Pressure Anisotropy in Polymer Brushes and Its Effects on Wetting.

Polymer brushes, coatings consisting of densely grafted macromolecules, experience an intrinsic lateral compressive pressure, originating from chain elasticity and excluded volume interactions. This lateral pressure complicates a proper definition of the interface and, thereby, the determination and interpretation of the interfacial tension and its relation to the wetting behavior of brushes. Here, we study the link among grafting-induced compressive lateral pressure in polymer brushes, interfacial tension, and brush wettability using coarse-grained molecular dynamics simulations. We focus on grafting densities and polymer-liquid affinities such that the polymer and liquid do not tend to mix. For these systems, a central result is that the liquid contact angle is independent of the grafting density, which implies that the grafting-induced lateral compressive pressure in the brush does not influence its wettability. Although the definition of brush interfacial tensions is complicated by the grafting-induced pressure, the difference in the interfacial tension between wet and dry brushes is perfectly well-defined. We confirm explicitly from Young's law that this difference offers an accurate description of the brush wettability. We then explore a method to isolate the grafting-induced contribution to the lateral pressure, assuming the interfacial tension is independent of grafting density. This scenario indeed allows disentanglement of interfacial and grafting effects for a broad range of parameters, except close to the mixing point. We separately discuss the latter case in light of autophobic dewetting.

Charging and discharging a supercapacitor in molecular simulations.

As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.

A simple efficient algorithm for molecular simulations of constant potential electrodes.

Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.

Stress-dependent macromolecular crowding in the mitochondrial matrix.

Macromolecules of various sizes induce crowding of the cellular environment. This crowding impacts on biochemical reactions by increasing solvent viscosity, decreasing the water-accessible volume and altering protein shape, function, and interactions. Although mitochondria represent highly protein-rich organelles, most of these proteins are somehow immobilized. Therefore, whether the mitochondrial matrix solvent exhibits macromolecular crowding is still unclear. Here, we demonstrate that fluorescent protein fusion peptides (AcGFP1 concatemers) in the mitochondrial matrix of HeLa cells display an elongated molecular structure and that their diffusion constant decreases with increasing molecular weight in a manner typical of macromolecular crowding. Chloramphenicol (CAP) treatment impaired mitochondrial function and reduced the number of cristae without triggering mitochondrial orthodox-to-condensed transition or a mitochondrial unfolded protein response. CAP-treated cells displayed progressive concatemer immobilization with increasing molecular weight and an eightfold matrix viscosity increase, compatible with increased macromolecular crowding. These results establish that the matrix solvent exhibits macromolecular crowding in functional and dysfunctional mitochondria. Therefore, changes in matrix crowding likely affect matrix biochemical reactions in a manner depending on the molecular weight of the involved crowders and reactants.

The permeability of pillar arrays in microfluidic devices: an application of Brinkman's theory towards wall friction.

Darcy's law describes the flow of Newtonian fluids through bulk porous media as the product of the applied pressure difference, the fluid's viscosity and the medium's permeability. Brinkman extended Darcy's law with a viscous stress term, thereby enabling boundary conditions to the flow field at the surface of the medium. The validity of Brinkman's term, and the value of its effective viscosity, have been heavily debated since their introduction nearly 75 years ago. We use experiments and Multibody Dissipative Particle Dynamics (MDPD) simulations to study flows through ordered and disordered pillar arrays in microfluidic channels of limited height. We find that the simulated velocity profiles are well described by an expedient interpretation of Brinkman's theory. Depending on the solid volume fraction and pillar arrangement, the effective viscosity varies between two and three times the bulk fluid viscosity. The calculated effective permeabilities of the flow devices, combining the flow resistances due to the pillars and the walls by Brinkman's theory, agree well with the experimental data. This approach enables fast and accurate estimates of the effective permeability of micropillared chips. The simulated force distributions over the walls and pillars require an effective viscosity equal to the bulk viscosity and an elevation-dependent permeability of the pillar array.

Cancer immune therapy using engineered ?tail-flipping' nanoliposomes targeting alternatively activated macrophages.

Alternatively-activated, M2-like tumor-associated macrophages (TAM) strongly contribute to tumor growth, invasiveness and metastasis. Technologies to disable the pro-tumorigenic function of these TAMs are of high interest to immunotherapy research. Here we show that by designing engineered nanoliposomes bio-mimicking peroxidated phospholipids that are recognised and internalised by scavenger receptors, TAMs can be targeted. Incorporation of phospholipids possessing a terminal carboxylate group at the sn-2 position into nanoliposome bilayers drives their uptake by M2 macrophages with high specificity. Molecular dynamics simulation of the lipid bilayer predicts flipping of the sn-2 tail towards the aqueous phase, while molecular docking data indicates interaction of the tail with Scavenger Receptor Class B type 1 (SR-B1). In vivo, the engineered nanoliposomes are distributed specifically to M2-like macrophages and, upon delivery of the STAT6 inhibitor (AS1517499), zoledronic acid or muramyl tripeptide, these cells promote reduction of the premetastatic niche and/or tumor growth. Altogether, we demonstrate the efficiency and versatility of our engineered "tail-flipping" nanoliposomes in a pre-clinical model, which paves the way to their development as cancer immunotherapeutics in humans.

