Phase diagram and tie-line determination for the ternary mixture DOPC/eSM/cholesterol.

We propose a novel, to our knowledge, method for the determination of tie lines in a phase diagram of ternary lipid mixtures. The method was applied to a system consisting of dioleoylphosphatidylcholine (DOPC), egg sphingomyelin (eSM), and cholesterol (Chol). The approach is based on electrofusion of single- or two-component homogeneous giant vesicles in the fluid phase and analyses of the domain areas of the fused vesicle. The electrofusion approach enables us to create three-component vesicles with precisely controlled composition, in contrast to conventional methods for giant vesicle formation. The tie lines determined in the two-liquid-phase coexistence region are found to be not parallel, suggesting that the dominant mechanism of lipid phase separation in this region changes with the membrane composition. We provide a phase diagram of the DOPC/eSM/Chol mixture and predict the location of the critical point. Finally, we evaluate the Gibbs free energy of transfer of individual lipid components from one phase to the other.

Nonisomorphic nucleation pathways arising from morphological transitions of liquid channels.

Motivated by unexpected morphologies of the emerging liquid phase (channels, bulges, droplets) at the edge of thin, melting alkane terraces, we propose a new heterogeneous nucleation pathway. The competition between bulk and interfacial energies and the boundary conditions determine the growth and shape of the liquid phase at the edge of the solid alkane terraces. Calculations and experiments reveal a "precritical" shape transition (channel-to-bulges) of the liquid before reaching its critical volume along a putative shape-conserving path. Bulk liquid emerges from the new shape, and, depending on the degree of supersaturation, the new pathway may have two, one, or zero energy barriers. The findings are broadly relevant for many heterogeneous nucleation processes because the novel pathway is induced by common, widespread surface topologies (scratches, steps, etc.).

Operation modes of the molecular motor kinesin.

The velocity and the adenosine triphosphate (ATP) hydrolysis rate of the molecular motor kinesin are studied using a general network representation for the motor, which incorporates both the energetics of ATP hydrolysis and the experimentally observed separation of time scales between chemical and mechanical transitions. Both the motor velocity and its hydrolysis rate can be expressed as superpositions of excess fluxes for the directed cycles (or dicycles) of the network. The sign of these dicycle excess fluxes depends only on two thermodynamic control parameters as provided by the load force F and the chemical energy Deltamicro released during the hydrolysis of a single ATP molecule. In contrast, both the motor velocity and its hydrolysis rate depend, in general, on the load force F as well as on the three concentrations of ATP, adenosine diphosphate (ADP), and inorganic phosphate (P), separately. Thus, in order to represent the different operation modes of the motor in the (F,Deltamicro) plane, one has to specify two concentrations such as the product concentrations [ADP] and [P]. As a result, we find four different operation modes corresponding to the four possible combinations of ATP hydrolysis or synthesis with forward or backward mechanical steps. Our operation diagram implies in particular that backward steps are coupled to ATP hydrolysis for sufficiently large ATP concentrations, but to ATP synthesis for sufficiently large ADP and/or P concentrations.

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 gamma , which strongly attracts this membrane. If the vesicle is larger than the attractive gamma 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 gamma 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 gamma 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 gamma 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.

Stochastic resonance for adhesion of membranes with active stickers.

The behavior of two membranes that interact by active adhesion molecules or stickers is studied theoretically using mean-field theory and Monte Carlo simulations. The stickers are anchored in one of the membranes and undergo conformational transitions between on and off states. In their on states, the stickers can bind to ligands that are anchored in the other membrane. The transitions between the on and off states arise from the coupling of the stickers to some active, energy-releasing process, which keeps the system out of equilibrium. As one varies the transition rates of this active process, the membrane separation undergoes a stochastic resonance: this separation is maximal at intermediate rates of the sticker transitions and considerably smaller both at high and at low transition rates. This implies that the effective, fluctuation-induced repulsion between the membranes contains a rate-dependent contribution that arises from the switching of the active stickers.

Two-component membrane material properties and domain formation from dissipative particle dynamics.

