Morphology of Polymer Brushes in the Presence of Attractive Nanoparticles: Effects of Temperature.

We study the role of temperature on the structure of pure polymer brushes and their mixture with attractive nanoparticles in flat and cylindrical geometries. It has previously been established that the addition of such nanoparticles causes the polymer brush to collapse and the intensity of the collapse depends on the attraction strength, the nanoparticle diameter, and the grafting density. In this work, we carry out molecular dynamics simulation under good solvent conditions to show how the collapse transition is affected by the temperature, for both plane grafted and inside-cylinder grafted brushes. We first examine the pure brush morphology and verify that the brush height is insensitive to temperature changes in both planar and cylindrical geometries, as expected for a polymer brush in a good solvent. On the other hand, for both system geometries, the brush structure in the presence of attractive nanoparticles is quite responsive to temperature changes. Generally speaking, for a given nanoparticle concentration, increasing the temperature causes the brush height to increase. A brush which contracts when nanoparticles are added eventually swells beyond its pure brush height as the system temperature is increased. The combination of two easily controlled external parameters, namely, concentration of nanoparticles in solution and temperature, allows for sensitive and reversible adjustment of the polymer brush height, a feature which could be exploited in designing smart polymer devices.

The Role of Cohesiveness in the Permeability of the Spatial Assemblies of FG Nucleoporins.

Nuclear pore complexes (NPCs) conduct selective, bidirectional transport across the nuclear envelope. The NPC passageway is lined by intrinsically disordered proteins that contain hydrophobic phenylalanine-glycine (FG) motifs, known as FG nucleoporins (FG nups), that play the key role in the NPC transport mechanism. Cohesive interactions among the FG nups, which arise from the combination of hydrophobic, electrostatic, and other forces, have been hypothesized to control the morphology of the assemblies of FG nups in the NPC, as well as their permeability with respect to the transport proteins. However, the role of FG nup cohesiveness is still vigorously debated. Using coarse-grained polymer theory and numerical simulations, we study the effects of cohesiveness on the selective permeability of in vitro FG nup assemblies in different geometries that have served as proxies for the morphological and transport properties of the NPC. We show that in high-density FG nup assemblies, increase in cohesiveness leads to the decrease in their permeability, in accordance with the accepted view. On the other hand, the permeability of low-density assemblies is a nonmonotonic function of the cohesiveness, and a moderate increase in cohesiveness can enhance permeability. The density- and cohesiveness-dependent effects on permeability are explained by considering the free-energy cost associated with penetrating the FG nup assemblies. We discuss the implications of these findings for the organization and function of the NPC.

Controlling the Surface Properties of Binary Polymer Brush-Coated Colloids via Targeted Nanoparticles.

This paper explores a novel mechanism for controlling the surface properties of polymer-coated colloids using targeted ("sticky") nanoparticles which attract monomers of certain polymer species. In our study, colloids are coated by two types of tethered polymer chains having different chemical properties. Attraction of nanoparticles to the monomers of one polymer type causes these polymer chains to contract toward the grafting surface, rendering the other type more exposed to the environment. Thus, the effective surface properties of the colloid are dominated by the intended polymer type. We use coarse-grained molecular dynamics (CGMD) simulation to demonstrate that introducing nanoparticles which interact preferentially with certain types of polymers makes it possible to switch between different surface properties of the colloid. This mechanism can in principle be exploited in drug delivery systems and self-assembly applications.

Driven water/ion transport through narrow nanopores: a molecular dynamics perspective.

