Dynamic simulations of many-body electrostatic self-assembly

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process.This article is part of the theme issue 'Modern theoretical chemistry'.

Repulsion between oppositely charged rod-shaped macromolecules: Role of overcharging and ionic confinement

The interaction between two oppositely charged rod-shaped macro-ions in a micro-ion solution is investigated via Monte Carlo simulations of the primitive model. The focus is on the asymmetry in rod and/or ion charge, i.e., conditions where oppositely charged objects can repel one another. For equally and oppositely charged rods with asymmetric z:1 micro-ions, repulsion may be induced by overcharging one of the rods with the z valent ions. For asymmetrically charged rods in a symmetric z:z micro-ion solution, a repulsive interaction-at separation of the order of one ion diameter-can arise via an unbalanced osmotic pressure contribution from the ionic atmosphere in the inter-rod space, and an attractive interaction-at a smaller separation-may occur due to a "squeezing out" of the micro-ions from the space between the rods (with a consequent gain in entropy). The thermodynamics of each mechanism is investigated in terms of rod charge and size and micro-ion valence, size, and concentration. Our findings contribute to the understanding of the complex role of charge asymmetry on the interaction of, for example, oppositely charged polyelectrolytes, functionalized nanotubes, and rod-like biomolecules, e.g., viruses.

Interaction modes between asymmetrically and oppositely charged rods

The interaction of oppositely and asymmetrically charged rods in salt-a simple model of (bio)macromolecular assembly-is observed via simulation to exhibit two free energy minima, separated by a repulsive barrier. In contrast to similar minima in the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the governing mechanism includes electrostatic attraction at large separation, osmotic repulsion at close range, and depletion attraction near contact. A model accounting for ion condensation and excluded volume is shown to be superior to a mean-field treatment in predicting the effect of charge asymmetry on the free-energy profile.

Ligand-modulated interactions between charged monolayer-protected Au144(SR)60 gold nanoparticles in physiological saline

In order to determine how functionalized gold nanoparticles (AuNPs) interact in a near-physiological environment, we performed all-atom molecular dynamics simulations on the icosahedral Au144 nanoparticles each coated with a homogeneous set of 60 thiolates selected from one of these five (5) types: 11-mercapto-1-undecanesulfonate -SC11H22(SO3(-)), 5-mercapto-1-pentanesulfonate -SC5H10(SO3(-)), 5-mercapto-1-pentaneamine -SC5H10(NH3(+)), 4-mercapto-benzoate -SPh(COO(-)), or 4-mercapto-benzamide -SPh(CONH3(+)). These thiolates were selected to elucidate how the aggregation behavior of AuNPs depends on ligand parameters, including the charge of the terminal group (anionic vs. cationic), and its length and conformational flexibility. For this purpose, each functionalized AuNP was paired with a copy of itself, placed in an aqueous cell, neutralized by 120 Na(+)/Cl(-) counter-ions and salinated with a 150 mM concentration of NaCl, to form five (5) systems of like-charged AuNPs pairs in a saline. We computed the potential of mean force (the reversible work of separation) as a function of the intra-pair distance and, based on which, the aggregation affinities. We found that the AuNPs coated with negatively charged, short ligands have very high affinities. Structurally, a significant number of Na(+) counter-ions reside on a plane between the AuNPs, mediating the interaction. Each such ion forms a "salt bridge" (or "ionic bonds") to both of the AuNPs when they are separated by its diameter plus 0.2-0.3 nm. The positively charged AuNPs have much weaker affinities, as Cl(-) counter-ions form fewer and weaker salt bridges between the AuNPs. In the case of Au144(SC11H22(SO3(-)))60 pair, the flexible ligands fluctuate much more than the other four cases. The large fluctuations disfavor the forming of salt bridges between two AuNPs, but enable hydrophobic contact between the exposed hydrocarbon chains of the two AuNPs, which are subject to an effective attraction at a separation much greater than the AuNP diameter and involve a higher concentration of counter ions in the inter-pair space.

