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Background: Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain., Results: Here we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices., Conclusions: We have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue the need for a deeper understanding of the microscopic activities underpinning macroscopic self-organization in active gels and urge further experiments to help bridge these lengths.

In order to study the dynamics of colloidal suspensions with viscoelastic solvents, a simple mesoscopic model of the solvent is required. We propose to extend the multiparticle collision dynamics (MPC) technique--a particle-based simulation method, which has been successfully applied to study the hydrodynamic behavior of many complex fluids with Newtonian solvent--to shear-thinning viscoelastic solvents. Here, the normal MPC particles are replaced by dumbbells with finite-extensible nonlinear elastic (FENE) springs. We have studied the properties of FENE-dumbbell fluids under simple shear flow with shear rate ̇γ. The stress tensor is calculated, and the viscosity η and the first normal-stress coefficient Ψ(1) are obtained. Shear-thinning behavior is found for reduced shear rates Γ= ̇γτ>1, where τ is a characteristic dumbbell relaxation time. Here, both η and Ψ(1) display power-law behavior in the shear-thinning regime. Thus, the FENE-dumbbell fluid with MPC collisions provides a good description of viscoelastic fluids. As a first application, we study the flow behavior of a colloid in a shear-thinning viscoelastic fluid in two dimensions. A slowing down of the colloid rotation in a viscoelastic fluid compared to a Newtonian fluid is obtained, in agreement with recent numerical calculations and experimental results., (© 2011 American Institute of Physics)

The dynamical deformation of ultrasoft colloids as well as their dynamic frictional forces are numerically investigated, when one colloid is dragged past another at constant velocity. Hydrodynamic interactions are captured by a particle-based mesoscopic simulation method. At vanishing relative velocity, the equilibrium repulsive force-distance curve is obtained. At large drag velocities, in contrast, we find an apparent attractive force for departing colloids along the dragging direction. The deformation, in the close encounter of colloids, and the energy dissipation are examined as a function of the drag velocity and their separation.

Nonequilibrium structure formation and dynamics in suspensions of superparamagnetic colloids driven by an external rotating magnetic field are studied by particle-based mesoscale hydrodynamics simulations in confined geometry. We address the fundamental question how the rotation of the colloids about their own axes can be converted into a translational motion by breaking the symmetry of the confining geometry. We study a two-dimensional system of colloids with short-range repulsive interactions, which mimics flow in shallow microchannels. In straight channels, we observe a two-way traffic but--for symmetry reasons--no net transport. However, by keeping some colloids fixed near one of the two walls, net transport can be achieved. This approach allows the control and switchability of the flow in complex microchannel networks. A minimal geometry that fulfills the requirement of broken symmetry are ring channels. We determine the translational velocity of the spinning colloids and study its dependence on the channel width for various median radii. We conclude that spinning colloids present a promising alternative for flow generation and control in microfluidic devices.

The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood's microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit. We explicitly represent cell-cell interactions and identify the types and sizes of reversible rouleaux structures that yield a tremendous increase of blood viscosity at low shear rates. We also present the first quantitative estimates of the magnitude of adhesive forces between red cells. In addition, our simulations support the hypothesis, previously deduced from experiments, of yield stress as an indicator of cell aggregation. This non-Newtonian behavior is analyzed and related to the suspension's microstructure, deformation, and dynamics of single red blood cells. The most complex cell dynamics occurs in the intermediate shear rate regime, where individual cells experience severe deformation and transient folded conformations. The generality of these cell models together with single-cell measurements points to the future prediction of blood-viscosity anomalies and the corresponding microstructures associated with various diseases (e.g., malaria, AIDS, and diabetes mellitus). The models can easily be adapted to tune the properties of a much wider class of complex fluids including capsule and vesicle suspensions.

The flow behavior of a semiflexible polymer in microchannels is studied using multiparticle collision dynamics, a particle-based hydrodynamic simulation technique. Conformations, distributions, and radial cross-streamline migration are investigated for various bending rigidities, with persistence lengths L(p) in the range 0.5 ≤ L(p)/L(r) ≤ 30. The flow behavior is governed by the competition between a hydrodynamic lift force and steric repulsion from the wall, which lead to migration away from the wall, and a locally varying flow induced orientation, which drives the polymer away from the channel center and towards the wall. The different dependences of these effects on the polymer bending rigidity and the flow velocity results in a complex dynamical behavior. However, a generic effect is the appearance of a maximum in the monomer and the center-of-mass distributions, which occurs at the channel center for small flow velocities, but moves off-center at higher velocities.

