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Biomedical subjects

G Gompper

Publications and source records attributed to G Gompper.

At least 19 recordsLinked to original sources
PubMed2006

Star polymers in shear flow.

Linear and star polymers in solution are studied in the presence of shear flow. The solvent is described by a particle-based mesoscopic simulation technique, which accounts for hydrodynamic interactions. The scaling properties of the average gyration tensor, the orientation angle, and the rotation frequency are investigated for various arm lengths and arm numbers. With increasing functionality f, star polymers exhibit a crossover in their flow properties from those of linear polymers to a novel behavior, which resembles the tank-treading motion of elastic capsules.

Elasticity↗
PubMed2006

Forced crumpling of self-avoiding elastic sheets.

Thin elastic sheets are important materials across length scales ranging from mesoscopic (polymerized membranes, clay platelets, virus capsids) to macroscopic (paper, metal foils). The crumpling of such sheets by external forces is characterized by the formation of a complex pattern of folds. We have investigated the role of self-avoidance, the fact that the sheets cannot self-intersect, for the crumpling process by large-scale computer simulations. At moderate compression, the force-compression relations of crumpled sheets for both self-avoiding and phantom sheets are found to obey universal power-law behaviours. However, self-avoiding sheets are much stiffer than phantom sheets and, for a given compression, develop many more folds. Moreover, self-avoidance is relevant already at very small volume fractions. The fold-length distribution for crumpled sheets is determined, and is found to be well-described by a log-normal distribution. The stiffening owing to self-avoidance is reflected in the changing nature of the sheet-to-sheet contacts from line-like to two-dimensionally extended with increasing compression.

Biocompatible Materials↗
PubMed2005

Dynamics of polymers in a particle-based mesoscopic solvent.

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.

Journal Article↗
PubMed2005

Dynamic regimes of fluids simulated by multiparticle-collision dynamics.

We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the "particle regime" in which the dynamics is gaslike and the "collective regime" where the dynamics is fluidlike. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecular-chaos assumption, are found to describe the simulation data very well in the particle regime, but important deviations are found in the collective regime. These deviations are due to hydrodynamic correlations. The model is then extended in order to investigate self-diffusion in colloidal dispersions. We study first the transport properties of heavy pointlike particles in the mesoscopic solvent, as a function of their mass and number density. Second, we introduce excluded-volume interactions among the colloidal particles and determine the dependence of the diffusion coefficient on the colloidal volume fraction for different solvent mean-free paths. In the collective regime, the results are found to be in good agreement with previous theoretical predictions based on Stokes hydrodynamics and the Smoluchowski equation.

Journal Article↗
PubMed2004

Helical polymer in cylindrical confining geometries.

Using an algorithm for simulating equilibrium configurations, we study a fluctuating helical polymer either (i) contained in a cylindrical pore or (ii) wound around a cylindrical rod. We work in the regime where both the contour length and the persistence length of the helical polymer are much larger than the diameter of the cylinder. In case (i) we calculate the free energy of confinement and interpret it in terms of a wormlike chain in a pore with an effective diameter that depends on the parameters of the helix. In case (ii) we consider the possibility that one end of the helical polymer escapes from the rod and wanders away. The average numbers of turns at which the helix escapes or intersects the rod are measured in the simulations, as a function of the pitch p(0) . The behavior for large and small p(0) is explained with simple scaling arguments.

Journal Article↗
PubMed2004

Attraction between DNA molecules mediated by multivalent ions.

The effective force between two parallel DNA molecules is calculated as a function of their mutual separation for different valencies of counterion and salt ions and different salt concentrations. Computer simulations of the primitive model are used and the shape of the DNA molecules is accurately modeled using different geometrical shapes. We find that multivalent ions induce a significant attraction between the DNA molecules whose strength can be tuned by the averaged valency of the ions. The physical origin of the attraction is traced back either to electrostatics or to entropic contributions. For multivalent counterions and monovalent salt ions, we find a salt-enhanced repulsion effect: the force is first attractive but gets repulsive with increasing salt concentration. Furthermore, we show that the multivalent-ion-induced attraction does not necessarily correlate with DNA overcharging.

Binding Sites↗
PubMed2003

Budding of crystalline domains in fluid membranes.

Crystalline domains embedded in fluid membrane vesicles are studied by Monte Carlo simulations of dynamically triangulated surfaces and by scaling arguments. A budding transition from a caplike state to a budded shape is observed for increasing spontaneous curvature C0 of the crystalline domain as well as increasing line tension lambda. The location of the budding transition is determined as a function of C0, lambda, and the radius R(A) of the crystalline domain. In contrast to previous theoretical predictions, it is found that budding occurs at a value of the spontaneous curvature C0, that is always a decreasing function of the domain size R(A). Several characteristic scaling regimes are predicted. The distribution of five- and sevenfold disclinations as the budding transition is approached is determined, and the dynamics of the generation of defects is studied.

