Interplay between structure and density anomaly for an isotropic core-softened ramp-like potential

Using molecular dynamics simulations and integral equations we investigate the structure, the thermodynamics and the dynamics of a system of particles interacting through a continuous core- softened ramp-like interparticle potential. We found density, dynamic and structural anomalies similar to that found in water. Analysis of the radial distribution function for several temperatures at fixed densities show a pattern that may be related to the origin of density anomaly.Comment: 7 pages, 3 figure

Attraction of like-charged macroions in the strong-coupling limit

Like-charged macroions attract each other as a result of strong electrostatic correlations in the presence of multivalent counterions or at low temperatures. We investigate the effective electrostatic interaction between i) two like-charged rods and ii) two like-charged spheres using the recently introduced strong-coupling theory, which becomes asymptotically exact in the limit of large coupling parameter (i.e. for large counterion valency, low temperature, or high surface charge density on macroions). Since we deal with curved surfaces, an additional parameter, referred to as Manning parameter, is introduced, which measures the ratio between the radius of curvature of macroions to the Gouy-Chapman length and controls the counterion-condensation process that directly affects the effective interactions. For sufficiently large Manning parameters (weakly-curved surfaces), we find a strong long-ranged attraction between two macroions that form a closely-packed bound state with small surface-to-surface separation of the order of the counterion diameter in agreement with recent simulations. For small Manning parameters (highly-curved surfaces), on the other hand, the equilibrium separation increases and the macroions unbind from each other as the confinement volume increases to infinity. This occurs via a continuous universal unbinding transition for two charged rods at a threshold Manning parameter of 2/3, while the transition is discontinuous for spheres because of a pronounced potential barrier at intermediate distances.Comment: 16 pages, 10 figure

Quantitative prediction of multivalent ligand–receptor binding affinities for influenza, cholera, and anthrax inhibition

Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biology and promising for the synthesis of high-affinity inhibitors of pathogens. We present a molecular model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing experimental designs. The calculated binding affinities quantitatively agree with experimental studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equilibrium end-to-end distance that is slightly longer than the geometric separation between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity

Beyond Poisson-Boltzmann: Fluctuations and Correlations

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations and correlations are included by a loop-wise expansion around this saddle point. We show that the Poisson equation is obeyed at each order in the loop expansion and explicitly give the expansion of the Gibbs potential up to two loops. We then apply our formalism to the case of an impenetrable, charged wall, and obtain the fluctuation corrections to the electrostatic potential and counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. We also calculate effective interactions between charged particles, which reflect counter-ion correlation effects.Comment: 12 pages, 8 postscript figure

Variational charge renormalization in charged systems

We apply general variational techniques to the problem of the counterion distribution around highly charged objects where strong condensation of counterions takes place. Within a field-theoretic formulation using a fluctuating electrostatic potential, the concept of surface-charge renormalization is recovered within a simple one-parameter variational procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for a single charge planar surface both in the weak-charge and strong-charge regime. We then apply our techniques to non-planar geometries where closed-form solutions of the non-linear Poisson-Boltzmann equation are not available. In the cylindrical case, the Manning charge renormalization result is obtained in the limit of vanishing salt concentration. However, for intermediate salt concentrations a slow crossover to the non-charge-renormalized regime (at high salt) is found with a quasi-power-law behavior which helps to understand conflicting experimental and theoretical results for the electrostatic persistence length of polyelectrolytes. In the spherical geometry charge renormalization is only found at intermediate salt concentrations

Plectoneme creation reduces the rotational friction of a polymer

The torsional dynamics of a semiflexible polymer with a contour length $L$ larger than its persistence length L_p that is rotated at fixed frequency omega_0 at one end is studied by scaling arguments and hydrodynamic simulations. We find a non-equilibrium transition at a critical frequency omega_*: In the linear regime, omega_0 < omega_*, axial spinning is the dominant dissipation mode. In the non-linear regime, omega_0 > omega_*, the twist-dissipation mode involves the continuous creation of plectonemes close to the driven end and the rotational friction is substantially reduced

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.Comment: 22 pages, 9 figures; revised version with additional calculations and experimental comparison; accepted for publication in Macromolecule

Roughness-Induced Wetting

We investigate theoretically the possibility of a wetting transition induced by geometric roughness of a solid substrate for the case where the flat substrate does not show a wetting layer. Our approach makes use of a novel closed-form expression which relates the interaction between two sinusoidally modulated interfaces to the interaction between two flat interfaces. Within the harmonic approximation, we find that roughness-induced wetting is indeed possible if the substrate roughness, quantified by the substrate surface area, exceeds a certain threshold. In addition, the molecular interactions between the substrate and the wetting substance have to satisfy several conditions. These results are expressed in terms of a lower bound on the wetting potential for a flat substrate in order for roughness-induced wetting to occur. This lower bound has the following properties: A minimum is present at zero or very small separation between the two interfaces, as characteristic for the non-wetting situation in the flat case. Most importantly, the wetting potential needs to have a pronounced maximum at a separation comparable to the amplitude of the substrate roughness. These findings are in agreement with the experimental observation of roughness-induced surface premelting at a glass-ice interface as well as the calculation of the dispersion interaction for the corresponding glass-water-ice system.Comment: 17 pages, 8 figure