The multiscale coarse-graining method. X. Improved algorithms for constructing coarse-grained potentials for molecular systems

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.

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Systematic Coarse-Grained Models for Molecular Systems Using Entropy

Proceedings ◽

10.3390/ecea-5-06710 ◽

2020 ◽

Vol 46 (1) ◽

pp. 27

Author(s):

Evangelia Kalligiannaki ◽

Vagelis Harmandaris ◽

Markos Katsoulakis

Keyword(s):

Bootstrap Method ◽

Coarse Graining ◽

Research Area ◽

Potential Of Mean Force ◽

Coarse Grained ◽

Molecular Systems ◽

Matching Methods ◽

Force Matching ◽

Mesoscopic Models ◽

Body Potential

The development of systematic coarse-grained mesoscopic models for complex molecular systems is an intense research area. Here we first give an overview of different methods for obtaining optimal parametrized coarse-grained models, starting from detailed atomistic representation for high dimensional molecular systems. We focus on methods based on information theory, such as relative entropy, showing that they provide parameterizations of coarse-grained models at equilibrium by minimizing a fitting functional over a parameter space. We also connect them with structural-based (inverse Boltzmann) and force matching methods. All the methods mentioned in principle are employed to approximate a many-body potential, the (n-body) potential of mean force, describing the equilibrium distribution of coarse-grained sites observed in simulations of atomically detailed models. We also present in a mathematically consistent way the entropy and force matching methods and their equivalence, which we derive for general nonlinear coarse-graining maps. We apply, and compare, the above-described methodologies in several molecular systems: A simple fluid (methane), water and a polymer (polyethylene) bulk system. Finally, for the latter we also provide reliable confidence intervals using a statistical analysis resampling technique, the bootstrap method.

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Minimalist models for proteins: a comparative analysis

Quarterly Reviews of Biophysics ◽

10.1017/s0033583510000132 ◽

2010 ◽

Vol 43 (3) ◽

pp. 333-371 ◽

Cited By ~ 79

Author(s):

Valentina Tozzini

Keyword(s):

Phase Diagram ◽

Comparative Analysis ◽

Amino Acid ◽

Degrees Of Freedom ◽

Predictive Power ◽

Coarse Graining ◽

Coarse Grained ◽

Molecular Systems ◽

Modern Molecular Biology ◽

Functional Forms

AbstractThe last decade has witnessed a renewed interest in the coarse-grained (CG) models for biopolymers, also stimulated by the needs of modern molecular biology, dealing with nano- to micro-sized bio-molecular systems and larger than microsecond timescale. This combination of size and timescale is, in fact, hard to access by atomic-based simulations. Coarse graining the system is a route to be followed to overcome these limits, but the ways of practically implementing it are many and different, making the landscape of CG models very vast and complex.In this paper, the CG models are reviewed and their features, applications and performances compared. This analysis, restricted to proteins, focuses on the minimalist models, namely those reducing at minimum the number of degrees of freedom without losing the possibility of explicitly describing the secondary structures. This class includes models using a single or a few interacting centers (beads) for each amino acid.From this analysis several issues emerge. The difficulty in building these models resides in the need for combining transferability/predictive power with the capability of accurately reproducing the structures. It is shown that these aspects could be optimized by accurately choosing the force field (FF) terms and functional forms, and combining different parameterization procedures. In addition, in spite of the variety of the minimalist models, regularities can be found in the parameters values and in FF terms. These are outlined and schematically presented with the aid of a generic phase diagram of the polypeptide in the parameter space and, hopefully, could serve as guidelines for the development of minimalist models incorporating the maximum possible level of predictive power and structural accuracy.

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On the three-dimensional spatial correlations of curved dislocation systems

Materials Theory ◽

10.1186/s41313-020-00026-w ◽

2021 ◽

Vol 5 (1) ◽

Author(s):

Joseph Pierre Anderson ◽

Anter El-Azab

Keyword(s):

Correlation Function ◽

Slip System ◽

Correlation Functions ◽

Mean Field ◽

Coarse Graining ◽

Dislocation Dynamics ◽

Coarse Grained ◽

Spatial Correlation Function ◽

Line System ◽

Dislocation Densities

AbstractCoarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

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THE SIMULATION OF POLYSTYRENE/NANOPARTICLES COMPOSITE MICROSPHERES USING DISSIPATIVE PARTICLE DYNAMICS

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633612501118 ◽

2013 ◽

Vol 12 (02) ◽

pp. 1250111 ◽

Cited By ~ 4

Author(s):

HAILONG XU ◽

QIUYU ZHANG ◽

HEPENG ZHANG ◽

BAOLIANG ZHANG ◽

CHANGJIE YIN

Keyword(s):

Dissipative Particle Dynamics ◽

Sodium Dodecyl ◽

Coarse Graining ◽

Particle Dynamics ◽

Coarse Grained ◽

Polystyrene Nanoparticles ◽

Coarse Grained Model ◽

Composite Microspheres ◽

Polystyrene Matrix ◽

Materials Studio

Dissipative particle dynamics (DPD) was initially used to simulate the polystyrene/nanoparticle composite microspheres (PNCM) in this paper. The coarse graining model of PNCM was established. And the DPD parameterization of the model was represented in detail. The DPD repulsion parameters were calculated from the cohesive energy density which could be calculated by amorphous modules in Materials Studio. The equilibrium configuration of the simulated PNCM shows that the nanoparticles were actually "modified" with oleic acid and the modified nanoparticles were embedded in the bulk of polystyrene. As sodium dodecyl sulfate (SDS) was located in the interface between water and polystyrene, the hydrophilic head of SDS stretched into water while the hydrophobic tailed into polystyrene. All simulated phenomena were consistent with the experimental results in preparation of polystyrene/nanoparticles composite microspheres. The effect of surface modification of nanoparticles on its dispersion in polystyrene matrix was also studied by adjusting the interaction parameters between the OA and NP beads. The final results indicated that the nanoparticles removed from the core of composite microsphere to the surface with increase of a OA-NP . All the simulated results demonstrated that our coarse–grained model was reasonable.