Animals↗
PubMed2003

Adsorption of monovalent and multivalent cations and anions on DNA molecules.

Adsorption of monovalent and multivalent cations and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modeled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modeled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major-groove cationic charge is independent of the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salts. Simulations for larger ion radii, which mimic the effect of ion hydration, indicate an increased adsorbtion of cations in the major groove.

Anions↗
PubMed2002

Elastic properties of polymer interfaces: aggregation of pure diblock, mixed diblock, and triblock copolymers.

Block copolymers adsorbing to an interface between two immiscible homopolymers modify the elastic constants of this interface. Within self-consistent field calculations for Gaussian chains, we determine how the bending constants vary in dependence on the block copolymer concentration and architecture. Four phenomena are discussed. (i) When a tricritical or isotropic Lifshitz critical point is approached in a ternary mixture by varying the concentration of diblock copolymers or changing temperature, the elastic constants vanish. We determine the corresponding power laws, and show that the de Gennes-Taupin criterium for the stability of lamellar phases against undulations and the Ginzburg-Landau criterium for bulk fluctuations yield identical predictions for the validity of the mean-field approximation. (ii) Addition of a small amount of diblock copolymers modifies the bending rigidity. If the diblock copolymers are comparable in length to the homopolymers, adsorption of the diblocks reduces the bending rigidity. If the diblocks are much longer, they increase the bending rigidity. Only for an extreme ratio of chain lengths (>100), the predictions for polymers tethered to an infinitely thin, impenetrable sheet become accurate. (iii) Mixtures of short and long symmetric diblock copolymers are studied, as well as mixtures of two asymmetric diblocks, which are obtained by exchanging the long and short ends. The saddle-splay modulus is found to be the same in both mixtures, while the bending rigidity is significantly smaller in the latter case. (iv) The role of the block copolymer architecture is studied by comparing the effect of triblock copolymers with the effect of diblocks with the same overall length and composition. We propose that triblock copolymers are a very efficient way to control the spontaneous curvature of an interface.

Journal Article↗
PubMed2002

Mesoscopic solvent simulations: multiparticle-collision dynamics of three-dimensional flows.

A recently developed mesoscopic solvent model with multiparticle-collision dynamics is applied to three-dimensional solvent flows in a channel with and without a spherical obstacle. The advantage of a gravitationally driven flow of the solvent over the flow induced by a pressure gradient in the calculation of the solvent viscosity is demonstrated. Three different algorithms for stochastic collision steps are investigated and compared. In particular, we have examined an alternative algorithm with relative velocities drawn from a Maxwell-Boltzmann distribution at each collision step. This algorithm increases the numerical efficiency of the mesoscopic model for solvent flows with low and intermediate Reynolds numbers. Our simulation results for the recirculation length of stationary vortices behind a spherical obstacle are in good agreement with the previous experimental measurements.

Journal Article↗
PubMed2002

Numerical study of the flow around a cylinder using multi-particle collision dynamics.

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.

Journal Article↗
PubMed2001

Semiflexible polymer in a uniform force field in two dimensions.

The conformational properties of a semiflexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point, and field strength.

Journal Article↗
PubMed2001

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.

Journal Article↗
PubMed2000

Stability of inverse bicontinuous cubic phases in lipid-water mixtures

We investigate the stability of seven inverse bicontinuous cubic phases [ G, D, P, C(P), S, I-WP, F-RD] in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only G, D, and P are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acid/DLPC.

Journal Article↗
PubMed2000

Membrane decoration by amphiphilic block copolymers in bicontinuous microemulsions.

The effect of various amphiphilic block copolymers of different molar masses on the structure and phase behavior of ternary amphiphilic systems (water, oil, and nonionic surfactant) is investigated. Small amounts of PEP-PEO block copolymer lead to a dramatic increase in the volumes of oil and water, which can be solubilized in a bicontinuous microemulsion. High-precision neutron scattering experiments with a sophisticated contrast variation technique demonstrate that the polymers form uniformly distributed mushroom conformations on the surfactant membrane. Based on these observations, we propose a universal mechanism for the swelling behavior, which is due to the variation of the membrane curvature elasticity.

Cell Membrane↗
PubMed1999

Systematic approach to bicontinuous cubic phases in ternary amphiphilic systems.

The Fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures in the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both single and double structures are investigated; they correspond to systems with one or two monolayers in a unit cell, respectively. We show how and why single structures can be made to approach triply periodic minimal surfaces very closely, and give improved nodal approximations for G, D, I-WP, and P surfaces. We demonstrate that the relative stability of the single structures can be calculated from the geometrical properties of their interfaces only. The single gyroid G turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity. The representations are used to calculate distributions of the Gaussian curvature and 2H-nuclear-magnetic-resonance band shapes for C(P), C(D), S, C(Y), and F-RD surfaces.

Journal Article↗
PubMed1999

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.

Cell Membrane↗