Spontaneous self-assembly of diblock copolymers in nanoconfined geometries by dissipative particle dynamics

We performed dissipative particle dynamics (DPD) simulations to reproduce phase separation morphologies of diblock copolymers for directed self-assembly (DSA) lithography. DSA is a promising technique to overcome the current photolithography resolution limit. The Flory–Huggins χ parameter estimated from a small-angle X-ray scattering experiment was used for the DPD simulations owing to the multiple degrees of coarse-graining. The degree of coarse-graining and the bond parameter for the spring force were optimised to represent the experimental result of the number of lamellar layers formed in a trench guide. The DPD simulations using these parameters can also represent the diameter of the central cylinder domain that is formed by phase separation in the cylindrical hole. It was found that the bond parameter considering the spreading of polymer segments in a coarse-grained particle gives good quantitative agreement between the results of the simulations and the experimental data.     

Self-aggregation of trehalose in the mixed solvents of 1,3-dimethylimidazolium ionic liquid and water

Abstract

Conformational variations of solvated trehaloses in binary mixtures of 1,3-dialkylimidazolium ([dmim]Cl) ionic liquids and trehalose as well as ternary mixtures of trehalose, [dmim]Cl and water have been studied by molecular dynamics (MD) simulations with and without polarisable force fields. The interaction energy between anion Cl^? and water is stronger than that between water itself in the [dmim]Cl-water mixtures. Isolated water clusters were found in the binary [dmim]Cl-water mixtures with 60.0 and 75.0% mole fraction of water, but a continuous water network appears when the concentration of the mixture increases to 99.9%. In the case of binary mixtures of trehalose and [dmim]Cl, both non-polarisable and polarisable models demonstrated that the pyranose rings of trehalose displayed chair conformations. MD simulations with polarisation model could sample larger conformation space than that with non-polarisable model. A self-aggregation behaviour of trehalose was found in the ternary trehalose-[dmim]Cl-water mixtures, which can be rationalised by the stronger non-bonded interaction energy between trehalose molecules and anion Cl^? than that between trehalose molecules and water.     

Predicting large-scale conformational changes in proteins using energy-weighted normal modes

We report the development of a method to improve the sampling of protein conformational space in molecular simulations. It is shown that a principal component analysis of energy-weighted normal modes in Cartesian coordinates can be used to extract vectors suitable for describing the dynamics of protein substructures. The method can operate with either atomistic or user-defined coarse-grained models of protein structure. An implicit reverse coarse-graining allows the dynamics of all-atoms to be recovered when a coarse-grained model is used. For an external test set of four proteins, it is shown that the new method is more successful than normal mode analysis in describing the large-scale conformational changes observed on ligand binding. The method has potential applications in protein-ligand and protein-protein docking and in biasing molecular dynamics simulations.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

Molecular Renormalization Group Coarse-Graining of Polymer Chains: Application to Double-Stranded DNA

Coarse-graining of atomistic force fields allows us to investigate complex biological problems, occurring at long timescales and large length scales. In this work, we have developed an accurate coarse-grained model for double-stranded DNA chain, derived systematically from atomistic simulations. Our approach is based on matching correlators obtained from atomistic and coarse-grained simulations, for observables that explicitly enter the coarse-grained Hamiltonian. We show that this requirement leads to equivalency of the corresponding partition functions, resulting in a one-step renormalization. Compared to prior works exploiting similar ideas, the main novelty of this work is the introduction of a highly compact set of Hamiltonian basis functions, based on molecular interaction potentials. We demonstrate that such compactification allows us to reproduce many-body effects, generated by one-step renormalization, at low computational cost. In addition, compact Hamiltonians greatly increase the likelihood of finding unique solutions for the coarse-grained force-field parameter values. By successfully applying our molecular renormalization group coarse-graining technique to double-stranded DNA, we solved, for the first time, a long-standing problem in coarse-graining polymer systems, namely, how to accurately capture the correlations among various polymeric degrees of freedom. Excellent agreement is found among atomistic and coarse-grained distribution functions for various structural observables, including those not included in the Hamiltonian. We also suggest higher-order generalization of this method, which may allow capturing more subtle correlations in biopolymer dynamics.     

