Theory of myelin coiling

A new model is proposed to explain coiling of myelins composed of fluid bilayers. This model allows the constituent bilayer cylinders of a myelin to be non-coaxial and the bilayer lateral tension to vary from bilayer to bilayer. The calculations show that a myelin would bend or coil to lower its free energy when the bilayer lateral tension is sufficiently large. From a mechanical point of view, the proposed coiling mechanism is analogous to the classical Euler buckling of a thin elastic rod under axial compression. The analysis of a simple two-bilayer case suggests that a bilayer lateral tension of about 1 dyne/cm can easily induce coiling of myelins of typical lipid bilayers. This model signifies the importance of bilayer lateral tension in determining the morphology of myelinic structures.     

Role of dislocation loops on the elastic constants of lyotropic lamellar phases

We study the role of dislocation loops defects on the elasticity of lamellar phases by investigating the variation of the lamellar elastic constants, ˉ and K, induced by the proliferation of these defects. We focus our interest on one particular lamellar phase made up of a mixture of C₁₂E₅ and DMPC in water, which is already well-characterised. This lamellar phase undergoes a second-order (or weakly first-order) lamellar-to-nematic phase transition at about 19^°C and dislocation loops are seen to proliferate within the lamellar structure when temperature is decreased below 30^°C. The values of both elastic constants of this given lamellar phase are measured as a function of temperature, approaching the lamellar-to-nematic transition, with the help of Quasi-Elastic Light Scattering (QELS) on oriented lamellar phases. Very surprisingly we observe a strong and rapid increase in both ˉ and K as the lamellar-to-nematic transition temperature is approached. These increases are seen to start as soon as dislocation loops can be observed in the lamellar phase. We interpret our results as being the consequence of the appearance and proliferation of dislocation loops within the lamellar structure. According to a simple model we developped we show that ˉ and K are proportional to the density of dislocation loops in the lamellar phase.     

Universality classes of self-avoiding fixed-connectivity membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is ν = 0.95(5) (Hausdorff dimension d _H = 2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes --the roughness exponent in three dimensions is ξ = 0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally, we address some theoretical and experimental implications of our work. Received 23 June 2000 and Received in final form 25 October 2000     

Flory radius of polymers in a periodic field: An exact analytic theory

We found an exact expression for the Flory radius R _F of Gaussian polymers placed in an external periodic field. This solution is expressed in terms of the two parameters η and a that describe the reduced strength of an external field and the period of the field to the polymer gyration radius ratio, respectively. R _F is found to be a decaying function of η for any values of a . Provided that the gyration radius is of the order of the period of an external field or less, the ground-state (GS) approximation of the exact result for R _F is shown to give qualitatively incorrect results. In addition to the “ground-state” contribution, the exact solution for R _F contains an additional term that is overlooked by the GS approximation. This term gives rise to the fact that R _F as a function of η exhibits power law behavior (rather than exponential decay obtained from the GS result) once η exceeds the threshold value η_con .     

Effects of properties of the surfactant on its aggregate behavior

The effects of the solvent-surfactant interaction, chain length and stiffness of surfactants on the formation of aggregates and the aggregation degree of surfactants in the two-dimension solution have been investigated using discontinuous molecular-dynamics simulations. When the tail-water repulsion increases or the head-water attraction decreases, the aggregation degree increases. Increasing the chain length and raising the stiffness of surfactants lead to the increment of the aggregation degree. Received 25 July 2001 and Received in final form 7 May 2002     

Two direct methods to calculate fluctuation forces between rigid objects embedded in fluid membranes

The fluctuation-induced attractive interaction of rigid flat objects embedded in a fluid membrane is calculated for a pair of parallel strips and a pair of equal circular disks. Assuming flat boundary conditions, we derive the interaction from the entropy of the suppressed boundary angle fluctuation modes. Each mode entropy is computed in two ways: from the boundary angles themselves and from the mean-curvature mode functions. A formula for the entropy loss of suppressing one or more mean-curvature modes is developed and applied. For the pair of disks we recover the result of Goulian et al. and Golestanian et al. in a direct manner, avoiding any mappings by Hubbard-Stratonovitch transformations. The mode-by-mode agreement of the two computed entropies in both systems confirms an earlier claim that mean curvature is the natural measure of integration for fluid membranes. Received 15 December 2000     

