Early stages of clathrin aggregation at a membrane in coarse-grained simulations.

The self-assembly process of clathrin coated pits during endocytosis has been simulated by combining and extending coarse grained models of the clathrin triskelion, the adaptor protein AP2, and a flexible network membrane. The AP2's core, upon binding to membrane and cargo, releases a motif that can bind clathrin. In conditions where the core-membrane-cargo binding is weak, the binding of this motif to clathrin can result in a stable complex. We characterize the conditions and mechanisms resulting in the formation of clathrin lattices that curve the membrane, i.e., clathrin coated pits. The mechanical properties of the AP2 ß linker appear crucial to the orientation of the curved clathrin lattice relative to the membrane, with wild-type short linkers giving rise to the inward curving buds enabling endocytosis while long linkers produce upside-down cages and outward curving bulges.

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles.

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Coarse grain forces in star polymer melts.

An analysis is presented of forces acting on the centers of mass of three-armed star polymers in the molten state. The arms consist of 35 Kremer-Grest beads, which is slightly larger than needed for one entanglement mass. For a given configuration of the centers of mass, instantaneous forces fluctuate wildly around averages which are two orders of magnitude smaller than their root mean square deviations. Average forces are well described by an implicit many-body potential, while pair models fail completely. The fluctuating forces are modelled by means of dynamical variables quantifying the degree of mixing of the various polymer pairs. All functions and parameters in a coarse grain model based on these concepts are obtained from the underlying small scale simulation. The coarse model reproduces both the diffusion coefficient and the shear relaxation modulus. Ways to improve the model suggest themselves on the basis of our findings.

Mesoscale modeling of shear-thinning polymer solutions.

We simulate the linear and nonlinear rheology of two different viscoelastic polymer solutions, a polyisobutylene solution in pristane and an aqueous solution of hydroxypropylcellulose, using a highly coarse-grained approach known as Responsive Particle Dynamics (RaPiD) model. In RaPiD, each polymer has originally been depicted as a spherical particle with the effects of the eliminated degrees of freedom accounted for by an appropriate free energy and transient pairwise forces. Motivated by the inability of this spherical particle representation to entirely capture the nonlinear rheology of both fluids, we extended the RaPiD model by introducing a deformable particle capable of elongation. A Finite-Extensible Non-Linear Elastic potential provides a free energy penalty for particle elongation. Upon disentangling, this deformability allows more time for particles to re-entangle with neighbouring particles. We show this process to be integral towards recovering the experimental nonlinear rheology, obtaining excellent agreement. We show that the nonlinear rheology is crucially dependent upon the maximum elongation and less so on the elasticity of the particles. In addition, the description of the linear rheology has been retained in the process.

Coarse-grained simulations of moderately entangled star polyethylene melts.

In this paper, a previous coarse-grain model [J. T. Padding and W. J. Briels, J. Chem. Phys. 117, 925 (2002)] to simulate melts of linear polymers has been adapted to simulate polymers with more complex hierarchies. Bond crossings between highly coarse-grained soft particles are prevented by applying an entanglement algorithm. We first test our method on a virtual branch point inside a linear chain to make sure it works effectively when linking two linear arms. Next, we apply our method to study the diffusive and rheological behaviors of a melt of three-armed stars. We find that the diffusive behavior of the three-armed star is very close to that of a linear polymer with the same molecular weight, while its rheological properties are close to those of a linear chain with molecular mass equal to that of the longest linear sub-chain in the star.

Inducement by directional fields of rotational and translational phase ordering in polymer liquid-crystals.

The effects of aligning fields on models of polymer liquid crystals were simulated using the dissipative particle dynamics method. Exposing a liquid crystal of rod-like particles to a directional field causes a stabilization of the phases with orientational order, shifts the isotropic-nematic and nematic-smectic-A phase transitions to higher temperatures, makes the transitions continuous beyond a critical field strength, and induces weak para-nematic alignment in the zero-field isotropic phase. The interplay of liquid-crystalline ordering, microphase separation, and an alignment field endows the diblock and triblock copolymers studied here with rich phase behavior. The simulations suggest that field-induced orientational ordering can give rise to positional ordering. Reversely, positional ordering resulting from rod-coil demixing may be accompanied by orientational ordering, which is enhanced by external fields. For highly asymmetric rod-coil copolymers, the microphase separation pattern formed by the rigid segments can be altered by an aligning field.

The origin of flow-induced alignment of spherical colloids in shear-thinning viscoelastic fluids.

We have studied the poorly understood process of flow-induced structure formation by colloids suspended in shear-thinning fluids. These viscoelastic fluids contain long flexible chains whose entanglements appear and disappear continuously as a result of brownian motion and the applied shear flow. Responsive particle dynamics simulates each chain as a single smooth brownian particle, with slowly evolving inter-particle degrees of freedom accounting for the entanglements. The colloids mixed homogeneously in all simulated quiescent dispersions and they remain dispersed under slow shear flow. Beyond a critical shear rate, which varies depending on the fluid, the colloids aggregate and form flow-aligned strings in the bulk of the fluid. In this work we explore the physical origins of this hitherto unexplained ordering phenomena, both by systematically varying the parameters of the simulated fluids and by analyzing the flow-induced effective colloidal interactions. We also present an expression for the critical shear rate of the studied fluids.

Alignment of particles in sheared viscoelastic fluids.

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.

Microphase separation and liquid-crystalline ordering of rod-coil copolymers.

Microphase separation and liquid-crystalline ordering in diblock and triblock rod-coil copolymers (with rod-to-coil fraction f=0.5) were investigated using the dissipative particle dynamics method. When the isotropic disordered phases of these systems were cooled down below their order-disorder transition temperatures T(ODT), lamellar structures were observed. For rod-coil diblock copolymers, the lamellar layers were obtained below T=2.0. This temperature was found to be higher than the T(ODT) for normal coil-coil diblock copolymers. Significant ordering of the rods was observed only below T=0.9 which is the isotropic-nematic transition temperature for rodlike fluids. For the triblock rod-coil copolymers, both microphase separation and rod ordering occurred at T=0.9. Normal coil-coil triblock copolymers were found to undergo microphase separation at T=0.8, which is about half the T(ODT) of the normal diblock copolymers. Investigations of the mean square displacement and the parallel and the perpendicular components of the spatial distribution function revealed that at low temperatures, the rod-coil diblock copolymers exhibit smectic-A and crystalline phases, while the triblock copolymers show smectic-C and crystalline phases. No nematic phases were observed at the density and interaction parameters used in this study.