Atomistic Molecular Dynamics (MD) simulations provide numerous insights into the process whereby water is driven through a narrow nanopore (diameter on the order of a few water molecules) by application of hydrostatic pressure. If there are ions in the water, e.g., from dissolved salt, these may be swept along with the flowing water. If the surface of the nanopore is charged, electrostatic interaction between the surface charges and the ions as well as with partial charges on the water molecules will influence the details of the water/ion flow through the channel. Water and ion permeability depend on the geometry of the channel and the degree to which it is charged. Interesting collective features of the water molecules such as water wires that form along the pore axis and rings of water molecules that can insert into the pore perpendicular to the channel axis strongly influence the permeation process, thus emphasizing the importance of molecular level interactions in the mechanism of water and ion flow through conduits with dimensions on the molecular scale.

Calculating tracer currents through narrow ion channels: beyond the independent particle model.

Discrete state models of single-file ion permeation through a narrow ion channel pore are employed to analyze the ratio of forward to backward tracer current. Conditions under which the well-known Ussing formula for this ratio hold are explored in systems where ions do not move independently through the channel. Building detailed balance into the rate constants for the model in such a way that under equilibrium conditions (equal rate of forward versus backward permeation events) the Nernst equation is satisfied, it is found that in a model where only one ion can occupy the channel at a time, the Ussing formula is always obeyed for any number of binding sites, reservoir concentrations of the ions and electric potential difference across the membrane which the ion channel spans, independent of the internal details of the permeation pathway. However, numerical analysis demonstrates that when multiple ions can occupy the channel at once, the nonequilibrium forward/backward tracer flux ratio deviates from the prediction of the Ussing model. Assuming an appropriate effective potential experienced by ions in the channel, we provide explicit formulae for the rate constants in these models.

Effects of cross-linking on partitioning of nanoparticles into a polymer brush: Coarse-grained simulations test simple approximate theories.

The effect of cohesive contacts or, equivalently, dynamical cross-linking on the equilibrium morphology of a polymer brush infiltrated by nanoparticles that are attracted to the polymer strands is studied for plane-grafted brushes using coarse-grained molecular dynamics and approximate statistical mechanical models. In particular, the Alexander-de Gennes (AdG) and Strong Stretching Theory (SST) mean-field theory (MFT) models are considered. It is found that for values of the MFT cross-link strength interaction parameter beyond a certain threshold, both AdG and SST models predict that the polymer brush will be in a compact state of nearly uniform density packed next to the grafting surface over a wide range of solution phase nanoparticle concentrations. Coarse grained molecular dynamics simulations confirm this prediction, for both small nanoparticles (nanoparticle volume = monomer volume) and large nanoparticles (nanoparticle volume = 27 × monomer volume). Simulation results for these cross-linked systems are compared with analogous results for systems with no cross-linking. At the same solution phase nanoparticle concentration, strong cross-linking results in additional compression of the brush relative to the non-crosslinked analog and, at all but the lowest concentrations, to a lesser degree of infiltration by nanoparticles. For large nanoparticles, the monomer density profiles show clear oscillations moving outwards from the grafting surface, corresponding to a degree of layering of the absorbed nanoparticles in the brush as they pack against the grafting surface.

Free Energy of Nanoparticle Binding to Multivalent Polymeric Substrates.

Characterization of the interactions between nanosize ligands and polymeric substrates is important for predictive design of nanomaterials and in biophysical applications. The multivalent nature of the polymer-nanoparticle interaction and the dynamics of multiple internal conformations of the polymer chains makes it difficult to infer microscopic interactions from macroscopic binding assays. Using coarse-grained simulations, we estimate the free energy of binding between a nanoparticle and a surface-grafted polymeric substrate as a function of pertinent parameters such as polymer chain length, nanoparticle size, and microscopic polymer-nanoparticle attraction. We also investigate how the presence of the nanoparticle affects the internal configurations of the polymeric substrate, and estimate the entropic cost of binding. The results have important implications for the understanding of complex macromolecular assemblies.

Simple biophysics underpins collective conformations of the intrinsically disordered proteins of the Nuclear Pore Complex.

