Efficient solvent-free dissipative particle dynamics for lipid bilayers.

We rigorously derived effective potentials for solvent-free DPD simulation of lipid bilayers. The derivation relies on an earlier developed hybrid particle/field method and is based on the idea that the solvent is always in local equilibrium on a coarse-grained time scale, given the instantaneous templates set by the self-assembly structure. By relating the parameters in the effective implicit-solvent potentials directly to the lipid-solvent interactions and membrane properties for the explicit solvent DPD model, we constitute an efficient and general procedure for reformulating any DPD membrane model in an implicit-solvent form. Here, we determined these membrane properties for two existing DPD models, via an analysis of membrane fluctuation spectra. Equivalent single-processor implicit- and explicit-solvent calculations show the trade-mark of implicit solvent simulation: a 20-fold reduction of the total simulation time for a system containing 92% solvent. This increased efficiency enabled us to realistically simulate the spontaneous formation of a ∼20 nm diameter vesicle on a single processor overnight. We believe that this work will contribute to an enhanced computational study of large vesicles and thus a better understanding of experimental liposome dynamics.

Stochastic quasi-Newton method: application to minimal model for proteins.

Knowledge of protein folding pathways and inherent structures is of utmost importance for our understanding of biological function, including the rational design of drugs and future treatments against protein misfolds. Computational approaches have now reached the stage where they can assess folding properties and provide data that is complementary to or even inaccessible by experimental imaging techniques. Minimal models of proteins, which make possible the simulation of protein folding dynamics by (systematic) coarse graining, have provided understanding in terms of descriptors for folding, folding kinetics, and folded states. Here we focus on the efficiency of equilibration on the coarse-grained level. In particular, we applied a new regularized stochastic quasi-Newton (S-QN) method, developed for accelerated configurational space sampling while maintaining thermodynamic consistency, to analyze the folding pathway and inherent structures of a selected protein, where regularization was introduced to improve stability. The adaptive compound mobility matrix B in S-QN, determined by a factorized secant update, gives rise to an automated scaling of all modes in the protein, in particular an acceleration of protein domain dynamics or principal modes and a slowing down of fast modes or "soft" bond constraints, similar to lincs/shake algorithms, when compared to conventional Langevin dynamics. We used and analyzed a two-step strategy. Owing to the enhanced sampling properties of S-QN and increased barrier crossing at high temperatures (in reduced units), a hierarchy of inherent protein structures is first efficiently determined by applying S-QN for a single initial structure and T=1>T(θ), where T(θ) is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature (T=0.01

Stochastic quasi-Newton molecular simulations.

We report a new and efficient factorized algorithm for the determination of the adaptive compound mobility matrix B in a stochastic quasi-Newton method (S-QN) that does not require additional potential evaluations. For one-dimensional and two-dimensional test systems, we previously showed that S-QN gives rise to efficient configurational space sampling with good thermodynamic consistency [C. D. Chau, G. J. A. Sevink, and J. G. E. M. Fraaije, J. Chem. Phys. 128, 244110 (2008)]. Potential applications of S-QN are quite ambitious, and include structure optimization, analysis of correlations and automated extraction of cooperative modes. However, the potential can only be fully exploited if the computational and memory requirements of the original algorithm are significantly reduced. In this paper, we consider a factorized mobility matrix B=JJ(T) and focus on the nontrivial fundamentals of an efficient algorithm for updating the noise multiplier J . The new algorithm requires O(n2) multiplications per time step instead of the O(n3) multiplications in the original scheme due to Choleski decomposition. In a recursive form, the update scheme circumvents matrix storage and enables limited-memory implementation, in the spirit of the well-known limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method, allowing for a further reduction of the computational effort to O(n). We analyze in detail the performance of the factorized (FSU) and limited-memory (L-FSU) algorithms in terms of convergence and (multiscale) sampling, for an elementary but relevant system that involves multiple time and length scales. Finally, we use this analysis to formulate conditions for the simulation of the complex high-dimensional potential energy landscapes of interest.

Improved configuration space sampling: Langevin dynamics with alternative mobility.

We present a new and efficient method for determining optimal configurations of a large number (N) of interacting particles. We use a coarse-grained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton's method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface Phi. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of Phi. We employ a Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.

Design of chimaeric polymersomes.

