time of chain rupture, <τ> follows an Arrhenian behavior with temperature T, and depends on the number of bonds N in the polymer as <τ> ∝ N(-1). In contrast, the rupture rates of the individual bonds along the polymer backbone indicate clearly the presence of self-induced inhomogeneity resulting from the interplay of thermal noise and nonlinearity. Eventually we examine the fragmentation kinetics during thermolysis. We demonstrate that both the probability distribution function of fragment sizes as well as the mean length of fragments at subsequent times t characterize degradation as predominantly a first order reaction.

Thermal breakage and self-healing of a polymer chain under tensile stress.

We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer multidimensional theory and by extensive molecular dynamics simulations in one dimension (1D) and three dimension (3D) space. Comparison with simulation data in one and three dimensions demonstrates that the Kramers-Langer theory provides good qualitative description of the process of bond scission as caused by a collective unstable mode. We derive distributions of the probability for scission over the successive bonds along the chain which reveal the influence of chain ends on rupture in good agreement with theory. The breakage time distribution of an individual bond is found to follow an exponential law as predicted by theory. Special attention is focused on the recombination (self-healing) of broken bonds. Theoretically derived expressions for the recombination time and distance distributions comply with MD observations and indicate that the energy barrier position crossing is not a good criterion for true rupture. It is shown that the fraction of self-healing bonds increases with rising temperature and friction.

Pulling an adsorbed polymer chain off a solid surface.

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain-ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain-end is kept fixed at height h over the solid plane at different adsorption strength [Formula: see text]. The phase diagram in the h-[Formula: see text] plane is calculated both analytically and by Monte Carlo simulations. We demonstrate that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than f is used as an independent control parameter.

Polymer desorption under pulling: a dichotomic phase transition.

The structural properties and phase behavior of a self-avoiding polymer chain on an adhesive substrate, subject to pulling at the chain end, are described by means of a grand canonical ensemble approach. We derive analytical expressions for the probability distributions of the basic structural units of an adsorbed polymer, such as loops, trains, and tails, in terms of the adhesive potential and applied pulling force f . In contrast to conventional, f=0 , polymer adsorption, the chain detachment transition under pulling turns out to be of first (rather than second) order, albeit it is dichotomic, i.e., no coexistence of different phase states exists. Also, the hitherto controversial value of the critical adsorption exponent varphi is found to depend essentially on the degree of interaction between different loops so that 0.34< or =varphi< or =0.59 . The theoretical predictions are verified by means of extensive Monte Carlo simulations.

Comment on 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and other recent papers by D Panja, G Barkema and R Ball.

In a recent publication of Panja et al (2007 J. Phys.: Condens. Matter 19 432202) they suggested a new interpretation of the translocation problem of polymer chain threading through a narrow pore. Here we point out some contradictions and inconsistencies in this treatment which question the plausibility of the obtained results.

Dynamics of a stretched nonlinear polymer chain.

We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modeled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond nonlinearity on the relaxation dynamics of the polymer at different degrees of stretching is treated analytically within the Gaussian self-consistent (GSC) approach and then compared to simulation results derived from two different methods: Monte Carlo (MC) and Molecular Dynamics (MD). At low and medium degrees of chain elongation we find good agreement between GSC predictions and the MC simulations. However, for strongly stretched chains, the MD method, which takes into account inertial effects, reveals two important aspects of the nonlinear interaction between monomers: (i) a coupling and energy transfer between the damped, oscillatory normal modes of the chain and (ii) the appearance of nonvanishing contributions of a continuum of frequencies around the characteristic modes in the power spectrum of the normal mode correlation functions.

Adsorption kinetics of a single polymer on a solid plane.

We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a "stem-flower" polymer conformation, and the related mechanism of "zipping" during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of (1+nu)-1, where nu approximately 3/5 is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we also study regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.

Polymer translocation through a nanopore: a showcase of anomalous diffusion.

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one-dimensional anomalous diffusion process in terms of the reaction coordinate s (i.e., the translocated number of segments at time t ) and shown to be governed by a universal exponent alpha=2(2nu+2-gamma(1), where nu is the Flory exponent and gamma(1) is the surface exponent. Remarkably, it turns out that the value of alpha is nearly the same in two and three dimensions. The process is described by a fractional diffusion equation which is solved exactly in the interval 02, which provide a full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

Preferential adsorption of hydrophobic-polar model proteins on patterned surfaces.

