Simulations Of Coarse-grained Model Research Articles

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus

ABSTRACT Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a “wetting”-like interaction. In contrast, fluctuations are insensitive to heterochromatin’s internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.

Coarse-grained simulation model of protein TDP-43 liquid-liquid phase separation behavior

Coarse-grained simulation model of protein TDP-43 liquid-liquid phase separation behavior

Efficient generation of random rotation matrices in four dimensions.

Four-dimensional (4D) rotations have applications in the fields of robotics, computer vision, and rigid-body mechanics. In the latter, they can be used to transform between equimomental systems of point masses. Here we provide an efficient algorithm to generate random 4D rotation matrices covering an arbitrary, predefined range of rotation angles. These matrices can be combined with Monte Carlo methods for the efficient sampling of the SO(4) group of 4D rotations. The matrices are unbiased and constructed such that repeated rotations result in uniform sampling over SO(4). The algorithm can be used to optimize the mass partitioning in coarse-grained simulation models of molecules involving coupled constraints for stable time integration.

Dynamical coarse-grained models of molecular liquids and their ideal and non-ideal mixtures.

Coarse-grained (CG) simulation models of condensed-phase systems can be derived with well-established methods that perform coarse-graining in space and provide an effective Hamiltonian with which some of the structural and thermodynamic properties of the underlying fine-grained (FG) reference system can be represented. Coarse-graining in time potentially provides CG models that furthermore represent dynamic properties. However, systematic efforts in this direction have so far been limited, especially for moderately coarse-grained, chemistry-specific systems with complicated conservative interactions. With the aim of representing structural, thermodynamic, and dynamic properties in CG simulations of multi-component molecular systems, we investigated a recently introduced method in which the force on a CG particle originates from conservative interactions with surrounding particles and non-Markovian dissipative interactions, the latter introduced by means of a colored-noise thermostat. We examined two different methods to derive isotropic memory kernels required for integrating the corresponding generalized Langevin equation (GLE) of motion, based on the orthogonal dynamics of the FG forces and on an iterative optimization scheme. As a proof of concept, we coarse-grain single-component molecular liquids (cyclohexane, tetrachloromethane) and ideal and non-ideal binary mixtures of cyclohexane/tetrachloromethane and ethanol/tetrachloromethane, respectively. We find that for all systems, the FG single particle velocity auto-correlation functions and, consequently, both the short time and long time diffusion coefficients can be quantitatively reproduced with the CG-GLE models. We furthermore demonstrate that the present GLE-approach leads to an improved description of the rate with which the spatial correlations decay, which is artificially accelerated in the absence of dissipation.

Compression of a confined semiflexible polymer under direct and oscillating fields.

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Theory and Simulation of Multiphase Coexistence in Biomolecular Mixtures.

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase behavior of heterogeneous biomolecular mixtures are only beginning to be explored. Theory and simulation provide invaluable tools for probing the relationship between molecular determinants, such as protein and RNA sequences, and the emergence of phase-separated condensates in such complex environments. This review covers recent advances in the prediction and computational design of biomolecular mixtures that phase-separate into many coexisting phases. First, we review efforts to understand the phase behavior of mixtures with hundreds or thousands of species using theoretical models and statistical approaches. We then describe progress in developing analytical theories and coarse-grained simulation models to predict multiphase condensates with the molecular detail required to make contact with biophysical experiments. We conclude by summarizing the challenges ahead for modeling the inhomogeneous spatial organization of biomolecular mixtures in living cells.

Coarse-Grained Modeling of EUV Patterning Process Reflecting Photochemical Reactions and Chain Conformations.

Enabling extreme ultraviolet lithography (EUVL) as a viable and efficient sub-10 nm patterning tool requires addressing the critical issue of reducing line edge roughness (LER). Stochastic effects from random and local variability in photon distribution and photochemical reactions have been considered the primary cause of LER. However, polymer chain conformation has recently attracted attention as an additional factor influencing LER, necessitating detailed computational studies with explicit chain representation and photon distribution to overcome the existing approach based on continuum models and random variables. We developed a coarse-grained molecular simulation model for an EUV patterning process to investigate the effect of chain conformation variation and stochastic effects via photon shot noise and acid diffusion on the roughness of the pattern. Our molecular simulation demonstrated that final LER is most sensitive to the variation in photon distributions, while material distributions and acid diffusion rate also impact LER; thus, the intrinsic limit of LER is expected even at extremely suppressed stochastic effects. Furthermore, we proposed and tested a novel approach to improve the roughness by controlling the initial polymer chain orientation.