Nuclear Pore Complexes (NPCs) are key cellular transporter that control nucleocytoplasmic transport in eukaryotic cells, but its transport mechanism is still not understood. The centerpiece of NPC transport is the assembly of intrinsically disordered polypeptides, known as FG nucleoporins, lining its passageway. Their conformations and collective dynamics during transport are difficult to assess in vivo. In vitro investigations provide partially conflicting results, lending support to different models of transport, which invoke various conformational transitions of the FG nucleoporins induced by the cargo-carrying transport proteins. We show that the spatial organization of FG nucleoporin assemblies with the transport proteins can be understood within a first principles biophysical model with a minimal number of key physical variables, such as the average protein interaction strengths and spatial densities. These results address some of the outstanding controversies and suggest how molecularly divergent NPCs in different species can perform essentially the same function.

Water and ion permeability of a claudin model: A computational study.

At present, the three-dimensional structure of the multimeric paracellular claudin pore is unknown. Using extant biophysical data concerning the size of the pore and permeation of water and cations through it, two three-dimensional models of the pore are constructed in silico. Molecular Dynamics (MD) calculations are then performed to compute water and sodium ion permeation fluxes under the influence of applied hydrostatic pressure. Comparison to experiment is made, under the assumption that the hydrostatic pressure applied in the simulations is equivalent to osmotic pressure induced in experimental measurements of water/ion permeability. One model, in which pore-lining charged is distributed evenly over a selectivity filter section 10-16 Å in length, is found to be generally consistent with experimental data concerning the dependence of water and ion permeation on channel pore diameter, pore length, and the sign and magnitude of pore lining charge. The molecular coupling mechanism between water and ion flow under conditions where hydrostatic pressure is applied is computationally elucidated.

A Polymer-Brush-Based Nanovalve Controlled by Nanoparticle Additives: Design Principles.

Polymer-grafted surfaces and channels are increasingly used for the design of responsive materials and sensors due to robust performance and ease of use. Various strategies for the control of the nanoscale morphologies of such materials and devices are being tested. Entropic repulsion between the polymer chains in a grafted brush of sufficient density causes the chains to extend in the direction perpendicular to the grafting surface in comparison to the position of unattached polymers. When nanoparticles having attractive interactions with the polymers are introduced into the solvent, these nanoparticles tend to infiltrate into the brush and reduce its extension. Under certain conditions, a sharp reduction in brush height extension can occur over a narrow range of nanoparticle concentrations in solution. We describe a way of controlling transport through polymer-functionalized nanochannels with nanoparticle additives, relying on the physics of nanoparticles and polymer brushes under confinement, and we suggest a blueprint for the creation of a tunable nanovalve. The nanovalve is modeled as a cylinder with a polymer brush grafted on its inside surface. Brush properties such as the chain length and the grafting density are chosen so that the brush chains extend into the center of the cylinder in the absence of nanoparticles, occluding the flux of analyte molecules through the pore. When nanoparticles that are attracted to the polymers are introduced into solution, they infiltrate into the brush and partially collapse it against the cylindrical grafting surface, opening space in the center of the cylinder through which analyte molecules can flow. The operation of such a nanovalve is analyzed via self-consistent field theory calculations in the strong-stretching approximation. Self-consistent field analysis is supported by Langevin dynamics simulations of the underlying coarse-grained model of the polymer-nanoparticle system.

Calculation of iron transport through human H-chain ferritin.

Influx of ferrous ions from the cytoplasm through 3-fold pores in the shell of ferritin protein is computed using a 3-dimensional Poisson-Nernst-Planck electrodiffusion model, with inputs such as the pore structure and the diffusivity profile of permeant Fe(2+) ions extracted from all-atom molecular dynamics (MD) simulations. These calculations successfully reproduce experimental estimates of the transit time of Fe(2+) through the ferritin coat, which is on the millisecond time scale and hence much too long to be directly simulated via all-atom MD. This is also much longer than the typical time scale for ion transit in standard membrane spanning ion channels whose pores bear structural similarity to that of the 3-fold ferritin pore. The slow time scale for Fe(2+) transport through ferritin pores is traced to two features that distinguish the ferritin pore system from standard ion channels, namely, (i) very low concentration of cytoplasmic Fe(2+) under physiological conditions and (ii) very small internal diffusion coefficients for ions inside the ferritin pore resulting from factors that include the divalent nature of Fe(2+) and two rings of negatively charged amino acids surrounding a narrow geometric obstruction within the ferritin pore interior.