Interaction between functionalized gold nanoparticles in physiological saline

The interactions between functionalized noble-metal particles in an aqueous solution are central to applications relying on controlled equilibrium association. Herein, we obtain the potentials of mean force (PMF) for pair-interactions between functionalized gold nanoparticles (AuNPs) in physiological saline. These results are based upon >1000 ns experiments in silico of all-atom model systems under equilibrium and non-equilibrium conditions. Four types of functionalization are built by coating each globular Au144 cluster with 60 thiolate groups: GS-AuNP (glutathionate), PhS-AuNP (thiophenol), CyS-AuNP (cysteinyl), and p-APhS-AuNP (para-amino-thiophenol), which are, respectively, negatively charged, hydrophobic (neutral-nonpolar), hydrophilic (neutral-polar), and positively charged at neutral pH. The results confirm the behavior expected of neutral (hydrophilic or hydrophobic) particles in a dilute aqueous environment, however the PMF curves demonstrate that the charged AuNPs interact with one another in a unique way-mediated by H2O molecules and an electrolyte (Na(+), Cl(-))-in a physiological environment. In the case of two GS-AuNPs, the excess, neutralizing Na(+) ions form a mobile (or 'dynamic') cloud of enhanced concentration between the like-charged GS-AuNPs, inducing a moderate attraction (∼25 kT) between them. Furthermore, to a lesser degree, for a pair of p-APhS-AuNPs, the excess, neutralizing Cl(-) ions (less mobile than Na(+)) also form a cloud of higher concentration between the two like-charged p-APhS-AuNPs, inducing weaker yet significant attractions (∼12 kT). On combining one GS- with one p-APhS-AuNP, the direct, attractive Coulombic force is completely screened out while the solvation effects give rise to moderate repulsion between the two unlike-charged AuNPs.

Ion-mediated interactions in suspensions of oppositely charged nanoparticles

The structure of oppositely charged spherical nanoparticles (polyions), dispersed in ionic solutions with continuous solvent (primitive model), is investigated by Monte Carlo (MC) simulations, within explicit and implicit microion representations, over a range of polyion valences and densities, and microion concentrations. Systems with explicit microions are explored by semigrand canonical MC simulations, and allow density-dependent effective polyion pair potentials v(alphabeta) (eff)(r) to be extracted from measured partial pair distribution functions. Implicit microion MC simulations are based on pair potentials of mean force v(alphabeta) ((2))(r) computed by explicit microion simulations of two charged polyions, in the low density limit. In the vicinity of the liquid-gas separation expected for oppositely charged polyions, the implicit microion representation leads to an instability against density fluctuations for polyion valences mid R:Zmid R: significantly below those at which the instability sets in within the exact explicit microion representation. Far from this instability region, the v(alphabeta) ((2))(r) are found to be fairly close to but consistently more repulsive than the effective pair potentials v(alphabeta) (eff)(r). This is corroborated by additional calculations of three-body forces between polyion triplets, which are repulsive when one polyion is of opposite charge to the other two. The explicit microion MC data were exploited to determine the ratio of salt concentrations c and c(o) within the dispersion and the reservoir (Donnan effect). c/c(o) is found to first increase before finally decreasing as a function of the polyion packing fraction.

Nonspecific DNA-protein interaction: why proteins can diffuse along DNA

Recent single molecule experiments have reported that DNA binding proteins (DNA-BPs) can diffuse along DNA. This suggests that interactions between proteins and DNA play a role during the target search even far from their specific site on DNA. Here we show by means of Monte Carlo simulations and analytical calculations that there is a counterintuitive repulsion between the two oppositely charged macromolecules at a nanometer range. For the concave shape of DNA-BPs, and for realistic protein charge densities, we find that the DNA-protein interaction free energy has a minimum at a finite surface-to-surface separation, in which proteins can easily slide. When a protein encounters its target, the free energy barrier is completely counterbalanced by the H-bond interaction, thus enabling the sequence recognition.