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. A specific example of this is seen in solutions of lipid mixtures where the two species form lamellar structures and spherical micelles, respectively. Here, vesicles connected by threadlike micelles can form in a narrow concentration range of the sphere-forming lipid. We present a study of these structures based on self-consistent field theory (SCFT), a coarse-grained model of amphiphiles. First, we show that the addition of sphere-forming lipid to a solution of lamella-former can lower the free energy of cylindrical, threadlike micelles and hence encourage their formation. Next, we demonstrate the coupling between composition and curvature; specifically, that increasing the concentration of sphere-former in a system of two bilayers connected by a thread leads to a transfer of amphiphile to the thread. We further show that the two species are segregated within the structure, with the concentration of sphere-former being significantly higher in the thread. Finally, the addition of larger amounts of sphere-former is found to destabilize the junctions linking the bilayers to the cylindrical micelle, leading to a breakdown of the connected structures. The degree of segregation of the amphiphiles and the amount of sphere-former required to destabilize the junctions is shown to be sensitive to the length of the hydrophilic block of the sphere-forming amphiphiles.

The swimming behavior of self-propelled microorganisms is studied by particle-based mesoscale simulations. The simulation technique includes both hydrodynamics and thermal fluctuations that are both essential for the dynamics of microswimmers. The swimmers are modeled as squirmers, i.e., spherical objects with a prescribed tangential surface velocity, where the focus of thrust generation can be tuned from pushers to pullers. For passive squirmers (colloids), we show that the velocity autocorrelation function agrees quantitatively with the Boussinesq approximation. Single active squirmers show a persistent random-walk behavior, determined by forward motion, lateral diffusion, and orientational fluctuations, in agreement with theoretical predictions. For pairs of squirmers, which are initially swimming in parallel, we find an attraction for pushers and a repulsion for pullers, as expected. The hydrodynamic force between squirmer pairs is calculated as a function of the center-to-center distances d(cm) and is found to be consistent with a logarithmic distance dependence for d(cm) less than about two sphere diameters; here, the force is considerably stronger than expected from the far-field expansion. The dependence of the force strength on the asymmetry of the polar surface velocity is obtained. During the collision process, thermal fluctuations turn out to be very important and to strongly affect the postcollision velocity directions of both squirmers.

We consider an inextensible, semiflexible polymer or wormlike chain, with persistence length P and contour length L, fluctuating in a cylindrical channel of diameter D. In the regime D< occupied by the polymer and the mean-square deviation from the average vary as =[1-α(∘)(D/P)(2/3)]L and <ΔR(∥)(2)>=β(∘)(D(2)P)L , respectively, where α(∘) and β(∘) are dimensionless amplitudes. In earlier work we determined α(∘) and the analogous amplitude α(square) for a channel with a rectangular cross section from simulations of very long chains. In this paper, we estimate β(∘) and β(square) from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of R(∥) or radial distribution function, which is asymptotically exact for large L and has the skewed shape seen experimentally.

Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems: self-propelled rods interacting via volume exclusion and sinusoidally beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are gaussian distributed with a nonzero average. These systems are studied by brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are varied. By distinguishing three types of cluster-size probability density functions, we obtain a phase diagram of different swarm behaviors. The properties of clusters such as their configuration, lifetime, and average size are analyzed. We find that the swarm behavior of the two systems, characterized by several effective power laws, is very similar. However, a more careful analysis reveals several differences. Clusters of self-propelled rods form due to partially blocked forward motion and are therefore typically wedge shaped. At higher rod density and low noise, a giant mobile cluster appears, in which most rods are mostly oriented toward the center. In contrast, flagella become hydrodynamically synchronized and attract each other; their clusters are therefore more elongated. Furthermore, the lifetime of flagella clusters decays more quickly with cluster size than of rod clusters.

