Coarse-grained Dynamics Research Articles

Coarse-grained CFD-DEM study of Gas-solid flow in gas cyclone

Gas cyclones are common device in various industries to separate solid particles and/or droplets from gas streams. Nonetheless, the mathematical modelling of gas cyclone has been very challenging since huge number of multi-sized particles are involved in the system. In this work, a numerical study of the gas–solid flow in a gas cyclone with wide range of particle size distribution (from 1 to 200 µm) is carried out by developing a coarse-grained combined Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) model. It shows that the coarse-grained CFD-DEM model is able to capture the typical flow features in a gas cyclone including the solid strands and dust ceiling phenomena. It also shows that modelling of van der Waals force is critical for the prediction of separation efficiency in gas cyclone especially for fine particles. Furthermore, it is tried to explain how the dust ceiling is formed.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules.

Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Coarse-grained Dynamics Simulation in Polymer Systems: from Structures to Material Properties

Coarse-grained Dynamics Simulation in Polymer Systems: from Structures to Material Properties

Application of projection operator method to coarse-grained dynamics with transient potential.

We show that the coarse-grained dynamics model with the time-dependent and fluctuating potential (transient potential) can be derived from the microscopic Hamiltonian dynamics. The concept of the transient potential was first introduced rather phenomenologically, and its relation to the underlying microscopic dynamics has not been clarified yet. This is in contrast to the generalized Langevin equation, the relation of which to the microscopic dynamics is well-established. In this work, we show that the dynamic equationswith the transient potential can be derived for the coupled oscillator model, without any approximations. It is known that the dynamics of the coupled oscillator model can be exactly described by the generalized Langevin-type equations. This fact implies that the dynamic equationswith the transient potential can be utilized as a coarse-grained dynamics model in a similar way to the generalized Langevin equation. Then we show that the dynamic equationsfor the transient potential can also be formally derived for the microscopic Hamiltonian dynamics, without any approximations. We use the projection operator method for the coarse-grained variables and transient potential. The dynamic equationsfor the coarse-grained positions and momenta are similar to those in the Hamiltonian dynamics, but the interaction potential is replaced by the transient potential. The dynamic equationfor the transient potential is the generalized Langevin equationwith the memory effect. Our result justifies the use of the transient potential to describe the coarse-grained dynamics. We propose several approximations to obtain the simplified dynamics model. We show that, under several approximations, the dynamic equationfor the transient potential reduces to the relatively simple Markovian dynamic equationfor the potential parameters. We also show that with several additional approximations, the approximate dynamics model further reduces to the Markovian Langevin-type equationswith the transient potential.

Coarse-Grained Entanglement and Operator Growth in Anomalous Dynamics.

In two-dimensional Floquet systems, many-body localized dynamics in the bulk may give rise to a chaotic evolution at the one-dimensional edges that is characterized by a nonzero chiral topological index. Such anomalous dynamics is qualitatively different from local-Hamiltonian evolution. Here we show how the presence of a nonzero index affects entanglement generation and the spreading of local operators, focusing on the coarse-grained description of generic systems. We tackle this problem by analyzing exactly solvable models of random quantum cellular automata (QCA) that generalize random circuits. We find that a nonzero index leads to asymmetric butterfly velocities with different diffusive broadening of the light cones and to a modification of the order relations between the butterfly and entanglement velocities. We propose that these results can be understood via a generalization of the recently introduced entanglement membrane theory, by allowing for a spacetime entropy current, which in the case of a generic QCA is fixed by the index. We work out the implications of this current on the entanglement "membrane tension" and show that the results for random QCA are recovered by identifying the topological index with a background velocity for the coarse-grained entanglement dynamics.

Coarse-Grained Dynamically Accurate Simulations of Ionic Liquids: [pyr14][TFSI] and [EMIM][BF4

In this work, coarse-grained (CG) models for two different sets of ionic liquids were developed from atomistic molecular dynamics (MD) reference systems, expanding their system size and time duration capabilities. The bonded force field of the CG systems was built using harmonic oscillator potential (HOP) fitting, while the nonbonded force field was generated with the multiscale coarse-graining (MS-CG) approach based on force matching. The dynamics of each system were corrected using the probability distribution function-based coarse-grained molecular dynamics (PDF-based CGMD) method. The structure and dynamics of each system were proven to match reference system data at two temperature scales. CG models and force fields for these liquids were developed to exemplify a general purpose methodology for producing MD results of ionic liquids and other fluids with accurate structural as well as dynamic properties. As an application, developed ionic liquids CG models were then applied to study vacuum-interface interaction. Density profile results of vacuum-interface exposure show significant deviation from bulk behavior. At the interface, multilayer ordering of ionic liquids is predicted to be similar to those observed from an experimental work. This ordering is intensified by decreasing temperature and use of the PDF-based CGMD method as opposed to conventional CG methods.

