On the reliability of mean-field methods in polymer statistical mechanics

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mean-field theory (LMFT) method to statistically exact results from two independent numerical Monte Carlo simulations for the problems of a polymer chain moving in a spherical cavity and a polymer chain partitioning between two confining spheres of different radii. It is shown that in some cases the agreement between the LMFT and the simulation results is excellent, while in others, such as the case of strongly fluctuating monomer repulsion fields, the LMFT results agree with the simulations only qualitatively. Various approximations of the LMFT method are systematically estimated, and the quantitative discrepancy between the two sets of results is explained with the diminished accuracy of the saddle-point approximation, implicit in the mean-field method, in the case of strongly fluctuating fields.Comment: 27 pages, 9 figure

The Role of the Dielectric Barrier in Narrow Biological Channels: a Novel Composite Approach to Modeling Single-channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory

Partitioning of a polymer chain between a confining cavity and a gel

A lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E 60, 4257, (1999)] is applied to the study of a polymer chain contained in a spherical cavity but able to diffuse into a surrounding gel. The distribution of the polymer chain between the cavity and the gel is described by its partition coefficient, which is computed as a function of the number of monomers in the chain, the monomer charge, and the ion concentrations in the solution.Comment: 17 pages, 6 figure

Cumulant Methods and Short Time Propagators

The present paper clarifies a number of issues concerning the general problem of constructing improved short time quantum mechanical propagators. Cumulant methods are shown to be a particularly convenient tool for this task. Numerical results comparing methods based on partial averaging and on gradient approaches are presented for simple model problems and for many particle quantum fluids

Partial Averaging Approach to Fourier Coefficient Path Integration

The recently introduced method of partial averaging is developed in a general formalism for computing simple Cartesian path integrals. Examples of its application to both harmonic and anharmonic systems are given. For harmonic systems, where analytical results can be derived, both imaginary and complex time evolution is discussed. For two representative anharmonic systems, Monte Carlo path integral simulations of the imaginary time propagator (statistical density matrix) are presented. Connections with other Cartesian path integral techniques are stressed

Adsorption of Polymer-Grafted Nanoparticles on Curved Surfaces

Nanometer-curved surfaces are abundant in biological systems as well as in nano-sized technologies. Properly functionalized polymer-grafted nanoparticles (PGNs) adhere to surfaces with different geometries and curvatures. This work explores some of the energetic and mechanical characteristics of the adhesion of PGNs to surfaces with positive, negative and zero curvatures using Coarse-Grained Molecular Dynamics (CGMD) simulations. Our calculated free energies of binding of the PGN to the curved and flat surfaces as a function of separation distance show that curvature of the surface critically impacts the adhesion strength. We find that the flat surface is the most adhesive, and the concave surface is the least adhesive surface. This somewhat counterintuitive finding suggests that while a bare nanoparticle is more likely to adhere to a positively curved surface than a flat surface, grafting polymer chains to the nanoparticle surface inverts this behavior. Moreover, we studied the rheological behavior of PGN upon separation from the flat and curved surfaces under external pulling force. The results presented herein can be exploited in drug delivery and self-assembly applications