scholarly journals Exploring the landscape of model representations

2020 ◽  
Vol 117 (39) ◽  
pp. 24061-24068 ◽  
Author(s):  
Thomas T. Foley ◽  
Katherine M. Kidder ◽  
M. Scott Shell ◽  
W. G. Noid
Keyword(s):  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Coarse Graining ◽  
Order Parameters ◽  
Microscopic Model ◽  
Coarse Grained ◽  
Proper Order ◽  
Complex Phenomena ◽  
Protein Fluctuations

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

Diffusion Wavelet Decomposition for Coarse-Graining of Polymer Chains

2015 ◽  
Vol 1753 ◽  
Author(s):  
B. Christopher Rinderspacher ◽  
Jaydeep P. Bardhan ◽  
Ahmed E. Ismail
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Coarse Graining ◽  
Polymer Chains ◽  
Coarse Grained ◽  
Small Scale ◽  
Bonding Structure ◽  
Ring Structures ◽  
Spatial Coordinates ◽  
Molecular Bonding

ABSTRACTHere we present an alternative approach to coarse graining, based on the multiresolution diffusion-wavelet approach to operator compression, which does not require explicit atomistic-to-coarse-grained mappings. Our diffusion-wavelet method takes as input the topology and sparsity of the molecular bonding structure of a system, and returns as output a hierarchical set of degrees of freedom (DoFs) of system-specific coarse-grained variables. Importantly, the hierarchical compression provides a clear framework for modeling at many model scales (levels), beyond the common two-level CG representation. Our results show that the resulting hierarchy separates localized modes, such as a single C-C vibrational mode, from larger-scale motions, e.g., long-range concerted backbone vibrational modes. Our approach correctly captures small-scale chemical features, such as cellulose ring structures, and alkane side chains or CH2 units, as well as large-scale features of the backbone. In particular, the new method’s finest-scale modes describe DoFs similar to united atom models and other chemically-defined CG models. Modes at coarser levels describe increasingly large connected portions of the target polymers. For polyethylene and polystyrene, spatial coordinates and their associated forces were compressed by up to two orders of magnitude. The compression in forces is of particular interest as this allows larger timesteps as well as reducing the number of DoFs.

A new spectral coarse-graining algorithm based on K-means clustering in complex networks

2019 ◽  
Vol 33 (01) ◽  
pp. 1850421 ◽  
Author(s):  
Lang Zeng ◽  
Zhen Jia ◽  
Yingying Wang
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Dynamic Properties ◽  
Coarse Graining ◽  
Kuramoto Model ◽  
Coarse Grained ◽  
Original Network ◽  
Topological Information ◽  
Real World Applications ◽  
Large Scale Networks

Coarse-graining of complex networks is one of the important algorithms to study large-scale networks, which is committed to reducing the size of networks while preserving some topological information or dynamic properties of the original networks. Spectral coarse-graining (SCG) is one of the typical coarse-graining algorithms, which can keep the synchronization ability of the original network well. However, the calculation of SCG is large, which limits its real-world applications. And it is difficult to accurately control the scale of the coarse-grained network. In this paper, a new SCG algorithm based on K-means clustering (KCSCG) is proposed, which cannot only reduce the amount of calculation, but also accurately control the size of coarse-grained network. At the same time, KCSCG algorithm has better effect in keeping the network synchronization ability than SCG algorithm. A large number of numerical simulations and Kuramoto-model example on several typical networks verify the feasibility and effectiveness of the proposed algorithm.

scholarly journals Coarse-graining for fast dynamics of order parameters in the phase-field model

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170203 ◽  
Author(s):  
D. Jou ◽  
P. K. Galenko
Keyword(s):  
Master Equation ◽  
Thermodynamic Equilibrium ◽  
Phase Field ◽  
Order Parameter ◽  
Field Model ◽  
Local Thermodynamic Equilibrium ◽  
Phase Field Model ◽  
Coarse Graining ◽  
Order Parameters ◽  
Coarse Grained

