Scaling perspectives of underscreening in concentrated electrolyte solutions.

We present a scaling view of underscreening observed in salt solutions in the range of concentrations greater than about 1 M, in which the screening length increases with concentration. The system consists of hydrated clusters of positive and negative ions with a single unpaired ion as suggested by recent simulations. The environment of this ion is more hydrated than average which leads to a self-similar situation in which the size of this environment scales with the screening length. The prefactor involves the local dielectric constant and the cluster density. The scaling arguments as well as the cluster model lead to scaling of the screening length with the ion concentration, in agreement with observations.

Flexible, charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity.

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of 0.66±0.02. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a "jacket" of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

Polyelectrolyte Conformation Controlled by a Trivalent-Rich Ion Jacket.

The configuration of charged polymers is heavily dependent on interactions with surrounding salt ions, typically manifesting as a sensitivity to the bulk ionic strength. Here, we use single-molecule mechanical measurements to show that a charged polysaccharide, hyaluronic acid, shows a surprising regime of insensitivity to ionic strength in the presence of trivalent ions. Using simulations and theory, we propose that this is caused by the formation of a "jacket" of ions, tightly associated with the polymer, whose charge (and thus effect on configuration) is robust against changes in solution composition.

Compressing Θ-Chain in Slit Geometry.

When compressed in a slit of width D, a Θ-chain that displays the scaling of size R0 (diameter) with respect to the number of monomers N, R0 ∼ aN1/2, expands in the lateral direction as R|| ∼ aNν(a/D)2ν-1. Provided that the Θ condition is strictly maintained throughout the compression, the well-known scaling exponent of Θ-chain in two dimensions, ν = 4/7, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from R0/D < 1 to R0/D ≫ 1, ν gradually deviates from ν = 1/2 and plateaus at ν = 3/4, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the Θ condition under confinement because of two major effects. First, as the dimension is reduced from three to two dimensions, the contributions of higher order virial terms, which can be ignored in three dimensions at large N, become significant, making the perturbative expansion used in Flory-type approach inherently problematic. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the second virial coefficient (B2) changes from B2 = 0 (Θ condition) in free space to B2 > 0 (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.

Dynamics of Charged Species in Ionic-Neutral Block Copolymer and Surfactant Complexes.

Structure-property relationships of ionic block copolymer (BCP) surfactant complexes are critical toward the progress of favorable engineering design of efficient charge-transport materials. In this article, molecular dynamics simulations are used to understand the dynamics of charged-neutral BCP and surfactant complexes. The dynamics are examined for two different systems: charged-neutral double-hydrophilic and hydrophobic-hydrophilic block copolymers with oppositely charged surfactant moieties. The dynamics of the surfactant head, tails, and charges are studied for five different BCP volume fractions. We observe that the dynamics of the different species solely depend on the balance between electrostatic and entropic interactions between the charged species and the neutral monomers. The favorable hydrophobic-hydrophobic interactions and the unfavorable hydrophobic-hydrophilic interactions determine the mobilities of the monomers. The dynamical properties of the charge species influence complex formation. Structural relaxations exhibit length-scale dependent behavior, with slower relaxation at the radius of gyration length-scale and faster relaxation at the segmental length-scale, consistent with previous results. The dynamical analysis correlates ion-exchange kinetics to the self-assembly behavior of the complexes.

Effects of Dimethyl Sulfoxide on Surface Water near Phospholipid Bilayers.

Despite much effort to probe the properties of dimethyl sulfoxide (DMSO) solution, the effects of DMSO on water, especially near plasma membrane surfaces, still remain elusive. By performing molecular dynamics simulations at varying DMSO concentrations (XDMSO), we study how DMSO affects structural and dynamical properties of water in the vicinity of phospholipid bilayers. As proposed by a number of experiments, our simulations confirm that DMSO induces dehydration from bilayer surfaces and disrupts the H-bond structure of water. However, DMSO-enhanced water diffusivity at solvent-bilayer interfaces, an intriguing discovery reported by a spin-label measurement, is not confirmed in our simulations. To resolve this discrepancy, we examine the location of the spin label (Tempo) relative to the solvent-bilayer interface. In accord with the evidence in the literature, our simulations, which explicitly model Tempo-phosphatidylcholine, find that the Tempo moiety is equilibrated at ∼8-10 Å below the bilayer surface. Furthermore, the DMSO-enhanced surface-water diffusion is confirmed only when water diffusion is analyzed around the Tempo moiety that is immersed below the bilayer surface, which implies that the experimentally detected signal of water using Tempo stems from the interior of bilayers, not from the interface. Our analysis finds that the increase of water diffusion below the bilayer surface is coupled to the increase of area per lipid with an increasing XDMSO(≲10mol%). Underscoring the hydrophobic nature of the Tempo moiety, our study calls for careful re-evaluation of the use of Tempo in measurements on lipid bilayer surfaces.