Sperm are propelled by an actively beating tail, and display a wide variety of swimming patterns. When confined between two parallel walls, sperm swim either in circles or on curvilinear trajectories close to the walls. We employ mesoscale hydrodynamics simulations in combination with a mechanical sperm model to study the swimming behavior near walls. The simulations show that sperm become captured at the wall due to the hydrodynamic flow fields which are generated by the flagellar beat. The circular trajectories are determined by the chiral asymmetry of the sperm shape. For strong (weak) chirality, sperm swim in tight (wide) circles, with the beating plane of the flagellum oriented perpendicular (parallel) to the wall. For comparison, we also perform simulations based on a local anisotropic friction of the flagellum. In this resistive force approximation, surface adhesion and circular swimming patterns are obtained as well. However, the adhesion mechanism is now due to steric repulsion, and the orientation of the beating plane is different. Our model provides a theoretical framework that explains several distinct swimming behaviors of sperm near and far from a wall. Moreover, the model suggests a mechanism by which sperm navigate in a chemical gradient via a change of their shape., (2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The effects of embedded proteins on the dynamical properties of lipid bilayer membranes are studied in shear flow. Coarse-grained molecular simulations are employed, in which lipids are modeled as short polymers consisting of hydrophilic head groups and hydrophobic tail monomers; similarly, transmembrane proteins are modeled as connected hydrophobic double- or triple-chain molecules with hydrophilic groups at both ends. In thermal equilibrium, rigid proteinlike molecules aggregate in a membrane of flexible lipids, while flexible proteins do not aggregate. In shear flow parallel to the membrane, the monolayers of lipid bilayer slide over each other. The presence of transmembrane proteins enhances the intermonolayer friction. The friction coefficient depends on the chain lengths of lipids, the membrane tension, the length of the protein, and the cluster size. It is found to increase with protein length (with positive mismatch, i.e., proteins which are longer than the membrane thickness) and protein cluster size. In flow, proteins get oriented in the flow direction to reduce friction, with large fluctuations of the orientation angle.

The sedimentation of an initially inhomogeneous distribution of hard-sphere colloids confined in a slit is simulated using the multi-particle collision dynamics scheme which takes into account hydrodynamic interactions mediated by the solvent. This system is an example for soft matter driven out of equilibrium where various length and time scales are involved. The initial laterally homogeneous density profiles exhibit a hydrodynamic Rayleigh-Taylor-like instability. Solvent backflow effects lead to an intricate non-linear behaviour which is analyzed via the solvent flow field and the colloidal velocity correlation function. Our simulation data are in good agreement with real-space microscopy experiments.

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membrane-mediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities etain and etaout inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast etain/etaout. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance ycm of the vesicle center of mass from the wall is well described by an effective power law ycm(-2) for intermediate distances 0.8Rp< approximately ycm< approximately 3Rp with vesicle radius Rp. The boundary-integral calculation indicates that the lift force decays asymptotically as 1/[ycm ln(ycm)] far from the wall.

We study the structure and phase behavior of fullerene-cubane C(60) x C(8)H(8) by Monte Carlo simulation. Using a simple potential model capturing the icosahedral and cubic symmetries of its molecular constituents, we reproduce the experimentally observed phase transition from a cubic to an orthorhombic crystal lattice and the accompanying rotational freezing of the C(60) molecules. We elaborate a scheme to identify the low-temperature orientations of individual molecules and to detect a pattern of orientational ordering similar to the arrangement of C(60) molecules in solid C(60). Our configuration of orientations supports a doubled periodicity along one of the crystal axes.

The recent development of microfluidic devices allows the investigation and manipulation of individual liquid microdroplets, capsules, and cells. The collective behavior of several red blood cells (RBCs) or microcapsules in narrow capillaries determines their flow-induced morphology, arrangement, and effective viscosity. Of fundamental interest here is the relation between the flow behavior and the elasticity and deformability of these objects, their long-range hydrodynamic interactions in microchannels, and thermal membrane undulations. We study these mechanisms in an in silico model, which combines a particle-based mesoscale simulation technique for the fluid hydrodynamics with a triangulated-membrane model. The 2 essential control parameters are the volume fraction of RBCs (the tube hematocrit, H(T)), and the flow velocity. Our simulations show that already at very low H(T), the deformability of RBCs implies a flow-induced cluster formation above a threshold flow velocity. At higher H(T) values, we predict 3 distinct phases: one consisting of disordered biconcave-disk-shaped RBCs, another with parachute-shaped RBCs aligned in a single file, and a third with slipper-shaped RBCs arranged as 2 parallel interdigitated rows. The deformation-mediated clustering and the arrangements of RBCs and microcapsules are relevant for many potential applications in physics, biology, and medicine, such as blood diagnosis and cell sorting in microfluidic devices.

