Molecular dynamics simulation of the spontaneous formation of a small DPPC vesicle in water in atomistic detail

Molecular dynamics simulations have been used to study the spontaneous aggregation of a concentrated solution of dipalmitoylphosphatidylcholine (DPPC) molecules in water into a small vesicle. The molecules were represented in atomistic detail. Starting from a DPPC solution in water, an oblong vesicle with a long axis of 15 nm and short axes of 10 nm was formed spontaneously. After 90 ns of simulation, the vesicle contained a number of water pores. Water pores were shown to facilitate exchange of lipids between inner and outer leaflets. Lipid tails were shown to be less ordered in the inner leaflet of the vesicle, as compared to those in the outer leaflet of the vesicle and an equilibrated lamellar bilayer.     

Comparison of thermodynamic properties of coarse-grained and atomic-level simulation models.

Thermodynamic data are often used to calibrate or test amomic-level (AL) force fields for molecular dynamics (MD) simulations. In contrast, the majority of coarse-grained (CG) force fields do not rely extensively on thermodynamic quantities. Recently, a CG force field for lipids, hydrocarbons, ions, and water, in which approximately four non-hydrogen atoms are mapped onto one interaction site, has been proposed and applied to study various aspects of lipid systems. To date, no extensive investigation of its capability to describe salvation thermodynamics has been undertaken. In the present study, a detailed picture of vaporization, solvation, and phase-partitioning thermodynamics for liquid hydrocarbons and water was obtained at CG and AL resolutions, in order to compare the two types or models and evaluate their ability to describe thermodynamic properties in the temperature range between 263 and 343 K. Both CG and AL models capture the experimental dependence of the thermodynamic properties on the temperature, albeit a systematically weaker dependence is found for the CG model. Moreover, deviations are found for solvation thermodynamics and for the corresponding enthalpy-entropy compensation for the CG model. Particularly water/oil repulsion seems to be overestimated. However, the results suggest that the thermodynamic properties considered should be reproducible by a CG model provided it is reparametrized on the basis of these liquid-phase properties.     

Adaptive resolution simulation of an atomistic DNA molecule in MARTINI salt solution

We present a dual-resolution model of a deoxyribonucleic acid (DNA) molecule in a bathing solution, where we concurrently couple atomistic bundled water and ions with the coarse-grained MARTINI model of the solvent. We use our fine-grained salt solution model as a solvent in the inner shell surrounding the DNA molecule, whereas the solvent in the outer shell is modeled by the coarse-grained model. The solvent entities can exchange between the two domains and adapt their resolution accordingly. We critically asses the performance of our multiscale model in adaptive resolution simulations of an infinitely long DNA molecule, focusing on the structural characteristics of the solvent around DNA. Our analysis shows that the adaptive resolution scheme does not produce any noticeable artifacts in comparison to a reference system simulated in full detail. The effect of using a bundled-SPC model, required for multiscaling, compared to the standard free SPC model is also evaluated. Our multiscale approach opens the way for large scale applications of DNA and other biomolecules which require a large solvent reservoir to avoid boundary effects.     

Curvature-dependent elastic properties of liquid-ordered domains result in inverted domain sorting on uniaxially compressed vesicles

Using a coarse-grained molecular model we study the spatial distribution of lipid domains on a 20-nm-sized vesicle. The lipid mixture laterally phase separates into a raftlike, liquid-ordered (l(o)) phase and a liquid-disordered phase. As we uniaxially compress the mixed vesicle keeping the enclosed volume constant, we impart tension onto the membrane. The vesicle adopts a barrel shape, which is composed of two flat contact zones and a curved edge. The l(o) domain, which exhibits a higher bending rigidity, segregates to the highly curved edge. This inverted domain sorting switches to normal domain sorting, where the l(o) domain prefers the flat contact zone, when we release the contents of the vesicle. We rationalize this domain sorting by a pronounced reduction of the bending rigidity and area compressibility of the l(o) phase upon bending.     

