Development of a bottom-up coarse-grained model for interactions of lipids with TiO 2 nanoparticles.

Understanding interactions of inorganic nanoparticles with biomolecules is important in many biotechnology, nanomedicine, and toxicological research, however, the size of typical nanoparticles makes their direct modeling by atomistic simulations unfeasible. Here, we present a bottom-up coarse-graining approach for modeling titanium dioxide (TiO 2 ) nanomaterials in contact with phospholipids that uses the inverse Monte Carlo method to optimize the effective interactions from the structural data obtained in small-scale all-atom simulations of TiO 2 surfaces with lipids in aqueous solution. The resulting coarse-grained models are able to accurately reproduce the structural details of lipid adsorption on different titania surfaces without the use of an explicit solvent, enabling significant computational resource savings and favorable scaling. Our coarse-grained simulations show that small spherical TiO 2 nanoparticles ( r = 2 nm) can only be partially wrapped by a lipid bilayer with phosphoethanolamine headgroups, however, the lipid adsorption increases with the radius of the nanoparticle. The current approach can be used to study the effect of the size and shape of TiO 2 nanoparticles on their interactions with cell membrane lipids, which can be a determining factor in membrane wrapping as well as the recently discovered phenomenon of nanoquarantining, which involves the formation of layered nanomaterial-lipid structures.

Biomolecular Adsorption on Nanomaterials: Combining Molecular Simulations with Machine Learning.

Adsorption free energies of 32 small biomolecules (amino acids side chains, fragments of lipids, and sugar molecules) on 33 different nanomaterials, computed by the molecular dynamics - metadynamics methodology, have been analyzed using statistical machine learning approaches. Multiple unsupervised learning algorithms (principal component analysis, agglomerative clustering, and K-means) as well as supervised linear and nonlinear regression algorithms (linear regression, AdaBoost ensemble learning, artificial neural network) have been applied. As a result, a small set of biomolecules has been identified, knowledge of adsorption free energies of which to a specific nanomaterial can be used to predict, within the developed machine learning model, adsorption free energies of other biomolecules. Furthermore, the methodology of grouping of nanomaterials according to their interactions with biomolecules has been presented.

Multiscale modeling reveals the ion-mediated phase separation of nucleosome core particles.

Due to the vast length scale inside the cell nucleus, multiscale models are required to understand chromatin folding, structure, and dynamics and how they regulate genomic activities such as DNA transcription, replication, and repair. We study the interactions and structure of condensed phases formed by the universal building block of chromatin, the nucleosome core particle (NCP), using bottom-up multiscale coarse-grained (CG) simulations with a model extracted from all-atom MD simulations. In the presence of the multivalent cations Mg(H2O)62+ or CoHex3+, we analyze the internal structures of the NCP aggregates and the contributions of histone tails and ions to the aggregation patterns. We then derive a "super" coarse-grained (SCG) NCP model to study the macroscopic scale phase separation of NCPs. The SCG simulations show the formation of NCP aggregates with Mg(H2O)62+ concentration-dependent densities and sizes. Variation of the CoHex3+ concentrations results in highly ordered lamellocolumnar and hexagonal columnar phases in agreement with experimental data. The results give detailed insights into nucleosome interactions and for understanding chromatin folding in the cell nucleus.

Neutron scattering study of polyamorphic THF·17(H2O) - toward a generalized picture of amorphous states and structures derived from clathrate hydrates.

From crystalline tetrahydrofuran clathrate hydrate, THF-CH (THF·17H2O, cubic structure II), three distinct polyamorphs can be derived. First, THF-CH undergoes pressure-induced amorphization when pressurized to 1.3 GPa in the temperature range 77-140 K to a form which, in analogy to pure ice, may be called high-density amorphous (HDA). Second, HDA can be converted to a densified form, VHDA, upon heat-cycling at 1.8 GPa to 180 K. Decompression of VHDA to atmospheric pressure below 130 K produces the third form, recovered amorphous (RA). Results from neutron scattering experiments and molecular dynamics simulations provide a generalized picture of the structure of amorphous THF hydrates with respect to crystalline THF-CH and liquid THF·17H2O solution (∼2.5 M). Although fully amorphous, HDA is heterogeneous with two length scales for water-water correlations (less dense local water structure) and guest-water correlations (denser THF hydration structure). The hydration structure of THF is influenced by guest-host hydrogen bonding. THF molecules maintain a quasiregular array, reminiscent of the crystalline state, and their hydration structure (out to 5 Å) constitutes ∼23H2O. The local water structure in HDA is reminiscent of pure HDA-ice featuring 5-coordinated H2O. In VHDA, the hydration structure of HDA is maintained but the local water structure is densified and resembles pure VHDA-ice with 6-coordinated H2O. The hydration structure of THF in RA constitutes ∼18 H2O molecules and the water structure corresponds to a strictly 4-coordinated network, as in the liquid. Both VHDA and RA can be considered as homogeneous.