A systematic methodology for defining coarse-grained sites in large biomolecules

Coarse-grained (CG) models of biomolecules have recently attracted considerable interest because they enable the simulation of complex biological systems on length-scales and timescales that are inaccessible for atomistic molecular dynamics simulation. A CG model is defined by a map that transforms an atomically detailed configuration into a CG configuration. For CG models of relatively small biomolecules or in cases that the CG and all-atom models have similar resolution, the construction of this map is relatively straightforward and can be guided by chemical intuition. However, it is more challenging to construct a CG map when large and complex domains of biomolecules have to be represented by relatively few CG sites. This work introduces a new and systematic methodology called essential dynamics coarse-graining (ED-CG). This approach constructs a CG map of the primary sequence at a chosen resolution for an arbitrarily complex biomolecule. In particular, the resulting ED-CG method variationally determines the CG sites that reflect the essential dynamics characterized by principal component analysis of an atomistic molecular dynamics trajectory. Numerical calculations illustrate this approach for the HIV-1 CA protein dimer and ATP-bound G-actin. Importantly, since the CG sites are constructed from the primary sequence of the biomolecule, the resulting ED-CG model may be better suited to appropriately explore protein conformational space than those from other CG methods at the same degree of resolution.     

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg²⁺) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg²⁺ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg²⁺ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg²⁺-excess concentrations and comparison with fluorescence titration measurements shows that on average 20–30% of the Mg²⁺ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.     

Spectral signatures of heterogeneous protein ensembles revealed by MD Simulations of 2DIR spectra

A model for the calculation of amide I FTIR and 2DIR spectra taking into account fluctuations in hydrogen bonding and structure from molecular dynamics (MD) simulations is tested on three systems. It is found that although the homogeneous lineshape approximation yields satisfactory FTIR spectra, 2DIR spectra are sensitive to the inhomogeneity naturally present in any solvated protein and the common approximations of a static structure and averaged-effect solvent are invalid. By building on the local amide Hamiltonian and incorporating site energy variation with electrostatic-based models and disorder from MD trajectories, good agreement is obtained between calculated and measured 2DIR spectra. The largest contribution to the observed inhomogeneity is found to be the fluctuating site energies, which in turn are most sensitive to the water solvent. With the ability to accurately predict 2DIR spectra from atomistic simulations, new opportunities to test force fields and mechanistic predictions from MD are revealed.     

Nanopore-facilitated, voltage-driven phosphatidylserine translocation in lipid bilayers--in cells and in silico

Nanosecond, megavolt-per-meter pulses--higher power but lower total energy than the electroporative pulses used to introduce normally excluded material into biological cells--produce large intracellular electric fields without destructively charging the plasma membrane. Nanoelectropulse perturbation of mammalian cells causes translocation of phosphatidylserine (PS) to the outer face of the cell, intracellular calcium release, and in some cell types a subsequent progression to apoptosis. Experimental observations and molecular dynamics (MD) simulations of membranes in pulsed electric fields presented here support the hypothesis that nanoelectropulse-induced PS externalization is driven by the electric potential that appears across the lipid bilayer during a pulse and is facilitated by the poration of the membrane that occurs even during pulses as brief as 3 ns. MD simulations of phospholipid bilayers in supraphysiological electric fields show a tight association between PS externalization and membrane pore formation on a nanosecond time scale that is consistent with experimental evidence for electropermeabilization and anode-directed PS translocation after nanosecond electric pulse exposure, suggesting a molecular mechanism for nanoelectroporation and nanosecond PS externalization: electrophoretic migration of the negatively charged PS head group along the surface of nanometer-diameter electropores initiated by field-driven alignment of water dipoles at the membrane interface.     