Determining equilibrium constants for dimerization reactions from molecular dynamics simulations

With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form ΔG ∝ ln(P(1) /P(0) ). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics.     

Electrophoretic mobility does not always reflect the charge on an oil droplet

Electrophoresis is widely used to determine the electrostatic potential of colloidal particles. Oil droplets in pure water show negative or positive electrophoretic mobilities depending on the pH. This is commonly attributed to the adsorption of hydroxyl or hydronium ions, resulting in a negative or positive surface charge, respectively. This explanation, however, is not in agreement with the difference in isoelectric point and point of zero charge observed in experiment. Here we present molecular dynamics simulations of oil droplets in water in the presence of an external electric field but in the absence of any ions. The simulations reproduce the negative sign and the order of magnitude of the oil droplet mobilities at the point of zero charge in experiment. The electrostatic potential in the oil with respect to the water phase, induced by anisotropic dipole orientation in the interface, is positive. Our results suggest that electrophoretic mobility does not always reflect the net charge or electrostatic potential of a suspended liquid droplet and, thus, the interpretation of electrophoresis in terms of purely continuum effects may need to be reevaluated.     

Antimicrobial peptides in action

Molecular dynamics simulations of the magainin MG-H2 peptide interacting with a model phospholipid membrane have been used to investigate the mechanism by which antimicrobial peptides act. Multiple copies of the peptide were randomly placed in solution close to the membrane. The peptide readily bound to the membrane, and above a certain concentration, the peptide was observed to cooperatively induce the formation of a nanometer-sized, toroidally shaped pore in the bilayer. In sharp contrast with the commonly accepted model of a toroidal pore, only one peptide was typically found near the center of the pore. The remaining peptides lay close to the edge of the pore, maintaining a predominantly parallel orientation with respect to the membrane.     

Lipids out of equilibrium: energetics of desorption and pore mediated flip-flop

The potential of mean force (PMF) of a phospholipid in a bilayer is a key thermodynamic property that describes the energetic cost of localized lipid defects. We have calculated the PMF by umbrella sampling using molecular dynamics simulations. The profile has a deep minimum at the equilibrium position in the bilayer and steeply rises for displacements both deeper into the bilayer and moving away from the bilayer. As the lipid loses contact with the bilayer, the profile abruptly flattens without a significant barrier. The calculated free energy difference of 80 kJ/mol between the minimum of the PMF and the value in water agrees well with the free energy difference calculated from the experimentally measured critical micelle concentration. Significant water/lipid defects form when a lipid is forced into the bilayer interior, in the form of a small water pore that spans the membrane. The energy required to form such a water pore is also found to be 80 kJ/mol. On the basis of this energy, we estimate the lipid flip-flop rate and permeability rate of sodium ions. The resulting rates are in good agreement with experimental measurements, suggesting lipid flip-flop and basal permeability of ions are pore mediated.     

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure–property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Multiscale modeling resolves the molecular structure of a synthetic light-harvesting complex, unraveling the microscopic origin of its photophysical properties.