Between Two Walls: Modeling the Adsorption Behavior of β-Glucosidase A on Bare and SAM-Functionalized Gold Surfaces.

The efficient immobilization of enzymes on surfaces remains a complex but central issue in the biomaterials field, which requires us to understand this process at the atomic level. Using a multiscale approach combining all-atom molecular dynamics and coarse-grain Brownian dynamics simulations, we investigated the adsorption behavior of β-glucosidase A (βGA) on bare and self-assembled monolayer (SAM)-functionalized gold surfaces. We monitored the enzyme position and orientation during the molecular dynamics (MD) trajectories and measured the contacts it forms with both surfaces. While the adsorption process has little impact on the protein conformation, it can nonetheless perturb its mechanical properties and catalytic activity. Our results show that compared to the SAM-functionalized surface, the adsorption of βGA on bare gold is more stable, but less specific, and more likely to disrupt the enzyme's function. This observation emphasizes the fact that the structural organization of proteins at the solid interface is a key point when designing devices based on enzyme immobilization, as one must find an acceptable stability-activity trade-off.

Mathematical Framework for Breathing Chimera States

About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence–incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott–Antonsen reduction technique.

Interactions of Crosslinked Polyacrylic Acid Polyelectrolyte Gels with Nonionic and Ionic Surfactants.

The morphology and stability of surfactant-loaded polyelectrolyte gels are of great interest for a variety of personal care, cosmetic, and pharmaceutical products. However, the mechanisms of surfactant interactions with gel-forming polymers are poorly understood and experimentally challenging. The aim of this work is to explore in silico the specifics of surfactant absorption within polyelectrolyte gels drawing on the examples of typical non-ionic octaethylene glycol monooctyl ether (C8E8) and anionic sodium dodecyl sulfate (SDS) surfactants and polyacrylic acid modified with hydrophobic sidechains mimicking the practically important Carbopol polymer. Using the systematically parameterized coarse-grained dissipative particle dynamics models, we generate and characterize the equilibrium conformations and swelling of the polymer films in aqueous solutions with the surfactant concentrations varied up to the critical micelle concentration (cmc). We discover the striking difference in interactions of Carbopol-like polymers with nonionic and ionic surfactants under mildly acidic conditions. The sorption of C8E8 within the polymer film is found substantial. As the surfactant concentration increases, the polymer film swells and, close to cmc, becomes unstable due to the formation and growth of water pockets filled with surfactant micelles. Sorption of SDS at the same bulk concentrations is found much lower, with only about 1% of surfactant mass fraction achieved at cmc. As the SDS concentration increases further, a lamellae structure is formed within the film, which remains stable. Reduced swelling and higher stability indicate better prospects of using SDS-type surfactants with Carbopol-based gels in formulations for detergents and personal care products.

Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

Memory retrieval dynamics and storage capacity of a modular network model of association cortex with featural decomposition

The primate heteromodal cortex presents an evident functional modularity at a mesoscopic level, with physiological and anatomical evidence pointing to it as likely substrate of long-term memory. In order to investigate some of its properties, a model of multimodular autoassociator is studied. Each of the many modules represents a neocortical functional ensemble of recurrently connected neurons and operates as a Hebbian autoassociator, storing a number of local features which it can recall upon cue. The global memory patterns are made of combinations of features sparsely distributed across the modules. Intermodular connections are modelled as a finite-connectivity random graph. Any pair of features in any respective pair of modules is allowed to be involved in several memory patterns; the coarse-grained modular network dynamics is defined in such a way as to overcome the consequent ambiguity of associations. Effects of long-range homeostatic synaptic scaling on network performance are also assessed.The dynamical process of cued retrieval almost saturates a natural upper bound while producing negligible spurious activation. The extent of finite-size effects on storage capacity is quantitatively evaluated. In the limit of infinite size, the functional relationship between storage capacity and number of features per module reduces to that which other authors found by methods from equilibrium statistical mechanics, which suggests that the origin of the functional form is of a combinatorial nature. In contrast with its apparent inevitability at intramodular level, long-range synaptic scaling results to be of minor relevance to both retrieval and storage capacity, casting doubt on its existence in the neocortex. A conjecture is also posited about how statistical fluctuation of connectivity across the network may underpin spontaneous emergence of semantic hierarchies through learning.

Shock-induced interfacial instabilities of granular media

This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

Estimating Entropy Production from Waiting Time Distributions.

