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Notes: Abstract: We formulate the exact 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 of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the 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. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level.

Notes: We study a simple model of a random heteropolymer, without excluded volume, in layered fluid systems of the form (i) ABA or ABC, where A, B, C denote three immiscible fluids, (ii) AB+hard wall, (iii) ABABA... . The quenched randomness is contained in the affinities {ξj; j=1,2,...,N} of the N links of the chain with the different fluids: these affinities are taken as random independent variables. Case (i) may be of interest for the localization of proteins in membranes, and (ii) pertains to the adsorption onto a wall. Using a replica-symmetric theory with a Hartree variational procedure, we study the behavior of the chain as a function of temperature. Various transitions [localization in case (i), adsorption in (ii)] are then exhibited. In the periodic situation (iii), the quenched and annealed randomness lead to the same results.

Notes: We use a nondynamical Monte Carlo method to simulate chains with charged monomers interacting via Coulomb potentials and short-range excluded volume potentials. An ensemble of chains of length N is created by adding monomers to the end of chains in an existing ensemble of length N−1. This is done in such a way that the ensemble remains at equilibrium at each stage of the process. For a weakly charged polyelectrolyte in a θ solvent the chain remains Gaussian for short lengths (R2∼N) but becomes linear (R2∼N2) for N greater than a "blob'' size N0. The crossover point N0 decreases with increasing charge density. The results support the predictions of scaling theories and show that the "electrostatic blob'' idea can be taken quite literally. For a polyelectrolyte in a poor solvent the Coulomb repulsions are in competition with attractive short-range interactions. The chain configuration is found to be collapsed (R2∼N2/3) for N〈Nτ and linear (R2∼N2) for N〉Nτ, where the blob size Nτ is a function of a charge density and the excluded volume. If the Coulomb interactions are screened then there is a configurational change of the polymer when the screening length κ−1 is reduced to the electrostatic blob radius. This is shown to happen very gradually over a range of κ−1 for the θ solvent case, but abruptly for the poor solvent case, again in agreement with theory. We also consider a neutral polyampholyte chain containing an equal number of positive and negative charges. The effect of the Coulomb interactions is shown to be attractive, but we are unable to see the long-chain scaling behavior for the chains of length 220 generated here. We discuss the statistical errors and correlations in the ensemble growth method. The efficiency of the method compares favorably with dynamical Monte Carlo methods (e.g., reptation algorithm) since it permits the whole range of lengths 1−N to be studied in a single run.

Notes: We consider a lattice model of a semiflexible homopolymer chain in a bad solvent. Beside the temperature T, this model is described by (i) a curvature energy εh, representing the stiffness of the chain; (ii) a nearest-neighbor attractive energy εv, representing the solvent; and (iii) the monomer density ρ=N/Ω, where N and Ω denote, respectively, the number of monomers and the number of lattice sites. This model is a simplified view of the protein folding problem, which encompasses the geometrical competition between secondary structures (the curvature term modelling helix formation) and the global compactness (modeled here by the attractive energy), but contains no side chain information. By allowing the monomer density ρ to depart from unity one has made a first (albeit naive) step to include the role of the water. In previous analytical studies, we considered only the (fully compact) case ρ=1, and found a first order freezing transition towards a crystalline ground state (also called the native state in the protein literature). In this paper, we extend this calculation to the description of both compact and noncompact phases. The analysis is done first at a mean-field level. We then find that the transition from the high temperature swollen coil state to the crystalline ground state is a two-step process for which (i) there is first a θ collapse transition towards a compact "liquid'' globule, and (ii) at low temperature, this "liquid'' globule undergoes a discontinuous freezing transition. The mean-field value of the θ collapse temperature is found to be independent of the curvature energy εh. This mean-field analysis is improved by a variational bound, which confirms the independence of the θ collapse temperature with respect to εh. This result is confirmed by a Monte Carlo simulation, although with a much lower value of the θ temperature. This lowering of the collapse transition allows the possibility (for large εh) of a direct first order freezing transition, from a swollen coil to the crystalline ground state. For small values of εh, the mean-field two-step mechanism remains valid. In the protein folding problem, the "liquid'' compact phase is likely to be related to the "molten globule'' phase. The properties of this model system thus suggest that, even though side chain disordering is not taken into account, disordering of the backbone of a protein may still be a sufficient mechanism to drive the system from the native state into the molten globule state. © 1996 American Institute of Physics.