Twist grain boundaries in bicontinuous cubic surfactant phases are studied by employing a Ginzburg-Landau model of ternary amphiphilic systems. Calculations are performed on a discrete real-space lattice with periodic boundary conditions for the lamellar L(alpha), gyroid G, diamond D, and the Schwarz P phases for various twist angles. An isosurface analysis of the scalar order parameter reveals the structure of the surfactant monolayer at the interfaces between the oil-rich and water-rich regions. The curvature distributions show that the grain boundaries are minimal surfaces. The interfacial free energy per unit area is determined as a function of the twist angle for the G, D, P, and lamellar phases using two complementary approaches: the Ginzburg-Landau free-energy functional and a geometrical approach based on the curvature energy of a monolayer. For the L(alpha), G, and D phases the interfacial free energy per unit area is very small, has the same order of magnitude, and exhibits a nonmonotonic dependence on the twist angle. The P phase is found to be unstable with respect to the nucleation of grain boundaries.

Sperm swimming at low Reynolds number have strong hydrodynamic interactions when their concentration is high in vivo or near substrates in vitro. The beating tails not only propel the sperm through a fluid, but also create flow fields through which sperm interact with each other. We study the hydrodynamic interaction and cooperation of sperm embedded in a two-dimensional fluid by using a particle-based mesoscopic simulation method, multiparticle collision dynamics. We analyze the sperm behavior by investigating the relationship between the beating-phase difference and the relative sperm position, as well as the energy consumption. Two effects of hydrodynamic interaction are found, synchronization and attraction. With these hydrodynamic effects, a multisperm system shows swarm behavior with a power-law dependence of the average cluster size on the width of the distribution of beating frequencies.

The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multiparticle collision dynamics (MPC), and dissipative particle dynamics, are investigated, both with and without angular-momentum conservation. Analytical results are derived for fluids with an ideal-gas equation of state and a finite-time-step dynamics, and compared with simulation data. In particular, the viscosity is derived in a general form for all variants of the MPC method. In general, very good agreement between theory and simulations is obtained.

In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multiparticle collision (MPC) dynamics model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated. Attractive wall potentials are applied to obtain a nearly uniform density everywhere in the simulation box. We find that both in steady and oscillatory shear flows, a boundary layer develops near the wall, with a higher velocity gradient than in the bulk. The thickness of this layer is proportional to the average dumbbell size. We determine the zero-shear viscosities as a function of the spring constant of the dumbbells and the mean free path. For very high shear rates, a very weak "shear thickening" behavior is observed. Moreover, storage and loss moduli are calculated in oscillatory shear, which show that the viscoelastic properties at low and moderate frequencies are consistent with a Maxwell fluid behavior. We compare our results with a kinetic theory of dumbbells in solution, and generally find good agreement.

The angular momentum is conserved in fluids with a few exceptions such as ferrofluids. However, it can be violated locally in fluid simulations to reduce computational costs. The effects of this violation are investigated using a particle-based simulation method, multiparticle collision dynamics, which can switch on or off angular-momentum conservation. To this end, we study circular Couette flows between concentric and eccentric cylinders, where nonphysical torques due to the lack of the angular-momentum conservation are found whereas the velocity field is not affected. In addition, in simulations of fluids with different viscosities in contact and star polymers in solvent, incorrect angular velocities occur. These results quantitatively agree with the theoretical predictions based on the macroscopic stress tensor.

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D<

The crystallography of two-dimensional particle packings on flexible surfaces of spherical topology is investigated. Examples are viral capsids and crystalline vesicles. Computer simulations of dynamically triangulated surfaces are employed to study the shape and structure of lattice defects as a function of the Föppl-von Kármán number gamma. We find that grain-boundary scars become much more fuzzy with increasing temperature, that the size of grain-boundary scars saturates with increasing vesicle radius, and that the buckling transition shifts to higher values of gamma due to the presence of scars.

