Coarse-grained Molecular Dynamics Model Research Articles

Dynamics of micelle–nanoparticle systems undergoing shear: a coarse-grained molecular dynamics approach

Recent work has shown that polymeric micelles can template nanoparticles via interstitial sites in shear-ordered micelle solutions. In this work, we report results based on a coarse-grained molecular dynamics (CGMD) model of a solvent/polymer/nanoparticle system. Our results demonstrate the importance of polymer concentration and the micelle corona length in 2D shear-ordering of neat polymer solutions. Although our results do not show strong 3D ordering during shear, we find that cessation of shear allows the system to relax into a 3D configuration of greater order than without shear. It is further shown that this post-shear relaxation is strongly dependent on the length of the micelle corona. For the first time, we demonstrate the presence and importance of a flow disturbance surrounding micelles in simple shear flow at moderate Peclet numbers. This disturbance is similar to what is observed around simulated star polymers and ellipsoids. The extent of the flow disturbance increases as expected with a longer micelle corona length. It is further suggested that without proper consideration of these dynamics, a stable nanoparticle configuration would be difficult to obtain.

Molecular Dynamics Simulations of Creatine Kinase and Adenine Nucleotide Translocase in Mitochondrial Membrane Patch

Interaction between mitochondrial creatine kinase (MtCK) and adenine nucleotide translocase (ANT) can play an important role in determining energy transfer pathways in the cell. Although the functional coupling between MtCK and ANT has been demonstrated, the precise mechanism of the coupling is not clear. To study the details of the coupling, we turned to molecular dynamics simulations. We introduce a new coarse-grained molecular dynamics model of a patch of the mitochondrial inner membrane containing a transmembrane ANT and an MtCK above the membrane. The membrane model consists of three major types of lipids (phosphatidylcholine, phosphatidylethanolamine, and cardiolipin) in a roughly 2:1:1 molar ratio. A thermodynamics-based coarse-grained force field, termed MARTINI, has been used together with the GROMACS molecular dynamics package for all simulated systems in this work. Several physical properties of the system are reproduced by the model and are in agreement with known data. This includes membrane thickness, dimension of the proteins, and diffusion constants. We have studied the binding of MtCK to the membrane and demonstrated the effect of cardiolipin on the stabilization of the binding. In addition, our simulations predict which part of the MtCK protein sequence interacts with the membrane. Taken together, the model has been verified by dynamical and structural data and can be used as the basis for further studies.

A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172-180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473-2480, 2005; Hale et al. in Soft Matter 5:3603-3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528-540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature.

Two-Component Coarse-Grained Molecular-Dynamics Model for the Human Erythrocyte Membrane

We present a two-component coarse-grained molecular-dynamics model for simulating the erythrocyte membrane. The proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and the elastic properties of the erythrocyte cytoskeleton. In this model, three types of coarse-grained particles are introduced to represent clusters of lipid molecules, actin junctions, and band-3 complexes, respectively. The proposed model facilitates simulations that span large length scales (approximately micrometers) and timescales (approximately milliseconds). By tuning the interaction potential parameters, we were able to control the diffusivity and bending rigidity of the membrane model. We studied the membrane under shearing and found that at a low shear strain rate, the developed shear stress was due mainly to the spectrin network, whereas the viscosity of the lipid bilayer contributed to the resulting shear stress at higher strain rates. In addition, we investigated the effects of a reduced spectrin network connectivity on the shear modulus of the membrane.

Preparation, structure, and a coarse-grained molecular dynamics model for dodecanethiol-stabilized gold nanoparticles

Thiol-stabilized metal nanoparticles possess unique properties in the comparison with larger-scale materials, which enable their use in many promising chemical and biological applications. We have synthesized thiol-coated colloidal gold nanoparticles (AuNP) soluble in non-polar organic solvents by a simplified procedure, in which AuCl 4 - was initially reduced in aqueous phase and then coated with thiol residues and transferred to organic phase. Using the transmission electron micrograph (TEM) imaging, the average diameter of a dodecanethiol-stabilized AuNP was estimated to be 3.75 ± 0.06 nm. Based on the experimental TEM data, a new coarse-grained molecular dynamics model of AuNP was developed. The model was applied for studying self-assembly of AuNPs on a flat graphite surface, enabling further elucidating the structure and packing of the ligand shell around the spherical nanoparticle core.

