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.

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.

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.

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.

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.

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.

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.

Molecular dynamics investigation of Cl- and water transport through a eukaryotic CLC transporter.

Early crystal structures of prokaryotic CLC proteins identified three Cl(-) binding sites: internal (S(int)), central (S(cen)), and external (S(ext)). A conserved external GLU (GLU(ex)) residue acts as a gate competing for S(ext). Recently, the first crystal structure of a eukaryotic transporter, CmCLC, revealed that in this transporter GLU(ex) competes instead for S(cen). Here, we use molecular dynamics simulations to investigate Cl(-) transport through CmCLC. The gating and Cl(-)/H(+) transport cycle are inferred through comparative molecular dynamics simulations with protonated and deprotonated GLU(ex) in the presence/absence of external potentials. Adaptive biasing force calculations are employed to estimate the potential of mean force profiles associated with transport of a Cl(-) ion from S(ext) to S(int), depending on the Cl(-) occupancy of other sites. Our simulations demonstrate that protonation of GLU(ex) is essential for Cl(-) transport from S(ext) to S(cen). The S(cen) site may be occupied by two Cl(-) ions simultaneously due to a high energy barrier (∼8 Kcal/mol) for a single Cl(-) ion to translocate from S(cen) to S(int). Binding two Cl(-) ions to S(cen) induces a continuous water wire from S(cen) to the extracellular solution through the side chain of the GLU(ex) gate. This may initiate deprotonation of GLU(ex), which then drives the two Cl(-) ions out of S(cen) toward the intracellular side via two putative Cl(-) transport paths. Finally, a conformational cycle is proposed that would account for the exchange stoichiometry.

Calcium inhibits paracellular sodium conductance through claudin-2 by competitive binding.

Claudins form paracellular pores at the tight junction in epithelial cells. Profound depletion of extracellular calcium is well known to cause loosening of the tight junction with loss of transepithelial resistance. However, moderate variations in calcium concentrations within the physiological range can also regulate transepithelial permeability. To investigate the underlying molecular mechanisms, we studied the effects of calcium on the permeability of claudin-2, expressed in an inducible MDCK I cell line. We found that in the physiological range, calcium acts as a reversible inhibitor of the total conductance and Na(+) permeability of claudin-2, without causing changes in tight junction structure. The effect of calcium is enhanced at low Na(+) concentrations, consistent with a competitive effect. Furthermore, mutation of an intrapore negatively charged binding site, Asp-65, to asparagine partially abrogated the inhibitory effect of calcium. This suggests that calcium competes with Na(+) for binding to Asp-65. Other polyvalent cations had similar effects, including La(3+), which caused severe and irreversible inhibition of conductance. Brownian dynamics simulations demonstrated that such inhibition can be explained if Asp-65 has a relatively high charge density, thus favoring binding of Ca(2+) over that of Na(+), reducing Ca(2+) permeation by inhibiting its dissociation from this site, and decreasing Na(+) conductance through repulsive electrostatic interaction with Ca(2+). These findings may explain why hypercalcemia inhibits Na(+) reabsorption in the proximal tubule of the kidney.

Discrete-state representation of ion permeation coupled to fast gating in a model of CLC-chloride channels: analytic estimation of the state-to-state rate constants.

Analytical estimation of state-to-state rate constants is carried out for a recently developed discrete state model of chloride ion motion in a CLC chloride channel (Coalson and Cheng, J. Phys. Chem. B 2010, 114, 1424). In the original presentation of this model, the same rate constants were evaluated via three-dimensional Brownian dynamics simulations. The underlying dynamical theory is an appropriate single- or multiparticle three-dimensional Smoluchowski equation. Taking advantage of approximate geometric symmetries (based on the details of the model channel geometry), well-known formulas for state-to-state transition rates are appealed to herein and adapted as necessary to the problem at hand. Rates of ionic influx from a bulk electrolyte reservoir to the nearest binding site within the channel pore are particularly challenging to compute analytically because they reflect multi-ion interactions (as opposed to single-ion dynamics). A simple empirical correction factor is added to the single-ion rate constant formula in this case to account for the saturation of influx rate constants with increasing bulk Cl(-) concentration. Overall, the agreement between all analytically estimated rate constants is within a factor of 2 of those computed via three-dimensional Brownian dynamics simulations, and often better than this. Current-concentration curves obtained using rate constants derived from these two different computational approaches agree to within 25%.

Molecular dynamics and brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel.

