Molecular dynamics simulations of grafted layers of bottle-brush polyelectrolytes

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer.     

Molecular dynamics simulations of multilayer films of polyelectrolytes and nanoparticles

We performed molecular dynamics simulations of multilayer assemblies of flexible polyelectrolytes and nanoparticles. The film was constructed by sequential adsorption of oppositely charged polymers and nanoparticles in layer-by-layer fashion from dilute solutions. We have studied multilayer films assembled from oppositely charged polyelectrolytes, oppositely charged nanoparticles, and mixed films containing both nanoparticles and polyelectrolytes. For all studied systems, the multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness. The multilayer films assembled from nanoparticles show better layer stratification but at the same time have higher film roughness than those assembled from flexible polyelectrolytes.     

Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls

Molecular dynamics simulations of polyelectrolytes grafted to two apposing surfaces were performed. Bead-spring polymer models are used to treat flexible chains [e.g., sodium poly(styrene sulfonate)] and stiff chains (double-stranded DNA). The counterions are explicitly treated. The effect of the surface density of the grafted polymer, the chain length, and the gap width on the structure and the pressure were studied. Results are compared to experimental measurements and to simulations of polyelectrolyte brushes on a single surface. The density profiles exhibit a maximum not found in single surface data. The maximum is due to the brushes shrinking to avoid interpenetration.     

Molecular dynamics simulations of spontaneous bile salt aggregation

Bile salts are surfactants in bile that facilitate digestion, adsorption and excretion of various compounds. They have planar hydrophobic and hydrophilic faces and therefore exhibit some unusual properties; including the shape and size of the micelles that they form. Molecular dynamics simulations of the spontaneous aggregation of six bile salts (cholate (CHD), glycocholate (GCH), taurocholate (TCH), glycochenodeoxycholate (GCD), glycodeoxycholate (GDX) and glycolithocholate (GLC)) were performed in an aqueous phase to gain insight into their micellar structure. The aggregates that formed spontaneously from a random distribution of molecules ranged in size from 8 to 17 molecules. The structures are highly dynamic in nature and are on average oblate, but can vary from oblate, to spherical or prolate. Intermolecular hydrogen bonding within the micelles was found to be an important factor in determining the micelle size, structure and dynamics. The molecular arrangement within the micelles maximises the hydration of the hydrophilic chains and some favourable orientations for adjacent molecules were acquired. The dynamics of the micelles were investigated using the hydrogen-bond lifetime autocorrelation function correlation time, which exhibited a relationship with the degree of hydroxylation. Comparison of the proposed model to the three literature models showed some features of the disk shaped models of Cary and Small [M.C. Cary, D.M. Small, Arch. Intern. Med. 130 (1972) 506–527] and Kawamura et al. [H. Kawamura, Y. Murata, T. Yamaguchi, H. Igimi, M. Tanaka, G. Sugihara, J.P. Kratohvil, J. Phys. Chem. 93 (1989) 3321–3326], whereas the third, inverted helix model of Giglio et al. [E. Giglio, S. Loreti, N.V. Pavel, J. Phys. Chem. 92 (1988) 2858–2862] can be discounted. The proposed model is better than the existing models, which assumed a rigid and structured molecular arrangement.     

Molecular dynamics simulations of the characteristics of sodium carboxymethyl cellulose with different degrees of substitution in a salt solution

Sodium carboxymethyl cellulose (SCMC) with different degrees of substitution (DS) possesses structural characteristics and physicochemical properties that are important in broad areas of industrial applications. This reported work investigated the structural characteristics, including the effective length (L _ef), the radius of gyration (R _g), and the hydrodynamic radius (R _H), and the physicochemical properties, including intrinsic viscosity ([η]) and salt tolerance, of SCMC with a DS more than 1.0 in NaCl solution using molecular dynamics (MD) simulations. In the MD simulations, the DS of SCMC varied from 1.2 to 2.8, and the NaCl concentration varied from 0 to 1.4 mol/L. MD simulation results showed that with the increment of NaCl concentration, the L _ef (or R _g or R _H) of SCMC decreased; with the increment of the DS, the L _ef of SCMC increased. Also, the variation tendency of [η] in the NaCl solution was consistent with its L _ef (or R _g or R _H). It was noted that the salt tolerance (represented by D) of SCMC increased as the DS increased. In addition, the sharp variation of the D value of SCMC occurred in the range of DS of 1.6 to 2.0, which agreed with the reported experimental results. Radial distribution function analyses showed that the Na⁺ cations had a stronger interaction with the carboxyl groups in SCMC with lower DS when it was present in a salt solution of higher concentration, which also reasonably explained the variation of L _ef, R _g, R _H, [η], and D of SCMC in NaCl solution.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