All-Atom and Coarse-Grained Molecular Dynamics Simulations of a Membrane Protein Stabilizing Polymer

Amphipathic polymers called amphipols (APols) have been developed as an alternative to detergents for stabilizing membrane proteins (MPs) in aqueous solutions. APols provide MPs with a particularly mild environment and, as a rule, keep them in a native functional state for longer periods than do detergents. Amphipol A8-35, a derivative of polyacrylate, is widely used and has been particularly well studied experimentally. In aqueous solutions, A8-35 molecules self-assemble into well-defined globular particles with a mass of ∼40 kDa and a R(g) of ∼2.4 nm. As a first step towards describing MP/A8-35 complexes by molecular dynamics (MD), we present three sets of simulations of the pure APol particle. First, we performed a series of all-atom MD (AAMD) simulations of the particle in solution, starting from an arbitrary initial configuration. Although AAMD simulations result in stable cohesive particles over a 45 ns simulation, the equilibration of the particle organization is limited. This motivated the use of coarse-grained MD (CGMD), allowing us to investigate processes on the microsecond time scale, including de novo particle assembly. We present a detailed description of the parametrization of the CGMD model from the AAMD simulations and a characterization of the resulting CGMD particles. Our third set of simulations utilizes reverse coarse-graining (rCG), through which we obtain all-atom coordinates from a CGMD simulation. This allows a higher-resolution characterization of a configuration determined by a long-timescale simulation. Excellent agreement is observed between MD models and experimental, small-angle neutron scattering data. The MD data provides new insight into the structure and dynamics of A8-35 particles, which is possibly relevant to the stabilizing effects of APols on MPs, as well as a starting point for modeling MP/A8-35 complexes.

Coarse-grained molecular dynamics simulation of DNA translocation in chemically modified nanopores.

Solid-state nanopores provide a direct means to detect and analyze DNA and proteins. In a typical setup, the DNA molecules travel through a nanopore under electrophoretic voltage bias. The nanopore is sandwiched between two chambers that are filled with ionic solution. A major challenge in using solid-state nanopores for DNA sequencing and gene detection is to improve their selectivity and detection sensitivity. To achieve these goals, one solution is to functionalize the nanopores by chemically modifying the pore walls with silanes or nucleic acids. However, little is known about molecular interactions in functionalized nanopores. This paper presents DNA translocation dynamics and the mechanism of DNA sequencing in a functionalized nanopore through a coarse-grained molecular dynamics model. The DNA nucleotide is coarse-grained into two interaction sites: one site corresponds to the base group and the other encompasses the phosphate and sugar groups. The water molecules are included in the model implicitly through Langevin dynamics. The coarse-grained model immensely improves the computational efficiency while still capturing the essential translocation dynamics. The model characterizes important physical properties of functionalized nanopores such as the effective pore diameter and effect of biasing voltage on the DNA translocation dynamics. The model reveals a nonlinear relationship between translocation speed of DNA and applied voltage. Moreover, DNA translocation in nanopores functionalized with hairpin-loop (HPL) DNA and single-stranded DNA (ss-DNA) shows significant differences: a target DNA is found to translocate through a ss-DNA coated nanopore 9 times faster than through an HPL coated one at a bias of 100 mV, putatively from lower stiffness of ss-DNA than that for HPL. The DNA translocation speed is also largely influenced by interaction potential between the DNA and surface-tethered molecules. The results reveal that such selective translocation, distinctly different translocation dynamics of target DNA molecules largely stem from the flexibility and orientation of the surface-tethered molecules. These findings can significantly impact the rational design of DNA transport experiments leading to rapid molecule-level diagnostics.