Ab Initio Derived Classical Force Field for Molecular Dynamics Simulations of ZnO Surfaces in Biological Environment.

Zinc oxide nanostructures are used in an ever increasing line of applications in technology and biomedical fields. This requires a detailed understanding of the phenomena that occur at the surface particularly in aqueous environments and in contact with biomolecules. In this work, we used ab initio molecular dynamics (AIMD) simulations to determine structural details of ZnO surfaces in water and to develop a general and transferable classical force field for hydrated ZnO surfaces. AIMD simulations show that water molecules dissociate near unmodified ZnO surfaces, forming hydroxyl groups at about 65% of the surface Zn atoms and protonating 3-coordinated surface oxygen atoms, while the rest of the surface Zn atoms bind molecularly adsorbed waters. Several force field atom types for ZnO surface atoms were identified by analysis of the specific connectivities of atoms. The analysis of the electron density was then used to determine partial charges and Lennard-Jones parameters for the identified force field atom types. The obtained force field was validated by comparison with AIMD results and with available experimental data on adsorption and immersion enthalpies, as well as adsorption free energies of several amino acids in methanol. The developed force field can be used for modeling of ZnO in aqueous and other fluid environments and in interaction with biomolecules.

First principles characterisation of bio-nano interface.

Nanomaterials possess a wide range of potential applications due to their novel properties and exceptionally high activity as a result of their large surface to volume ratios compared to bulk matter. The active surface may present both advantage and risk when the nanomaterials interact with living organisms. As the overall biological impact of nanomaterials is triggered and mediated by interactions at the bio-nano interface, an ability to predict those from the atomistic descriptors, especially before the material is produced, can present enormous advantage for the development of nanotechnology. Fast screening of nanomaterials and their variations for specific biological effects can be enabled using computational materials modelling. The challenge lies in the range of scales that needs to be crossed from the material-specific atomistic representation to the relevant length scales covering typical biomolecules (proteins and lipids). In this work, we present a systematic multiscale approach that allows one to evaluate crucial interactions at the bionano interface from the first principles without any prior information about the material and thus establish links between the details of the nanomaterials structure to protein-nanoparticle interactions. As an example, an advanced computational characterization of titanium dioxide nanoparticles (6 different surfaces of rutile and anatase polymorphs) has been performed. We computed characteristics of the titanium dioxide interface with water using density functional theory for electronic density, used these parameters to derive an atomistic force field, and calculated adsorption energies for essential biomolecules on the surface of titania nanoparticles via direct atomistic simulations and coarse-grained molecular dynamics. Hydration energies, as well as adsorption energies for a set of 40 blood proteins are reported.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level.

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex3+). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex3+ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

Effect of lipid saturation on amyloid-beta peptide partitioning and aggregation in neuronal membranes: molecular dynamics simulations.

