Simulations of Stretching a Strong, Flexible Polyelectrolyte

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Overlap Concentration of Sodium Polystyrene Sulfonate in Solution

The overlap concentration c* of sodium polystyrene sulfonate in water is calculated using multichain atomistic and coarse grained (CG) simulations for a range of chain lengths. Fully atomistic molecular dynamics simulations are carried out for N = 32-192 monomers. The CG model was parameterized to match the end-to-end distance from the atomistic simulations at small N and allows us to simulate a much larger N. Treating the hydrophobic backbone by inclusion of attraction between monomers is an essential addition to the CG model. The simulation c* are in agreement with experimental data, yet at c*, the chains are not fully stretched, even for N as large as 1200. This implies that none of the experimental systems are in the scaling regime and to reach the scaling regime for NaPSS chains much longer than N = 1200 are required.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte that is, proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included. This model can be regarded as a kind of “minimal” in the sense that it contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both, with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 at low pH-values (Pincus regime) is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to the changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Electric-field-induced stretching of surface-tethered polyelectrolytes in a microchannel

We study the stretching of a surface-tethered polyelectrolyte confined between parallel surfaces under the application of a dc electric field. We explore the influence of the electric-field strength, the length of the polyelectrolyte, and the degree of confinement on the conformation of the polyelectrolyte by single-molecule experiments and coarse-grained coupled lattice-Boltzmann molecular-dynamics simulations. The fractional extension of the polyelectrolyte is found to be a universal function of the product of the applied electric field and the molecular contour length, which is explained by simple scaling arguments. The degree of confinement does not have any significant influence on the stretching. We also confirm that an electrohydrodynamic equivalence principle relating the stretching in an electric field to that in a flow field is applicable.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ∼ cs (-0.5) as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Sequence-dependent elasticity and electrostatics of single-stranded DNA: signatures of base-stacking

Base-stacking is a key factor in the energetics that determines nucleic acid structure. We measure the tensile response of single-stranded DNA as a function of sequence and monovalent salt concentration to examine the effects of base-stacking on the mechanical and thermodynamic properties of single-stranded DNA. By comparing the elastic response of highly stacked poly(dA) and that of a polypyrimidine sequence with minimal stacking, we find that base-stacking in poly(dA) significantly enhances the polymer's rigidity. The unstacking transition of poly(dA) at high force reveals that the intrinsic electrostatic tension on the molecule varies significantly more weakly on salt concentration than mean-field predictions. Further, we provide a model-independent estimate of the free energy difference between stacked poly(dA) and unstacked polypyrimidine, finding it to be ∼-0.25 kBT/base and nearly constant over three orders of magnitude in salt concentration.

The snakelike chain character of unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod "wormlike chain" (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a "snakelike chain," characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.

Global force-torque phase diagram for the DNA double helix: structural transitions, triple points, and collapsed plectonemes

We present a free energy model for structural transitions of the DNA double helix driven by tensile and torsional stress. Our model is coarse grained and is based on semiflexible polymer descriptions of B-DNA, underwound L-DNA, and highly overwound P-DNA. The statistical-mechanical model of plectonemic supercoiling previously developed for B-DNA is applied to semiflexible polymer models of P- and L-DNA to obtain a model of DNA structural transitions in quantitative accord with experiment. We identify two distinct plectonemic states, one "inflated" by electrostatic repulsion and thermal fluctuations and the other "collapsed," with the two double helices inside the supercoils driven to close contact. We find that supercoiled B and L are stable only in the inflated form, while supercoiled P is always collapsed. We also predict the behavior and experimental signatures of highly underwound "Q"-DNA, the left-handed analog of P-DNA; as for P, supercoiled Q is always collapsed. Overstretched "S"-DNA and strand-separated "stress-melted" DNA are also included in our model, allowing prediction of a global phase diagram for forces up to 1000 pN and torques between ±60 pN nm, or, in terms of linking number density, from σ=-5 to +3.