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.

The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables

The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can be obtained from the dynamics of the underlying microscopic system and in which cases it makes sense to introduce a potential of mean force. We discuss shortcomings of previous derivations presented in the literature and demonstrate the implications of our derivation for the structure of memory terms and for generalized fluctuation-dissipation relations. We show, in particular, that the widely used, simple structure which contains a potential of mean force, a memory term which is linear in the observable, and a fluctuating force which is related to the memory term by a fluctuation-dissipation relation, is neither exact nor can it, in general, be derived as a controlled approximation to the exact dynamics.

Site of Cholesterol Oxidation Impacts Its Localization and Domain Formation in the Neuronal Plasma Membrane.

Cholesterol is integral to the structure of mammalian cell membranes. Oxidation of cholesterol alters how it behaves in the membrane and influences the membrane biophysical properties. Elevated levels of oxidized cholesterol are associated with neurodegenerative diseases such as Alzheimer's disease, Parkinson's disease, multiple sclerosis, and Huntington's disease. Previous work has investigated the impact of oxidized cholesterol in the context of simple model membrane systems. However, there is a growing body of literature that shows that complex membranes possessing physiological phospholipid distributions have different properties from those of binary or trinary model membranes. In the current work, the impact of oxidized cholesterol on the biophysical properties of a complex neuronal plasma membrane is investigated using coarse-grained Martini molecular dynamics simulations. Comparison of the native neuronal membrane to neuronal membranes containing 10% tail-oxidized or 10% head-oxidized cholesterol shows that the site of oxidization changes the behavior of the oxidized cholesterol in the membrane. Furthermore, species-specific domain formation is observed between each oxidized cholesterol and minor lipid classes. Although both tail-oxidized and head-oxidized cholesterols modulate the biophysical properties of the membrane, smaller changes are observed in the complex neuronal membrane than seen in the previous work on simple binary or trinary model membranes. This work highlights the presence of compensatory effects of lipid diversity in the complex neuronal membrane. Overall, this study improves our molecular-level understanding of the effects of oxidized cholesterol on the properties of neuronal tissue and emphasizes the importance of studying membranes with realistic lipid compositions.

High Adsorption of α-Glucosidase on Polymer Brush-Modified Anisotropic Particles Acquired by Electrospraying-A Combined Experimental and Simulation Study.

In this particular contribution, we aim to immobilize a model enzyme such as α-glucosidase onto poly(DMAEMA) [poly(2-dimethyl amino ethyl methacrylate)] brush-modified anisotropic (cup- and disc-shaped) biocompatible polymeric particles. The anisotropic particles comprising a blend of PLA [poly(lactide)] and poly(MMA-co-BEMA) [poly((methyl methacrylate)-co-(2-(2-bromopropionyloxy) ethyl methacrylate)] were acquired by electrospraying, a scalable and convenient technique. We have also demonstrated the role of a swollen polymer brush grafted on the surface of cup-/disc-shaped particles via surface-initiated atom transfer radical polymerization in immobilizing an unprecedentedly high loading of enzyme [441 mg/g (cup)-589 mg/g (disc) of particles, 15-20 times higher than that of the literature-reported system] as compared to non-brush-modified particles. Circular dichroism spectroscopy was used to predict the structural changes of the enzyme upon immobilization onto the carrier particles. An enormously high amount of enzymes with preserved activity (∼85 ± 13% for cups and ∼78 ± 15% for discs) was found to adhere onto brush-modified particles at pH 7 via electrostatic adsorption. These findings were further explored at the atomistic level using a coarse-grained dissipative particle dynamics simulation approach, which exhibited excellent correlation with experimental results. In addition, accelerated particle separation was also achieved via magnetic force-induced aggregation within 20 min (without a centrifuge) by incorporating magnetic nanoparticles into disc-shaped particles while electrojetting. This further strengthens the technical feasibility of the process, which holds immense potential to be applied for various enzymes intended for several applications.

Rapid prototyping of arbitrary 2D and 3D wireframe DNA origami.

