Translocation of Hydrophobic Polyelectrolytes under Electrical Field: Molecular Dynamics Study.

We studied the translocation of polyelectrolyte (PE) chains driven by an electric field through a pore by means of molecular dynamics simulations of a coarse-grained HP model mimicking high salt conditions. Charged monomers were considered as polar (P) and neutral monomers as hydrophobic (H). We considered PE sequences that had equally spaced charges along the hydrophobic backbone. Hydrophobic PEs were in the globular form in which H-type and P-type monomers were partially segregated and they unfolded in order to translocate through the narrow channel under the electric field. We provided a quantitative comprehensive study of the interplay between translocation through a realistic pore and globule unraveling. By means of molecular dynamics simulations, incorporating realistic force fields inside the channel, we investigated the translocation dynamics of PEs at various solvent conditions. Starting from the captured conformations, we obtained distributions of waiting times and drift times at various solvent conditions. The shortest translocation time was observed for the slightly poor solvent. The minimum was rather shallow, and the translocation time was almost constant for medium hydrophobicity. The dynamics were controlled not only by the friction of the channel, but also by the internal friction related to the uncoiling of the heterogeneous globule. The latter can be rationalized by slow monomer relaxation in the dense phase. The results were compared with those from a simplified Fokker-Planck equation for the position of the head monomer.

Polyelectrolytes: From Seminal Works to the Influence of the Charge Sequence.

We propose a selected tour of the physics of polyelectrolytes (PE) following the line initiated by de Gennes and coworkers in their seminal 1976 paper. The early works which used uniform charge distributions along the PE backbone achieved tremendous progress and set most milestones in the field. Recently, the focus has shifted to the role of the charge sequence. Revisited topics include PE complexation and polyampholytes (PA). We develop the example of a random PE in poor solvent forming pearl-necklace structures. It is shown that the pearls typically adopt very asymmetric mass and charge distributions. Individual sequences do not necessarily reflect the ensemble statistics and a rich variety of behaviors emerges (specially for PA). Pearl necklaces are dynamic structures and switch between various types of pearl-necklace structures, as described for both PE and PA.

Partially Globular Conformations from Random Charge Sequences.

Overall charged polymers with quenched charge sequences often adopt partially globular structures which result from the interplay between the disorder in charge sequences and thermal fluctuations. Simple energetic considerations show that structures consisting of alike (equal-size-equal-charge) globules are not favorable: the structures are intrinsically heterogeneous. We predict the globule distributions with the lowest energies in the size-charge space. The favorable structures comprise large (undercharged) and a majority of small (overcharged) globules. These distributions build a well characterized compact subset, which suggests some order. We also perform large scale molecular dynamics simulations on random quenched +/- sequences. Simulation results show that, despite disorder, the random charge sequences preferentially visit the predicted low energy structures and the predicted order emerges in the pearl-size distribution. This good agreement validates a posteriori the simple expression used for the energy. Implications for polyampholytes, polyelectrolytes, and intrinsically disordered proteins are discussed.

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.

Sequence Blockiness Controls the Structure of Polyampholyte Necklaces.

A scaling theory of statistical (Markov) polyampholytes is developed to understand how sequence correlations, that is, the blockiness of positive and negative charges, influences conformational behavior. An increase in the charge patchiness leads to stronger correlation attractions between oppositely charged monomers, but simultaneously, it creates a higher charge imbalance in the polyampholyte. A competition between effective short-range attractions and long-range Coulomb repulsions induces globular, pearl-necklace, or fully stretched chain conformations, depending on the average length of the block of like charges. The necklace structure and the underlying distribution of the net charge are also controlled by the sequence. Sufficiently long blocks allow for charge migration from globular beads (pearls) to strings, thereby providing a nonmonotonic change in the number of necklace beads as the blockiness increases. The sequence-dependent structure of polyampholyte necklaces is confirmed by molecular dynamics simulations. The findings presented here provide a framework for understanding the sequence-encoded conformations of synthetic polyampholytes and intrinsically disordered proteins (IDPs).

The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions.

We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.

Grand-canonical polymers under confinement: Dense solutions.