A Coarse-Grained Model for Unfolded Proteins

There is increasing evidence that natively-unfolded proteins play a key role in many important biological processes, including nucleocytoplasmic transport. In this work we propose an implicit solvent one-bead per amino-acid coarse-grained molecular dynamics model to study the characteristics of unfolded proteins. Experimentally-obtained Ramachandran plots for the coil regions of proteins are converted into distributions of pseudo-bond and pseudo-dihedral angles between neighboring alpha-carbons in the polypeptide chain. These are then used to derive bending and torsion potentials, which are residue- and sequence-specific. We show that the radius of gyration of denatured proteins can be well predicted by the developed potentials. Figure 1 shows the radius of gyration (Rg) as a function of the number of residues (N) for a range of denatured proteins. Both our simulation results and experimental data can be well fitted to a power-law relation with a similar exponent. The experimental data are slightly overestimated, which could be explained by the presence of hydrophobic clusters and residual structures for the used experimental conditions. In future work our model will be extended to include hydrophobic and electrostatic effects as well.

Molecular dynamics simulation of ribosome jam

We propose a coarse-grained molecular dynamics model of ribosome molecules to study the dependence of translation process on environmental parameters. We found the model exhibits traffic jam property, which is consistent with an ASEP model. We estimated the influence of the temperature and concentration of molecules on the hopping probability used in the ASEP model. Our model can also treat environmental effects on the translation process that cannot be explained by such cellular automaton models.

Development and modeling of arsenic-trioxide–loaded thermosensitive liposomes for anticancer drug delivery

In this article, a novel delivery system for the anticancer drug, arsenic trioxide (ATO), is characterized. The release of ATO from DPPC liposomes with MPPC lysolipid incorporated into the bilayer was measured. Upon heating the liposomes to 37°C, there was a 15–25% release over 24 hours. The ATO release from the DPPC and DPPC:MPPC (5%) systems leveled off after 10 hours at 37°C, whereas the DPPC:MPPC (10%) liposomes continue to release ATO over the 24-hour time span. Upon heating the liposomes rapidly to 42°C, the release rate was substantially increased. The systems containing lysolipids exhibited a very rapid release of a significant amount of arsenic in the first hour. In the first hour, the DPPC:MPPC (5%) liposomes released 40% of the arsenic and the DPPC:MPPC (10%) liposomes released 55% of the arsenic. Arsenic release from pure DPPC liposomes was comparable at 37 and 42°C, indicating that the presence of a lysolipid is necessary for a significant enhancement of the release rate. A coarse-grained molecular dynamics (CGMD) model was used to investigate the enhanced permeability of lysolipid-incorporated liposomes and lipid bilayers. The CG liposomes did not form a gel phase when cooled due to the high curvature; however, permeability was still significantly lower below the liquid-to-gel phase-transition temperature. Simulations of flat DPPC:MPPC bilayers revealed that a peak in the permeability did coincide with the phase transition from the gel to LC state when the lysolipid, MPPC, was present. No pores were observed in the simulations, so it is unlikely this was the permeability-enhancing mechanism.

Mechanical Properties of Coarse-Grained Bilayers Formed by Cardiolipin and Zwitterionic Lipids.

Lipid shape and charge are connected with the physical properties and the biological function of membranes. Cardiolipin, a double phospholipid with four chains and the potential of changing its charge with pH, is crucially connected with mitochondrial inner membrane shape, and recent experiments suggest that local pH changes allow highly curved local geometries. Here, we use a coarse-grained molecular dynamics model to investigate the mechanical properties of cardiolipin bilayers, systematically varying the headgroup charge and the composition in mixtures with zwitterionic 1,2-dioleoyl-glycero-3-phosphatidylcholine (DOPC) or 1,2-dioleoyl-glycero-3-phosphatidylethanolamine (DOPE). Low cardiolipin charge, corresponding to low pH, was found to induce bending moduli on the order of kBT and curved microdomains. On the length scale investigated, in contrast to continuum theoretical models, we found the area modulus and bending modulus to be inversely correlated for mixtures of cardiolipin and DOPC/DOPE, explainable by changes in the effective headgroup volume.

