pH response of sequence-controlled polyampholyte brushes.

We use molecular simulation to investigate the pH response of sequence-controlled polyampholyte brushes (PABs) with polymer chains consisting of alternating blocks of weakly acidic and basic monomers. Changes in the ionization state, height, lateral structure, and chain conformations of PABs with pH are found to differ qualitatively from those observed for polyelectrolyte brushes. Grafting density has a relatively modest effect on PAB properties. By contrast, monomer sequence strongly affects the pH response, with the extent of the response increasing with the block size. This trend is attributed to strong electrostatic attractions between oppositely charged blocks, which lead to an increase in chain backfolding as block size increases. This behavior is consistent with that observed for polyampholytes with similar monomer sequences in solution in previous studies. Our study shows that monomer sequence can be used to tune the pH response of weak PABs to generate stimuli-responsive surfaces.

Dynamic arrest of adhesive hard rod dispersions.

The phenomenon of dynamic arrest, more commonly referred to as gel and glass formation, originates as particle motion slows significantly. Current understanding of gels and glasses stems primarily from dispersions of spherical particles, but much less is known about how particle shape affects dynamic arrest transitions. To better understand the effects of particle shape anisotropy on gel and glass formation, we systematically measure the rheology, particle dynamics, and static microstructure of thermoreversible colloidal dispersions of adhesive hard rods (AHR). First, the dynamic arrest transitions are mapped as a function of temperature T, aspect ratio L/D≈ 3 to 7, and volume fraction φ≈ 0.1 to 0.5. The critical gel temperature Tgel and glass volume fraction φg are determined from the particle dynamics and rheology. Second, an effective orientation-averaged, short-range attraction between rods is quantified from small-angle scattering measurements and characterized by a reduced temperature τ. Similar τ is found at low rod concentrations, indicating that rod gelation occurs at similar effective attraction strength independent of L/D. Monte Carlo simulations reveal a similar convergence in τ when rods cluster and percolate with an average bond coordination number 〈nc〉≈ 2.4, supporting the link between physical gelation and rigidity percolation. Lastly, AHR results are mapped onto a dimensionless state diagram to compare with previous predictions of attraction-driven gels, repulsion-driven glasses, and liquid crystal phases.

Parallel Prefetching for Canonical Ensemble Monte Carlo Simulations.

In order to enable large-scale molecular simulations, algorithms must efficiently utilize multicore processors that continue to increase in total core count over time with relatively stagnant clock speeds. Although parallelized molecular dynamics (MD) software has taken advantage of this trend in computer hardware, single-particle perturbations with Monte Carlo (MC) are more difficult to parallelize than system-wide updates in MD using domain decomposition. Instead, prefetching reconstructs the serial Markov chain after computing multiple MC trials in parallel. Canonical ensemble MC simulations of a Lennard-Jones fluid with prefetching resulted in up to a factor of 1.7 speedup using 2 threads, and a factor of 3 speedup using 4 threads. Strategies for maximizing efficiency of prefetching simulations are discussed, including the potentially counterintuitive benefit of reduced acceptance probabilities. Determination of the optimal acceptance probability for a parallel simulation is simplified by theoretical prediction from serial simulation data. Finally, complete open-source code for parallel prefetch simulations was made available in the Free Energy and Advance Sampling Simulation Toolkit (FEASST).

Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density.

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.

Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles.

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.

Tabular Potentials for Monte Carlo Simulation of Supertoroids with Short-Range Interactions.

We describe a methodology for constructing tabular potentials of supertoroids with short-range interactions, which requires the calculation of the volume of overlap of these shapes for many relative positions and orientations. Recent advances in the synthesis of anisotropic colloids have made experimental realizations of such particles feasible and have increased the practical impact of fundamental simulation studies of these families of shapes. This extends our recent work on superquadric potentials to now include a family of ring-like shapes with a hole in the middle. Along with the addition of supertoroids, the ability to make tables for nonidentical particles and particle pairs with multiple, disconnected overlap volumes was added. Using newly developed extensions to a previously published algorithm, we produced tabular potentials for all of these new cases. The algorithmic developments in this work will enable Monte Carlo simulations of a wider variety of shapes to predict thermodynamic properties over a range of conditions.

