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.

A Bottom-Up Coarse-Grained Model for Nucleosome-Nucleosome Interactions with Explicit Ions.

The nucleosome core particle (NCP) is a large complex of 145-147 base pairs of DNA and eight histone proteins and is the basic building block of chromatin that forms the chromosomes. Here, we develop a coarse-grained (CG) model of the NCP derived through a systematic bottom-up approach based on underlying all-atom MD simulations to compute the necessary CG interactions. The model produces excellent agreement with known structural features of the NCP and gives a realistic description of the nucleosome-nucleosome attraction in the presence of multivalent cations (Mg(H2O)62+ or Co(NH3)63+) for systems comprising 20 NCPs. The results of the simulations reveal structural details of the NCP-NCP interactions unavailable from experimental approaches, and this model opens the prospect for the rigorous modeling of chromatin fibers.

Bottom-Up Coarse-Grained Modeling of DNA.

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

Modeling DNA Flexibility: Comparison of Force Fields from Atomistic to Multiscale Levels.

Accurate parametrization of force fields (FFs) is of ultimate importance for computer simulations to be reliable and to possess a predictive power. In this work, we analyzed, in multi-microsecond simulations of a 40-base-pair DNA fragment, the performance of four force fields, namely, the two recent major updates of CHARMM and two from the AMBER family. We focused on a description of double-helix DNA flexibility and dynamics both at atomistic and at mesoscale level in coarse-grained (CG) simulations. In addition to the traditional analysis of different base-pair and base-step parameters, we extended our analysis to investigate the ability of the force field to parametrize a CG DNA model by structure-based bottom-up coarse-graining, computing DNA persistence length as a function of ionic strength. Our simulations unambiguously showed that the CHARMM36 force field is unable to preserve DNA's structural stability at over-microsecond time scale. Both versions of the AMBER FF, parmbsc0 and parmbsc1, showed good agreement with experiment, with some bias of parmbsc0 parameters for intermediate A/B form DNA structures. The CHARMM27 force field provides stable atomistic trajectories and overall (among the considered force fields) the best fit to experimentally determined DNA flexibility parameters both at atomistic and at mesoscale level.

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.

All-Atom MD Simulation of DNA Condensation Using Ab Initio Derived Force Field Parameters of Cobalt(III)-Hexammine.

It is well established that the presence of the trivalent cobalt(III)-hexammine cation (CoHex3+) at submillimolar concentrations leads to bundling (condensation) of double-stranded DNA molecules, which is caused by DNA-DNA attraction induced by the multivalent counterions. However, the detailed mechanism of this process is still not fully understood. Furthermore, in all-atom molecular dynamics (MD) simulations, spontaneous aggregation of several DNA oligonucleotides in the presence of CoHex3+ has previously not been demonstrated. In order to obtain a rigorous description of CoHex3+-nucleic acid interactions and CoHex3+-induced DNA condensation to be used in MD simulations, we have derived optimized force field parameters of the CoHex3+ ion. They were obtained from Car-Parrinello molecular dynamics simulation of a single CoHex3+ ion in the presence of 125 water molecules. The new set of force field parameters reproduces the experimentally known transition of DNA from B- to A-form, and qualitatively describes changes of DNA and RNA persistence lengths. We then carried out a 2 µs long atomistic simulation of four DNA oligomers each consisting of 36 base pairs in the presence of CoHex3+. We demonstrate that, in this system, DNA molecules display attractive interactions and aggregate into bundle-like structures. This behavior depends critically on the details of the CoHex3+ interaction with DNA. A control simulation with a similar setup but in the presence of Mg2+ does not induce DNA-DNA attraction, which is also in agreement with experiment.

Multiscale Modelling of Bionano Interface.

We present a framework for coarse-grained modelling of the interface between foreign nanoparticles (NP) and biological fluids and membranes. Our model includes united-atom presentations of membrane lipids and globular proteins in implicit solvent, which are based on all-atom structures of the corresponding molecules and parameterised using experimental data or atomistic simulation results. The NPs are modelled by homogeneous spheres that interact with the beads of biomolecules via a central force that depends on the NP size. The proposed methodology is used to predict the adsorption energies for human blood plasma proteins on NPs of different sizes as well as the preferred orientation of the molecules upon adsorption. Our approach allows one to rank the proteins by their binding affinity to the NP, which can be used for predicting the composition of the NP-protein corona for the corresponding material. We also show how the model can be used for studying NP interaction with a lipid bilayer membrane and thus can provide a mechanistic insight for modelling NP toxicity.

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.

MagiC: Software Package for Multiscale Modeling.