Coarse grain lipid-protein molecular interactions and diffusion with MsbA flippase

Coarse-grained (CG) modeling has proven effective for simulating lipid bilayer dynamics on scales of biological interest. Modeling the dynamics of flexible membrane proteins within the bilayer, on the other hand, poses a considerable challenge due to the complexity of the folding or conformational landscape. In the present work, the multiscale coarse-graining method is applied to atomistic peptide-lipid "soup" simulations to develop a general set of CG protein-lipid interaction potentials. The reduced model was constructed to be compatible with recent solvent-free CG models developed for protein-protein folding and lipid-lipid model bilayer interactions. The utility of the force field was demonstrated by molecular dynamics simulation of the MsbA ABC transporter in a mixed DOPC/DOPE bilayer. An elastic network was parameterized to restrain the MsbA dimer in its open, closed and hydrolysis intermediate conformations and its impact on domain flexibility was examined. Conformational stability enabled long-time dynamics simulation of MsbA freely diffusing in a 25 nm membrane patch. Three-dimensional density analysis revealed that a shell of weakly bound "annular lipids" solvate the membrane accessible surface of MsbA and its internal substrate-binding chamber. The annular lipid binding modes, along with local perturbations in head group structure, are a function of the orientation of grooves formed between transmembrane helices and may influence the alternating access mechanism of substrate entry and translocation.     

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.     

Molecular dynamics simulations of concentrated aqueous electrolyte solutions

Transport properties of concentrated electrolytes have been analysed using classical molecular dynamics simulations with the algorithms and parameters typical of simulations describing complex electrokinetic phenomena. The electrical conductivity and transport numbers of electrolytes containing monovalent (KCl), divalent (MgCl₂), a mixture of both (KCl+MgCl₂) and trivalent (LaCl₃) cations have been obtained from simulations of the electrolytes in electric fields of different magnitude. The results obtained for different simulation parameters have been discussed and compared with experimental measurements of our own and from the literature. The electroosmotic flow of water molecules induced by the ionic current in different cases has been calculated and interpreted with the help of the hydration properties extracted from the simulations.     

A comparison of the electromechanical properties of structurally diverse proteins by molecular dynamics simulation

Proteins are subjected to electric fields both within the cell and during routine biochemical analysis. We have used atomistic molecular dynamics simulations to study conformational changes within three structurally diverse proteins subjected to high electric fields. At electric fields in excess of .5?V/nm, major structural changes were observed in all three proteins due to charge redistribution within the biomolecule. However, the electromechanical resilience was found to be highly dependent on the protein secondary structure, with α-helices showing a particularly high susceptibility to deformation by the applied electric field.     

A structurally relevant coarse-grained model for cholesterol

Detailed atomistic computer simulations are now widely used to study biological membranes, including increasingly mixed lipid systems that involve, for example, cholesterol, which is a key membrane lipid. Typically, simulations of these systems start from a preassembled bilayer because the timescale on which self-assembly occurs in mixed lipid systems is beyond the practical abilities of fully atomistic simulations. To overcome this limitation and study bilayer self-assembly, coarse-grained models have been developed. Although there are several coarse-grained models for cholesterol reported in the literature, these generally fail to account explicitly for the unique molecular features of cholesterol that relate to its function and role as a membrane lipid. In this work, we propose a new coarse-grained model for cholesterol that retains the molecule's unique features and, as a result, can be used to study crystalline structures of cholesterol. In the development of the model, two levels of coarse-graining are explored and the importance of retaining key molecular features in the coarse-grained model that are relevant to structural properties is investigated.     

The dielectric properties of water within model transbilayer pores.

Ion channels contain extended columns of water molecules within their transbilayer pores. The dynamic properties of such intrapore water have been shown to differ from those of water in its bulk state. In previous molecular dynamics simulations of two classes of model pore (parallel bundles of Ala20 alpha-helices and antiparallel barrels of Ala10 beta-strands), a substantially reduced translational and rotational mobility of waters was observed within the pore relative to bulk water. Molecular dynamics simulations in the presence of a transpore electrostatic field (i.e., a voltage drop along the pore axis) have been used to estimate the resultant polarization (due to reorientation) of the intrapore water, and hence to determine the local dielectric behavior within the pore. It is shown that the local dielectric constant of water within a pore is reduced for models formed by parallel alpha-helix bundles, but not by those formed by beta-barrels. This result is discussed in the context of electrostatics calculations of ion permeation through channels, and the effect of the local dielectric of water within a helix bundle pore is illustrated with a simple Poisson-Boltzmann calculation.     

