Henri Orland

STERIC EFFECTS IN ELECTROLYTES : A MODIFIED POISSON-BOLTZMANN EQUATION

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson-Boltzmann equation which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments.

Theory of critical micelle concentration for solutions of block copolymers

A simple microscopic model for micellar formation in mixtures of block copolymers and homopolymers is presented. The size, number of chains, and energy of formation of micelle are calculated. The fraction of copolymer chains aggregating into micelles is computed as a function of the overall copolymer content. A critical micelle concentration behavior is found for low copolymer contents even for weak incompatibilities of species. The similarity with an aborted phase transition is underlined.

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

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.

Dipolar Poisson-Boltzmann Equation: Ions and Dipoles Close to Charge Interfaces

We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic expansion. It is applied to a two-plate system with oppositely charged surfaces. The ion distribution and profiles in the dipolar order parameter are calculated and can result in a large correction to the interplate pressure.

Dielectric constant of ionic solutions: a field-theory approach.

We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods, we expand the Gibbs free energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles.

Topological Classification of RNA Structures

We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non-planar diagrams correspond to pseudoknotted structures and have higher genus. The topological genus allows for the definition of topological folding motifs, similar in spirit to those introduced and commonly used in protein folding. We analyze real RNA structures from the databases Worldwide Protein Data Bank and Pseudobase and classify them according to their topological genus. For simplicity, we limit our analysis by considering only Watson-Crick complementary base pairs and G-U wobble base pairs. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.

Field theory for charged fluids and colloids.

Charged systems are considered using field theoretic methods which include fluctuations and correlations via a systematic expansion in powers of the local electrostatic potential. At the Gaussian level we recover the classical Debye-Huckel (DH) theory, which is found to exhibit the full hierarchy of multibody correlations determined by pair-distribution functions given by the screened DH potential. Higher-order corrections can lead to attractive pair interactions between similarly charged particles in asymmetric ionic environments. The phase diagram for an ionic fluid shows a critical point of demixing. The critical temperature and critical density exhibit pronounced deviations from DH theory for highly asymmetric ionic systems.

RNA folding and large N matrix theory

We formulate the RNA folding problem as an N × N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N →∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the 1/N 2 corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.  2002 Published by Elsevier Science B.V.

Quantitative protein dynamics from dominant folding pathways

We develop a theoretical approach to the protein-folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps are removed, and simulating the entire reaction in atomistic details using existing computers becomes feasible. We discuss how to determine the most probable folding pathway, identify configurations representative of the transition state, and compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine dipeptide, within an all-atom model based on the empiric GROMOS96 force field.

Polyelectrolyte Solutions between Charged Surfaces

The effect of electrostatic interactions on the distribution of polymers in a good solvent is investigated for semi-dilute solutions containing charged polymers (polyelectrolytes) and small ions. A mean field approach is used to derive two coupled differential equations: a modified Poisson-Boltzmann equation for the electrostatic potential, and a self-consistent field equation for the polymer order parameter. We compare several monomer charge distributions; smeared, annealed and quenched. The polymers are confined between two charged surfaces, and are in contact with a reservoir of polymers and electrolyte. This makes the annealed and quenched cases equivalent. Non-monotonous profiles are obtained for the case of competing surface interactions: electrostatic adsorption vs. short-range desorption.