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically triangulated surfaces, as well as a theoretical approach based on two variables: a shape parameter and the inclination angle, which has no adjustable parameters. We show that, between the well-known tank-treading and tumbling states, a new "swinging" state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.

The dynamics of membranes is studied on the basis of a particle-based meshless surface model, which was introduced earlier [Phys. Rev. E 73, 021903 (2006)]. The model describes fluid membranes with bending energy and-in the case of membranes with boundaries-line tension. The effects of hydrodynamic interactions are investigated by comparing Brownian dynamics with a particle-based mesoscale solvent simulation (multiparticle collision dynamics). Particles self-assemble into vesicles via disk-shaped membrane patches. The time evolution of assembly is found to consist of three steps: particle assembly into discoidal clusters, aggregation of clusters into larger membrane patches, and finally vesicle formation. The time dependence of the cluster distribution and the mean cluster size is evaluated and compared with the predictions of Smoluchowski rate equations. On the other hand, when the line tension is suddenly decreased (or the temperature is increased), vesicles dissolve via pore formation in the membrane. Hydrodynamic interactions are found to speed up the dynamics in both cases. Furthermore, hydrodynamics makes vesicle more spherical in the membrane-closure process.

Virus capsids and crystalline surfactant vesicles are two examples of self-assembled shells in the nano- to micrometer size range. Virus capsids are particularly interesting since they have to sustain large internal pressures while encapsulating and protecting the viral DNA. We therefore study the mechanical properties of crystalline shells of icosahedral symmetry on a substrate under a uniaxial applied force by computer simulations. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number of elementary building blocks N (the capsomers in the case of viral shells), the Föppl-von Kármán number gamma (which characterizes the relative importance of shear and bending elasticity), and the confining geometry. In particular, we show that whereas large shells are well described by continuum elasticity-theory, small shells of the size of typical viral capsids behave differently already for small deformations. Our results are essential to extract quantitative information about the elastic properties of viruses and vesicles from deformation experiments.

A meshless particle-based membrane model is proposed. The particles possess no internal degree of freedom and interact via a potential, which has three different contributions: a short-range repulsive pair potential, an attractive multibody potential, and a curvature potential based on the moving least-squares method. Brownian dynamics simulations are employed to demonstrate that the particles self-assemble into a membrane and to study equilibrium properties, such as bending rigidity, surface tension, line tension, and diffusion constant. The bending rigidity and line tension are shown to depend on different potential parameters and can therefore be varied independently. The finite-size effects of nearly planar membranes are investigated. This model is well suited to study the membrane dynamics with topological changes.

The dynamics of fluid vesicles and red blood cells (RBCs) in cylindrical capillary flow is studied by using a three-dimensional mesoscopic simulation approach. As flow velocity increases, a model RBC is found to transit from a nonaxisymmetric discocyteto an axisymmetric parachute shape (coaxial with the flow axis), while a fluid vesicle is found to transit from a discocyte to a prolate ellipsoid. Both shape transitions reduce the flow resistance. The critical velocities of the shape transitions are linearly dependent on the bending rigidity and on the shear modulus of the membrane. Slipper-like shapes of the RBC model are observed around the transition velocities. Our results are in good agreement with experiments on RBCs.

The effect of linear homopolymers, diblock copolymers, and star polymers anchored to a membrane on the membrane's fluctuation spectrum is investigated for low grafting densities. Due to the nonlocality of the polymer-membrane interaction, the effective bending rigidity kappa(eff)(q) of the composite membrane is found to depend strongly on the wave vector q of the membrane undulations. Analytical calculations for ideal linear chains and simulations for ideal and self-avoiding linear chains as well as for star polymers are presented. The analytical calculations are based on the Green's function approach of Bickel and Marques [Eur. Phys. J. E 9, 349 (2002)]; for the simulations the Monte Carlo method is used. The functional form of kappa(eff)(q) differs for end-grafted chains and diblock copolymers. In general, the polymer effect is most pronounced for undulations on length scales larger than or comparable to the polymer size, and decreases rapidly for smaller undulation wavelengths. Anchored linear chains always increase kappa; anchored star polymers may increase as well as decrease kappa, depending on whether they are anchored symmetrically or asymmetrically to the membrane.