Nanostructures of colloidal complexes formed in oppositely charged polyelectrolyte/surfactant dilute aqueous solutions

Small-angle neutron scattering measurements were performed on dilute solutions of carboxymethylcellulose/DTAB complexes in water in order to determine their size, shape and internal structures. At low polymer content, the complexes are spherical, rather monodisperse and probably made of polymer chains intercalated between surfactant micelles. Moreover, we show that these micelles have a similar cubic arrangement than found in polymer/surfactant precipitates formed at higher surfactant concentrations. At larger polymer content, in the semi-dilute polyelectrolyte regime, the complexes are larger, softer and polydisperse. However, they possess a similar internal structure in both regimes. Carboxymethylcellulose/CTAB complexes are also large, soft and polydisperse but do not seem to exhibit well-defined internal structures.     

Small-angle neutron scattering studies of aqueous solutions of short-chain amphiphiles

We present small angle neutron scattering measurements on binary aqueous solutions of some short-chain amphiphiles (diols, triols, glycols and diglycols) at room temperature. The spectra were analysed in terms of the Teubner-Strey phenomenological formula which allows to obtain a measure for the amphiphilicity strength of each system (amphiphilicity factor f _a). In some systems, however, other models, valid for micellar solutions, give also a good representation of the spectra. As a result, we find that, independently of the type of hydrophilic group side (oxydrilic or oxirane), these systems cover the entire accessible amphiphilicity scale ( -1 < f _a < 1). Some disordered systems ( f _a > 1) presumably are able to form micelle-like aggregates. Received 12 June 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: giovanni.darrigo@uniroma1.it     

Size and viscoelasticity of spatially confined multilamellar vesicles

We studied viscoelastic properties and scaling behavior of multilamellar vesicles (MLVs) confined between two parallel plates as a function of the shear rate and sample thickness (gap size between parallel plates). The rheological properties are classified into two regimes; the shear-thinning regime at high shear rates and the shear-thickening regime at low shear rates. In the former, the MLV radius results from the mechanical balance between the effective surface tension σ_eff and viscous stress force. The MLV radius is independent of the gap size. σ_eff estimated by van der Linden model is 2.1 ±0.15 ×10^-4 Nm^-1 corresponding to the same value obtained by SANS measurement. Power law exponents for the steady state viscosity and yield stress against pre-shear rate ( , ) well agree with prediction based on the layering of membranes. Therefore, viscoelastic properties in this regime could be modeled by assuming that the dynamics of MLVs are driven by layering of MLV polydomains, which could be accompanied by the viscous dissipation, i.e., the stress relaxation on the MLV, induced by continuous sequence of yields of MLVs. The flow curve is empirically explained by the assumption of a relaxation time for the MLV shape. In the latter, however, scaling laws observed in the shear-thinning regime break down. The MLV radius increases when the gap size is reduced below the threshold value and MLV is no longer formed at very small gap sizes. Different dynamics from the shear-thinning regime seem to dominate the viscoelasticity.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

Brownian motion of particles embedded in a solution of giant micelles

We have measured the mean-square displacement of colloidal particles embedded in a semi-dilute solution of worm-like micelles, using diffusing wave spectroscopy. This allowed us to describe their rheological properties over a very wide time range. At very short times, the particles diffuse freely in the solvent, and then, they experience the characteristic relaxation times of the living chains. We deduced directly, from the mean-square displacement of the particles, the mechanical properties of the micellar solution, not only in the high-frequency regime, but also in the low-frequency range, in which we compared our results with direct mechanical measurements, and found good agreement. Received 22 March 2002 and Received in final form 5 June 2002     

Pearling instabilities in water-dispersed copolymer cylinders with charged brushes

We investigate the structural behavior of a poly(styrene)-block-poly(acrylic acid) diblock copolymer which forms hexagonally-packed PS cylinders (C-phase) in the melt state. The water dispersion of this structure provides hairy cylinders which comprise a PAA swollen cylindrical brush with a height h tunable via its degree of ionization and the ionic strength in the solution, and a water-free, PS cylindrical core of constant radius R_C. Such system constitutes an out-of-equilibrium frustrated model system: the selective swelling of the PAA brush results in a frustration of the interface curvature, which the ratio h/R_C allows to quantify. Upon heating at a temperature higher than the glass transition temperature of the PS core, the glassiness of the core is relieved and the mechanical constraints arising from the selective swelling of the structure can be relaxed: the cylinders undergo a cylinder-to-sphere transition upon annealing at high temperature, when above a frustration threshold h/R_C 1.8. Thanks to a careful mapping of the transition diagram, an undulating cylindrical morphology (UC) is identified between unchanged cylinders ( h/R_C 1.8) and spheres ( h/R_C 2.0), which appears to result from a Rayleigh-like pearling instability of the copolymer cylinders.     

