We conducted molecular dynamics simulations combined with distance-based umbrella sampling and forward flux sampling to investigate the early stages of protein crystallization. Formation of contacts with long-range interactions and/or an exposed position on the protein surface was kinetically preferred over more stable hydrophobic contacts with a shorter attractive range, while the thermodynamic stability of the protein crystal was provided by hydrophobic interactions. Contacts with a large interaction area showed complex dissociation pathways that were not detected by distance-based umbrella sampling. Instead, forward flux sampling simulations of contact dissociation identified long-range attractive interactions.

Entropic forces tend to demix polymers in confinement, which has been argued to at least facilitate DNA segregation in cylindrical bacteria. Ring polymers as found in modern bacteria such as Escherichia coli experience even stronger segregating forces than linear ones due to the fact that rings additionally constrain themselves. Using a territorial "renormalized" Flory approach we obtain a scaling prediction for the segregation force and speed of ring polymers and confirm this prediction by molecular dynamics simulations. The ring topology also affects the induction phase, when the initial symmetry is broken before segregation sets in. We show that the induction time still scales exponentially with the chain length and thus dominates the overall time scale of entropic segregation, although it is significantly shorter than the one for linear chains.

We report simulations on the homogeneous liquid-fcc nucleation of charged colloids for both low and high contact energy values. As a precursor for crystal formation, we observe increased local order at the position where the crystal will form, but no correlations with the local density. Thus, the nucleation is driven by order fluctuations rather than density fluctuations. Our results also show that the transition involves two stages in both cases, first a transition of liquid → bcc, followed by a bcc → hcp/fcc transition. Both transitions have to overcome free energy barriers, so that a spherical bcc-like cluster is formed first, in which the final fcc structure is nucleated mainly at the surface of the crystallite. This means that the second stage bcc-fcc phase transition is a heterogeneous nucleation in the partially grown solid phase, even though we start from a homogeneous bulk liquid. The height of the bcc → hcp/fcc free energy barrier strongly depends on the contact energies of the colloids. For low contact energy this barrier is low, so that the bcc → hcp/fcc transition occurs spontaneously. For the higher contact energy, the second barrier is too high to be crossed spontaneously by the colloidal system. However, it was possible to ratchet the system over the second barrier and to transform the bcc nuclei into the stable hcp/fcc phase. The transitions are dominated by the first liquid-bcc transition and can be described by classical nucleation theory using an effective surface tension.

While the phenomenon of like-charge attraction of DNA is clearly observed experimentally and in simulations, mean-field theories fail to predict it. Kornyshev et al. argued that like-charge attraction is due to DNA's helical geometry and hydration forces. Strong-coupling (SC) theory shows that attraction of like-charged rods is possible through ion correlations alone at large coupling parameters, usually by multivalent counterions. However for SC theory to be applicable, counterion-counterion correlations perpendicular to the DNA strands need to be sufficiently small, which is not a priori the case for DNA even with trivalent counterions. We study a system containing infinitely long DNA strands and trivalent counterions by computer simulations employing varying degrees of coarse-graining. Our results show that there is always attraction between the strands, but its magnitude is indeed highly dependent on the specific shape of the strand. While discreteness of the charge distribution has little influence on the attractive forces, the role of the helical charge distribution is considerable: charged rods maintain a finite distance in equilibrium, while helices collapse to close contact with a phase shift of π, in full agreement with SC predictions. The SC limit is applicable because counterions strongly bind to the charged sites of the helices, so that helix-counterion interactions dominate over counterion-counterion interactions. Thus DNA's helical geometry is not crucial for like-charge DNA attraction, but strongly enhances it, and electrostatic interactions in the strong-coupling limit are sufficient to explain this attraction.

With the help of a recently developed non-equilibrium approach, we investigate the ionic strength dependence of the Hubbard-Onsager dielectric decrement. We compute the depolarization of water molecules caused by the motion of ions in sodium chloride solutions from the dilute regime (0.035 M) up close to the saturation concentration (4.24 M), and find that the kinetic decrement displays a strong non-monotonic behavior, in contrast to the prediction of available models. We introduce a phenomenological modification of the Hubbard-Onsager continuum theory, which takes into account the screening due to the ionic cloud at the mean-field level and, which is able to describe the kinetic decrement at high concentrations including the presence of a pronounced minimum.

Crystallization of macroions happens in many applications like protein purification, photonic crystals or structure determination. However, the mechanism of crystallization in these systems is only poorly understood. We thus study homogeneous nucleation and crystallization of charged spherical particles using molecular dynamics (MD) computer simulations with the software package ESPResSo.