Assembly of three-dimensional binary superlattices from multi-flavored particles.

Binary superlattices constructed from nano- or micron-sized colloidal particles have a wide variety of applications, including the design of advanced materials. Self-assembly of such crystals from their constituent colloids can be achieved in practice by, among other means, the functionalization of colloid surfaces with single-stranded DNA sequences. However, when driven by DNA, this assembly is traditionally premised on the pairwise interaction between a single DNA sequence and its complement, and often relies on particle size asymmetry to entropically control the crystalline arrangement of its constituents. The recently proposed "multi-flavoring" motif for DNA functionalization, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids, can be used to experimentally realize a binary mixture in which all pairwise interactions are independently controllable. In this work, we use various computational methods, including molecular dynamics and Wang-Landau Monte Carlo simulations, to study a multi-flavored binary system of micron-sized DNA-functionalized particles modeled implicitly by Fermi-Jagla pairwise interactions. We show how self-assembly of such systems can be controlled in a purely enthalpic manner, and by tuning only the interactions between like particles, demonstrate assembly into various morphologies. Although polymorphism is present over a wide range of pairwise interaction strengths, we show that careful selection of interactions can lead to the generation of pure compositionally ordered crystals. Additionally, we show how the crystal composition changes with the like-pair interaction strengths, and how the solution stoichiometry affects the assembled structures.

Predicting structural properties of fluids by thermodynamic extrapolation.

We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.

A methodology to calculate small-angle scattering profiles of macromolecular solutions from molecular simulations in the grand-canonical ensemble.

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier's plots at high molecular concentrations, beyond what the traditional limits are for such analysis.

Assembly of multi-flavored two-dimensional colloidal crystals.

We systematically investigate the assembly of binary multi-flavored colloidal mixtures in two dimensions. In these mixtures all pairwise interactions between species may be tuned independently. This introduces an additional degree of freedom over more traditional binary mixtures with fixed mixing rules, which is anticipated to open new avenues for directed self-assembly. At present, colloidal self-assembly into non-trivial lattices tends to require either high pressures for isotropically interacting particles, or the introduction of directionally anisotropic interactions. Here we demonstrate tunable assembly into a plethora of structures which requires neither of these conditions. We develop a minimal model that defines a three-dimensional phase space containing one dimension for each pairwise interaction, then employ various computational techniques to map out regions of this phase space in which the system self-assembles into these different morphologies. We then present a mean-field model that is capable of reproducing these results for size-symmetric mixtures, which reveals how to target different structures by tuning pairwise interactions, solution stoichiometry, or both. Concerning particle size asymmetry, we find that domains in this model's phase space, corresponding to different morphologies, tend to undergo a continuous "rotation" whose magnitude is proportional to the size asymmetry. Such continuity enables one to estimate the relative stability of different lattices for arbitrary size asymmetries. Owing to its simplicity and accuracy, we expect this model to serve as a valuable design tool for engineering binary colloidal crystals from multi-flavored components.

Communication: Predicting virial coefficients and alchemical transformations by extrapolating Mayer-sampling Monte Carlo simulations.

Virial coefficients are predicted over a large range of both temperatures and model parameter values (i.e., alchemical transformation) from an individual Mayer-sampling Monte Carlo simulation by statistical mechanical extrapolation with minimal increase in computational cost. With this extrapolation method, a Mayer-sampling Monte Carlo simulation of the SPC/E (extended simple point charge) water model quantitatively predicted the second virial coefficient as a continuous function spanning over four orders of magnitude in value and over three orders of magnitude in temperature with less than a 2% deviation. In addition, the same simulation predicted the second virial coefficient if the site charges were scaled by a constant factor, from an increase of 40% down to zero charge. This method is also shown to perform well for the third virial coefficient and the exponential parameter for a Lennard-Jones fluid.

