Adhesion of fluid vesicles at chemically structured substrates

The adhesion of fluid vesicles at chemically structured substrates is studied theoretically via Monte Carlo simulations. The substrate surface is planar and repels the vesicle membrane apart from a single surface domain γ , which strongly attracts this membrane. If the vesicle is larger than the attractive γ domain, the spreading of the vesicle onto the substrate is restricted by the size of this surface domain. Once the contact line of the adhering vesicle has reached the boundaries of the γ domain, further deflation of the vesicle leads to a regime of low membrane tension with pronounced shape fluctuations, which are now governed by the bending rigidity. For a circular γ domain and a small bending rigidity, the membrane oscillates strongly around an average spherical cap shape. If such a vesicle is deflated, the contact area increases or decreases with increasing osmotic pressure, depending on the relative size of the vesicle and the circular γ domain. The lateral localization of the vesicle's center of mass by such a domain is optimal for a certain domain radius, which is found to be rather independent of adhesion strength and bending rigidity. For vesicles adhering to stripe-shaped surface domains, the width of the contact area perpendicular to the stripe varies nonmonotonically with the adhesion strength.     

Compressing a rigid filament: Buckling and cyclization

We study elastic properties of rigid filaments modeled as stiff chains shorter than their persistence length. By rigid filaments we mean that fluctuations around the optimal filament shape are weak and that low-order expansions (quadratic or quartic) in the deviation from the optimal shape are sufficient to describe them. Our main interest lies in the profiles of force vs. projected filament length, closure probability and weakly buckled states. Results may be relevant to experiments on self-assembled biological (microtubules, actin filaments) and synthetic (organo-gelators) filaments, carbon nanotubes and polymers grafted with strongly repelling side chains, some of which are discussed here.     

Budding and fission of a multiphase vesicle

We present a model of bi-phasic vesicles in the limit of large surface tension. In this regime, the vesicle is completely stretched and well described by two spherical caps with a fold, which concentrates the membrane stress. The conservation laws and geometric constraints restrict the space of possible shapes to a pair of solutions labeled by a parameter given by line tension/pressure. For a given value of , the two solutions differ by the length of the interface between domains. For a critical value, , the two vesicle shapes become identical and no connected solution exists above this critical value. This model sheds new light on two proposed mechanisms (osmotic shocks and molecule absorption) to explain the budding and the fission in recent experiments.     

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     

Contribution of the Nernst potential to stiffness constants: The asymmetrical case

Inside biological membranes, one of the fundamental functions of active proteins such as pumps is to generate some electrochemical gradient across the membrane and then, to establish a new stationary state. The membrane electric potential generated by activity modifies the stiffness constants of the membrane. A spontaneous curvature appears if the inner and outer Debye lengths are different. The corresponding characteristic radius falls in the range from 0.08μm to 50μm. The bending elastic modulus is always increased. This effect is only noticeable in the limit of large Debye length from 0.5μm to 0.09μm. For a Nernst potential of 100mV and a Debye length of 0.2μ m, the bending modulus can reach 40k_BT. An erratum to this article is available at .     

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.     

Vesicle self-reproduction: The involvement of membrane hydraulic and solute permeabilities

Conditions for self-reproduction are sought for a growing vesicle with its growth defined by an exponential increase of vesicle membrane area and by adequate flow of the solution across the membrane. In the first step of the presumed vesicle self-reproduction process, the initially spherical vesicle must double its volume in the doubling time of the membrane area and, through the appropriate shape transformations, attain the shape of two equal spheres connected by an infinitesimally thin neck. The second step involves separation of the two spheres and relies on conditions that cause the neck to be broken. In this paper we consider the first step of this self-reproduction process for a vesicle suspended in a solution whose solute can permeate the vesicle membrane. It is shown that vesicle self-reproduction occurs only for certain combinations of the values of membrane hydraulic and solute permeabilities and the external solute concentration, these quantities being related to the mechanical properties of the membrane and the membrane area doubling time. The analysis includes also the relaxation of a perturbed system towards stationary self-reproduction behavior and the case where the final shape consists of two connected spheres of different radii.     