Aggregation of amyloid-[Formula: see text] (Aß) peptides, cleaved from the amyloid precursor protein, is known as a precursor of the Alzheimer's disease (AD). It is also known that Alzheimer's disease is characterized by a substantial decrease of the amount of polyunsaturated lipids in the neuronal membranes of the frontal gray matter. To get insight into possible interconnection of these phenomena, we have carried out molecular dynamics simulations of two fragments of A[Formula: see text] peptide, A[Formula: see text][Formula: see text] and A[Formula: see text][Formula: see text], in four different lipid bilayers: two monocomponent ones (14:0-14:0 PC, 18:0-22:6 PC), and two bilayers containing mixtures of 18:0-18:0 PE, 22:6-22:6 PE, 16:0-16:0 PC and 18:1-18:1 PC lipids of composition mimicking neuronal membranes in a "healthy" and "AD" brain. The simulations showed that the presence of lipids with highly unsaturated 22:6cis fatty acids chains strongly affects the interaction of amyloid-[Formula: see text] peptides with lipid membranes. The polyunsaturated lipids cause stronger adsorption of A[Formula: see text]-peptides by the membrane and lead to weaker binding between peptides when the latter form aggregates. This difference in the behaviour observed in monocomponent bilayers is propagated in a similar fashion to the mixed membranes mimicking composition of neuronal membranes in "healthy" and "AD" brains, with "healthy" membrane having higher fraction of polyunsaturated lipids. Our simulations give strong indication that it can be physical-chemical background of the interconnection between amyloid fibrillization causing Alzheimer's disease, and content of polyunsaturated lipids in the neuronal membranes.

Curvature sensing by cardiolipin in simulated buckled membranes.

Cardiolipin is a non-bilayer phospholipid with a unique dimeric structure. It localizes to negative curvature regions in bacteria and is believed to stabilize respiratory chain complexes in the highly curved mitochondrial membrane. Cardiolipin's localization mechanism remains unresolved, because important aspects such as the structural basis and strength for lipid curvature preferences are difficult to determine, partly due to the lack of efficient simulation methods. Here, we report a computational approach to study curvature preferences of cardiolipin by simulated membrane buckling and quantitative modeling. We combine coarse-grained molecular dynamics with simulated buckling to determine the curvature preferences in three-component bilayer membranes with varying concentrations of cardiolipin, and extract curvature-dependent concentrations and lipid acyl chain order parameter profiles. Cardiolipin shows a strong preference for negative curvatures, with a highly asymmetric chain order parameter profile. The concentration profiles are consistent with an elastic model for lipid curvature sensing that relates lipid segregation to local curvature via the material constants of the bilayers. These computations constitute new steps to unravel the molecular mechanism by which cardiolipin senses curvature in lipid membranes, and the method can be generalized to other lipids and membrane components as well.

Unperturbed hydrocarbon chains and liquid phase bilayer lipid chains: a computer simulation study.

In this work, the properties of saturated and unsaturated fatty acid acyl chains 16:0, 18:0, 18:1(n-9)cis, 18:2(n-6)cis, 18:3(n-3)cis, 18:4(n-3)cis, 18:5(n-3)cis, 20:4(n-6)cis, 20:5(n-3)cis and 22:6(n-3)cis in a bilayer liquid crystalline state and similar hydrocarbon chains (with CH[Formula: see text] terminal groups instead of C=O groups) in the unperturbed state characterised by a lack of long-range interaction were investigated. The unperturbed hydrocarbon chains were modelled by Monte Carlo simulations at temperature [Formula: see text] K; sixteen fully hydrated homogeneous liquid crystalline phosphatidylcholine bilayers containing these chains were studied by molecular dynamics simulations at the same temperature. To eliminate effects of the simulation parameters, the molecular dynamics and Monte Carlo simulations were carried out using the same structural data and force field coefficients. From these computer simulations, the average distances between terminal carbon atoms of the chains (end-to-end distances) were calculated and compared. The trends in the end-to-end distances obtained for the unperturbed chains were found to be qualitatively similar to those obtained for the same lipid chains in the bilayers. So, for understanding of a number of processes in biological membranes (e.g., changes in fatty acid composition caused by environmental changes such as temperature and pressure), it is possible to use, at least as a first approximation, the relationships between the structure and properties for unperturbed or isolated hydrocarbon chains.

Cholesterol in phospholipid bilayers: positions and orientations inside membranes with different unsaturation degrees.