We present software package MagiC, which is designed to perform systematic structure-based coarse graining of molecular models. The effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from the modeling of the system in a high resolution (atomistic) description. The software supports coarse-grained tabulated intramolecular bond and angle interactions, as well as tabulated nonbonded interactions between different site types in the coarse-grained system, with the treatment of long-range electrostatic forces by the Ewald summation. Two methods of effective potential refinement are implemented: iterative Boltzmann inversion and inverse Monte Carlo, the latter accounting for cross-correlations between pair interactions. MagiC uses its own Metropolis Monte Carlo sampling engine, allowing parallel simulation of many copies of the system with subsequent averaging of the properties, which provides fast convergence of the method with nearly linear scaling at parallel execution.

Circadian profiles of focal epileptic seizures: a need for reappraisal.

Circadian rhythm of seizure is underestimated in the study of focal epilepsies. A review of the current literature revealed a clear correlation between cortical epileptogenic focus and the circadian phase of seizure peak occurrence in adult patients. A single diurnal peak at 19:00 was found in seizures originating from the occipital lobe, between 5:00 and 7:00 in frontal lobe seizures, and between 16:00 and 17:00 h in temporal lobe seizures. Two diurnal peaks, between 5:00 and 7:00, and at 23:00 are reported in seizures from the parietal lobe, and between 7:00 to 8:00 and 16:00 to 17:00 in mesial temporal onset seizures. This circadian character of seizure occurrence in focal epilepsies may not be unique to partial seizures since recent clinical and experimental data indicate that generalized seizures also demonstrate circadian effects. The clinical evidence on generalized seizures and epilepsies is not recent, but a formal integration of circadian rhythmicity in our understanding and clinical management of epilepsies may be warranted.

Effective solvent mediated potentials of Na+ and Cl- ions in aqueous solution: temperature dependence.

The effective solvent-mediated potentials for Na(+) and Cl(-) ions in aqueous solution were calculated in a wide range of temperatures from 0 to 100 °C. The potentials have been determined using the inverse Monte Carlo approach, from the ion-ion radial distribution functions computed in 50 ns molecular dynamics simulations of ions and explicit water molecules. We further separated the effective potentials into a short-range part and an electrostatic long-range part represented by a coulombic potential with some dielectric permittivity. We adjusted the value of the dielectric permittivity to provide the fastest possible decay of the short-range potentials at larger distances. The obtained temperature dependence of the dielectric permittivity follows well the experimental data. We show also that the largest part of the temperature dependence of the effective potentials can be attributed to the temperature-dependent dielectric permittivity.

Molecular dynamics investigation of dipeptide-transition metal salts in aqueous solutions.

Molecular dynamics (MD) simulations of glycylglycine dipeptide with transition metal ions (Mn(2+), Fe(2+), Co(2+), Ni(2+), Cu(2+), and Zn(2+)) in aqueous solutions have been carried out to get an insight into the solvation structure, intermolecular interactions, and salt effects in these systems. The solvation structure and hydrogen bonding were described in terms of radial distribution function (RDF) and spatial distribution function (SDF). The dynamical properties of the solvation structure were also analyzed in terms of diffusion and residence times. The simulation results show the presence of a well-defined first hydration shell around the dipeptide, with water molecules forming hydrogen bonds to the polar groups of the dipeptide. This shell is, however, affected by the strong electric field of divalent metal ions, which at higher ion concentrations lead to the shift in the dipeptide-water RDFs. Higher salt concentrations lead also to increased residence times and slower diffusion rates. In general, smaller ions (Cu(2+), Zn(2+)) demonstrate stronger binding to dipeptide than the larger ones (Fe(2+), Mn(2+)). Simulations do not show any stronger association of peptide molecules indicating their dissolution in water. The above results may be of potential interest to future researchers on these molecular interactions.

Systematic coarse-graining of molecular models by the Newton inversion method.

Systematic construction of coarse-grained molecular models from detailed atomistic simulations, and even from ab initio simulations is discussed. Atomistic simulations are first performed to extract structural information about the system, which is then used to determine effective potentials for a coarse-grained model of the same system. The statistical-mechanical equations expressing the canonical properties in terms of potential parameters can be inverted and solved numerically according to the iterative Newton scheme. In our previous applications, known as the Inverse Monte Carlo, radial distribution functions were inverted to reconstruct pair potential, while in a more general approach the targets can be other canonical averages. We have considered several examples of coarse-graining; for the united atom water model we suggest an easy way to overcome the known problem of high pressure. Further, we have developed coarse-grained models for L- and D-prolines, dissolved here in an organic solvent (dimethylsulfoxide), keeping their enantiomeric properties from the corresponding all-atom proline model. Finally, we have revisited the previously developed coarse-grained lipid model based on an updated all-atomic force field. We use this model in large-scale meso-scale simulations demonstrating spontaneous formation of different structures, such as vesicles, micelles, and multi-lamellar structures, depending on thermodynamical conditions.