We present the software package FRESHS (http://www.freshs.org) for parallel simulation of rare events using sampling techniques from the ‘splitting’ family of methods. Initially, Forward Flux Sampling (FFS) and Stochastic Process Rare Event Sampling (SPRES) have been implemented. These two methods together make rare event sampling available for both quasi-static and full non-equilibrium regimes. Our framework provides a plugin system for software implementing the underlying physics of the system of interest. At present, example plugins exist for our framework to steer the popular MD packages GROMACS, LAMMPS and ESPResSo, but due to the simple interface of our plugin system, it is also easy to attach other simulation software or self-written code. Use of our framework does not require recompilation of the simulation program. The modular structure allows the flexible implementation of further sampling methods or physics engines and creates a basis for objective comparison of different sampling algorithms. Our code is designed to make optimal use of available compute resources. System states are managed using standard database technology so as to allow checkpointing, scaling and flexible analysis. The communication within the framework uses plain TCP/IP networking and is therefore suited to high-performance parallel hardware as well as to distributed or even heterogeneous networks of inexpensive machines. For FFS we implemented an automatic interface placement that ensures optimal, nearly constant flux through the interfaces. We introduce ‘ghost’ (or ‘look-ahead’) runs that remedy the bottleneck which occurs when progressing to the next interface. FRESHS is open-source, providing a publicly available parallelized rare event sampling system.

Colloidal suspensions are often argued to be an ideal model for studying phase transitions such as crystallization, as they have the advantage of tunable interactions and experimentally tractable time and length scales. Because crystallization is assumed to be unaffected by details of particle transport other than the bulk diffusion coefficient, findings are frequently argued to be transferable to pure melts without solvent. In this article, we present molecular dynamics simulations of crystallization in a suspension of colloids with Yukawa interactions which challenge this assumption. In order to investigate the role of hydrodynamic interactions mediated by the solvent, we model the solvent both implicitly and explicitly, using Langevin dynamics and the fluctuating lattice Boltzmann method, respectively. Our simulations show a significant reduction of the crystal growth velocity due to hydrodynamic interactions even at moderate hydrodynamic coupling. This slowdown is accompanied by a reduction of the width of the layering region in front of the growing crystal. Thus the dynamics of a colloidal suspension differ strongly from that of a melt, making it less useful as a model for solvent-free melts than previously thought.

In confinement, overlapping polymers experience entropic segregating forces that tend to demix them. This plays a role during cell replication, where it facilitates the segregation of daughter chromosomes. It has been argued that these forces are strong enough to explain chromosome segregation in elongated bacteria such as E. coli without the need for additional active mechanisms [S. Jun and B. Mulder, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 12388]. However, entropic segregation can only set in after the initial symmetry has been broken. We demonstrate that the timescale for this induction phase is exponentially growing in the chain length, while the actual segregation time scales only quadratically in the chain length. Thus the induction quickly becomes the dominating, slow process, and makes entropic segregation much less efficient than previously thought. The slow induction might also explain the long delay in chromosome segregation observed in experiments on E. coli.

Transition paths characterize chemical reaction mechanisms. In this paper, we present a new method to find mean reaction paths based on the free energy. A nudged elastic band (NEB) is optimized using gradients and Hessians of the free energy, which are obtained from umbrella integration. The transition state can be refined by a Newton-Raphson search starting from the highest point of the NEB path. All optimizations are done using Cartesian coordinates. Independent molecular dynamics (MD) runs are performed at each image used to discretize the path. This makes the method intrinsically parallel. In contrast to other free energy methods, the algorithm does not become more expensive when including more degrees of freedom in the active space. The method is applied to the alanine-dipeptide as a test case and compared to pathways that have been derived from metadynamics and forward flux sampling.

In the late 1970s, Hubbard and Onsager predicted that adding salt to a polar solution would result in a reduced dielectric permittivity that arises from the unexpected tendency of solvent dipoles to align opposite to the applied field. Here we develop a novel non-equilibrium molecular dynamics simulation approach to determine this decrement accurately. Using a thermodynamic consistent all-atom force field we show that for an aqueous solution containing sodium chloride around 4.8 mol/l, this effect accounts for 12% of the total dielectric permittivity. The dielectric decrement can be strikingly different if a less accurate force field for the ions is used. Using the widespread GROMOS parameters, we observe in fact an increment of the dielectric permittivity rather than a decrement, caused by ion pairing and introduced by a too low dispersion force.