How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks.

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.

A coarse-grained simulation model for colloidal self-assembly via explicit mobile binders.

Colloidal particles with mobile binding molecules constitute a powerful platform for probing the physics of self-assembly. Binding molecules are free to diffuse and rearrange on the surface, giving rise to spontaneous control over the number of droplet-droplet bonds, i.e., valence, as a function of the concentration of binders. This type of valence control has been realized experimentally by tuning the interaction strength between DNA-coated emulsion droplets. Optimizing for valence two yields droplet polymer chains, termed 'colloidomers', which have recently been used to probe the physics of folding. To understand the underlying self-assembly mechanisms, here we present a coarse-grained molecular dynamics (CGMD) model to study the self-assembly of this class of systems using explicit representations of mobile binding sites. We explore how valence of assembled structures can be tuned through kinetic control in the strong binding limit. More specifically, we optimize experimental control parameters to obtain the highest yield of long linear colloidomer chains. Subsequently tuning the dynamics of binding and unbinding via a temperature-dependent model allows us to observe a heptamer chain collapse into all possible rigid structures, in good agreement with recent folding experiments. Our CGMD platform and dynamic bonding model (implemented as an open-source custom plugin to HOOMD-Blue) reveal the molecular features governing the binding patch size and valence control, and opens the study of pathways in colloidomer folding. This model can therefore guide programmable design in experiments.

United atom and coarse grained models for crosslinked polydimethylsiloxane with applications to the rheology of silicone fluids.

Siloxane systems consisting primarily of polydimethylsiloxane (PDMS) are versatile, multifaceted materials that play a key role in diverse applications. However, open questions exist regarding the correlation between their varied atomic-level properties and observed macroscale features. To this effect, we have created a systematic workflow to determine coarse-grained simulation models for crosslinked PDMS in order to further elucidate the effects of network changes on the system's rheological properties below the gel point. Our approach leverages a fine-grained united atom model for linear PDMS, which we extend to include crosslinking terms, and applies iterative Boltzmann inversion to obtain a coarse-grain "bead-spring-type" model. We then perform extensive molecular dynamics simulations to explore the effect of crosslinking on the rheology of silicone fluids, where we compute systematic increases in both density and shear viscosity that compare favorably to experiments that we conduct here. The kinematic viscosity of partially crosslinked fluids follows an empirical linear relationship that is surprisingly consistent with Rouse theory, which was originally derived for systems comprised of a uniform distribution of linear chains. The models developed here serve to enable quantitative bottom-up predictions for curing- and age-induced effects on macroscale rheological properties, allowing for accurate prediction of material properties based on fundamental chemical data.

Kinetic frustration by limited bond availability controls the LAT protein condensation phase transition on membranes.

LAT is a membrane-linked scaffold protein that undergoes a phase transition to form a two-dimensional protein condensate on the membrane during T cell activation. Governed by tyrosine phosphorylation, LAT recruits various proteins that ultimately enable condensation through a percolation network of discrete and selective protein-protein interactions. Here, we describe detailed kinetic measurements of the phase transition, along with coarse-grained model simulations, that reveal that LAT condensation is kinetically frustrated by the availability of bonds to form the network. Unlike typical miscibility transitions in which compact domains may coexist at equilibrium, the LAT condensates are dynamically arrested in extended states, kinetically trapped out of equilibrium. Modeling identifies the structural basis for this kinetic arrest as the formation of spindle arrangements, favored by limited multivalent binding interactions along the flexible, intrinsically disordered LAT protein. These results reveal how local factors controlling the kinetics of LAT condensation enable formation of different, stable condensates, which may ultimately coexist within the cell.

Microscopic Interface and Multiscale Failure Analysis of Proposed Molecular Chain Polymers Based on Aifantis Strain Gradient Theory.

A study on the microscopic morphology of real-world polymer blends and its mechanism of change showed that the microscopic morphology of equiproportional mixtures gradually changed from a dense body structure to a network structure with the addition of the total polymer concentration up to 20%; the microscopic morphology of mixtures with different proportions was characterized by the most uniform network structure of equiproportional mixtures when the total polymer concentration was 20%. The polymer acts as a defoamer in the mixed system. In this paper, the relationship between the microscopic morphology of each mixture and the physicochemical behavior of the two polymer chains in the mixed system was investigated on the basis of the Aifantis strain gradient theory. Molecular polymer microscopic interface and multiscale failure analysis are proposed. It is shown that for the dihedral angle distribution of four consecutive coarse-grained particles, the peaks obtained from all atomic-scale simulation data are reproduced in the coarse-grained model simulations. The deviation is within 2.5% in most places, except for the local area where the deviation exceeds 5%. Therefore, we have achieved good results for large-scale failures.