Specific biomembrane adhesion --Indirect lateral interactions between bound receptor molecules

We studied biomembrane adhesion using the micropipet aspiration technique. Adhesion was caused by contact site A, a laterally mobile and highly specific cell adhesion molecule from Dictyostelium discoideum, reconstituted in lipid vesicles of DOPC (L-α-dioleoylphosphatidylcholine) with an addition of 5 mol % DOPE-PEG₂₀₀₀ (1,2-diacyl-sn-glycero-3-phosphatidylethanolamine-N-[poly(ethyleneglycol) 2000]). The “fuzzy” membrane mimics the cellular plasma membrane including the glycocalyx. We found adhesion and subsequent receptor migration into the contact zone. Using membrane tension jumps to probe the equation of state of the two-dimensional “gas” of bound receptor pairs within the contact zone, we found strong, attractive lateral interactions. Received 16 February 2001     

Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2+

We present a study of the fractal dimension of clusters of large unilamellar vesicles (LUVs) formed by egg yolk phosphatidylcholine (EYPC), dimyristoylphosphocholine (DMPC) and dipalmitoylphosphocholine (DPPC) induced by Ca²⁺ . Fractal dimensions were calculated by application of two methods, measuring the angular dependency of the light scattered by the clusters and following the evolution of the cluster size. In all cases, the fractal dimensions fell in the range from 2.1 to 1.8, corresponding to two regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). Whereas DMPC clusters showed a typical transition from the RLCA to the DLCA aggregation, EYPC exhibited an unusual behaviour, since the aggregation was limited for a higher concentration than the critical aggregation concentration. The behaviour of DPPC was intermediate, with a transition from the RLCA to the DLCA regimes with cluster sizes depending on Ca²⁺ concentration. Studies on the reversibility of the aggregates show that EYPC and DPPC clusters can be re-dispersed by dilution with water. DMPC does not present reversibility. Reversibility is evidence of the existence of secondary minima in the DLVO potential between two liposomes. To predict these secondary minima, a correction of the DLVO model was necessary taking into account a repulsive force of hydration.     

Structure and interaction potentials in solid-supported lipid membranes studied by X-ray reflectivity at varied osmotic pressure

Highly oriented solid-supported lipid membranes in stacks of controlled number N ≃ 16 (oligo-membranes) have been prepared by spin-coating using the uncharged lipid model system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The samples have been immersed in aqueous polymer solutions for control of osmotic pressure and have been studied by X-ray reflectivity. The bilayer structure and fluctuations have been determined by modelling the data over the full q-range. Thermal fluctuations are described using the continuous smectic Hamiltonian with the appropriate boundary conditions at the substrate and at the free surface of the stack. The resulting fluctuation amplitudes and the pressure-distance relation are discussed in view of the inter-bilayer potential.     

Collective alignment of polar filaments by molecular motors

We study the alignment of polar biofilaments, such as microtubules and actin, subject to the action of multiple molecular motors attached simultaneously to more than one filament. Focusing on a paradigm model of only two filaments interacting with multiple motors, we were able to investigate in detail the alignment dynamics. While almost no alignment occurs in the case of a single motor, the filaments become rapidly aligned due to the collective action of the motors. Our analysis shows that the alignment time is governed by the number of bound motors and the magnitude of the motors’ stepping fluctuations. We predict that the time scale of alignment is in the order of seconds, much faster than that reported for passive crosslink-induced bundling. In vitro experiments on the alignment of microtubules by multiple-motor covered beads are in qualitative agreement. We also discuss another mode of fast alignment of filaments, namely the cooperation between motors and passive crosslinks.     

Diffusion in supported lipid bilayers: Influence of substrate and preparation technique on the internal dynamics

The diffusion law of DMPC and DPPC in Supported Lipid Bilayers (SLB), on different substrates, has been investigated in details by Fluorescence Recovery After Patterned Photobleaching (FRAPP). Over micrometer length scales, we demonstrate the validity of a purely Brownian diffusive law both in the gel and the fluid phases of the lipids. Measuring the diffusion coefficient as a function of temperature, we characterize the gel-to-liquid phase transition of DMPC and DPPC. It is shown that, depending on the type of substrate and the method used for bilayer preparation, completely different behaviours can be observed. On glass substrates, using the Langmuir-Blodgett deposition technique, both leaflets of the bilayer have the same dynamics. On mica, the dynamics of the proximal leaflet is slower than the dynamics of the distal leaflet, although the transition temperature is the same for both layers. Preparing bilayers from vesicle fusion in same conditions leads to more random behaviours and shifted transition temperatures.     