Cholesterol is an essential component of all animal cell membranes and plays an important role in maintaining the membrane structure and physical-chemical properties necessary for correct cell functioning. The presence of cholesterol is believed to be responsible for domain formation (lipid rafts) due to different interactions of cholesterol with saturated and unsaturated lipids. In order to get detailed atomistic insight into the behaviour of cholesterol in bilayers composed of lipids with varying degrees of unsaturation, we have carried out a series of molecular dynamics simulations of saturated and polyunsaturated lipid bilayers with different contents of cholesterol, as well as well-tempered metadynamics simulations with a single cholesterol molecule in these bilayers. From these simulations we have determined distributions of cholesterol across the bilayer, its orientational properties, free energy profiles, and specific interactions of molecular groups able to form hydrogen bonds. Both molecular dynamics and metadynamics simulations showed that the most unsaturated bilayer with 22:6 fatty acid chains shows behaviour which is most different from other lipids. In this bilayer, cholesterol is relatively often found in a "flipped" configuration with the hydroxyl group oriented towards the membrane middle plane. This bilayer has also the highest (least negative) binding free energy among liquid phase bilayers, and the lowest reorientation barrier. Furthermore, cholesterol molecules in this bilayer are often found to form head-to-tail contacts which may lead to specific clustering behaviour. Overall, our simulations support ideas that there can be a subtle interconnection between the contents of highly unsaturated fatty acids and cholesterol, deficiency or excess of each of them is related to many human afflictions and diseases.

Force Field Development for Lipid Membrane Simulations.

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Quantum chemical and molecular dynamics modelling of hydroxylated polybrominated diphenyl ethers.

A series of 19 hydroxylated polybrominated diphenyl ethers (OH-PBDEs) have been studied using density functional theory (DFT) and molecular dynamics simulations with the purpose of investigating eventual correlations between their physicochemical properties and toxic action. Dissociation constants (pKa), solvation free energies and octanol-water partition coefficients (log P) have been computed. Additionally, metadynamics simulations of OH-PBDEs passing through a lipid bilayer have been carried out for four OH-PBDE species. No correlations between computed pKa values and toxicity data have been found. Medium correlations were found between partition coefficients and the ability of OH-PBDEs to alter membrane potential in cell cultures, which is attributed to higher uptake of molecules with larger log P parameters. It was also demonstrated that in lipid bilayers, OH-PBDE molecules differ in their orientational distributions and can adopt different conformations which can affect the uptake of these molecules and influence the pathways of their toxic action.

Diffusion and reaction pathways of water near fully hydrated TiO2 surfaces from ab initio molecular dynamics.

Ab initio molecular dynamics simulations are reported for water-embedded TiO2 surfaces to determine the diffusive and reactive behavior at full hydration. A three-domain model is developed for six surfaces [rutile (110), (100), and (001), and anatase (101), (100), and (001)] which describes waters as "hard" (irreversibly bound to the surface), "soft" (with reduced mobility but orientation freedom near the surface), or "bulk." The model explains previous experimental data and provides a detailed picture of water diffusion near TiO2 surfaces. Water reactivity is analyzed with a graph-theoretic approach that reveals a number of reaction pathways on TiO2 which occur at full hydration, in addition to direct water splitting. Hydronium (H3O+) is identified to be a key intermediate state, which facilitates water dissociation by proton hopping between intact and dissociated waters near the surfaces. These discoveries significantly improve the understanding of nanoscale water dynamics and reactivity at TiO2 interfaces under ambient conditions.

Binding energy calculations for hevein-carbohydrate interactions using expanded ensemble molecular dynamics simulations.

Accurate estimation of protein-carbohydrate binding energies using computational methods is a challenging task. Here we report the use of expanded ensemble molecular dynamics (EEMD) simulation with double decoupling for estimation of binding energies of hevein, a plant lectin with its monosaccharide and disaccharide ligands GlcNAc and (GlcNAc)2, respectively. In addition to the binding energies, enthalpy and entropy components of the binding energy are also calculated. The estimated binding energies for the hevein-carbohydrate interactions are within the range of ±0.5 kcal of the previously reported experimental binding data. For comparison, binding energies were also estimated using thermodynamic integration, molecular dynamics end point calculations (MM/GBSA) and the expanded ensemble methodology is seen to be more accurate. To our knowledge, the method of EEMD simulations has not been previously reported for estimating biomolecular binding energies.

Systematic hierarchical coarse-graining with the inverse Monte Carlo method.

We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730-3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.

Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids.

We have used systematic structure-based coarse graining to derive effective site-site potentials for a 10-site coarse-grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse-grained model the same site-site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid-water molar ratios. It was shown that there is a non-negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid-like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse-grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self-aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles.

