Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Ionic distribution and polymer conformation, near phase separation, in sodium polyacrylate/divalent cations mixtures: small angle X-ray and neutron scattering

Anomalous small angle X-ray scattering experiments show that before demixion in sodium polyacrylate/cobalt and sodium polyacrylate/calcium mixtures all the divalent counterions are in the close vicinity of the polyacrylate chain. The present results are consistent with previous UV/VIS spectroscopy, which have shown that all cobalt ions are chemically associated with acrylate groups. The chemical association dehydrates the acrylate monomers. However, the hydrophobicity of the complexed monomers is not strong enough to induce a collapse of the polymer chain at small spatial scale before the demixion. Indeed, the scattered intensity (X-ray and neutron scattering) decreases with the scattering vector q as q^-x with for q > 0.1 nm ^-1 which indicates that the local conformation of the chain is Gaussian. Received 21 January 1999     

A neural network model composed of two-state and three-state neurons

A neural network model composed of two-state (1 and -1) and three-state (1, 0 and -1) neurons is proposed. The two-state neurons are connected with the three-state ones only and vice versa. We derive dynamic equations for the model under the assumption of non-symmetrical dilution of connections. A zero-noise phase diagram is obtained and a region in which two fixed point solutions can coexist is found. Basins of attraction for the solutions are also investigated. Received 26 October 1998 and Received in final form 12 February 1999     

The distribution of counterions around synthetic rod-like polyelectrolytes in solution

An investigation of the radial distribution of the counterions of a synthetic rodlike polyelectrolyte in aqueous solution is presented. The cationic polyelectrolyte used here has a poly(p-phenylene) backbone. For typical molecular weights the macroion comprises approximately one persistence length (ca. 20 nm) and effects of finite stiffness may be disregarded. Each repeating unit bears four charges which leads to a charge parameter of ξ = 6.65. The distribution of the iodide counterions around this highly charged macroion is studied by small-angle X-ray scattering (SAXS) in dilute aqueous solution. These investigations are supplemented by measurements using anomalous small-angle X-ray scattering (ASAXS) that furnishes additional information about the contrast of the macroion. Data taken at high scattering angles give indication for contributions caused by the longitudinal fluctuations of the counterions. After correction for this effect the experimental results are compared to intensities calculated by use of the Poisson-Boltzmann (PB)-cell model. It is found that the PB-cell model describes the corrected data at intermediate and high scattering angles. Deviations at low scattering angle are attributed to the mutual interaction of the rod-like polyelectrolyte that can be described in terms of an effective structure factor. Data taken at lowest scattering angles point to a weak attraction between the rod-like macroions. Received: 27 July 2001 and Received in final form 27 March 2002     

Fibril stability in solutions of twisted -sheet peptides: a new kind of micellization in chiral systems

The problem of fibril (fibre) formation in chiral systems is explored theoretically being supported by experiments on synthetic de novo 11-mer peptide forming self-assembled -sheet tapes. Experimental data unambiguously indicate that the tapes form fibrils of nearly monodisperse thickness ca . 8-10 nm. Fibril formation and stabilisation are attributed to inter-tape face-to-face attraction and their intrinsic twist, correspondingly. The proposed theory is capable of predicting the fibril aggregation number and its equilibrium twist in terms of molecular parameters of the primary tapes. The suggested novel mechanism of twist stabilisation of finite aggregates (fibrils) is different to the well-known stabilisation of micelles in amphiphilic systems, and it is likely to explain the formation and stability of fibrils in a wide variety of systems including proteinaceous amyloid fibres, sickle-cell hemoglobin fibres responsible for HbS anemia, corkscrew threads found in chromonics in the presence of chiral additives and native cellulose microfibrillar crystallites. The theory also makes it possible to extract the basic molecular parameters of primary tapes (inter-tape attraction energy, helical twist step, elastic moduli) from the experimental data. Received 7 May 1999 and Received in final form 15 February 2000     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density (“dilute limit”), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the “dilute limit”, to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions. Received 3 June 1999 and Received in final form 29 July 1999     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002     

Simulations of counterions at charged plates

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open). Received 6 November 2001     

Thermodynamic Properties of a Simple Model of Like-Charged Attracting Rods

We study the thermodynamic properties of a simple model for the possible mechanism of attraction between like charged rod-like polyions inside a polyelectrolyte solution. We consider two polyions in parallel planes, with Z charges each, in a solution containing multivalent counterion of valence . The model is solved exactly for Z13 for a general angle between the rods and supposing that n counterions are condensed onto each polyion. The free energy has two minima, one at =0 (parallel rods) and another at =/2 (perpendicular rods). The stability of the parallel and perpendicular configurations is analyzed.     

Quantum backaction of optical observations on Bose-Einstein condensates

Impressive pictures of moving Bose-Einstein condensates have been taken using phase-contrast imaging [M.R. Andrews et al., Science 273, 84 (1996)]. We calculate the quantum backaction of this measurement technique, assuming the absence of residual absorption. We find that the condensate gets gradually depleted at a universal rate that is proportional to the light intensity and to the inverse cube of the optical wave length. The fewer atoms are condensed the higher is the required intensity to see a picture, and, consequently, the higher is the induced backaction. To describe the quantum physics of phase-contrast imaging we put forward a new approach to quantum-optical propagation. We develop an effective field theory of paraxial optics in a fully quantized atomic medium. Received 25 February 1999     

Virial expansion for charged colloids and electrolytes

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d₊ and d_- and charge valences q₊ and q_- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d ₊∼d _- and q ₊∼q _-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient. Received 6 September 2001 / Received in final form 20 May 2002 Published online 24 September 2002     

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.     