Molecular dynamics simulations of dendrimer-encapsulated alpha-Keggin ions in trichloromethane solution

We report on molecular dynamics simulations of dendrimer-encapsulated alpha-Keggin ions in trichloromethane solution. The simulations were done within the NVE ensemble at temperatures around T = 300 K. The eight examined systems are model compounds for dendrizymes, a hybrid material where a polyoxometalate ion (the core) is surrounded by amphiphilic cationic dendrimers (the shell) such that the complete system may exhibit enzyme-like regioselectivity and substrate selectivity, e.g., in olefin oxidation. The influence of dendrimer type, dendrimer generation, and number of dendritic cations bound by electrostatic interaction to the polyoxometalate core on the structure and dynamics of the shell has been studied. It is shown that the resulting distribution of trichloromethane molecules within the shell may serve as an indicator for the shell's permeability for small molecules. The dendritic shell causes a size exclusion effect that influences the access of small molecules to the central polyoxometalate ion, i.e., to that part where the enzyme-like reaction of a dendrizyme is supposed to take place.     

Molecular dynamics studies of anchored polyelectrolytes

We study polyelectrolytes end-grafted to a surface in a model which includes counterions explicitly and treats the full long-range Coulomb interaction. For strongly charged polyelectrolytes the counterions are localized inside the brush and electroneutrality is satisfied locally. Under these conditions, we find that the brush thickness is linearly proportional to the chain length and the grafting density. The counterion distribution is strongly inhomogeneous, and counterion condensation can be observed although the Bjerrum length is smaller than the average bond length. Varying the Bjerrum length we find a non-monotonic behaviour of the brush height. Counterion diffusion is anisotropic, and is enhanced at higher grafting densities. For partially charged polyelectrolytes we obtain a crossover from quasi-neutral behaviour to the strongly charged behaviour reported above.     

Computer simulations of diffusion and dynamics of short-chain polyelectrolytes

Brownian dynamics simulations are conducted to investigate the diffusional and dynamic properties of polyelectrolytes in dilute salt-free solutions. The polyelectrolyte molecule is represented by a bead-spring chain in a primitive model. The long-range hydrodynamic and Coulomb interactions are both taken into consideration through the Ewald summations for the first time. The major finding of our simulations is that the dependence of the long-time chain diffusivity on the Coulomb interaction strength is very different from that of the Kirkwood short-time diffusivity, which simply shows a trend nearly opposite to the chain size. When ignoring the hydrodynamic interaction (HI), the coupling effect between the chain and its counterions gives rise to a noticeable increase in the long-time diffusivity at intermediate electrostatic interaction strengths. However, the incorporation of HI suppresses this effect to a degree that one can no longer discern it. Moreover, the rotational relaxation is found to show a dependence opposite to that of the gyration radius relaxation.     

Molecular dynamics simulations of oligonucleotides in solution: Visualisation of intrinsic curvature

Summary We have undertaken molecular dynamics simulations on the d(CGCAAAAAAGCG)d(CGCTTTTTTGCG) dodecamer in solution. In this study, we focus on aspects of conformation and dynamics, including the possibility of cross-strand hydrogen bonds. We compare our results with those from crystallography as well as infrared, Raman and NMR spectroscopy and cyclization kinetics. Our method of analysis allows us to visualise the curvature of the helix as a function of time during the simulation. We find that the major distortions of the helix axis path occur at the junctions between the (essentially straight) A-tract and the CG-and GC-tracts, although at one junction this is due to hyperflexibility (i.e., regions of high flexibility with no preferred direction of curvature), while at the other junction a static curvature is found (i.e., a preferred, sustained direction of curvature).     