Revealing the role of hydrogen bonding in polyurea with multiscale simulations

ABSTRACT Typically, polyurea is a polymer forming microphase-separated structures. Various coarse-grained (CG) simulation models have been developed to study the microphase structure and viscoelastic properties of polyurea. However, since the hydrogen atoms were modelled implicitly in the existing CG models, the anisotropic hydrogen bonding between urea groups in the hard domain might not be treated properly. Here, we introduce a hybrid all-atom/coarse-grained (AA/CG) model for polyurea, the CGU model, in which atomistic resolution are preserved for the urea groups. This model is proven to reproduce the results of the AA model, despite 24 times faster to run. By comparing the traditional CG model and the CGU model, we found that hydrogen bonding leads to a head-to-tail arrangement of the urea groups and a significant slowdown of the hard segment dynamics. Non-equilibrium simulations of stress relaxation process indicate that hydrogen bonding causes a broad relaxation time spectrum, which is consistent with experiment results.

Coarse grained simulation of the aggregation and structure control of polyethylene nanocrystals

Polyethylene (PE) telechelics with carboxylate functional groups at both ends have been shown to assemble into hexagonal nanocrystal platelets with a height defined by their chain length in basic CsOH-solution. In this coarse grained (CG) simulation study we show how properties of the functional groups alter the aggregation and crystallization behavior of those telechelics. Systematic variation of the parameters of the CG model showed that important factors which control nanoparticle stability and structure are the PE chain length and the hydrophilicity and the steric demand of the head groups. To characterize the aggregation process we analyzed the number and size of the obtained aggregates as well as intramolecular order and intermolecular alignment of the polymer chains. By comparison of CG and atomistic simulation data, it could be shown that atomistic simulations representing different chemical systems can be emulated with specific, different CG parameter sets. Thus, the results from the (generic) CG simulation models can be used to explain the effect of different head groups and different counterions on the aggregation of PE telechelics and the order of the obtained nanocrystals.

Dynamical properties across different coarse-grained models for ionic liquids

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation–anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Comperhensive Characterization of Active and Inactive Chromatin in Human Cells by Superresolution Microscopy and Computer Simulations

In chromatin DNA is wrapped around histone proteins forming so-called nucleosomes. These are the basic building blocks that organizes the DNA packaging. The nucleosome chain folds into a structure termed chromatin and is distinguished into active DNA comprising euchromatin and inactive DNA comprising heterochromatin. To better understand the underlaying processes and dynamics of these structures, two 5 kb regions (active, inactive) on chromosom 11 of the human genome were chosen by our collaboration partners in Munich. For these regions end to end measurements were executed repeatedly with the help of 3D STED microscopy. To verify the experimental data, our coarse-grained computer simulation model of chromatin was consolidated. In these nucleosomes are modelled as spherocylinders connected by elastic segments describing linker DNA. Interactions include stretching, bending, torsion, electrostatic and internucleosomal interactions. Configurations are sampled applying Metropolis Monte Carlo and replica exchange algorithms. One of the Results is indicating that an active region has different nucleosome occupancies in different cells. For this purpose, we first simulate the full nucleosome occupied active region and decreased the number of nucleosomes by one and simulate it again until 5 nucleosomes were deleted. After that, the end to end (Euclidean distance) distances of the lowest Temperature were measured and compared with the experimental histograms. The most interesting fact is that the addition of all histograms leads to a result which is much closer to the experimental one.

Unveiling the phase behavior of CiEj non-ionic surfactants in water through coarse-grained molecular dynamics simulations.