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

Modern Physics Letters B ◽

10.1142/s0217984918504213 ◽

2019 ◽

Vol 33 (01) ◽

pp. 1850421 ◽

Cited By ~ 1

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.

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Swarm-CG: Automatic Parametrization of Bonded Terms in Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

10.26434/chemrxiv.12613427 ◽

2020 ◽

Author(s):

Charly Empereur-mot ◽

Luca Pesce ◽

Davide Bochicchio ◽

Claudio Perego ◽

Giovanni M. Pavan

Keyword(s):

Particle Swarm Optimization ◽

State Of The Art ◽

Structural Complexity ◽

Coarse Grained ◽

Complex Molecules ◽

Swarm Optimization ◽

Molecular Systems ◽

Self Tuning ◽

User Friendly ◽

Python Package

We present Swarm-CG, a versatile software for the automatic parametrization of bonded parameters in coarse-grained (CG) models. By coupling state-of-the-art metaheuristics to Boltzmann inversion, Swarm-CG performs accurate parametrization of bonded terms in CG models composed of up to 200 pseudoatoms within 4h-24h on standard desktop machines, using an AA trajectory as reference and default<br>settings of the software. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of molecular systems interesting for bio- and nanotechnology.<br>Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity and size. Swarm-CG usage is ideal in combination with popular CG force<br>fields, such as e.g. MARTINI. However, we anticipate that in principle its versatility makes it well suited for the optimization of models built based also on other CG schemes. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Tutorials and demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

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Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture

Quantum Information and Computation ◽

10.26421/qic13.5-6-3 ◽

2013 ◽

Vol 13 (5&6) ◽

pp. 393-429

Author(s):

Matthew Hastings

Keyword(s):

Ground State ◽

Coding Theory ◽

Energy State ◽

Ground States ◽

Coarse Graining ◽

Quantum Circuit ◽

Technical Condition ◽

Two Dimensions ◽

Low Energy ◽

Coarse Grained

We consider the entanglement properties of ground states of Hamiltonians which are sums of commuting projectors (we call these commuting projector Hamiltonians), in particular whether or not they have ``trivial" ground states, where a state is trivial if it is constructed by a local quantum circuit of bounded depth and range acting on a product state. It is known that Hamiltonians such as the toric code only have nontrivial ground states in two dimensions. Conversely, commuting projector Hamiltonians which are sums of two-body interactions have trivial ground states\cite{bv}. Using a coarse-graining procedure, this implies that any such Hamiltonian with bounded range interactions in one dimension has a trivial ground state. In this paper, we further explore the question of which Hamiltonians have trivial ground states. We define an ``interaction complex" for a Hamiltonian, which generalizes the notion of interaction graph and we show that if the interaction complex can be continuously mapped to a $1$-complex using a map with bounded diameter of pre-images then the Hamiltonian has a trivial ground state assuming one technical condition on the Hamiltonians holds (this condition holds for all stabilizer Hamiltonians, and we additionally prove the result for all Hamiltonians under one assumption on the $1$-complex). While this includes the cases considered by Ref.~\onlinecite{bv}, we show that it also includes a larger class of Hamiltonians whose interaction complexes cannot be coarse-grained into the case of Ref.~\onlinecite{bv} but still can be mapped continuously to a $1$-complex. One motivation for this study is an approach to the quantum PCP conjecture. We note that many commonly studied interaction complexes can be mapped to a $1$-complex after removing a small fraction of sites. For commuting projector Hamiltonians on such complexes, in order to find low energy trivial states for the original Hamiltonian, it would suffice to find trivial ground states for the Hamiltonian with those sites removed. Such trivial states can act as a classical witness to the existence of a low energy state. While this result applies for commuting Hamiltonians and does not necessarily apply to other Hamiltonians, it suggests that to prove a quantum PCP conjecture for commuting Hamiltonians, it is worth investigating interaction complexes which cannot be mapped to $1$-complexes after removing a small fraction of points. We define this more precisely below; in some sense this generalizes the notion of an expander graph. Surprisingly, such complexes do exist as will be shown elsewhere\cite{fh}, and have useful properties in quantum coding theory.

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A scaled MP-PIC method for bubbling fluidization

10.22541/au.163253496.64565288/v1 ◽

2021 ◽

Author(s):

Xing Zhao ◽

Yong Jiang ◽

Fei Li ◽

Wei Wang

Keyword(s):

Fluidized Beds ◽

Volume Fraction ◽

Phase Particle ◽

Scaling Law ◽

Coarse Graining ◽

Coarse Grained ◽

Particle In Cell ◽

Wide Range ◽

Pic Method ◽

Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

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"Dividing and Conquering" and "Caching" in Molecular Modeling

10.20944/preprints202012.0081.v2 ◽

2021 ◽

Author(s):

Xiaoyong Cao ◽

Pu Tian

Keyword(s):

Molecular Modeling ◽

Degrees Of Freedom ◽

Materials Science ◽

Force Fields ◽

Coarse Graining ◽

Divide And Conquer ◽

Collective Variables ◽

Molecular Systems ◽

State Models ◽

Molecular Science

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, Most of important methodological advancements in more than half century of molecule modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science based on force fields parameterization by coarse graining, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but no transferability is available. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science and a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

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