Precision of free energies calculated by molecular dynamics simulations of peptides in solution

Errors in free energies for molecular replacement and for conformation change of a small model peptide have been determined empirically by repeated simulations from different starting points. All calculations have been done using thermodynamic integration, in which the system's potential energy is coupled to a parameter λ, that is increased or decreased by a small amount at each step of the simulation. The effects of several factors that may alter the precision are evaluated. These factors include: the length of the simulation, the dependence of the potential energy on λ, the use of conformational restraints, and their magnitude and form. The methods used for restraint and conformational forcing are described in detail. The free energy change, calculated as the mean from several successive simulations with alternately increasing and decreasing λ, is found to be independent of the length of the simulations. As expected, longer simulations produce more precise results. The variation of the calculated free energies is found to consist of two parts, a random error and a systematic hysteresis, i.e., a dependence on the direction in which λ changes. The hysteresis varies as the inverse of the length of the simulation and the random error as the inverse square root The advantage of the use of a different (nonlinear) dependence of the attractive and repulsive parts of the nonbonded potential energy on the coupling parameter when “creating” particles in solution is found to be very large. This nonlinear coupling was found to be superior to the use of linear coupling and a nonlinear change of the coupling parameter with the simulation time. The hysteresis in conformational free energy calculations is found to increase markedly if too weak a forcing restraint is chosen. It is shown how to deconvolute the contribution of a torsional restraint from the dependence of the free energy on a torsion angle.     

Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.     

Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.     

Interaction between brush layers of bottle-brush polyelectrolytes: molecular dynamics simulations

Interactions between tethered layers composed of aggrecan (charged bottle-brush) macromolecules are responsible for the molecular origin of cartilage biomechanical behavior. To elucidate the role of the electrostatic forces in interaction between bottle-brush layers, we have performed molecular dynamics simulations of charged and neutral bottle-brush macromolecules tethered to substrates. In the case of charged bottle-brush layers, the disjoining pressure P between two brush layers in salt-free solutions increases with decreasing distance D between substrates as P ∝ D(-1.8). A stronger dependence of the disjoining pressure P on the surface separation D was observed for neutral bottle-brushes, P ∝ D(-4.6), in the same interval of disjoining pressures. These scaling laws for dependence of disjoining pressure P on distance D are due to bending energy of the bottle-brush macromolecules within compressed brush layers. The weaker distance dependence observed in polyelectrolyte bottle-brushes is due to interaction between counterion clouds surrounding the bottle-brush macromolecules preventing strong brush overlap.     

Counterion associative behavior with flexible polyelectrolytes

At low ionic strength, organic counterions dress a flexible charged polymer as measured directly by small-angle neutron scattering and neutron spin-echo spectroscopy. This dressed state, quantified by the concentration dependence of the static correlation length, illustrates the polymer-counterion coupled nature on the nanometer length scale. The counterions, made visible by selective hydrogen and deuterium labeling, undress from the polymeric template by addition of sodium chloride. The addition of this electrolyte leads to two effects: increased Debye electrostatic screening and decoupled organic counterion-polymer correlations. Neutron spin-echo spectroscopy measures a slowing down of the effective diffusion coefficient of the labeled counterions at the length scale of 8 nm, the static correlation length, indicating the nanosecond counterion dynamics mimics the polymer. These experiments, performed with semidilute solutions of tetramethylammonium poly(styrene sulfonate) [(h-TMA(+)) d-PSS], apply to relevant biopolymers including single and double stranded DNA and unfolded proteins, which undergo orchestrated dynamics of counterions and chain segments to fold, unfold, and assemble.     

"Like-charge attraction" between anionic polyelectrolytes: molecular dynamics simulations

"Like-charge attraction" is a phenomenon found in many biological systems containing DNA or proteins, as well as in polyelectrolyte systems of industrial importance. "Like-charge attraction" between polyanions is observed in the presence of mobile multivalent cations. At a certain limiting concentration of cations, the negatively charged macroions cease to repel each other and even an attractive force between the anions is found. With classical molecular dynamics simulations it is possible to elucidate the processes that govern the attractive behavior with atomistic resolution. As an industrially relevant example we study the interaction of negatively charged carboxylate groups of sodium polyacrylate molecules with divalent cationic Ca2+ counterions. Here we show that Ca2+ ions initially associate with single chains of polyacrylates and strongly influence sodium ion distribution; shielded polyanions approach each other and eventually "stick" together (precipitate), contrary to the assumption that precipitation is initially induced by intermolecular Ca2+ bridging.     