Molecular Dynamics Simulation of Trimer Self-Assembly Under Shear.

The self-assembly of patchy trimer particles consisting of one attractive site and two repulsive sites is investigated with nonequilibrium molecular dynamics simulations in the presence of a velocity gradient, as would be produced by the application of a shear stress on the system. As shear is increased, globular-shaped micellar clusters increase in size and become more elongated. The globular clusters are also more stable at higher temperatures in the presence of shear than at equilibrium. These results help to increase our understanding of the effect of shear on self-assembly for a variety of applications.

Self-assembly of trimer colloids: effect of shape and interaction range.

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Depletion-driven crystallization of cubic colloids sedimented on a surface.

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Computational study of trimer self-assembly and fluid phase behavior.

The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled structures were obtained including spherical micelle-like clusters, elongated clusters, and densely packed cylinders, depending on both the state conditions and shape of the trimer. Advanced simulation techniques were employed to determine transitions between self-assembled structures and macroscopic phases using thermodynamic and structural definitions. Simple changes in particle geometry yield dramatic changes in phase behavior, ranging from macroscopic fluid phase separation to molecular-scale self-assembly. In special cases, both self-assembled, elongated clusters and bulk fluid phase separation occur simultaneously. Our work suggests that tuning particle shape and interactions can yield superstructures with controlled architecture.

Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal-Organic Frameworks.

Molecular simulations of water adsorption in porous materials often converge slowly due to sampling bottlenecks that follow from hydrogen bonding and, in many cases, the formation of water clusters. These effects may be exacerbated in metal-organic framework (MOF) adsorbents, due to the presence of pore spaces (cages) that promote the formation of discrete-size clusters and hydrophobic effects (if present), among other reasons. In Grand Canonical Monte Carlo (MC) simulations, these sampling challenges are typically manifested by low MC acceptance ratios, a tendency for the simulation to become stuck in a particular loading state (i.e., macrostates), and the persistence of specific clusters for long periods of the simulation. We present simulation strategies to address these sampling challenges, by applying flat-histogram MC (FHMC) methods and specialized MC move types to simulations of water adsorption. FHMC, in both Transition-matrix and Wang-Landau forms, drives the simulation to sample relevant macrostates by incorporating weights that are self-consistently adjusted throughout the simulation and generate the macrostate probability distribution (MPD). Specialized MC moves, based on aggregation-volume bias and configurational bias methods, separately address low acceptance ratios for basic MC trial moves and specifically target water molecules in clusters; in turn, the specialized MC moves improve the efficiency of generating new configurations which is ultimately reflected in improved statistics collected by FHMC. The combined strategies are applied to study the adsorption of water in CuBTC and ZIF-8 at 300 K, through examination of the MPD and the adsorption isotherm generated by histogram reweighting. A key result is the appearance of nontrivial oscillations in the MPD, which we show to be associated with water clusters in the adsorption system. Additionally, we show that the probabilities of certain clusters become similar in value near the boundaries of the isotherm hysteresis loop, indicating a strong connection between cluster formation/destruction and the thermodynamic limits of stability. For a hydrophobic MOF, the FHMC results show that the phase transition from low density to high density is suppressed to water pressure far above the bulk-fluid saturation pressure; this is consistent with results presented elsewhere. We also compare our FHMC simulation isotherm to one measured by a different technique but with ostensibly the same molecular interactions and comment on observed differences and the need for follow-up work. The simulation strategies presented here can be applied to the simulation of water in other MOFs using heuristic guidelines laid out in our text, which should facilitate the more consistent and efficient simulation of water adsorption in porous materials in future applications.

