Comparison of Simulations of Lipid Membranes with Membranes of Block Copolymers

Rupturing the hemi-fission intermediate in membrane fission under tension: Reaction coordinates, kinetic pathways, and free-energy barriers

Membrane fission is a fundamental process in cells, involved inter alia in endocytosis, intracellular trafficking, and virus infection. Its underlying molecular mechanism, however, is only incompletely understood. Recently, experiments and computer simulation studies have revealed that dynamin-mediated membrane fission is a two-step process that proceeds via a metastable hemi-fission intermediate (or wormlike micelle) formed by dynamin's constriction. Importantly, this hemi-fission intermediate is remarkably metastable, i.e., its subsequent rupture that completes the fission process does not occur spontaneously but requires additional, external effects, e.g., dynamin's (unknown) conformational changes or membrane tension. Using simulations of a coarse-grained, implicit-solvent model of lipid membranes, we investigate the molecular mechanism of rupturing the hemi-fission intermediate, such as its pathway, the concomitant transition states, and barriers, as well as the role of membrane tension. The membrane tension is controlled by the chemical potential of the lipids, and the free-energy landscape as a function of two reaction coordinates is obtained by grand canonical Wang-Landau sampling. Our results show that, in the course of rupturing, the hemi-fission intermediate undergoes a "thinning → local pinching → rupture/fission" pathway, with a bottle-neck-shaped cylindrical micelle as a transition state. Although an increase of membrane tension facilitates the fission process by reducing the corresponding free-energy barrier, for biologically relevant tensions, the free-energy barriers still significantly exceed the thermal energy scale k_BT.

How the Incorporation of Pluronic Block Copolymers Modulates the Response of Lipid Membranes to Mechanical Stress

We employ atomistic molecular dynamics simulations to investigate the effect that the incorporation of the nonionic amphiphilic copolymer known as Pluronic L64 has on the mechanical stability of a DPPC membrane. The simulations reveal that the incorporation of the polymer chains leads to membranes that can sustain increasing mechanical stresses. Analysis of mechanical, structural, and dynamic properties of the membrane shows that the polymer chains interact strongly with the lipids in the vicinity, restraining their mobility and imparting better mechanical stability to the membrane. The hybrid membranes under tension remain thicker, more ordered, and stiffer in comparison to their lipid analogues. Trans-bilayer lipid movements (flip-flop) are observed and appear to be triggered by the presence of the polymer chains. A careful analysis of the pore formation under high tensions reveals two distinctive mechanisms that depend on the distribution of the hydrophilic polymer blocks in the bilayer. Finally, the rate of growth of the formed membrane defects is slowed down in the presence of polymers. These findings show that Pluronic block copolymers could be exploited for the formation of optimized hybrid nanodevices with controlled elastic and dynamic properties.

Simulation of self-assembly of polyzwitterions into vesicles

Using the Langevin dynamics method and a coarse-grained model, we have studied the formation of vesicles by hydrophobic polymers consisting of periodically placed zwitterion side groups in dilute salt-free aqueous solutions. The zwitterions, being permanent charge dipoles, provide long-range electrostatic correlations which are interfered by the conformational entropy of the polymer. Our simulations are geared towards gaining conceptual understanding in these correlated dipolar systems, where theoretical calculations are at present formidable. A competition between hydrophobic interactions and dipole-dipole interactions leads to a series of self-assembled structures. As the spacing d between the successive zwitterion side groups decreases, single chains undergo globule → disk → worm-like structures. We have calculated the Flory-Huggins χ parameter for these systems in terms of d and monitored the radius of gyration, hydrodynamic radius, spatial correlations among hydrophobic and dipole monomers, and dipole-dipole orientational correlation functions. During the subsequent stages of self-assembly, these structures lead to larger globules and vesicles as d is decreased up to a threshold value, below which no large scale morphology forms. The vesicles form via a polynucleation mechanism whereby disk-like structures form first, followed by their subsequent merger.

Single-chain-in-mean-field simulations of weak polyelectrolyte brushes

Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pK_a value of the polymer.

Process-directed self-assembly of block copolymers: a computer simulation study

The free-energy landscape of self-assembling block copolymer systems is characterized by a multitude of metastable minima and concomitant protracted relaxation times of the morphology. Tailoring rapid changes (quench) of thermodynamic conditions, one can reproducibly trap the ensuing kinetics of self-assembly in a specific metastable state. To this end, it is necessary to (1) control the generation of well-defined, highly unstable states and (2) design the unstable state such that the ensuing spontaneous kinetics of structure formation reaches the desired metastable morphology. This process-directed self-assembly provides an alternative to fine-tuning molecular architecture by synthesis or blending, for instance, in order to fabricate complex network structures. Comparing our simulation results to recently developed free-energy techniques, we highlight the importance of non-equilibrium molecular conformations in the starting state and motivate the significance of the local conservation of density.

Coarse-graining poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) block copolymers using the MARTINI force field

The MARTINI coarse-grain (CG) force field is extended for a class of triblock block copolymers known as Pluronics. Existing MARTINI bead types are used to model the non-bonded part of the potential while single chain properties for both homopolymers, poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO), are used to develop the bonded interactions. The new set of force field parameters reproduces structural and dynamical properties of high molecular weight homo- and copolymers. The CG model is moderately transferable in solvents of different polarity and concentration; however, the PEO homopolymer model presents a reduced thermodynamic transferability especially in water probably due to the lack of hydrogen bonds with the solvent. Our simulations of a monolayer of Pluronic L44 show polymer-brush-like characteristics for the PEO segments which protrude into the aqueous phase. Other membrane properties not easily accessible using experimental techniques such as its membrane thickness are also calculated.