Molecular dynamics simulations of peptide-surface interactions

Proteins, which are bioactive molecules, adsorb on implants placed in the body through complex and poorly understood mechanisms and directly influence biocompatibility. Molecular dynamics modeling using empirical force fields provides one of the most direct methods of theoretically analyzing the behavior of complex molecular systems and is well-suited for the simulation of protein adsorption behavior. To accurately simulate protein adsorption behavior, a force field must correctly represent the thermodynamic driving forces that govern peptide residue-surface interactions. However, since existing force fields were developed without specific consideration of protein-surface interactions, they may not accurately represent this type of molecular behavior. To address this concern, we developed a host-guest peptide adsorption model in the form of a G(4)-X-G(4) peptide (G is glycine, X is a variable residue) to enable determination of the contributions to adsorption free energy of different X residues when adsorbed to functionalized Au-alkanethiol self-assembled monolayers (SAMs). We have previously reported experimental results using surface plasmon resonance (SPR) spectroscopy to measure the free energy of peptide adsorption for this peptide model with X = G and K (lysine) on OH and COOH functionalized SAMs. The objectives of the present research were the development and assessment of methods to calculate adsorption free energy using molecular dynamics simulations with the GROMACS force field for these same peptide adsorption systems, with an oligoethylene oxide (OEG) functionalized SAM surface also being considered. By comparing simulation results to the experimental results, the accuracy of the selected force field to represent the behavior of these molecular systems can be evaluated. From our simulations, the G(4)-G-G(4) and G(4)-K-G(4) peptides showed minimal to no adsorption to the OH SAM surfaces and the G(4)-K-G(4) showed strong adsorption to the COOH SAM surface, which is in agreement with our SPR experiments. Contrary to our experimental results, however, the simulations predicted a relatively strong adsorption of G(4)-G-G(4) peptide to the COOH SAM surface. In addition, both peptides were unexpectedly predicted to adsorb to the OEG surface. These findings demonstrate the need for GROMACS force field parameters to be rebalanced for the simulation of peptide adsorption behavior on SAM surfaces. The developed methods provide a direct means of assessing, modifying, and validating force field performance for the simulation of peptide and protein adsorption to surfaces, without which little confidence can be placed in the simulation results that are generated with these types of systems.     

Molecular dynamics simulations of biotin carboxylase

Biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin and is one component of the multienzyme complex acetyl-CoA carboxylase that catalyzes the first committed step in fatty acid synthesis in all organisms. Biotin carboxylase from Escherichia coli, whose crystal structures with and without ATP bound have been determined, has served as a model system for this component of the acetyl-CoA carboxylase complex. The two crystal structures revealed a large conformational change of one domain relative to the other domains when ATP is bound. Unfortunately, the crystal structure with ATP bound was obtained with an inactive site-directed mutant of the enzyme. As a consequence the structure with ATP bound lacked key structural information such as for the Mg2+ ions and contained altered conformations of key active-site residues. Therefore, nanosecond molecular dynamics studies of the wild-type biotin carboxylase were undertaken to supplant and amend the results of the crystal structures. Specifically, the protein-metal interactions of the two catalytically critical Mg2+ ions bound in the active site are presented along with a reevaluation of the conformations of active-site residues bound to ATP. In addition, the regions of the polypeptide chain that serve as hinges for the large conformational change were identified. The results of the hinge analysis complemented a covariance analysis that identified the individual structural elements of biotin carboxylase that change their conformation in response to ATP binding.     

Molecular dynamics simulations of cardiolipin bilayers

Cardiolipin is a key lipid component in the inner mitochondrial membrane, where the lipid is involved in energy production, cristae structure, and mechanisms in the apoptotic pathway. In this article we used molecular dynamics computer simulations to investigate cardiolipin and its effect on the structure of lipid bilayers. Three cardiolipin/POPC bilayers with different lipid compositions were simulated: 100, 9.2, and 0% cardiolipin. We found strong association of sodium counterions to the carbonyl groups of both lipid types, leaving in the case of 9.2% cardiolipin virtually no ions in the aqueous compartment. Although binding occurred primarily at the carbonyl position, there was a preference to bind to the carbonyl groups of cardiolipin. Ion binding and the small headgroup of cardiolipin gave a strong ordering of the hydrocarbon chains. We found significant effects in the water dipole orientation and water dipole potential which can compensate for the electrostatic repulsion that otherwise should force charged lipids apart. Several parameters relevant for the molecular structure of cardiolipin were calculated and compared with results from analyses of coarse-grained simulations and available X-ray structural data.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.