The material parameters (area stretch modulus and bending rigidity) of two-component amphiphilic membranes are determined from dissipative particle dynamics simulations. The preferred area per molecule for each species is varied so as to produce homogeneous mixtures or nonhomogeneous mixtures that form domains. If the latter mixtures are composed of amphiphiles with the same tail length, but different preferred areas per molecule, their material parameters increase monotonically as a function of composition. By contrast, mixtures of amphiphiles that differ in both tail length and preferred area per molecule form both homogeneous and nonhomogeneous mixtures that both exhibit smaller values of their material properties compared to the corresponding pure systems. When the same nonhomogeneous mixtures of amphiphiles are assembled into planar membrane patches and vesicles, the resulting domain shapes are different when the bending rigidities of the domains are sufficiently different. Additionally, both bilayer and monolayer domains are observed in vesicles. We conclude that the evolution of the domain shapes is influenced by the high curvature of the vesicles in the simulation, a result that may be relevant for biological vesicle membranes.

Effect of chain length and asymmetry on material properties of bilayer membranes.

Dissipative particle dynamics is used to extract the material parameters (bending and area stretch moduli) of a bilayer membrane patch. Some experiments indicate that the area stretch modulus of lipid vesicles varies little as the chain length of the lipids composing the bilayer increases. Here we show that making the interactions between the hydrophilic head groups of the model amphiphiles proportional to the hydrophobic tail length reproduces the above result for the area stretch modulus. We also show that the area stretch modulus of bilayers composed of amphiphiles with the same number of tail beads but with asymmetric chains is less than that of bilayers with symmetric chains. The effects on the bilayer density and lateral stress profiles of changes to the amphiphile architecture are also presented.

Activated dynamics of semiflexible polymers on structured substrates.

We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.

Stretching of semiflexible polymers with elastic bonds.

A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length. We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.

Lateral and transverse diffusion in two-component bilayer membranes.

We study the lateral and transverse diffusion of amphiphiles in two-component bilayer membranes, using a coarse-grained model for amphiphilic molecules and combined Monte Carlo-Molecular Dynamics simulations. Membrane structural properties, such as the mean thickness, are also measured. The dependence of such properties on membrane composition, inter-molecular interactions, and amphiphile stiffness is determined. In particular, we show that addition of shorter amphiphiles drives the model membrane towards a more fluid state, with increased amphiphile lateral diffusion rates. These results can be understood in the framework of a simple free-volume model. Furthermore, we observe an increase in the trans-membrane diffusion when the interaction energy of amphiphiles with their neighboring molecules is decreased.

Adhesion of membranes with competing specific and generic interactions.

Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. The membranes contain specific adhesion molecules (stickers) which are attracted by the second surface. In the absence of stickers, the trans-interaction between the membrane and the second surface is assumed to be repulsive at short separations. It is shown that the interplay of specific attractive and generic repulsive interactions can lead to the formation of a potential barrier. This barrier induces a line tension between bound and unbound membrane segments which results in lateral phase separation during adhesion. The mechanism for adhesion-induced phase separation is rather general, as is demonstrated by considering two distinct cases involving: i) stickers with a linear attractive potential, and ii) stickers with a short-ranged square-well potential. In both cases, membrane fluctuations reduce the potential barrier and, therefore, decrease the tendency of phase separation.

Random walks of cytoskeletal motors in open and closed compartments.

Random walks of molecular motors, which bind to and unbind from cytoskeletal filaments, are studied theoretically. The bound and unbound motors undergo directed and nondirected motion, respectively. Motors in open compartments exhibit anomalous drift velocities. Motors in closed compartments generate stationary nonequilibrium states with spatially varying densities of the motor concentrations and currents. "Traffic jams" on the filaments lead to a maximum of the motor current at an optimal motor concentration. Quantitative estimates based on experimental data for bound motors indicate that these transport phenomena are accessible to experiments.

Adhesion-induced phase behavior of multicomponent membranes.