Mesoscale modelling of polyelectrolyteelectrophoresis

The electrophoretic behaviour of flexible polyelectrolyte chains ranging from single monomers up to long fragments of hundred repeat units is studied by a mesoscopic simulation approach. Abstracting from the atomistic details of the polyelectrolyte and the fluid, a coarse-grained molecular dynamics model connected to a mesoscopic fluid described by the Lattice Boltzmann approach is used to investigate free-solution electrophoresis. Our study demonstrates the importance of hydrodynamic interactions for the electrophoretic motion of polyelectrolytes and quantifies the influence of surrounding ions. The length-dependence of the electrophoretic mobility can be understood by evaluating the scaling behavior of the effective charge and the effective friction. The perfect agreement of our results with experimental measurements shows that all chemical details and fluid structure can be safely neglected, and a suitable coarse-grained approach can yield an accurate description of the physics of the problem, provided that electrostatic and hydrodynamic interactions between all entities in the system, i.e., the polyelectrolyte, dissociated counterions, additional salt and the solvent, are properly accounted for. Our model is able to bridge the single molecule regime of a few nm up to macromolecules with contour lengths of more than 100 nm, a length scale that is currently not accessible to atomistic simulations.

Stretching and twisting of the DNA duplexes in coarse-grained dynamical models

Three coarse-grained molecular dynamics models of the double-stranded DNA are proposedand compared in the context of single molecule mechanical manipulation such as twistingand various schemes of stretching—unzipping, shearing, two-strand stretching andstretching of only one strand. The models differ in the number of effective beads (betweentwo and five) representing each nucleotide. They all show similar behaviour, but the biggerthe resolution, the more details in the force patterns. The models incorporate the effectiveLennard-Jones potentials in the couplings between two strands and harmonicpotentials to describe the structure of a single strand. The force patterns are shown todepend on the sequence studied. In particular, both shearing and unzipping for anall-AT sequence lead to lower forces than for an all-CG sequence. The unzippingpatterns and the corresponding scenario diagrams for the contact rupture eventsare found to reflect the sequential information if the temperature is moderateand initial transients are discarded. The derived torque–force phase diagram isfound to be qualitatively consistent with experiments and all-atom simulations.

Entangled chain dynamics of polymer knots in extensional flow

We formulate a coarse-grained molecular-dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in a strong extensional flow (Deborah number De=1.6 ). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the "natural," unraveling, and flow-induced chain motions. Moreover, the steady-state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.

Polyelectrolytes in electric fields: measuring the dynamical effective charge and effective friction

We use a coarse-grained molecular dynamics model to study the electrophoretic behaviour of flexible polyelectrolyte chains. We first characterize the static properties of the model with respect to the chain length, the polyelectrolyte concentration, additional salt and the influence of an applied external field. Next we investigate the dynamic behaviour in the oligomer range and find excellent correspondence of simulations to experimental observations when hydrodynamic interactions are accounted for in the simulations. We then present novel estimators for the dynamical effective charge during free-solution electrophoresis and compare them to static estimators. We find complete agreement between the static and the dynamic estimators. We further evaluate the scaling behaviour of the effective friction of the polyelectrolyte-counterion complex with the surrounding fluid. We identify a hydrodynamic screening length beyond which the friction during electrophoresis is linear depending on the chain length resulting in a constant mobility for long polyelectrolyte chains. Our results show a convincing agreement with experimental data and demonstrate that it is possible to model dynamic behaviour of polyelectrolytes using coarse-grained models, provided they include the effects of hydrodynamical interactions.

Coarse-grained molecular dynamics simulations of nanopatterning with multivalent inks

A coarse-grained molecular dynamics (MD) model is developed to study the multivalent, or multisite, binding of small functionalized dendrimer molecules to beta-cyclodextrin-terminated self-assembled monolayers, the so-called "molecular printboards" used to print "ink" molecules on surfaces with a high degree of positional control and specificity. Some current and future bionanotechnology applications are in the creation of nanoparticle assemblies, directed protein assembly, platforms for biosensing, and cell:surface attachment. The coarse-grained model allows us to probe up to microsecond timescales and model ink diffusion, crucial for the application of the printboard in, for example, medical diagnostics. Recent all-atom MD simulations identified and quantified the molecular strain limiting the stability of nanopatterns created with small dendrimer inks, and explained the different patterns obtained experimentally with different dendrimer inks. In the present work, the all-atom simulations are "scaled up" to longer timescales via coarse graining, without incurring significant additional computational expense, and, crucially, without significant loss in atom-scale detail, the coarse-grained MD simulations yielding properties similar to those obtained from the all-atom simulations. The anchoring of the ink molecules to the monolayer is of multivalent nature and the degree of multivalency shows a sharp dependence on temperature, control of temperature thus providing a further operational "switch" for directed molecular assembly. The computational protocol developed can, in principle, be extended to model any multivalent assembly, for example, virus-cell complexation.