In standard descriptions, the master equation can be obtained by coarse-graining with the application of the hypothesis of full local thermalization that is equivalent to the local thermodynamic equilibrium. By contrast, fast transformations proceed in the absence of local equilibrium and the master equation must be obtained with the absence of thermalization. In the present work, a non-Markovian master equation leading, in specific cases of relaxation to local thermodynamic equilibrium, to hyperbolic evolution equations for a binary alloy, is derived for a system with two order parameters. One of them is a conserved order parameter related to the atomistic composition, and the other one is a non-conserved order parameter, which is related to phase field. A microscopic basis for phenomenological phase-field models of fast phase transitions, when the transition is so fast that there is not sufficient time to achieve local thermalization between two successive elementary processes in the system, is provided. In a particular case, when the relaxation to local thermalization proceeds by the exponential law, the obtained coarse-grained equations are related to the hyperbolic phase-field model. The solution of the model equations is obtained to demonstrate non-equilibrium phenomenon of solute trapping which appears in rapid growth of dendritic crystals. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals Nature does not play Dice at the Planck scale

2020 ◽  
Vol 29 (14) ◽  
pp. 2043012
Author(s):  
Tejinder P. Singh
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Planck Scale ◽  
Coarse Graining ◽  
Lagrangian Dynamics ◽  
Time Intervals ◽  
Spacetime Geometry ◽  
The Status ◽  
Planck Time ◽  
Matter Fields

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.

Multipolar Expansion Methods for Coarse Grained Force Fields [PowerPoint Submission]

2006 ◽  
Vol 978 ◽  
Author(s):  
Sheng D. Chao
Keyword(s):  
Molecular Dynamics ◽  
Quantum Chemistry ◽  
Large Scale ◽  
Force Fields ◽  
Coarse Graining ◽  
Expansion Method ◽  
Distribution Functions ◽  
Coarse Grained ◽  
Quantum Chemistry Calculations ◽  
Multipolar Expansion

AbstractCurrent large scale atomistic simulations remain too computationally demanding to be generally applicable to industrial and bioengineering materials. It is desirable to develop multiscale modeling algorithms to perform efficient and informative mesoscopic simulations. Here we present a multipolar expansion method to construct coarse grained force fields (CGFF) for polymer nanostructures and nanocomposites. This model can effectively capture the stereochemical response to anisotropic long-range interactions and can be systematically improved upon adding higher order terms. The coarse-graining procedure forms the basis to perform a hierarchy of multiscale simulations starting with the quantum chemistry calculations to coarse grained molecular dynamics, hopefully toward continuum modeling. We have applied this procedure to molecular clusters such as alkane, benzene, and fullerene. For liquid alkane, molecular dynamics simulations using the CGFF can reproduce the pair distribution functions using atomistic force fields. Molecular mechanics simulations using the CGFF can well reproduce the energetics of benzene clusters from quantum chemistry electronic structure calculations. Subtle anisotropy in the interaction potentials of the fullerene dimer using the Brenner force field can also be well represented by the model. It is promising this procedure can be standardized and further extended.

NON-SPHERICAL VOIDS: THE BEST ALTERNATIVE TO DARK ENERGY?

2011 ◽  
Vol 20 (supp01) ◽  
pp. 94-101
Author(s):  
ROBERTO A SUSSMAN
Keyword(s):  
Dark Energy ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Observation Point ◽  
Coarse Grained ◽  
Spherical Void ◽  
Cosmological Observations ◽  
Definition Of ◽  
Almost All ◽  
Spherical Voids

If our cosmic location lies within a large-scale under–dense region or "void", then current cosmological observations can be explained without resorting to a cosmological constant or to an exotic and elusive source like "dark energy". If we further assume this void region to be spherical (as almost all current void models do), then fitting observational data severely constrains our position to be very near the void center, which is a very special and unlikely observation point. We argue in this article that existing spherical void models must be regarded as gross approximations that arise by smoothing out more realistic non–spherical configurations that may fit observations without the limitations imposed by spherical symmetry. In particular, the class of quasi–spherical Szekeres models provides sufficient degrees of freedom to describe the evolution of non–spherical inhomogeneities, including a configuration consisting of several elongated supercluster–like overdense filaments with large underdense regions between them. We summarize a recently published example of such configuration, showing that it yields a reasonable coarse-grained description of realistic observed structures. While the density distribution is not spherically symmetric, its proper volume average yields a spherical density void profile of 250 Mpc that roughly agrees with observations. Also, once we consider our location to lie within a non-spherical void, the definition of a "center" location becomes more nuanced, and thus the constraints placed by the fitting of observations on our position with respect to this location become less restrictive.