Wireframe DNA origami assemblies can now be programmed automatically from the top-down using simple wireframe target geometries, or meshes, in 2D and 3D, using either rigid, six-helix bundle (6HB) or more compliant, two-helix bundle (DX) edges. While these assemblies have numerous applications in nanoscale materials fabrication due to their nanoscale spatial addressability and high degree of customization, no easy-to-use graphical user interface software yet exists to deploy these algorithmic approaches within a single, standalone interface. Further, top-down sequence design of 3D DX-based objects previously enabled by DAEDALUS was limited to discrete edge lengths and uniform vertex angles, limiting the scope of objects that can be designed. Here, we introduce the open-source software package ATHENA with a graphical user interface that automatically renders single-stranded DNA scaffold routing and staple strand sequences for any target wireframe DNA origami using DX or 6HB edges, including irregular, asymmetric DX-based polyhedra with variable edge lengths and vertices demonstrated experimentally, which significantly expands the set of possible 3D DNA-based assemblies that can be designed. ATHENA also enables external editing of sequences using caDNAno, demonstrated using asymmetric nanoscale positioning of gold nanoparticles, as well as providing atomic-level models for molecular dynamics, coarse-grained dynamics with oxDNA, and other computational chemistry simulation approaches.

Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic differential equation (SDE) descriptions of realistically-sampled time series data, to understand finite-size effects in the Kuramoto model of coupled oscillators. We find that across the entire bifurcation diagram, the dynamics of the Kuramoto order parameter are statistically consistent with an SDE whose drift term has the form predicted by the Ott–Antonsen ansatz in the N→∞ limit. We find that the diffusion term is nearly independent of the bifurcation parameter, and has a magnitude decaying as N−1/2, consistent with the central limit theorem. This shows that the diverging fluctuations of the order parameter near the critical point are driven by a bifurcation in the underlying drift term, rather than increased stochastic forcing.

Mori-Zwanzig projection operator formalism: Particle-based coarse-grained dynamics of open classical systems far from equilibrium.

We present a generalized Langevin equation (GLE) of motion that governs exactly the time evolution of phase-space observables in finite open systems described by classical Hamiltonians with explicitly time-dependent potentials. This formalism is based on the Mori-Zwanzig projection operator (PO) method with a time-independent Zwanzig PO within a Heisenberg (Lagrangian) picture and reduced description of Hamiltonian systems in terms of canonical relevant and irrelevant coordinates. We demonstrate that, similarly to closed systems, GLE dynamics in Hamiltonian systems in the presence of time-dependent potentials is determined by conservative, dissipative memory, and projected force fields, and that the memory functions relate to the projected force, which is a two-time process, in a way that is reminiscent of the equilibrium second fluctuation-dissipation relation. We further show that, in the most general case, the memory kernel depends on the relevant momentum gradients of the (Boltzmann) entropy of the irrelevant subsystem. Using two Zwanzig operators which are, respectively, functionals of the canonical and generalized canonical probability densities, we then derive what we call canonical and generalized canonical GLEs. Further, we can formulate the particle-based, coarse-grained (CG) GLE dynamics by transitioning to Jacobi coordinates which corresponds to a particle set partitioning of the Hamiltonian system. The obtained canonical CG GLE of motion for the relevant momenta is a generalization of the CG equation of motion known for closed systems. Also, using a Markovian approximation of the canonical CG GLE, we can extend the dissipative particle dynamics equation to open systems. A distinctive feature of our extension is a use of explicitly time-dependent frictions, which reflect the changes in the dissipation rate caused by time-dependent coupling to an external bath. Our GLE formalism and workflow constitute a general and viable framework that can be readily used as a starting point to rigorously formulate microscopically informed CG treatments for a variety of phenomena in externally forced systems far from equilibrium.

A novel constrained genetic algorithm-based Boolean network inference method from steady-state gene expression data.

MotivationIt is a challenging problem in systems biology to infer both the network structure and dynamics of a gene regulatory network from steady-state gene expression data. Some methods based on Boolean or differential equation models have been proposed but they were not efficient in inference of large-scale networks. Therefore, it is necessary to develop a method to infer the network structure and dynamics accurately on large-scale networks using steady-state expression.ResultsIn this study, we propose a novel constrained genetic algorithm-based Boolean network inference (CGA-BNI) method where a Boolean canalyzing update rule scheme was employed to capture coarse-grained dynamics. Given steady-state gene expression data as an input, CGA-BNI identifies a set of path consistency-based constraints by comparing the gene expression level between the wild-type and the mutant experiments. It then searches Boolean networks which satisfy the constraints and induce attractors most similar to steady-state expressions. We devised a heuristic mutation operation for faster convergence and implemented a parallel evaluation routine for execution time reduction. Through extensive simulations on the artificial and the real gene expression datasets, CGA-BNI showed better performance than four other existing methods in terms of both structural and dynamics prediction accuracies. Taken together, CGA-BNI is a promising tool to predict both the structure and the dynamics of a gene regulatory network when a highest accuracy is needed at the cost of sacrificing the execution time.Availability and implementationSource code and data are freely available at https://github.com/csclab/CGA-BNI.Supplementary information Supplementary data are available at Bioinformatics online.