The dynamical behavior of vesicles is investigated in simple shear flow. A simulation technique is presented that combines a three-dimensional particle-based mesoscopic model (multiparticle collision dynamics) for the solvent with a dynamically triangulated surface model for the membrane. In this model, thermal fluctuations of the solvent and of the membrane are consistently taken into account. The membrane viscosity can be varied by changing the bond-flip rate of the dynamically triangulated surface. Vesicles are found to transit from steady tank-treading to unsteady tumbling motion with increasing membrane viscosity. At small reduced volumes, the shear induces a transformation from a discocyte to a prolate shape at low membrane viscosity. On the other hand, at high membrane viscosity, the shear induces a transformation from prolate to discocyte, or tumbling motion accompanied by shape oscillations between these two states. Thermal fluctuations induce intermittent tumbling and smooth out the transitions. This effect can be understood from a simplified stochastic model.

The effect of membrane viscosity on the dynamics of vesicles in shear flow is studied. We present a new simulation technique, which combines three-dimensional multiparticle collision dynamics for the solvent with a dynamically triangulated membrane model. Vesicles are found to transit from steady tank treading to unsteady tumbling motion with increasing membrane viscosity. Depending on the reduced volume and membrane viscosity, shear can induce both discocyte-to-prolate and prolate-to-discocyte transformations. This behavior can be understood from a simplified model.

The effect of anchored linear and star polymers in the mushroom regime on the curvature elasticity of membranes is investigated by Monte Carlo simulations and scaling arguments. We describe a simulation method to calculate the free energy of anchored polymers as a function of membrane curvature, which is accurate enough to extract reliable values for the polymer-induced spontaneous curvature Deltac(0), bending rigidity Deltakappa, and saddle-splay modulus Deltakappa;. For self-avoiding linear and star polymers, the universal amplitudes of the curvature moduli as well as the effects of finite chain lengths are determined, to our knowledge, for the first time. We find that star polymers have the unique property of strongly affecting c(0) and kappa, but leaving kappa; essentially unchanged. Furthermore, star polymers are shown to have a much stronger effect on membrane properties than an equivalent number of linear polymers.

The bending elasticity of a fluid membrane is characterized by its modulus and spontaneous curvature. We present a new method, advanced flicker spectroscopy of giant nonspherical vesicles, which makes it possible to simultaneously measure both parameters for the first time. Our analysis is based on the generation of a large set of reference data from Monte Carlo simulations of randomly triangulated surfaces. As an example of the potential of the procedure, we monitor thermal trajectories of vesicle shapes and discuss the elastic response of zwitterionic membranes to transmembrane pH gradients. Our technique makes it possible to easily characterize membrane curvature as a function of environmental conditions.

We have observed polymersomes of high genus with their vesicle wall organized on the micrometer scale either in a double bilayer connected by a lattice of passages or a tubular network with hexagonal symmetry. Experimentally found shape classes are identified within a theoretical phase diagram based on the bending energy of the polymer membrane. Pronounced morphological changes could be induced and controlled by temperature.

A novel mesoscopic simulation technique--multi-particle collision dynamics--which has been suggested very recently, is used to study the two-dimensional flow around a square and a circular cylinder. The method is described and new proper boundary conditions are proposed to deal with wall collisions. The flow is analyzed in a wide range of Reynolds numbers in order to cover both the steady and unsteady regimes, resulting in symmetric steady vortices and periodic vortex shedding, respectively. The numerical results for integral flow parameters, such as the recirculation length, the drag and lift coefficients, the Strouhal number, as well as the spatial dependence of the velocity field, are compared with previous numerical and experimental studies. The qualitative and quantitative agreement is very good, validating the method as a promising technique to describe the hydrodynamic effects of solvent on embedded particles.

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.

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.

The conformation and scaling properties of self-avoiding fluid membranes with an extrinsic bending rigidity kappa were studied with the use of Monte Carlo methods. For kappa = 0, the results are consistent with branched polymer behavior at large length scales. There is a smooth crossover from a crumpled to an extended state with increasing kappa, with a peak in the specific heat when the persistence length reaches the system size. The scale-dependent effective bending rigidity is a decreasing function of system size for all bare rigidities. These results indicate that fluid membranes are always crumpled at sufficiently long length scales.