We theoretically study dense polymer solutions under open (capillary and slit) and closed (box) confinement. The theory is formulated for grand-canonical polymers and corrections to the self-consistent mean-field results are discussed. In contrast to the mean-field prediction, we found that the partition function of a labeled chain is affected by confinement even under neutral von Neumann boundary conditions and the chain length distribution is biased to short chains. As the container size increases, the contribution of the transverse excited states to the free energy of a labeled chain is found to approach its bulk value nonmonotonically (through an extremum) for the box and the capillary confinement but not for the slit. So does the confinement free energy of a labeled chain. The confinement energy of the solution is well behaved for open confinement but formally diverges for a closed box in the limit that the average chain length goes to infinity. Counted per chain, the confinement energy of the dense solution is qualitatively weaker than for a single ideal chain under similarly strong confinement (by one power in transverse container size). The container boundary contributes a surface tension to the free energy, which makes the effective monomer-wall affinity more repulsive. This correction increases with the average chain length. If present, edge or vertex singularities also contribute to the grand potential of the solution.

Polymers grown in cavities: Vesicles and droplets.

In synthetic chemistry and biological or biomimetic systems, polymers are often grown in cavities. Polymerizations in microemulsions, biopolymers grown in cells, or in vesicles containing artificial organelles have an influence on the shape of liquid boundaries. We consider confined grand-canonical polymers to address equilibrium properties of annealed polymers. We calculate the concentration profiles established by annealed (star-) polymers inside a confining cavity. Our emphasis is on the description of pressure fields derived from the contact theorem. We further show how the pressure field exerted by a localized annealed polymer (or pair of polymers) deforms the confining vesicle/ microemulsions droplet.

Microscopic Structure of Compacted Polyelectrolyte Complexes: Insights from Molecular Dynamics Simulations.

We utilize atomistic molecular dynamics (MD) simulations to study local structural changes inside a polyelectrolyte complex consisting of poly(styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA) upon densification, in analogy to ultracentrifugation in experiments. In particular, we focus on the water content and on the reinforcement of the PSS-PDADMA network for various external accelerations. We demonstrate that apart from the formation of mesoscopic pores observed experimentally also the microscopic structure and the local relaxation processes likely affect the unique rheological properties of compacted polyelectrolyte complexes, as densification increases both the number of PSS-PDADMA coordinations and the intermixing of PSS and PDADMA. These processes slow down local rearrangements, thus further stabilizing the compacted state. We find that the concept of binary PSS-PDADMA salt bonds-relevant for theoretical models-is not strictly valid in the dense limit.

The Daoud and Cotton blob model and the interaction of star-shaped polymers.

Since it was first proposed in 1982, the Daoud and Cotton (DC) model for star-shaped polymers was intensively used also for self-assembled copolymers and small colloids grafted with long polymers. We try to clarify the position of the DC model and focus on the star partition function which plays a central role in self-assembly and gives access to the star-star interaction. While the predicted star-star interaction agrees with scattering data by Likos et al. (Phys. Rev. Lett. 80, 4450 (1998)), an extensive simulation by Hsu et al. (Macromolecules, 37, 4658 (2004)) does not recover the prediction for the partition function. We try to reconcile this seemingly conflicting results. We discuss star-star interactions, star free energy in θ -solvents, mixing of A/B branches in copolymer stars, within or beyond the Daoud and Cotton blob model.

Super-helical filaments at surfaces: dynamics and elastic responses.

Bio-filaments often behave in a way unexpected from the standard semi-flexible polymer chain model (WLC), when squeezed to a surface, confined in microfluidic channels or clamped by their end. This calls for the super-helical filament model, going beyond WLC, where the filament forms a helix much wider than its diameter. We study this model using Brownian dynamics simulations, focusing on filaments confined to a surface by a strong potential. We analyze shapes and shape fluctuations under tension where excited states comprising a number of inflection points (twist-kink) can be stabilized. Pulling/releasing experiments during a cycle of increasing/decreasing tension show hysteresis. We find that the excited state, once established, is long-lived and the life time grows with the filament length cubed. Twist-kink diffusion involves position (filament shape) dependent friction for which we provide analytical expression. Dynamic responses to tension are investigated via numerical simulations and several mechanisms of shape relaxation are found and rationalized.

Unveiling the pathway to Z-DNA in the protein-induced B-Z transition.