Capillary Imbibition of Binary Fluid Mixtures in Nanochannels.

Many-body Dissipative Particle Dynamics (MDPD) simulations of binary fluid mixtures imbibing cylindrical nanochannels reveal a strong segregation of fluids differing in their affinities to the pore walls. Surprisingly, the imbibition front furthest into the channel is highly enriched in the fluid with the lower affinity for the walls, i.e., the fluid less prone to enter the pore. This effect is caused by the more-wetting fluid forming a monolayer covering the walls of the pore, while the lesser-wetting fluid is expelled from the walls to the interior of the pore where the higher axial flow velocity carries it to the front. The fluids remix after cessation of the flow. Nonwetting fluids can be made to enter a pore by mixing with a small amount of wetting fluid. The imbibition depth of the mixtures scales with the square root of time, in agreement with Bell-Cameron-Lucas-Washburn theory for pure fluids.

Systematic approach for wettability prediction using molecular dynamics simulations.

We present a fast and efficient approach to predict the wettability and spreading of liquids on polymeric substrates. First, a molecular dynamics parameterization is proposed for the calculation of the solubility parameter for 74 compounds including surfactants typically used in inkjet printing. Then, we introduce a molecular geometrical factor to relate the solubility parameter to the surface tension, obtaining estimates in remarkable agreement with experiments. By using a modified Young-Fowkes equation, the contact angles of liquids on various polymeric substrates are determined and their dependence on the hydrogen bonding, dispersion and polar contribution of the solubility parameter are investigated. We find that wetting properties are obtained with a good accuracy when taking into account the hydrogen-bonding and polar interactions in the geometric sum of the solubility parameter. Based on these findings, a 3D wetting space is proposed to evaluate liquids wettability and judge their suitability for specific substrates. This will enable easy formulation of liquids with wettability tailored for a particular surface and application.

Fluctuating Brownian stresslets and the intrinsic viscosity of colloidal suspensions.

The interplay between Brownian colloidal particles and their suspending fluid is well understood since Einstein's seminal work of 1905: the fluid consists of atoms whose thermal motion gives rise to the Brownian motion of the colloids, while the colloids increase the viscosity of the suspension under shear. An alternative route to the viscosity, by exploring the thermal stress fluctuations in a quiescent fluid in the Green-Kubo formalism, however, reveals a marked inconsistency with the viscosity under shear. We show that an additional stress term, accounting for Brownian fluctuating stresslets and coupled to the Brownian forces by a generalized fluctuation-dissipation theorem, is required for the description of the stress and viscosity of a colloidal suspension. Whereas previous applications of the Green-Kubo method to colloidal systems were limited to the deterministic "thermodynamic" part of the stress, using other means to determine the remainder of the viscosity, the whole viscosity is now within the reach of equilibrium studies.

Intrinsic viscosities of non-spherical colloids by Brownian dynamics simulations.

A numerical study is presented on the intrinsic viscosities of sheared dilute suspensions of nonspherical Brownian colloidal particles. The simulations confirm theoretical predictions on the intrinsic viscosities of highly oblate and highly prolate spheroids in the limits of weak and strong Brownian noise (i.e., for low and high Péclet numbers). Numerical data and fit functions are provided covering the entire shear-thinning regime, for spheroids ranging from highly oblate to highly prolate. The tumbling motion and intrinsic viscosities of a hemispherical cap and a helix are briefly discussed.

Coarse-Grained Simulations of Three-Armed Star Polymer Melts and Comparison with Linear Chains.

Melts of three-armed star polymers have been simulated using a coarse-grained model parameterized by atomistic simulations of polyethylene. The bonds between the highly coarse-grained, and hence soft, polymer beads are explicitly prevented from crossing by the TWENTANGLEMENT algorithm. The three melts of symmetric stars, differing in the lengths of the arms, are compared against five melts of linear polymers with comparable dimensions to study the impact of branched architecture on self-diffusion and bulk rheological properties. Differently from the power-law relation between the viscosity and molecular mass of linear chains, the star polymers in our simulations follow an exponential mass-viscosity relation and show qualitative agreement with the storage and loss moduli for stars with far longer arms from experiments. The stress relaxation dynamics of the stars are also compared with theoretical analysis in terms of Rouse modes.

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix.

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

Intrinsic Conformational Preferences and Interactions in α-Synuclein Fibrils: Insights from Molecular Dynamics Simulations.