Bacterial Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) is activated to cation permeation upon lowering the solution pH. Its function can be modulated by anesthetic halothane. In the present work, we integrate molecular dynamics (MD) and Brownian dynamics (BD) simulations to elucidate the ion conduction, charge selectivity, and halothane modulation mechanisms in GLIC, based on recently resolved X-ray crystal structures of the open-channel GLIC. MD calculations of the potential of mean force (PMF) for a Na(+) revealed two energy barriers in the extracellular domain (R109 and K38) and at the hydrophobic gate of transmembrane domain (I233), respectively. An energy well for Na(+) was near the intracellular entrance: the depth of this energy well was modulated strongly by the protonation state of E222. The energy barrier for Cl(-) was found to be 3-4 times higher than that for Na(+). Ion permeation characteristics were determined through BD simulations using a hybrid MD/continuum electrostatics approach to evaluate the energy profiles governing the ion movement. The resultant channel conductance and a near-zero permeability ratio (P(Cl)/P(Na)) were comparable to experimental data. On the basis of these calculations, we suggest that a ring of five E222 residues may act as an electrostatic gate. In addition, the hydrophobic gate region may play a role in charge selectivity due to a higher dehydration energy barrier for Cl(-) ions. The effect of halothane on the Na(+) PMF was also evaluated. Halothane was found to perturb salt bridges in GLIC that may be crucial for channel gating and open-channel stability, but had no significant impact on the single ion PMF profiles.

Dynamic linear response theory for conformational relaxation of proteins.

Dynamic linear response theory is adapted to the problem of computing the time evolution of the atomic coordinates of a protein in response to the unbinding of a ligand molecule from a binding pocket within the protein. When the ligand dissociates from the molecule, the protein molecule finds itself out of equilibrium and its configuration begins to change, ultimately coming to a new stable configuration corresponding to equilibrium in a force field that lacks the ligand-protein interaction terms. Dynamic linear response theory (LRT) relates the nonequilibrium motion of the protein atoms that ensues after the ligand molecule dissociates to equilibrium dynamics in the force field, or equivalently, on the potential energy surface (PES) relevant to the unliganded protein. In general, the connection implied by linear response theory holds only when the ligand-protein force field is small. However, in the case where the PES of the unliganded protein system is a quadratic (harmonic oscillator) function of the coordinates, and the force of the ligand upon the protein molecule in the ligand-bound conformation is constant (the force on each atom in the protein is independent of the location of the atom), dynamic LRT is exact for any ligand-protein force field strength. An analogous statement can be made for the case where the atoms in the protein are subjected to frictional and random noise forces in accord with the Langevin equation (to account for interaction of the protein with solvent, for example). We numerically illustrate the application of dynamic LRT for a simple harmonic oscillator model of the ferric binding protein, and for an analogous model of T4 lysozyme. Using a physically appropriate value of the viscosity of water to guide the choice of friction parameters, we find relaxation time scales of residue-residue distances on the order of several hundred ps. Comparison is made to relevant experimental measurements.

Effectiveness of perturbation theory approaches for computing non-condon electron transfer dynamics in condensed phases.

A description of electron transfer in condensed-phase media requires models that adequately describe the coupling of the electronic degrees of freedom to the surrounding nuclear coordinates. The spin-boson model has been the canonical model used to understand quantum dynamic processes in condensed-phase media over the last 25 years. Inherent in the standard model of a two-state quantum system coupled to a bosonic bath is the assumption that the Condon approximation is valid. In this context, the Condon approximation assumes that the bath configurations (coordinates) have no effect on the nonadiabatic coupling matrix element. While this is a useful model for electron transfer in small molecular systems, the validity of this approximation is less likely when large-scale motions of solvent molecules are strongly coupled to the electron transfer event, e.g., in molecular clamps and long-range electron transfer in biopolymers. In the present paper a general model for two-state electron transfer which allows for system-bath coupling in both the diagonal and off-diagonal (nonadiabatic) terms is studied. Time-dependent perturbation theory for this Hamiltonian is developed using a small polaron transformation. As noted in several recent studies, in a certain regime of parameter space, the relevant Hamiltonian admits an exact solution, termed the exactly solvable non-Condon Hamiltonian (or NCE). This limit, for which exact solutions are available, is used to benchmark the short- and long-time accuracy of various perturbative approaches. The validated perturbation equations are subsequently used to explore the role of non-Condon effects on electron transfer by systematically increasing the strength of the non-Condon coupling term from zero (i.e., the canonical spin-boson model) to the value that pertains to the exactly solvable non-Condon model (where non-Condon effects are significant).

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.

Molecular dynamics simulations of ethanol binding to the transmembrane domain of the glycine receptor: implications for the channel potentiation mechanism.

