Charged Dendrimers with Finite-Size Counterions

Effect of Counterion Size on Knotted Polyelectrolyte Conformations

Using Langevin dynamics simulations and a coarse-grained primitive model of electrolytes, we show that the behavior of knotted circular strong polyelectrolytes (PEs) in diluted aqueous solution is largely affected by the diameter of the counterions (CIs), σCI. Indeed, we observe that both gyration radius and knot length vary nonmonotonically with σCI, with both small and bulky CIs favoring knot localization, while medium-sized ones promote delocalized knots. We also show that the conformational change from delocalized to tight knots occurs via the progressive coalescence of the knot's essential crossings. The emerging conformers correspond to the minima of the free energy landscape profiled as a function of the knot length or PE size. We demonstrate that different conformational states can coexist, the transition between them appearing first-order-like and controlled by the enthalpic and entropic trade-off of the amount of CIs condensed on the PE. Such balance can be further altered by varying CI concentrations, thus providing an additional and more convenient tuning parameter for the system properties. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and shape by choosing the nature of its CIs. Thus, they offer new intriguing possibilities for designing novel PE-based materials that are capable of responding to changes in ionic solution properties.

Effect of counterion size on polyelectrolyte conformations and thermodynamics

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.

Binding mechanisms in dendrimer-surfactant complexes

Molecular dynamics simulations were employed to investigate the impact of interactions between dendritic polyeclectrolytes and amphiphilic surfactants on the supramolecular complex formation. We recognize two crucial parameters that govern association of surfactants within dendrimers: surfactant hydrophobicity, ε^{*}, and dendrimer generation, G. We find that depending on the values of ε^{*} and G encapsulation of surfactants by dendrimers is either noncooperative or cooperative. The noncooperative binding is characterized by absorption of surfactants as unimers, whereas in cooperative binding absorption of unimers is followed by aggregate formation through hydrophobic attractions between the surfactant tails. Our results provide guidelines for controlled encapsulation of guest molecules in dendrimer-based guest-host complexes.

Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, [Formula: see text], which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, [Formula: see text], which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by [Formula: see text]. For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing [Formula: see text]. For strong electrostatic couplings the dendrimer deswells correspondingly to [Formula: see text]. In this regime a spatial separation of the counterions into core-shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions.

Mechanistic Understanding From Molecular Dynamics Simulation in Pharmaceutical Research 1: Drug Delivery

In this review, we outline the growing role that molecular dynamics simulation is able to play as a design tool in drug delivery. We cover both the pharmaceutical and computational backgrounds, in a pedagogical fashion, as this review is designed to be equally accessible to pharmaceutical researchers interested in what this new computational tool is capable of and experts in molecular modeling who wish to pursue pharmaceutical applications as a context for their research. The field has become too broad for us to concisely describe all work that has been carried out; many comprehensive reviews on subtopics of this area are cited. We discuss the insight molecular dynamics modeling has provided in dissolution and solubility, however, the majority of the discussion is focused on nanomedicine: the development of nanoscale drug delivery vehicles. Here we focus on three areas where molecular dynamics modeling has had a particularly strong impact: (1) behavior in the bloodstream and protective polymer corona, (2) Drug loading and controlled release, and (3) Nanoparticle interaction with both model and biological membranes. We conclude with some thoughts on the role that molecular dynamics simulation can grow to play in the development of new drug delivery systems.