We study the adsorption of a single hydrophobic-polar (HP) model protein under the influence of a flat but specially designed surface. A folded HP model protein is brought to the surface with a designed pattern consisting of certain attractive and repulsive sites for the different monomers (amino acids). In contrast to the deformation of a random sequence that is continuous, deformation of any protein-like sequences is unlikely and an energy gap is associated with it. The surface with a certain wavelength of pattern attracts a certain type of folded structure preferentially and the free energy of the combined system is reduced. The model presented here represents a minimal theoretical model for protein recognition.

Self-generated disorder and structural glass formation in homopolymer globules.

We have investigated the interrelation between spin glasses and structural glasses. Spin glasses in this case are p-spin interaction spin glasses (at p>2) or Potts glasses that contain quenched disorder, whereas the structural glasses are here exemplified by a homopolymeric globule, which can be viewed as a liquid of connected units on a nanoscale. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self-generated (in contrast to spin glasses) and can be related to competing interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated in the mean-field approximation the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.

Force-induced breakdown of flexible polymerized membrane.

We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a molecular-dynamics simulation with a Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphenelike hexagonal sheet for different pulling force f and temperature T. We find that bond rupture occurs almost always at the sheet periphery, and the first mean breakage time <τ> of bonds decays with membrane size as <τ> ∝N(-ß), where ß≈0.50±0.03 and N denotes the number of atoms in the membrane. The probability distribution of bond scission times t is given by a Poisson function W(t)∝t(1/3)exp(-t/<τ>). The mean failure time <τ(r)> necessary to rip off the sheet declines with growing size N as a power law <τ(r)>∝N(-φ(f)). We also find <τ(r)>∝exp(ΔU(0)/k(B)T), where the nucleation barrier for crack formation ΔU(0)∝f(-2), in agreement with Griffith's theory. <τ(r)> displays an Arrhenian dependence of <τ(r)> on temperature T. Our results indicate a rapid increase in crack spreading velocity with growing external tension f.

Forced translocation of a polymer: Dynamical scaling versus molecular dynamics simulation.

We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of a propagating front of tensile force along the chain backbone, suggested by Sakaue [Phys. Rev. E 76, 021803 (2007); Phys. Rev. E 81, 041808 (2010); Eur. Phys. J. E 34, 135 (2011)]. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation: trumpet, stem-trumpet, etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasistatic approximation), we derive an equation of motion for the tensile front position X(t). We show that the scaling law for the average translocation time 〈τ〉 changes from <τ> ∼ N2ν/f1/ν to <τ> ∼ N^1+ν/f (for the free-draining case) as the dimensionless force f[over ̃]R=aNνf/T (where a, N, ν, f, and T are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by molecular-dynamics simulation. Data from our computer experiment indicate indeed that the translocation scaling exponent α grows with the pulling force f[over ̃]R, albeit the observed exponent α stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations that are neglected in the quasistatic approximation.

Fractional Brownian motion approach to polymer translocation: the governing equation of motion.

We suggest a governing equation that describes the process of polymer-chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time t after the process has begun, and (ii) a subdiffusive increase of the distribution variance Δ(t) with elapsed time Δ(t)∝t(α). The latter quantity measures the mean-squared number s of polymer segments that have passed through the pore Δ(t)=([s(t)-s(t=0)](2)), and is known to grow with an anomalous diffusion exponent α<1. Our main assumption [i.e., a Gaussian distribution of the translocation velocity v(t)] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in 3D. We also numerically confirm the predictions made recently that the exponent α changes from 0.91 to 0.55 to 0.91 for short-, intermediate-, and long-time regimes, respectively.

Globular structures of a helix-coil copolymer: self-consistent treatment.

A self-consistent-field theory was developed in the grand canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field theory takes, in addition to the conventional Zimm-Bragg, [J. Chem. Phys. 31, 526 (1959)] parameters, also three-dimensional interaction terms into account. The appropriate differential equations which determine the self-consistent fields were solved numerically with finite element method. Three different phase states are found: open chain, amorphous globule, and nematic liquid-crystalline (LC) globule. The LC-globule formation is driven by the interplay between the hydrophobic helical segment attraction and the anisotropic globule surface energy of an entropic nature. The full phase diagram of the helix-coil copolymer was calculated and thoroughly discussed. The suggested theory shows a clear interplay between secondary and tertiary structures in globular homopolypeptides.

Aggregates of rod-coil diblock copolymers adsorbed at a surface.

The behavior of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adsorbs with the rods parallel to the surface the rods shift with respect to each other to allow for the chains to gain entropy. It is shown that this shift decays with increasing distance from the surface. The profile of this decay away from the surface is calculated by minimization of the total free energy of the system. The stability of such an adsorbed aggregate and other possible configurations are discussed as well.