Supramolecular structures may self-assemble from a variety of building blocks, resulting in a wide range of advanced materials with attractive biomimetic, sensing, catalytic, optoelectronic and photonic functionalities.^1–10 The close-packed nanoscale organization of the individual molecules within a supramolecular system, held together via noncovalent interactions, gives rise to the aggregate''s (collective) properties. Assemblies consisting of dye molecules often exhibit unique collective optical properties and are of interest for opto-electronic applications as well as artificial light-harvesting complexes that mimic natural antenna systems of photosynthetic bacteria and plants.^11–13 For example, chlorosomal antenna complexes of photosynthetic green sulfur bacteria are self-assembled into multilayer tubular structures having bacteriochlorophyll pigments as building blocks.^14–16 The structure of these antenna complexes and the underlying molecular arrangement ensures that the process of light-harvesting and excitation energy transport is very efficient, even under extremely low light conditions.^17,18 The quest to recreate such efficiency under laboratory conditions has sparked numerous studies of synthetic self-assembled systems mimicking natural chlorosomes, e.g. using porphyrins,¹⁹ zinc chlorin,²⁰ and cyanine dyes.²¹ Of particular interest are the tubular aggregates of 3,3′-bis(2-sulfopropyl)-5,5′,6,6′-tetrachloro-1,1′-dioctylbenzimidacarbocyanine (C8S3).^22–25 Cryo-TEM reveals a hierarchy of supramolecular architectures, including double-walled nanotubes; under certain conditions, bundles of nanotubes arise.²⁶ Thus, this system allows for the occurrence of electronic excitation energy transport at various levels: within one wall, between walls of one tube, and between different tubes, similar to the situation in natural systems.^27,28To understand how such supramolecular systems work, as well as propose design rules for new materials, it is essential to determine the relationship between molecular structure and optical properties. Current experimental techniques, however, are unable to resolve the structure at the molecular level. This, in combination with the sensitivity of spectral properties to the details of the molecular packing, leads to a crucial role for theoretical modeling.²⁹ For example, molecular dynamics (MD) simulations have been used to predict the molecular packing within a variety of supramolecular assemblies.^30–34 However, synthetic amphiphiles with aromatic groups, such as cyanine dyes—often used to prepare aggregates with optical functionality—tend to fall into kinetic traps during spontaneous self-assembly simulations and the packing of the aromatic chromophores remains highly disordered on the accessible time scale, leading to predicted (optical) spectra that are not consistent with experimental data.³⁵ This problem can be overcome by building assemblies based upon proposed architectures and assessing their stability in relatively short MD simulations.^36–38 The drawback of this approach is the requirement of a thorough understanding of what to use as a starting point and how to validate the structure. In any case, proper validation requires the modeling of the optical spectra of the obtained structure, and finally, comparing it to the experiment. The demanding character of such methods explains why an important role is played by phenomenological modeling, in which a molecular packing is guessed and the optics is obtained from parametrizing an exciton model that describes the collective excited states of the assembly with interactions dictated by the guessed packing. By comparing the calculated spectra to experimental ones, the structure and exciton model may be fine-tuned. While this method has been successful in describing spectra,^23,39 it is limited in its predictive power and also lacks access to essential microscopic parameters, such as tuning of the optical excitation energies imposed by the environment, disorder in these energies and structural heterogeneity.In this work, we use an advanced multiscale approach to determine structure–optical property relationships for the C8S3 double-walled nanotubes, guided by comparison to experiments. The optical spectrum of these aggregates, in which multiple exciton peaks may be discerned, suggests a rather complex underlying molecular packing. This fact, combined with their sheer size going up to many thousands of molecules, makes these systems exceptionally challenging to resolve and leaves important questions concerning structure–function relationships unanswered or under debate, for instance the origin of the splitting between the two lowest-energy spectral bands.^23,38 Here, we answer these questions by iteratively combining MD simulations to capture the details of molecular packing and structural disorder, an exciton Hamiltonian approach to calculate optical signatures, and explicit microelectrostatic calculations to estimate energetic disorder and solvent shifts. Previous attempts to reveal the structure of cyanine-based nanotubes were limited to small-scale system sizes,^37,38 modeling optical features phenomenologically rather than using atomistic information³⁸ or featuring simpler, single-walled systems.³⁷ In addition to answering important questions for the C8S3 double-walled nanotubes, our study opens the way to explain and predict at an unprecedented level of detail the functional properties of other highly complex molecular materials.     

Effects of bundling on the properties of the SPC water model

Simultaneous representation of molecules at an all-atom and coarse-grained level, as required by multiscaling molecular dynamics simulations, poses problems for the treatment of small molecules. If more than one of these molecules are mapped to a single coarse-grained interaction site, unrestricted movement in the all-atom representation can make a meaningful correspondence of the coordinates between the two representations impossible. Restricting the relative movement of molecules mapped to the same coarse-grained interaction site solves that problem, but will have consequences for the properties of the model. Here we investigate the effects of introducing bundling to the common simple point charge (SPC) water model and present a bundled water model that preserves important properties of SPC water relevant for multiscaling.