Molecular dynamics simulations demonstrate the regulation of DNA-DNA attraction by H4 histone tail acetylations and mutations.

The positively charged N-terminal histone tails play a crucial role in chromatin compaction and are important modulators of DNA transcription, recombination, and repair. The detailed mechanism of the interaction of histone tails with DNA remains elusive. To model the unspecific interaction of histone tails with DNA, all-atom molecular dynamics (MD) simulations were carried out for systems of four DNA 22-mers in the presence of 20 or 16 short fragments of the H4 histone tail (variations of the 16-23 a. a. KRHRKVLR sequence, as well as the unmodified fragment a. a.13-20, GGAKRHRK). This setup with high DNA concentration, explicit presence of DNA-DNA contacts, presence of unstructured cationic peptides (histone tails) and K(+) mimics the conditions of eukaryotic chromatin. A detailed account of the DNA interactions with the histone tail fragments, K(+) and water is presented. Furthermore, DNA structure and dynamics and its interplay with the histone tail fragments binding are analysed. The charged side chains of the lysines and arginines play major roles in the tail-mediated DNA-DNA attraction by forming bridges and by coordinating to the phosphate groups and to the electronegative sites in the minor groove. Binding of all species to DNA is dynamic. The structure of the unmodified fully-charged H4 16-23 a.a. fragment KRHRKVLR is dominated by a stretched conformation. The H4 tail a. a. fragment GGAKRHRK as well as the H4 Lys16 acetylated fragment are highly flexible. The present work allows capturing typical features of the histone tail-counterion-DNA structure, interaction and dynamics.

Exploring Carbamazepine Polymorph Crystal Growth in Water by Enhanced Sampling Simulations.

In this work, the polymorphism of the active pharmaceutical ingredient carbamazepine (CBZ) was investigated by using molecular dynamics simulations with an enhanced sampling scheme. A single molecule of CBZ attaching to flat surfaces of different polymorphs was used as a model for secondary nucleation in water. A novel approach was developed to compute the free energy profile characterizing the adsorption of molecules with orientation aligned with the crystal structure of the surface. The distribution of states that showed alignment was used to rescale the adsorption free energy to include only the contribution that is consistent with crystal growth. The resulting free energy surfaces showed favorable thermodynamics for the most stable form, Form III and the second most stable form, Form I. The primary crystallization product, a dihydrate, was found to be less favorable, implying a nonclassical crystallization pathway. We suggest that a major contribution determining the energetics is the hydrophobicity of the surface. This thermodynamic ranking provides valuable information about the molecular pathways of polymorph growth and will further contribute to the understanding of the crystallization process of CBZ, which is imperative since polymorph formation can alter the physical properties of a drug significantly.

Partial atomic charges and their impact on the free energy of solvation.

Free energies of solvation (ΔG) in water and n-octanol have been computed for common drug molecules by molecular dynamics simulations with an additive fixed-charge force field. The impact of the electrostatic interactions was investigated by computing the partial atomic charges with four methods that all fit the charges from the quantum mechanically determined electrostatic potential (ESP). Due to the redistribution of electron density that occurs when molecules are transferred from gas phase to condensed phase, the polarization impact was also investigated. By computing the partial atomic charges with the solutes placed in a conductor-like continuum, the charges were effectively polarized to take the polarization effects into account. No polarization correction term or similar was considered, only the partial atomic charges. Results show that free energies are very sensitive to the choice of atomic charges and that ΔG can differ by several k(B)T depending on the charge computing method. Inclusion of polarization effects makes the solutes too hydrophilic with most methods and in vacuo charges make the solutes too hydrophobic. The restrained-ESP methods together with effectively polarized charges perform well in our test set and also when applied to a larger set of molecules. The effect of water models is also highlighted and shows that the conclusions drawn are valid for different three-point models. Partitioning between an aqueous and a hydrophobic phase is also described better if the two environment's polarization is taken into account, but again the results are sensitive to the charge calculation method. Overall, the results presented here show that effectively polarized charges can improve the description of solvating a drug-like molecule in a solvent and that the choice of partial atomic charges is crucial to ensure that molecular simulations produce reliable results.