Left-handed Z-DNA is an extraordinary conformation of DNA, which can form by special sequences under specific biological, chemical or physical conditions. Human ADAR1, prototypic Z-DNA binding protein (ZBP), binds to Z-DNA with high affinity. Utilizing single-molecule FRET assays for Z-DNA forming sequences embedded in a long inactive DNA, we measure thermodynamic populations of ADAR1-bound DNA conformations in both GC and TG repeat sequences. Based on a statistical physics model, we determined quantitatively the affinities of ADAR1 to both Z-form and B-form of these sequences. We also reported what pathways it takes to induce the B-Z transition in those sequences. Due to the high junction energy, an intermediate B* state has to accumulate prior to the B-Z transition. Our study showing the stable B* state supports the active picture for the protein-induced B-Z transition that occurs under a physiological setting.

Local Chain Segregation and Entanglements in a Confined Polymer Melt.

The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends over mesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.

How bio-filaments twist membranes.

We study the deformations of a fluid membrane imposed by adhering stiff bio-filaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical bio-filaments. In particular, we analyse interface-mediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.

Competition between B-Z and B-L transitions in a single DNA molecule: Computational studies.

Under negative torsion, DNA adopts left-handed helical forms, such as Z-DNA and L-DNA. Using the random copolymer model developed for a wormlike chain, we represent a single DNA molecule with structural heterogeneity as a helical chain consisting of monomers which can be characterized by different helical senses and pitches. By Monte Carlo simulation, where we take into account bending and twist fluctuations explicitly, we study sequence dependence of B-Z transitions under torsional stress and tension focusing on the interaction with B-L transitions. We consider core sequences, (GC)_{n} repeats or (TG)_{n} repeats, which can interconvert between the right-handed B form and the left-handed Z form, imbedded in a random sequence, which can convert to left-handed L form with different (tension dependent) helical pitch. We show that Z-DNA formation from the (GC)_{n} sequence is always supported by unwinding torsional stress but Z-DNA formation from the (TG)_{n} sequence, which are more costly to convert but numerous, can be strongly influenced by the quenched disorder in the surrounding random sequence.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond.

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Disentanglement of Two Single Polymer Chains: Contacts and Knots.

Understanding the consequences of the noncrossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.

Annealed random copolymer model of the B-Z transition in DNA: torsional responses.

Both in vivo and in vitro, specific sequences in double-stranded DNA can adopt the left-handed Z-form when underwound. Recently, the B-Z transition of DNA has been studied in detail in magnetic tweezers experiments by several groups. We present a theoretical description of this transition, based on an annealed random copolymer model. The transition of a switchable sequence is discussed as a function of energetic and geometric parameters of the B- and Z-forms, of the applied boundary conditions, and of the characteristics of the B-Z interface. We address a possible torsional softening upon the B-Z transition. The model can be also applied to other biofilaments with annealed torsional/flexural degrees of freedom.

Topological energy storage of work generated by nanomotors.

Most macroscopic machines rely on wheels and gears. Yet, rigid gears are entirely impractical on the nano-scale. Here we propose a more useful method to couple any rotary engine to any other mechanical elements on the nano- and micro-scale. We argue that a rotary molecular motor attached to an entangled polymer energy storage unit, which together form what we call the "tanglotron" device, is a viable concept that can be experimentally implemented. We derive the torque-entanglement relationship for a tanglotron (its "equation of state") and show that it can be understood by simple statistical mechanics arguments. We find that a typical entanglement at low packing density costs around 6kT. In the high entanglement regime, the free energy diverges logarithmically close to a maximal geometric packing density. We outline several promising applications of the tanglotron idea and conclude that the transmission, storage and back-conversion of topological entanglement energy are not only physically feasible but also practical for a number of reasons.

Interactions between charged lamellae in aqueous solution.

Interactions between charged surfaces in aqueous solutions, widespread in soft matter and biology, are very complex and, despite many efforts, their full explanation remains challenging. We support the idea that, in contrast to extremely small separations (d≤2 nm), where many effects, prominently those linked to the structure of liquid water, interfere, electrostatics alone rules over larger distances (d≥5 nm) at low ionic strength. We set up specially designed surface force apparatus (SFA) experiments to measure the elastic compressibility modulus of a stack of charged membranes with monovalent counterions, directly and with high precision. We demonstrate that electrostatics alone, if implemented beyond Poisson-Boltzmann theory, fully accounts for the data, nonelectrostatic contributions playing at best a minor role.