Morphology of polymer brushes infiltrated by attractive nanoinclusions of various sizes.

Addition of nanoparticles can control the morphologies of grafted polymer layers that are important in a variety of natural and artificial systems. We study the morphologies of grafted polymer layers interacting attractively with nanoparticle inclusions, as a function of particle size and the interaction strength, using self-consistent field theory and Langevin dynamics simulations. We find that the addition of nanoparticles causes distinctive changes in the layer morphology. For sufficiently strong interaction/binding, increasing the concentration of nanoparticles causes a compression of the polymer layer into a compact, low height state, followed by a subsequent rebound and swelling at sufficiently high concentrations. For nanoparticles of small size, the compression of the layer is sharp and occurs over a narrow range of nanoparticle concentrations. The transition region widens as the nanoparticle size increases. The transition is initiated via a dense layer of tightly bound monomers and nanoparticles near the grafting surface, with a low density region above it. For nanoparticles much larger than the characteristic graft spacing in the brush, the behavior is reversed: the nanoparticles penetrate only the dilute region near the top of the polymer layer without causing the layer to collapse.

Overdamped dynamics of folded protein domains within a locally harmonic basin using coarse graining based on a partition of compact flexible clusters.

A coarse-graining method based on the partitioning of atoms into compact flexible clusters is used to formulate the dynamics of the nonequilibrium response of a protein to ligand dissociation. The α-carbon positions are used as the degrees of freedom. The net stiffness between each pair of neighboring α-carbons is calculated for the quasi-static, overdamped regime within the harmonic (quadratic potential energy surface) using the equivalent stiffness matrix of the network of atoms occupying the intervening space within the locally interacting region. This localized approach realizes a divide and conquer strategy that results in a substantial reduction in computational complexity while accurately predicting relaxations under general loading conditions. A close correlation between the shapes and time scales of the relaxation curves of the coarse-grained and all-atom instances of two medium-sized proteins, T4 lysozyme and ferric binding protein (each of which having known apo and holo structures), was observed for the holo to the apo transitions. Furthermore, for both proteins the dominant modes of motion and the decay rates of the temporal relaxation profiles monitoring the separation distance between select amino acid pairs were found to be nearly identical when calculated on the coarse-grained and all-atom scales.

Langevin dynamics simulation of 3D colloidal crystal vacancies and phase transitions.

We study the mechanism of vacancy migration and phase transitions of 3D crystalline colloidal arrays (CCA) using Langevin dynamics simulations. We calculate the self-diffusion coefficient of the colloid particles and the diffusion constant for vacancies as a function of temperature and DLVO potential parameters. We investigate the phase behavior of several systems with different interaction potential parameters using Voronoi analysis. Voronoi polyhedra tessellation, which is a useful method for characterizing the nearest neighbor environment around each atom, provides an efficient and effective way to identify phase transitions as well as geometrical changes in crystals. Using Voronoi analysis, we show that several neighboring particles are involved in the vacancy migration process that causes the vacancy to diffuse.

Metal binding sites of human H-chain ferritin and iron transport mechanism to the ferroxidase sites: a molecular dynamics simulation study.