Stretching to Understand Proteins—A Survey of the Protein Data Bank

We make a survey of resistance of 7510 proteins to mechanical stretching at constant speed as studied within a coarse-grained molecular dynamics model. We correlate the maximum force of resistance with the native structure, predict proteins which should be especially strong, and identify the nature of their force clamps.

Coarse-Grained Molecular Dynamics Modeling of Strongly Associating Fluids: Thermodynamics, Liquid Structure, and Dynamics of Symmetric Binary Mixture Fluids

Symmetric binary mixtures capable of strong association via a highly directional and saturable specific interaction between unlike molecules are investigated by canonical molecular dynamics simulations. The specific interaction of the molecules is defined in a new coarse-grained pair potential that can be applied in continuous molecular dynamics as well as in Monte Carlo simulations. The thermodynamic, structural, and dynamic properties of the associating mixture fluids are investigated as a function of density, temperature, and association strength of the specific interaction. Detailed analysis of the simulation data confirms a two-stage mechanism in the formation of specific bonds with increasing interaction strength, including a fast dimerization process and a subsequent stage of perfecting the bonds. A large heat capacity peak is found during the formation or breaking of the bonds, reflecting the large energy fluctuation introduced by the strong association. The fractions of nonbonded molecules obtained from the simulations as a function of density, temperature, and interaction strength are in excellent agreement with the predictions of Wertheim's thermodynamic perturbation theory. The translational and rotational dynamics of the Tmer mixture are effectively retarded with increasing association strength and are analyzed in terms of autocorrelation functions and a non-Gaussian parameter for the translational dynamics. The lifetimes of molecules in bonded and nonbonded states provide detailed information about the transformation of molecules between the bonded state and the nonbonded state. Finally, simulation sampling problems inherent to strongly interacting systems are easily overcome using the parallel tempering simulation technique. This latter result confirms that with the new continuous coarse-grained simulation potential we have a versatile and flexible interaction potential that can be used with many available molecular dynamics and Monte Carlo algorithms under various ensembles.

Polymorphic Phase Behavior of Cardiolipin Derivatives Studied by Coarse-Grained Molecular Dynamics

Cardiolipin (CL) is a negatively charged four acyl chain lipid, associated with energy production in bacterial and mitochondrial membranes. Due to the shape of CL, negative curvatures of aggregates are favorable if the charges in the head group can be reduced. The phase polymorphism of CL, and of associated derivatives with 2, 3, 4, or 5 chains, has been determined previously and offers a model system in which micellar, lamellar, and inverse hexagonal phases can be observed. We present an extension to a previously established coarse-grained molecular dynamics model with the aim of reproducing the different CL phases with two adjustable parameters: the number of acyl chains and the effective head group charge. With molecular dynamics simulations of large lipid systems, we observed transitions between different phases on the nanosecond to microsecond time scale. Charge screening by high salt or low pH was successfully modeled by a reduction of phosphate charge, which led to the adoption of aggregates with more negative curvature. Although specific ion binding at the interface and other atomistic details are sacrificed in the coarse-grained model, we found that it captures general phase features over a large range of aggregate geometries.

Laser ablation in a model two-phase system

Short pulse laser ablation of a model two-component system has been simulated using a coarse-grained molecular dynamics (MD) model. A system with two disparate components (hard and soft) has been considered, based broadly on the properties of hard tissue. The existence of distinct regimes of material ejection has been identified and the processes leading to the ablation have been investigated. In the lower fluence regime gaseous particles of the soft component stream from the hard matrix but there is no ejection of the hard component. In the higher fluence regime chunks of the hard component are ejected simultaneously with the soft component.