Aging kinetics of porous media due to freezing-thawing cycles

The two-dimensional Ausloos et al. model of fluid invasion, freezing and thawing in a porous medium is elaborated upon and investigated in order to take into account the pore volume redistribution and conservation during freezing. The results are qualitatively different from previous work, since the damaged pore sizes are found to be much less than the possible maximum value and is reached after a large number of invasion-freezing-thawing cycles, e.g. the material is “slowly damaged”. The pore size distribution is thus found in better agreement with expected practical findings. The successive invasion percolation clusters are still found to be self-avoiding with aging. The cluster size decreases with a power law as a function of invasion-frost-thaw iterations. The aging kinetics is also discussed through the normalized totally invaded pore volume. Received 24 September 1999 and Received in final form 5 January 2000     

Phase separation between phospholipids and grafted polymer chains onto a fluctuating membrane

We re-examine here the theoretical study of the phase separation between phospholipids and grafted long polymer chains onto a fluid membrane. The polymer chains are assumed to be anchored to the membrane by one extremity (anchor). The anchors are big amphiphile lipid molecules. The anchors and phospholipids forming the bilayer phase separate under the variation of a suitable parameter (temperature, pressure, membrane environment, ...). To investigate the demixtion transition, we elaborate a new approach that takes into account the membrane undulations. We show that these undulations have the tendency to induce additional attractive forces between anchors, and consequently, the separation transition is accentuated and occurs at high temperature. Quantitatively, we show that the membrane undulations contribute with an extra positive segregation parameter χ_m > 0 , which scales as χ_m κ^-2 , where κ is the bending rigidity constant. Therefore, the attraction phenomenon between species of the same kind is significant only for those membranes of small bending rigidity constant. Finally, the study is extended to the case where the lengths of the anchored polymer chains are randomly distributed. To achieve calculations, we choose a length distribution of fractal form. The essential conclusion is that the polydispersity increases the size of domains alternatively rich in phospholipids and anchors.     

Dynamics and structure of biopolyelectrolytes in repulsion regime characterized by dielectric spectroscopy

We overview the study of biopolyelectrolytes by dielectric spectroscopy technique by primarily focusing on the case of repulsive regime of intersegment interactions mediated by univalent counterions. Two observed dielectric relaxations in 100 Hz–100 MHz frequency range due to diffusive motion of counterions are related to polyelectrolyte structural properties: the high frequency mode probes the structural organization of the polyion network in solution, while the low frequency mode is correlated with single polyion conformational properties. Open issues are highlighted and prospects for further research with polyvalent counterions are designated in order to study the crossover from repulsive to attractive regime of intersegment interactions.     

Solubility of highly charged anionic polyelectrolytes in presence of multivalent cations: Specific interaction effect

Studies performed on strong polyelectrolytes and on a weak polyelectrolyte, sodium poly(acrylate), show that their stability in presence of multivalent cations depends on the chemical nature of the charged side groups of the polymer. For sulfonate groups (SO₃ ^-) or sulfate groups (OSO₃ ^-) phase separation generally occurs in presence of inorganic cations of valency 3 (as La³⁺) or larger and a resolubilization takes place at high salt concentration. The interactions of the polyelectrolyte with multivalent cations are of electrostatic origin and the phase diagrams are weakly dependent on the chemical nature of the polymer backbone and on the specificity of the counterions. For acrylate groups, (COO^-), the phase separation was observed with inorganic cations of valency 2 (as Ca²⁺) or larger without resolubilization at high salt concentration. The phase separation is due to a chemical association between cations and acrylate groups of two neighboring monomers of the same chain. This chemical association creates a hydrophobic complex by dehydrating both monomer and cation. With organic trivalent cation, as spermidine ⁺H₃N(CH₂)₄NH₂ ⁺(CH₂)₃NH₃ ⁺, where no chemical association occurs with the charged side groups COO^- or SO₃ ^- of the polyelectrolyte, similar phase diagrams were observed whatever was the polyelectrolyte with a resolubilization at high trivalent cation concentration. Received 3 March 1999 and Received in final form 2 September 1999     

Landau-Ginzburg treatment of nuclear matter at finite temperature

Based on recent studies of the temperature dependence of the energy and specific heat of liquid nuclear matter, a phase transition is suggested at a temperature ∼ 0.85 MeV. We apply the Landau-Ginzburg theory to this transition and determine the behaviour of the energy and specific heat close to the critical temperature in the condensed phase. Received: 29 July 2000 / Accepted: 20 October 2000     

On the observation of decoherence with a movable mirror

Following almost a century of debate on possible “independent of measurement" elements of reality, or “induced" elements of reality - originally invoked as an ad-hoc collapse postulate, we propose a novel line of interference experiments which may be able to examine the regime of induced elements of reality. At the basis of the proposed experiment, lies the hypothesis that models of “induced" elements of reality should exhibit symmetry breaking within quantum evolution. The described symmetry experiment is thus aimed at being able to detect and resolve spatial symmetry breaking signatures. The proposed experiment stands at the edge of present day technological abilities and will be, so we believe, realizable in the near future. Received 2 December 1999 and Received in final form 6 April 2000     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999