We study via all atom classical molecular dynamics (MD) simulation the process of uptake of ferrous ions (Fe(2+)) into the human ferritin protein and the catalytic ferroxidase sites via pores ("channels") in the interior of the protein. We observe that the three-fold hydrophilic channels serve as the main entrance pathway for the Fe(2+) ions. The binding sites along the ion pathway are investigated. Two strong binding sites, at the Asp131 and Glu134 residues and two weak binding sites, at the His118 and Cys130 are observed inside the three-fold channel. We also identify an explicit pathway for an ion exiting the channel into the central core of the protein as it moves to the ferroxidase site. The diffusion of an Fe(2+) ion from the inner opening of the channel to a ferroxidase site located in the interior region of the protein coat is assisted by Thr135, His136 and Tyr137. The Fe(2+) ion binds preferentially to site A of the ferroxidase site.

Energetics and ion permeation characteristics in a glutamate-gated chloride (GluCl) receptor channel.

An invertebrate glutamate-gated chloride channel (GluCl) has recently been crystallized in an open-pore state. This channel is homologous to the human Cys-loop receptor family of pentameric ligand-gated ion channels, including anion-selective GlyR and GABAR and cation-selective nAChR and 5HT(3). We implemented molecular dynamics (MD) in conjunction with an elastic network model to perturb the X-ray structure of GluCl and investigated the open channel stability and its ion permeation characteristics. Our study suggests that TM2 helical tilting may close GluCl near the hydrophobic constriction L254 (L9'), similar to its cation-selective homologues. Ion permeation characteristics were determined by Brownian dynamics simulations using a hybrid MD/continuum electrostatics approach to evaluate the free energy profiles for ion transport. Near the selectivity filter region (P243 or P-2'), the free energy barrier for Na(+) transport is over 4 k(B)T higher than that for Cl(-), indicating anion selectivity of the channel. Furthermore, three layers of positivity charged rings in the extracellular domain also contribute to charge selectivity and facilitate Cl(-) permeability over Na(+). Collectively, the charge selectivity of GluCl may be determined by overall electrostatic and ion dehydration effects, perhaps not deriving from a single region of the channel (the selectivity filter region near the intracellular entrance).

Morphological control of grafted polymer films via attraction to small nanoparticle inclusions.

Control of the morphologies of polymer films and layers by addition of nanosize particles is a novel technique for design of nanomaterials and is also at the core of some important biological processes. In order to facilitate the analysis of experimental data and enable predictive engineering of such systems, solid theoretical understanding is necessary. We study theoretically and computationally the behavior of plane-grafted polymer layers (brushes) in athermal solvent, decorated with small nanoparticle inclusions, using mean field theory and coarse-grained simulations. We show that the morphology of such layers is very sensitive to the interaction between the polymers and the nanoparticles and to the nanoparticle density. In particular, the mean field model shows that for a certain range of parameters, the nanoparticles induce a sharp transition in the layer height, accompanied by a sharp increase in the number of adsorbed nanoparticles. At other parameter values, the layer height depends smoothly on the nanoparticle concentration. Predictions of the theoretical model are verified by Langevin dynamics simulations. The results of the paper are in qualitative agreement with experiments on in vitro models of biological transport and suggest strategies for morphological control of nanocomposite materials.

Response of rotation-translation blocked proteins using Langevin dynamics on a locally harmonic landscape.

Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be successfully corrected by scaling each eigenvalue in the appropriate propagation matrix by the least-squares fitted slope of the blocked vs nonblocked eigenvalue spectra. The RTB responses for each test system were dominated by small eigenvalue overdamped Langevin modes. The large eigenvalue members of each response dissipated within the first 5 ps, after which the long time response was dominated by a modest set of low energy, overdamped normal modes, that were characterized by highly cooperative, functionally relevant displacements. The response assuming that the system is in the overdamped limit was compared to the full phase space Langevin dynamics results. The responses after the first 5 ps were nearly identical, confirming that the inertial components were significant only in the initial stages of the relaxation. Since the propagator matrix in the overdamped formulation is real-symmetric and does not require the inertial component in the propagator, the computation time and memory footprint was reduced by 1 order of magnitude.