Molecular mobility of confined phases in model mesoporous (MCM-41) and microporous (AlPO4-5 zeolite) host materials

This paper discusses the self-assembly of block copolymers into vesicular morphology. After a brief state of art of the field, a system based on an amphiphilic poly(butadiene)-b-poly(-L-glutamic acid) (PB-b-PGA) diblock copolymer in aqueous solution is discussed in detail. The aggregation behavior of this block copolymer has been investigated by means of fluorescence spectroscopy, dynamic (DLS) and static (SLS) light scattering as well as transmission electron microscopy (TEM). The diblock copolymer was found to form well-defined vesicles in water. The size of these so-called polymersomes or peptosomes could be reversibly manipulated as a function of both pH and ion strength. Depending on the pH of the aqueous solution, the hydrodynamic radii of these vesicles were found to vary from 100 nm to 150 nm. By cross-linking the 1,2-vinyl double bonds present in the polybutadiene block, the ability to transform a transient supramolecular self-organized aggregate into a permanent “shape-persistent stimuli-responsive nanoparticle” has been demonstrated. Received 25 June 2002 and Received in final form 22 October 2002 Published online: 11 March 2003     

Thermal undulations of quasi-spherical vesicles stabilized by gravity

The classical treatment of quasi-spherical vesicle undulations has, in the present work, been reviewed and extended to systems, which are affected by a gravitational field caused by a density difference across the membrane. The effects have been studied by the use of perturbation theory leading to corrections to the mean shape and the fluctuation correlation matrix. These corrections have been included in an analytical expression for the flicker spectrum to probe how the experimentally accessible spectrum changes with gravity. The results are represented in terms of the gravitational parameter, g ₀ = ΔρgR ⁴/κ. The contributions from gravity are in most experimental situations small and thus negligible, but for values of g₀ above a certain limit, the perturbational corrections must be included. Expressions for the relative error on the flicker spectrum have been worked out, so that it is possible to define the regime where gravity is negligible. An upper limit of g₀ has also been identified, where the error in all modes of the flicker spectrum is significant due to distortion of the mean shape. Received 9 July 2002 and Received in final form 15 November 2002 RID="a" ID="a"e-mail: jonas@kemi.dtu.dk RID="b" ID="b"e-mail: ipsen@memphys.sdu.dk     

Tilt angle of lipid acyl chains in unilamellar vesicles determined by ellipsometric light scattering

Ellipsometric light scattering (ELS) at room temperature is applied to unilamellar vesicles (~50 nm radius) of 1,2-Dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in the gel phase and of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) in the liquid-crystaline phase. A high sensitivity of this technique to the local anisotropy is found. From the resulting local birefringence, a lower limit of (29 ±0.5)^○ for the average tilt angle of the lipid chains of DPPC with respect to the membrane normal is estimated. This tilt angle value is slightly lower than literature values for the tilt angle in oriented lipid multi-bilayers on solid substrates.     

Membrane transistor with giant lipid vesicle touching a silicon chip

Lipid bilayers on silicon may become the matrix of future bioelectronic devices if the junction is sufficiently insulating. We touched the open gate of a field-effect transistor with a preformed giant lipid vesicle and bound the membrane by means of polyelectrolyte interaction. The sheet resistance along the junction was 100 GΩ and the membrane resistance was above 100 GΩ at a contact area of 1000 μm². The bilayer was fluid and smoothly followed the surface profile of the chip. The compound lipid–silicon structure is suitable to couple semiconductor and electroactive proteins. Received: 12 August 1999 / Accepted: 16 August 1999 / Published online: 6 October 1999     

Universal properties of shortest paths in isotropically correlated random potentials

We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations. Received 20 December 2002 / Received in final form 10 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: schorr@lusi.uni-sb.de     

Influence of membrane lipid composition on the activity of functionally reconstituted LmrA under high hydrostatic pressure

In cellular membranes, proteins and lipids are in sensitive macromolecular interaction influencing each other. To evaluate this interaction, the multi-drug transporter LmrA from Lactococcus lactis was functionally reconstituted in vesicles consisting of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), DMPC+10 mol% cholesterol and the model raft mixture DOPC/1,2-dipalmitoyl-sn-glycero-3-phosphocholine/cholesterol (1:2:1) and in natural membrane lipids at 30 °C. The lateral structure and organization of these proteoliposomes were modulated using high hydrostatic pressure. A sharp pressure-induced fluid-to-gel phase transition is observed without an extended two-phase region. The possibility for lipid sorting, such as for DMPC/cholesterol bilayers, has an inhibitory effect on the LmrA activity. A fluid-like membrane phase over the whole pressure range with suitable hydrophobic matching, such as for DOPC, prevents the membrane protein from high-pressure inactivation up to 200 MPa. Under high-pressure conditions, highest LmrA activities, exceeding those at ambient pressure, are achieved for heterogeneous lipid matrices with a small hydrophobic mismatch and the ability of lipid sorting.     

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.