The glycine receptor (GlyR) is potentiated by ethanol and other anesthetics. The potentiation mechanism at the molecular level is unknown and remains elusive, but mutagenic studies have shown that ethanol and other volatile anesthetics bind to a pocket between TM1, TM2, and TM3. The present study extends previous studies (Cheng et al., Proteins 2007;68:581-593) wherein we conducted homology modeling and molecular dynamics (MD) simulations to construct models of the homopentameric alpha1 subunits of the GlyR transmembrane domain in open and closed states. To understand the potentiation of GlyR by ethanol we compare the binding of ethanol molecules to the channel in these different states. We observe that ethanol stably resides inside solvent-accessible cavities found in the open state of GlyR that are formed by I229 (of TM1) in one subunit and S267 and A288 (of TM2 and TM3, respectively) in the adjacent subunit. The volume of these putative binding pockets is state-dependent. Selective binding to the open states of receptors has been proposed to explain the potentiating actions of this class of anesthetics. In accordance with this model, our MD simulations suggest that the potentiation of ethanol on GlyR may be effected through preferential binding of ethanol molecules to an inter-subunit binding pocket in the open state.

Water and deuterium oxide permeability through aquaporin 1: MD predictions and experimental verification.

Determining the mechanisms of flux through protein channels requires a combination of structural data, permeability measurement, and molecular dynamics (MD) simulations. To further clarify the mechanism of flux through aquaporin 1 (AQP1), osmotic p(f) (cm(3)/s/pore) and diffusion p(d) (cm(3)/s/pore) permeability coefficients per pore of H(2)O and D(2)O in AQP1 were calculated using MD simulations. We then compared the simulation results with experimental measurements of the osmotic AQP1 permeabilities of H(2)O and D(2)O. In this manner we evaluated the ability of MD simulations to predict actual flux results. For the MD simulations, the force field parameters of the D(2)O model were reparameterized from the TIP3P water model to reproduce the experimentally observed difference in the bulk self diffusion constants of H(2)O vs. D(2)O. Two MD systems (one for each solvent) were constructed, each containing explicit palmitoyl-oleoyl-phosphatidyl-ethanolamine (POPE) phospholipid molecules, solvent, and AQP1. It was found that the calculated value of p(f) for D(2)O is approximately 15% smaller than for H(2)O. Bovine AQP1 was reconstituted into palmitoyl-oleoyl-phosphatidylcholine (POPC) liposomes, and it was found that the measured macroscopic osmotic permeability coefficient P(f) (cm/s) of D(2)O is approximately 21% lower than for H(2)O. The combined computational and experimental results suggest that deuterium oxide permeability through AQP1 is similar to that of water. The slightly lower observed osmotic permeability of D(2)O compared to H(2)O in AQP1 is most likely due to the lower self diffusion constant of D(2)O.

In silico models for the human alpha4beta2 nicotinic acetylcholine receptor.

The neuronal alpha4beta2 nicotinic acetylcholine receptor (nAChR) is one of the most widely expressed nAChR subtypes in the brain. Its subunits have high sequence identity (54 and 46% for alpha4 and beta2, respectively) with alpha and beta subunits in Torpedo nAChR. Using the known structure of the Torpedo nAChR as a template, the closed-channel structure of the alpha4beta2 nAChR was constructed through homology modeling. Normal-mode analysis was performed on this closed structure and the resulting lowest frequency mode was applied to it for a "twist-to-open" motion, which increased the minimum pore radius from 2.7 to 3.4 A and generated an open-channel model. Nicotine could bind to the predicted agonist binding sites in the open-channel model but not in the closed one. Both models were subsequently equilibrated in a ternary lipid mixture via extensive molecular dynamics (MD) simulations. Over the course of 11 ns MD simulations, the open channel remained open with filled water, but the closed channel showed a much lower water density at its hydrophobic gate comprised of residues alpha4-V259 and alpha4-L263 and their homologous residues in the beta2 subunits. Brownian dynamics simulations of Na+ permeation through the open channel demonstrated a current-voltage relationship that was consistent with experimental data on the conducting state of alpha4beta2 nAChR. Besides establishment of the well-equilibrated closed- and open-channel alpha4beta2 structural models, the MD simulations on these models provided valuable insights into critical factors that potentially modulate channel gating. Rotation and tilting of TM2 helices led to changes in orientations of pore-lining residue side chains. Without concerted movement, the reorientation of one or two hydrophobic side chains could be enough for channel opening. The closed- and open-channel structures exhibited distinct patterns of electrostatic interactions at the interface of extracellular and transmembrane domains that might regulate the signal propagation of agonist binding to channel opening. A potential prominent role of the beta2 subunit in channel gating was also elucidated in the study.