Comparison of the potentials of mean force for alanine tetrapeptide between integral equation theory and simulation.

The dielectrically consistent reference interaction site model (DRISM) integral equation theory is applied to determine the potential of mean force (PMF) for an alanine tetramer. A stochastic dynamics simulation of the alanine tetramer using this PMF is then compared with an explicit water molecular dynamics simulation. In addition, comparison is also done with simulations using other solvent models like the extended reference interaction site model (XRISM) theory, constant dielectric and linear distance-dependent dielectric models. The results show that the DRISM method offers a fairly accurate and computationally inexpensive alternative to explicit water simulations for studies on small peptides.     

Interaction parameters between carbon nanotubes and water in Dissipative Particle Dynamics

Flow of water past an array of single-walled carbon nanotubes (SWNTs) is simulated in this work to determine the interaction parameters of carbon nanotubes (CNTs) and water using Dissipative Particle Dynamics (DPD). For this flow configuration, results from molecular dynamics simulations by Walther et al. are available and can be used for validation (Phys. Rev. E, 2004, 062201). The hydrodynamic properties for SWNT (32, 0) with diameter of 2.5 nm were determined in different Reynolds number flows. A set of appropriate DPD parameters was found so that the drag coefficients of the CNT agreed well with the Stokes–Oseen analytical solution and the fluid slip length on the CNT wall was comparable with the Walther et al. results. It was also found that it is feasible to apply these parameters in longer length and time scales by increasing the number of water molecules grouped into each DPD bead and still maintain the hydrodynamic properties of CNTs as well as their hydrophobic surface character.     

Protein orientation in time-dependent electric fields: orientation before destruction

Proteins often have nonzero electric dipole moments, making them interact with external electric fields and offering a means for controlling their orientation. One application that is known to benefit from orientation control is single-particle imaging with x-ray free-electron lasers, in which diffraction is recorded from proteins in the gas phase to determine their structures. To this point, theoretical investigations into this phenomenon have assumed that the field experienced by the proteins is constant or a perfect step function, whereas any real-world pulse will be smooth. Here, we explore the possibility of orienting gas-phase proteins using time-dependent electric fields. We performed ab initio simulations to estimate the field strength required to break protein bonds, with 45 V/nm as a breaking point value. We then simulated ubiquitin in time-dependent electric fields using classical molecular dynamics. The minimal field strength required for orientation within 10 ns was on the order of 0.5 V/nm. Although high fields can be destructive for the structure, the structures in our simulations were preserved until orientation was achieved regardless of field strength, a principle we denote “orientation before destruction.”     

Microscopic Kinetics of DNA Translocation through synthetic nanopores

We have previously demonstrated that a nanometer-diameter pore in a nanometer-thick metal-oxide-semiconductor-compatible membrane can be used as a molecular sensor for detecting DNA. The prospects for using this type of device for sequencing DNA are avidly being pursued. The key attribute of the sensor is the electric field-induced (voltage-driven) translocation of the DNA molecule in an electrolytic solution across the membrane through the nanopore. To complement ongoing experimental studies developing such pores and measuring signals in response to the presence of DNA, we conducted molecular dynamics simulations of DNA translocation through the nanopore. A typical simulated system included a patch of a silicon nitride membrane dividing water solution of potassium chloride into two compartments connected by the nanopore. External electrical fields induced capturing of the DNA molecules by the pore from the solution and subsequent translocation. Molecular dynamics simulations suggest that 20-basepair segments of double-stranded DNA can transit a nanopore of 2.2 x 2.6 nm(2) cross section in a few microseconds at typical electrical fields. Hydrophobic interactions between DNA bases and the pore surface can slow down translocation of single-stranded DNA and might favor unzipping of double-stranded DNA inside the pore. DNA occluding the pore mouth blocks the electrolytic current through the pore; these current blockades were found to have the same magnitude as the blockade observed when DNA transits the pore. The feasibility of using molecular dynamics simulations to relate the level of the blocked ionic current to the sequence of DNA was investigated.