Efficiency Comparison of Single- and Multiple-Macrostate Grand Canonical Ensemble Transition-Matrix Monte Carlo Simulations.

Recent interest in parallelizing flat-histogram transition-matrix Monte Carlo simulations in the grand canonical ensemble, due to its demonstrated effectiveness in studying phase behavior, self-assembly and adsorption, has led to the most extreme case of single-macrostate simulations, where each macrostate is simulated independently with ghost particle insertions and deletions. Despite their use in several studies, no efficiency comparisons of these single-macrostate simulations have been made with multiple-macrostate simulations. We show that multiple-macrostate simulations are up to 3 orders of magnitude more efficient than single-macrostate simulations, which demonstrates the remarkable efficiency of flat-histogram biased insertions and deletions, even with low acceptance probabilities. Efficiency comparisons were made for supercritical fluids and vapor-liquid equilibrium of bulk Lennard-Jones and a three-site water model, self-assembling patchy trimer particles and adsorption of a Lennard-Jones fluid confined in a purely repulsive porous network, using the open source simulation toolkit FEASST. By directly comparing with a variety of Monte Carlo trial move sets, this efficiency loss in single-macrostate simulations is attributed to three related reasons. First, ghost particle insertions and deletions in single-macrostate simulations incur the same computational expense as grand canonical ensemble trials in multiple-macrostate simulations, yet ghost trials do not reap the sampling benefit from propagating the Markov chain to a new microstate. Second, single-macrostate simulations lack macrostate change trials that are biased by the self-consistently converging relative macrostate probability, which is a major component of flat histogram simulations. Third, limiting a Markov chain to a single macrostate reduces sampling possibilities. Existing parallelization methods for multiple-macrostate flat-histogram simulations are shown to be more efficient than parallel single-macrostate simulations by approximately an order of magnitude or more in all systems investigated.

Role of Domain-Domain Interactions on the Self-Association and Physical Stability of Monoclonal Antibodies: Effect of pH and Salt.

Monoclonal antibodies (mAbs) make up a major class of biotherapeutics with a wide range of clinical applications. Their physical stability can be affected by various environmental factors. For instance, an acidic pH can be encountered during different stages of the mAb manufacturing process, including purification and storage. Therefore, understanding the behavior of flexible mAb molecules in acidic solution environments will benefit the development of stable mAb products. This study used small-angle X-ray scattering (SAXS) and complementary biophysical characterization techniques to investigate the conformational flexibility and protein-protein interactions (PPI) of a model mAb molecule under near-neutral and acidic conditions. The study also characterized the interactions between Fab and Fc fragments under the same buffer conditions to identify domain-domain interactions. The results suggest that solution pH significantly influences mAb flexibility and thus could help mAbs remain physically stable by maximizing local electrostatic repulsions when mAbs become crowded in solution. Under acidic buffer conditions, both Fab and Fc contribute to the repulsive PPI observed among the full mAb at a low ionic strength. However, as ionic strength increases, hydrophobic interactions lead to the self-association of Fc fragments and, subsequently, could affect the aggregation state of the mAb.

Molecular modeling of mechanical stresses on proteins in glassy matrices: formalism.

We present an expression for the calculation of microscopic stresses in molecular simulation, which is compatible with the use of electrostatic lattice sums such as the Ewald sum, with the presence of many-body interactions, and which allows local stresses to be calculated on surfaces of arbitrarily complex shape. The ultimate goal of this work is to investigate microscopic stresses on proteins in glassy matrices, which are used in the pharmaceutical industry for the long-term storage and stabilization of labile biomolecules. We demonstrate the formalism's usefulness through selected results on ubiquitin and an α-keratin fragment, in liquid and glassy states. We find that atomic-level normal stresses on hydrophilic side-chains exhibit a similar fingerprint in both proteins, and protein-level normal stresses increase upon vitrification. Both proteins experience compressive stresses of the order of 10(2) bar in the glassy state.