Fluctuation spectra of free and supported membrane pairs

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.     

Stimuli-responsive poly(ethylene oxide)-b-poly(2-vinylpyridine)-b-poly(ethylene oxide) triblock copolymers and complexation with poly(acrylic acid) at low pH

The self-organization of the double hydrophilic triblock copolymer poly(ethylene oxide)-b-poly(2-vinylpyridine)-b-poly(ethylene oxide), PEO-b-P2VP-b-PEO, was investigated in dilute aqueous solution under several experimental conditions using turbidimetry, as well as static and dynamic light scattering. As a result of the temperature-sensitive properties of the end PEO blocks and the p H-responsive properties of the middle P2VP block, the formation of large star-like micellar nanostructures is observed at high p H, while at low p H, but in the presence of salt and at high temperature, flower-like micelles are formed. Moreover, the viscosimetric and dynamic light scattering studies at low p H revealed that micelle-like nanostructures are formed upon mixing the triblock copolymer with poly(acrylic acid), PAA, due to hydrogen bonding interpolymer complexation.     

Undulated cylinders of charged diblock copolymers

We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.     

On coupling between the orientation and the shape of a vesicle under a shear flow

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, dψ/dt = A+Bcos(2 ψ) (ψ is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.     

Temperature and concentration dependence of SANS spectra of aqueous solutions of short-chain amphiphiles

The small-angle neutron scattering (SANS) of some aqueous solutions of short-chain amphiphiles (glycols, diglycols, diols) has been measured as a function of concentration and temperature. The analysis of the spectra in terms of the Teubner-Strey phenomelogical formula indicates that, on increasing the concentration of the amphiphile, the structure of all these systems evolves in a similar way, i.e. a transition from disordered structures toward correlated aggregates (microstructures). The transition is depressed by increasing the temperature.     

Diffusing wave spectroscopy in Maxwellian fluids

We present a critical assessment of the diffusing wave spectroscopy (DWS) technique for obtaining the characteristic lengths and for measuring the loss and storage moduli of a reasonable well-known wormlike micelle (WM) system. For this purpose, we tracked the Brownian motion of particles using DWS embedded in a Maxwellian fluid constituted by a wormlike micellar solution made of cetyltrimethylam-monium bromide (CTAB), sodium salicylate (NaSal), and water. We found that the motion of particles was governed by the viscosity of the solvent at short times and by the stress relaxation mechanisms of the giant micelles at longer times. From the time evolution of the mean square displacement of particles, we could obtain for the WM solution the cage size where each particle is harmonically bound at short times, the long-time diffusion coefficient, and experimental values for the exponent that accounts for the broad spectrum of relaxation times at the plateau onset time found in the 〈Δr ²(t)〉 vs. time curves. In addition, from the 〈Δr ²(t) vs. time curves, we obtained G′(ω) and G″(ω) for the WM solutions. All the DWS microreological information allowed us to estimate the characteristic lengths of the WM network. We compare our DWS microrheological results and characteristic lengths with those obtained with mechanical rheometers at different NaSal/CTAB concentration ratios and temperatures.     

Elasticity and shape equation of a liquid membrane

The density of the elastic energy of a deformed membrane in a liquid state is calculated. The thermodynamic equilibrium of its different parts is taken into account. The shape equation of a closed membrane is deduced. The quantity which keeps its value, when the variations of the energy of the system are calculated, is not the area of the deformed membrane, but its area in the flat tension free state. Because of this, additional terms appear in the second variation around the stable state. The case of a lipid bilayer and its fluctuations is examined for both free and blocked exchange of molecules between the monolayers, comprising the bilayer. Received 4 February 2002 / Received in final form 15 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: bivas@issp.bas.bg