Amyloid formation by the intrinsically disordered α-synuclein protein is the hallmark of Parkinson's disease. We present atomistic Molecular Dynamics simulations of the core of α-synuclein using enhanced sampling techniques to describe the conformational and binding free energy landscapes of fragments implicated in fibril stabilization. The theoretical framework is derived to combine the free energy profiles of the fragments into the reaction free energy of a protein binding to a fibril. Our study shows that individual fragments in solution have a propensity toward attaining non-ß conformations, indicating that in a fibril ß-strands are stabilized by interactions with other strands. We show that most dimers of hydrogen-bonded fragments are unstable in solution, while hydrogen bonding stabilizes the collective binding of five fragments to the end of a fibril. Hydrophobic effects make further contributions to the stability of fibrils. This study is the first of its kind where structural and binding preferences of the five major fragments of the hydrophobic core of α-synuclein have been investigated. This approach improves sampling of intrinsically disordered proteins, provides information on the binding mechanism between the core sequences of α-synuclein, and enables the parametrization of coarse grained models.

The attachment of α-synuclein to a fiber: A coarse-grain approach.

We present simulations of the amyloidogenic core of α-synuclein, the protein causing Parkinson's disease, as a short chain of coarse-grain patchy particles. Each particle represents a sequence of about a dozen amino acids. The fluctuating secondary structure of this intrinsically disordered protein is modelled by dynamic variations of the shape and interaction characteristics of the patchy particles, ranging from spherical with weak isotropic attractions for the disordered state to spherocylindrical with strong directional interactions for a ß-sheet. Flexible linkers between the particles enable sampling of the tertiary structure. This novel model is applied here to study the growth of an amyloid fibril, by calculating the free energy profile of a protein attaching to the end of a fibril. The simulation results suggest that the attaching protein readily becomes trapped in a mis-folded state, thereby inhibiting further growth of the fibril until the protein has readjusted to conform to the fibril structure, in line with experimental findings and previous simulations on small fragments of other proteins.

Clathrin Assembly Regulated by Adaptor Proteins in Coarse-Grained Models.

The assembly of clathrin triskelia into polyhedral cages during endocytosis is regulated by adaptor proteins (APs). We explore how APs achieve this by developing coarse-grained models for clathrin and AP2, employing a Monte Carlo click interaction, to simulate their collective aggregation behavior. The phase diagrams indicate that a crucial role is played by the mechanical properties of the disordered linker segment of AP. We also present a statistical-mechanical theory for the assembly behavior of clathrin, yielding good agreement with our simulations and experimental data from the literature. Adaptor proteins are found to regulate the formation of clathrin coats under certain conditions, but can also suppress the formation of cages.

A coarse grained protein model with internal degrees of freedom. Application to α-synuclein aggregation.

Particles in simulations are traditionally endowed with fixed interactions. While this is appropriate for particles representing atoms or molecules, objects with significant internal dynamics--like sequences of amino acids or even an entire protein--are poorly modelled by invariable particles. We develop a highly coarse grained polymorph patchy particle with the ultimate aim of simulating proteins as chains of particles at the secondary structure level. Conformational changes, e.g., a transition between disordered and ß-sheet states, are accommodated by internal coordinates that determine the shape and interaction characteristics of the particles. The internal coordinates, as well as the particle positions and orientations, are propagated by Brownian Dynamics in response to their local environment. As an example of the potential offered by polymorph particles, we model the amyloidogenic intrinsically disordered protein α-synuclein, involved in Parkinson's disease, as a single particle with two internal states. The simulations yield oligomers of particles in the disordered state and fibrils of particles in the "misfolded" cross-ß-sheet state. The aggregation dynamics is complex, as aggregates can form by a direct nucleation-and-growth mechanism and by two-step-nucleation through conversions between the two cluster types. The aggregation dynamics is complex, with fibrils formed by direct nucleation-and-growth, by two-step-nucleation through the conversion of an oligomer and by auto-catalysis of this conversion.

An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles.

Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Rotational Brownian dynamics simulations of clathrin cage formation.

The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.

Revisiting the Exact Relation between Potential of Mean Force and Free-Energy Profile.

Constraints are convenient in the calculation of free energy profiles via molecular dynamics simulations, but they subtly alter the phase space distribution. In a recent letter of a related title in this journal, Wong and York [J. Chem. Theory Comput. 2012, 8, 3998-4003] suggest replacing Fixman's mass-metric correction with its inverse and adding a Jacobian contribution to the potential of mean constraint force. This letter refutes both suggestions, discusses the underlying interpretation problems, and provides supporting numerical simulations.

The generation of curved clathrin coats from flat plaques.

Flat clathrin lattices or 'plaques' are commonly believed to be the precursors to clathrin-coated buds and vesicles. The sequence of steps carrying the flat hexagonal lattice into a highly curved polyhedral cage with exactly 12 pentagons remains elusive, however, and the large numbers of disrupted interclathrin connections in previously proposed conversion pathways make these scenarios rather unlikely. The recent notion that clathrin can make controlled small conformational transitions opens new avenues. Simulations with a self-assembling clathrin model suggest that localized conformational changes in a plaque can create sufficiently strong stresses for a dome-like fragment to break apart. The released fragment, which is strongly curved but still hexagonal, may subsequently grow into a cage by recruiting free triskelia from the cytoplasm, thus building all 12 pentagonal faces without recourse to complex topological changes. The critical assembly concentration in a slightly acidic in vitro solution is used to estimate the binding energy of a cage at 25-40 k(B) T/clathrin.