Effects of macromolecular crowding on the collapse of biopolymers.

Experiments show that macromolecular crowding modestly reduces the size of intrinsically disordered proteins even at a volume fraction (ϕ) similar to that in the cytosol, whereas DNA undergoes a coil-to-globule transition at very small ϕ. We show using a combination of scaling arguments and simulations that the polymer size R̅(g)(ϕ) depends on x=R̅(g)(0)/D, where D is the ϕ-dependent distance between the crowders. If x≲O(1), there is only a small decrease in R̅(g)(ϕ) as ϕ increases. When x≫O(1), a cooperative coil-to-globule transition is induced. Our theory quantitatively explains a number of experiments.

Repulsion between oppositely charged planar macroions.

The repulsive interaction between oppositely charged macroions is investigated using Grand Canonical Monte Carlo simulations of an unrestricted primitive model, including the effect of inhomogeneous surface charge and its density, the depth of surface charge, the cation size, and the dielectric permittivity of solvent and macroions, and their contrast. The origin of the repulsion is a combination of osmotic pressure and ionic screening resulting from excess salt between the macroions. The excess charge over-reduces the electrostatic attraction between macroions and raises the entropic repulsion. The magnitude of the repulsion increases when the dielectric constant of the solvent is lowered (below that of water) and/or the surface charge density is increased, in good agreement with experiment. Smaller size of surface charge and the cation, their discreteness and mobility are other factors that enhance the repulsion and charge inversion phenomenons.

Entropy-driven collective interactions in DNA brushes on a biochip.

Cell-free gene expression in localized DNA brushes on a biochip has been shown to depend on gene density and orientation, suggesting that brushes form compartments with partitioned conditions. At high density, the interplay of DNA entropic elasticity, electrostatics, and excluded volume interactions leads to collective conformations that affect the function of DNA-associated proteins. Hence, measuring the collective interactions in dense DNA, free of proteins, is essential for understanding crowded cellular environments and for the design of cell-free synthetic biochips. Here, we assembled dense DNA polymer brushes on a biochip along a density gradient and directly measured the collective extension of DNA using evanescent fluorescence. DNA of 1 kbp in a brush undergoes major conformational changes, from a relaxed random coil to a stretched configuration, following a universal function of density to ionic strength ratio with scaling exponent of 1/3. DNA extends because of the swelling force induced by the osmotic pressure of ions, which are trapped in the brush to maintain local charge neutrality, in competition with the restoring force of DNA entropic elasticity. The measurements reveal in DNA crossover between regimes of osmotic, salted, mushroom, and quasineutral brush. It is surprising to note that, at physiological ionic strength, DNA density does not induce collective stretch despite significant chain overlap, which implies that excluded volume interactions in DNA are weak.

Thermal fluctuation and elasticity of lipid vesicles interacting with pore-forming peptides.

The thermal fluctuation and elasticity of dioleoyl-phosphocholine large unilamellar vesicle interacting with pore-forming peptide, melittin, were investigated by neutron spin-echo measurements. The relaxation behavior of the membrane fluctuation with different peptide to lipid molar ratio P/L can be divided into three regions, resulting from characteristic changes of the effective bending modulus κ(˜) of the membrane which includes the effects of internal dissipation within the membrane. At low P/L, melittin is adsorbed parallel to the surface of membrane and κ(˜) decreases significantly due to perturbation of hydrocarbon chain packing. At a critical P/L, melittin forms pores in the membrane and κ(˜) starts to increase slightly due to high pore rigidity. At higher P/L where the repulsive interpore interaction becomes significant, κ(˜) increases rapidly.

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions.

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polyelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are pointlike, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also show that if the attractive interactions between the rods become frustrated as the bundle grows, finite-size bundles can be obtained with pointlike counterions.

Dielectric-induced counterion partitioning and its effect on membrane rigidity.

We report on a nonthermal mechanism for counterion partitioning driven by dielectric contrasts in a charged system. This mechanism allows objects to remain charged even in very low dielectric mediums and at low temperatures, if a nearby high dielectric environment can host its counterions. This nonthermal counterion partitioning leads to an attractive counterion pressure that is usually much larger than the van der Waals forces. In the context of a lipid membrane, this partitioning will stiffen the membrane by approximately k(B)T.