Poly(oxyethylene) alkyl ethers, usually denoted by CiEj surfactants, exhibit a rich phase behavior in water, self-assembling to form a variety of 3-D structures with a controllable morphology that find multiple applications across different industrial segments. Hence, being able to describe and understand the effect of molecular structure on the phase behavior of these systems is highly relevant for the efficient design of new materials and their applications. Considering the promising results obtained over the last decade using the MARTINI model to describe ethylene-oxide containing compounds, an extensive assessment of the ability of such a model to describe the phase behavior of CiEj in water was carried out and results are presented here. Given the overall poor temperature transferability of the MARTINI model, mostly due to the lack of an accurate representation of hydrogen bonding, simulations were carried out at a single temperature of 333 K, where most phases are expected to occur according to experiments. Different chain lengths of both the hydrophobic and hydrophilic moieties, spanning a wide range of hydrophilic-lipophilic balance values, were investigated and the phase diagrams of various CiEj surfactants explored over a wide concentration range. The model was able to satisfactorily describe the effect of surfactant structure and concentration on mesophase formation. The stability and dimensions of the obtained phases, and the prediction of some unique features such as the characterization of a singular lamellar phase are presented. The results obtained in this work highlight both the predictive ability and the transferability of the MARTINI forcefield in the description of such systems. Moreover, the model was shown to provide adequate descriptions of the micellar phase in terms of micelle dimensions, critical micelle concentration, and average aggregation number.

Magnetostriction in elastomers with mixtures of magnetically hard and soft microparticles: effects of nonlinear magnetization and matrix rigidity

Abstract In this contribution, a magnetoactive elastomer (MAE) of mixed content, i.e., a polymer matrix filled with a mixture of magnetically soft and magnetically hard spherical particles, is considered. The object we focus on is an elementary unit of this composite, for which we take a set consisting of a permanent spherical micromagnet surrounded by an elastomer layer filled with magnetically soft microparticles. We present a comparative treatment of this unit from two essentially different viewpoints. The first one is a coarse-grained molecular dynamics simulation model, which presents the composite as a bead-spring assembly and is able to deliver information of all the microstructural changes of the assembly. The second approach is entirely based on the continuum magnetomechanical description of the system, whose direct yield is the macroscopic field-induced response of the MAE to external field, as this model ignores all the microstructural details of the magnetization process. We find that, differing in certain details, both frameworks are coherent in predicting that a unit comprising magnetically soft and hard particles may display a nontrivial reentrant (prolate/oblate/prolate) axial deformation under variation of the applied field strength. The flexibility of the proposed combination of the two complementary frameworks enables us to look deeper into the manifestation of the magnetic response: with respect to the magnetically soft particles, we compare the linear regime of magnetization to that with saturation, which we describe by the Fröhlich–Kennelly approximation; with respect to the polymer matrix, we analyze the dependence of the reentrant deformation on its rigidity.

Measuring Internal Forces in Single-Stranded DNA: Application to a DNA Force Clamp.

We present a new method for calculating internal forces in DNA structures using coarse-grained models and demonstrate its utility with the oxDNA model. The instantaneous forces on individual nucleotides are explored and related to model potentials, and using our framework, internal forces are calculated for two simple DNA systems and for a recently published nanoscopic force clamp. Our results highlight some pitfalls associated with conventional methods for estimating internal forces, which are based on elastic polymer models, and emphasize the importance of carefully considering secondary structure and ionic conditions when modeling the elastic behavior of single-stranded DNA. Beyond its relevance to the DNA nanotechnological community, we expect our approach to be broadly applicable to calculations of internal force in a variety of structures-from DNA to protein-and across other coarse-grained simulation models.

Thermal Compaction of Disordered and Elastin-like Polypeptides: A Temperature-Dependent, Sequence-Specific Coarse-Grained Simulation Model.

Elastin-like polypeptides (ELPs) undergo a sharp solubility transition from low-temperature solvated phases to coacervates at elevated temperatures, driven by the increased strength of hydrophobic interactions at higher temperatures. The transition temperature, or "cloud point", critically depends on sequence composition, sequence length, and concentration of the ELPs. In this work, we present a temperature-dependent, implicit solvent, sequence-specific coarse-grained (CG) simulation model that reproduces the transition temperatures as a function of sequence length and guest residue identity of various experimentally probed ELPs to appreciable accuracy. Our model builds upon the self-organized polymer model introduced recently for intrinsically disordered polypeptides (SOP-IDP) and introduces a semi-empirical functional form for the temperature dependence of hydrophobic interactions. In addition to the fine performance for various ELPs, we demonstrate the ability of our model to capture the thermal compactions in dominantly hydrophobic IDPs, consistent with experimental scattering data. With the high computational efficiency afforded by the CG representation, we envisage that the model will be ideally suited for simulations of large-scale structures such as ELP networks and hydrogels, as well as agglomerates of IDPs.