Biomimetic membranes that contain several molecular components are studied theoretically. In contact with another surface, such as a solid substrate or another membrane, some of these intramembrane components are attracted by the second surface and, thus, act as local stickers. The cooperative behavior of these systems is characterized by the interplay of (i) attractive binding energies, (ii) entropic contributions arising from the shape fluctuations of the membranes, and (iii) the entropy of mixing of the stickers. A systematic study of this interplay, which starts from the corresponding partition functions, reveals that there are several distinct mechanisms for adhesion-induced phase separation within the membranes. The first of these mechanisms is effective for flexible stickers with attractive cis interactions (within the same membrane) and arises from the renormalization of these interactions by the confined membrane fluctuations. A second, purely entropic mechanism is found for rigid stickers without attractive cis interactions and arises from a fluctuation-induced line tension. Finally, a third mechanism is present if the membrane contains both stickers and repellers, i.e., nonadhesive molecules that protrude from the membrane surface. This third mechanism is based on an effective potential barrier and becomes less effective if the shape fluctuations of the membrane become more pronounced.

Budding dynamics of multicomponent membranes.

The budding of multicomponent membranes is studied by computer simulations and scaling arguments. The simulation algorithm combines dynamic triangulation with Kawasaki exchange dynamics. The budding process exhibits three distinct time regimes: (i) formation and growth of intramembrane domains; (ii) formation of many buds; and (iii) coalescence of small buds into larger ones. The coalescence regime (iii) is characterized by scaling laws which describe the long-time behavior. Thus, the number of buds, N(bud), decays as N(bud) approximately 1/t(theta) for large time t with theta = 1/2 and theta = 2/3 in the absence and the presence of hydrodynamic interactions, respectively.

Universal aspects of the chemomechanical coupling for molecular motors.

The directed movement of molecular motors is studied theoretically within a general class of nonuniform ratchet models in which the motor can attain M internal states and undergo transitions between these states at K spatial locations. The functional relationship between the motor velocity and the concentration of the fuel molecule is analyzed for arbitrary values of M and K. This relationship is found to exhibit universal features which depend on the number of unbalanced transitions per motor cycle arising from the enzymatic motor activity. This agrees with experimental results on dimeric kinesin and is predicted to apply to other cytoskeletal motors.

Unbinding transitions and phase separation of multicomponent membranes.

Multicomponent membranes in contact with another surface or wall are studied by a variety of theoretical methods and Monte Carlo simulations. The membranes contain adhesion molecules which are attracted to the wall and, thus, act as local stickers. It is shown that this system undergoes lateral phase separation leading to discontinuous unbinding transitions if the adhesion molecules are larger than the nonadhesive membrane components. This process is driven by an effective line tension which depends on the size of the stickers and arises from the interplay of shape fluctuations and sticker clusters.

Molecular motors and nonuniform ratchets.

Dimeric kinesin presumably moves in a "hand-over-hand" fashion via alternating steps of its two heads, which can cooperate in various ways. This motion is discussed in the framework of nonuniform ratchet models in which the molecular motor is described by M internal states and undergoes transitions at K spatial locations within the period of the molecular force potentials. Two subclasses of models with (M, K)=(3, 2) and (M, K)=(2, 2) are studied which correspond to weakly and strongly cooperative heads, respectively. Both subclasses lead to the same universal relationship between the motor velocity and the unbinding rate constant of the motor heads which is reminiscent of, but distinct from, Michaelis-Menten kinetics.

Liquid morphologies on structured surfaces: from microchannels to microchips

Liquid microchannels on structured surfaces are built up using a wettability pattern consisting of hydrophilic stripes on a hydrophobic substrate. These channels undergo a shape instability at a certain amount of adsorbed volume, from a homogeneous state with a spatially constant cross section to a state with a single bulge. This instability is quite different from the classical Rayleigh Plateau instability and represents a bifurcation between two different morphologies of constant mean curvature. The bulge state can be used to construct channel networks that could be used as fluid microchips or microreactors.

Modulated phases in multicomponent fluid membranes.

We investigate the behavior of flexible two-component bilayer and three-component monolayer membranes. The components are assumed to have different spontaneous curvatures, and to mutually phase separate in planar membranes. As a function of temperature, lateral tension and bending rigidity, a rich phase behavior is obtained. In particular, we find three different types of modulated phases. In symmetric bilayers, the excess component assembles at the boundary between oppositely curved domains; in sufficiently asymmetric bilayers, the excess component is found to preferentially assemble in a single layer, with no tendency for segregation to the domain boundaries. We show that the phase behavior of three-component monolayer strongly resembles the behavior of two-component bilayers. In fact, in a certain, restricted region of parameter space, the two models can be shown to be equivalent.