We discuss the development of hierarchical polymer particles, or variegated polymersome composites, in which at least two different components are phase separated within one polymersome chimaera. We briefly discuss the present status in experimental polymersome research, and then discuss a speculative design strategy, based on mesoscopic simulations with a dynamical variant of polymer self-consistent field theory (Mesodyn). The main conclusion is that the counter-intuitive co-assembly of demixing block copolymers is the key in controlling hierarchical structures on a mesoscopic scale. This is the classical paradox of a chimaera: the constituents live in the same scaffold, but apart. Block copolymers beyond a certain length will always split the assembly, and without further precautions, polymer based chimaerae are intrinsically unstable. To this end, we propose the application of a branched block copolymer as composite compatibilizer, glueing the separate domains together, and thereby stabilizing the chimaeric polymersome.

Structure formation in films of weakly charged block polyelectrolyte solutions.

A mean-field dynamic density functional theory is used to describe a phase diagram of concentrated solutions of weakly charged flexible block polyelectrolytes in a film. Electrostatics is taken into account by applying the local electroneutrality constraint (the Donnan membrane equilibrium approach). In the Donnan limit it is assumed that a salt added to the solution perfectly screens long-range electrostatic interactions. The phase diagram of a solution of a triblock polyelectrolyte in a film as a function of the solvent concentration and the charge of the polyelectrolyte (solvophilic) block is calculated for a given film thickness. The phase behavior of the block polyelectrolyte film arises from the interplay between surface-induced alignment and the electrostatically-driven structure formation. The observed mesoscopic structures (lamellar, perforated lamellar, cylindrical, micellar, and mixed phases) are oriented parallel to the surfaces for the considered case of morphologies unfrustrated by the film thickness. Structures with connections between parallel layers (bicontinuous, etc.) are not formed. As a result of surface-induced ordering, the region of ordered phases in a film is wider than in bulk and the phase boundary between ordered and disordered phases is more diffuse. As in the case of unconfined block polyelectrolyte solution, the solution in a film does not follow the lyotropic sequence of phases of such a block copolymer upon increase in the charge of the polyelectrolyte block. Upon changing the charge of the solvophilic copolymer block, transformations of copolymer morphology take place via change in curvature of polymeric domains. Due to confinement of a polyelectrolyte film, no swelling of solvophilic domains is observed.

Nematic-amorphous polymer interfaces in the presence of a compatibilizer.

We introduce and apply a variant of a dynamic self-consistent field simulation in two dimensions to predict the structure of interfaces between a nematic and an amorphous polymer compatibilized by a diblock copolymer. First, we investigate the effect of the nematic order on the polymer polymer interface without compatibilizer. Then we include the compatibilizer and consider two interfacial setups previously used in experiments, i.e., the bilayer setup and the trilayer setup. In the bilayer setup the diblock copolymer is mixed into the amorphous homopolymer and migrates to the interface in the course of the simulation forming a layered structure. We compare the amount of copolymer at the interface for initial concentrations of the copolymer below and above the critical micelle concentration. In the trilayer setup the initial thickness of the diblock copolymer is varied. The resulting interfacial morphology evolves in the competition between the lamellar structure induced by the interface and a micellar structure, which is intrinsic to the copolymer.

Microphase separation of weakly charged block polyelectrolyte solutions: Donnan theory for dynamic polymer morphologies.

A mean-field dynamic density functional theory for the phase behavior of concentrated weakly charged block polyelectrolyte solutions is developed, using the Donnan membrane equilibrium approach to account for electrostatic interactions. In this limit all long-range electrostatic interactions are canceled and the net charge density in any region on a coarse-grained scale is zero. The phase diagram of a model triblock polyelectrolyte in solution as a function of the charge of the solvophilic block and the solvent concentration is established. Different mesoscopic structures (lamellar, bicontinuous, hexagonal, micellar, and dispersed coexisting phases) are formed depending on the copolymer charge asymmetry. It is found that upon changing the charge of the solvophilic copolymer block the polyelectrolyte solution does not follow the lyotropic sequence of phases of this polymer. Upon increase in the charge of the solvophilic blocks, changes in copolymer morphology take place by means of change in curvature of polymeric domains.

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow.

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melts under reciprocating shear flow. We show that, similar to the steady shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the [parallel]--> [perpendicular] transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.