Nanoparticle agglomeration plays an important role in processes such as spray drying and particle flame synthesis. These processes have in common that nanoparticles collide at low concentrations and get irreversibly linked at the point of contact due to plastic deformation. In this article, we investigate several models of irreversible connections, which require only local interactions between the colliding nanoparticles and thus allow for scalable simulations. The models investigated here connect the particles upon collision by non-bonded strongly attractive interactions, bonded interactions or by binding agents placed at the point of contact. Models using spherically symmetric interactions form compact agglomerates and are therefore unsuitable to study agglomeration. In contrast, models that are either based on both central and angular potentials (type one) or on binding agents (type two) efficiently prevent restructuring of the agglomerates, and are therefore useful for modeling contacts formed by plastic deformation. Moreover, both types of models allow to control the rigidity and by that the degree of restructuring. The first type of model is computationally more efficient at low fractional dimensions of the aggregates, while the second gives easy access to local shear forces, which is important when breaking of agglomerates is to be considered. As example applications, we reproduce the well-known diffusion-limited agglomeration (DLA) and report results on soot aggregation.

Forward flux sampling (FFS) provides a convenient and efficient way to simulate rare events in equilibrium or non-equilibrium systems. FFS ratchets the system from an initial state to a final state via a series of interfaces in phase space. The efficiency of FFS depends sensitively on the positions of the interfaces. We present two alternative methods for placing interfaces automatically and adaptively in their optimal locations, on-the-fly as an FFS simulation progresses, without prior knowledge or user intervention. These methods allow the FFS simulation to advance efficiently through bottlenecks in phase space by placing more interfaces where the probability of advancement is lower. The methods are demonstrated both for a single-particle test problem and for the crystallization of Yukawa particles. By removing the need for manual interface placement, our methods both facilitate the setting up of FFS simulations and improve their performance, especially for rare events which involve complex trajectories through phase space, with many bottlenecks.

The partition coefficient of a substance measures its solubility in octanol compared with water and is widely used to estimate toxicity. If a substance is hardly soluble in octanol, then it is practically impossible for it to enter (human) cells and therefore is less likely to be toxic. For novel drugs it might be important to penetrate the cell through the membrane or even integrate into it. While for most simple substances the partition coefficient is concentration-independent at low concentrations, this is not true for a few important classes of complex molecules, such as ionic liquids or tensides. We present a simple association-dissociation model for concentration dependence of the partition coefficient of ionic liquids. Atomistic computer simulations serve to parametrize our model by calculating solvation free energies in water and octanol using thermodynamic integration. We demonstrate the validity of the method by reproducing the concentration-independent partition coefficients of small alcohols and the concentration-dependent partition coefficient of a commonly used ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C4MIM][NTf2]. The concentration dependence is accurately predicted in a concentration range of several orders of magnitude.

Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability.

The redesigned Extensible Simulation Package for Research on Soft matter systems (ESPResSo++) is a free, open-source, parallelized, object-oriented simulation package designed to perform many-particle simulations, principally molecular dynamics and Monte Carlo, of condensed soft matter systems. In addition to the standard simulation methods found in well-established packages, ESPResSo++ provides the ability to perform Adaptive Resolution Scheme (AdResS) simulations which are multiscale simulations of molecular systems where the level of resolution of each molecule can change on-the-fly. With the main design objective being extensibility, the software features a highly modular C++ kernel that is coupled to a Python user interface. This makes it easy to add new algorithms, setup a simulation, perform online analysis, use complex workflows and steer a simulation. The extreme flexibility of the software allows for the study of a wide range of systems. The modular structure enables scientists to use ESPResSo++ as a research platform for their own methodological developments, which at the same time allows the software to grow and acquire the most modern methods. ESPResSo++ is targeted for a broad range of architectures and is licensed under the GNU General Public License. (C) 2012 Elsevier B.V. All rights reserved.

Coarse-grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need to compute exact electrostatic interactions between charges in those systems is computationally demanding. We review here several algorithms developed by us that perform exactly this task. For planar dielectric surfaces in partial periodic boundary conditions, the arising image charges can be either treated with the MMM2D algorithm in a very efficient and accurate way or with the electrostatic layer correction term, which enables the user to use his favorite 3D periodic Coulomb solver. Arbitrarily-shaped interfaces can be dealt with using induced surface charges with the induced charge calculation (ICC*) algorithm. Finally, the local electrostatics algorithm, MEMD(Maxwell Equations Molecular Dynamics), even allows one to employ a smoothly varying dielectric constant in the systems. We introduce the concepts of these three algorithms and an extension for the inclusion of boundaries that are to be held fixed at a constant potential (metal conditions). For each method, we present a showcase application to highlight the importance of dielectric interfaces.