Mesoscale methods

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Large Scale ◽  
Equations Of Motion ◽  
Dissipative Particle Dynamics ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Collision Dynamics ◽  
Force Matching ◽  
Multiparticle Collision Dynamics ◽  
Long Time ◽  
Boltzmann Method

Coarse-graining is an increasingly commonplace approach to study, as economically as possible, large-scale, and long-time phenomena. This chapter covers the main methods. Brownian and Langevin dynamics are introduced, with practical details of the solution of the modified equations of motion. Several techniques which aim to bridge the gap to the hydrodynamic regime are described: these include dissipative particle dynamics, multiparticle collision dynamics, and the lattice Boltzmann method. Several examples of program code are provided. In the last part of the chapter, the derivation of a coarse-grained potential from an atomistic one is considered using force-matching and structure-matching, and the limitations of these approaches are discussed.

scholarly journals Bottom-Up Coarse-Grained Modeling of DNA

2021 ◽  
Vol 8 ◽  
Author(s):  
Tiedong Sun ◽  
Vishal Minhas ◽  
Nikolay Korolev ◽  
Alexander Mirzoev ◽  
Alexander P. Lyubartsev ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Deoxyribonucleic Acid ◽  
Persistence Length ◽  
Coarse Graining ◽  
Potential Of Mean Force ◽  
Coarse Grained ◽  
Bottom Up ◽  
Slow Dynamic ◽  
Molecular Systems ◽  
Fine Grained

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.

scholarly journals Less is more: Coarse-grained integrative modeling of large biomolecular assemblies with HADDOCK

2019 ◽  
Author(s):  
Jorge Roel-Touris ◽  
Charleen G. Don ◽  
Rodrigo V. Honorato ◽  
João P.G.L.M Rodrigues ◽  
Alexandre M.J.J. Bonvin
Keyword(s):  
Protein Interactions ◽  
Degrees Of Freedom ◽  
Energy Landscape ◽  
3D Structure ◽  
Coarse Graining ◽  
Protein Docking ◽  
Coarse Grained ◽  
Speed Increase ◽  
Less Is More ◽  
Similar Accuracy

ABSTRACTPredicting the 3D structure of protein interactions remains a challenge in the field of computational structural biology. This is in part due to difficulties in sampling the complex energy landscape of multiple interacting flexible polypeptide chains. Coarse-graining approaches, which reduce the number of degrees of freedom of the system, help address this limitation by smoothing the energy landscape, allowing an easier identification of the global energy minimum. They also accelerate the calculations, allowing to model larger assemblies. Here, we present the implementation of the MARTINI coarse-grained force field for proteins into HADDOCK, our integrative modelling platform. Docking and refinement are performed at the coarse-grained level and the resulting models are then converted back to atomistic resolution through a distance restraints-guided morphing procedure. Our protocol, tested on the largest complexes of the protein docking benchmark 5, shows an overall ~7-fold speed increase compared to standard all-atom calculations, while maintaining a similar accuracy and yielding substantially more near-native solutions. To showcase the potential of our method, we performed simultaneous 7 body docking to model the 1:6 KaiC-KaiB complex, integrating mutagenesis and hydrogen/deuterium exchange data from mass spectrometry with symmetry restraints, and validated the resulting models against a recently published cryo-EM structure.

Coarse-Grained Molecular Dynamics Simulation of Lysozyme Protein Crystals

2011 ◽  
Vol 6 (1) ◽  
Author(s):  
Nafiseh Farhadian ◽  
Mojtaba Shariaty-Niassar ◽  
Kourosh Malek ◽  
Ali Maghari
Keyword(s):  
Molecular Dynamics ◽  
Degrees Of Freedom ◽  
Coarse Graining ◽  
Dynamics Simulation ◽  
Coarse Grained ◽  
Protein Crystal ◽  
Protein Crystals ◽  
Biological Phenomena ◽  
The Stability ◽  
Coarse Grained Molecular Dynamics

Many biological phenomena of interest occur on a time scale that is too great to be studied by atomistic simulations. The use of coarse-graining methods to represent a system can alleviate this restriction by reducing the number of degrees of freedom thus extending the time and length scale in molecular modeling. Coarse-grained molecular dynamics (CGMD) technique was employed to simulate diffusion of water in the nanopores of lysozyme protein crystals. Good agreement was obtained between the atomistic and CG simulations in view of the stability of the protein crystal structure and water transport properties. Our simulations demonstrate that the CG method is a suitable technique for simulation the solvent diffusion process in the lysozyme protein crystal and also can be a good technique to predict the behavior of solvent and solutes in the biological systems at longer length and time scales.

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