Multiscale Coarse-graining Method Research Articles

Higher dose makes higher lethality? A dose–response model of pulsed electric fields inactivation from multiscale coarse-graining method

As an emerging technology in liquid inactivation, one of the main challenges of pulsed electric fields (PEFs) inactivation lies in quantitatively describing and predicting its lethality to microorganisms. However, due to its cross-scaled complexity and the consequent numerous regulatory factors, there is currently still no unified framework to understand the PEF dose–response relationship and the population dynamics theoretically. In this study, a simple yet powerful model from multiscale coarse-graining method is proposed to simulate the bacterial inactivation in suspensions during PEF processing. The complex dose–response effects at the macroscale are successfully reconstructed from simple evolution rules and several coarse-graining parameters, while considering the damage and death of a single bacterium at the microscale. Our model uncovers the seemingly chaotic and even controversial dose–response relationship of PEF in literatures and systematically explores the regulatory effect of experimental parameters in a unified framework. One of the interesting findings is that PEF with shorter pulsed width enhances lethality and reduces the minimal inhibitory time at a constant energy output per pulse, owing to the phase transitions in three bacterial population dynamics (Bistability mode, Avalanche mode, and Hybrid mode). Our study provides a new insight for numerically modeling PEF lethality in liquid inactivation and could serve as a guide for dosage management in practical applications.

Can a coarse-grained water model capture the key physical features of the hydrophobic effect?

Coarse-grained (CG) molecular dynamics can be a powerful method for probing complex processes. However, most CG force fields use pairwise nonbonded interaction potentials sets, which can limit their ability to capture complex multi-body phenomena such as the hydrophobic effect. As the hydrophobic effect primarily manifests itself due to the nonpolar solute affecting the nearby hydrogen bonding network in water, capturing such effects using a simple one CG site or “bead” water model is a challenge. In this work, we systematically test the ability of CG one site water models for capturing critical features of the solvent environment around a hydrophobe as well as the potential of mean force (PMF) of neopentane association. We study two bottom-up models: a simple pairwise (SP) force-matched water model constructed using the multiscale coarse-graining method and the Bottom-Up Many-Body Projected Water (BUMPer) model, which has implicit three-body correlations. We also test the top-down monatomic (mW) and the Machine Learned mW (ML-mW) water models. The mW models perform well in capturing structural correlations but not the energetics of the PMF. BUMPer outperforms SP in capturing structural correlations and also gives an accurate PMF in contrast to the two mW models. Our study highlights the importance of including three-body interactions in CG water models, either explicitly or implicitly, while in general highlighting the applicability of bottom-up CG water models for studying hydrophobic effects in a quantitative fashion. This assertion comes with a caveat, however, regarding the accuracy of the enthalpy–entropy decomposition of the PMF of hydrophobe association.

Coarse-Grained Water Model Development for Accurate Dynamics and Structure Prediction.

Several coarse-graining (CG) methods have been combined to develop a CG model of water capable of the accurate prediction of structure and dynamics properties. The multiscale coarse-graining (MS-CG) method based on force matching and the PDF-based coarse-graining method were used for accurate dynamics prediction. The iterative Boltzmann inversion (IBI) method was added for accurate structure representation. The approach is applied to bulk water, and the results show close reproduction of the CG structure when compared with the reference atomistic data. The combination of MS-CG and IBI methods facilitates the development of CG force fields at different temperatures based on a single MS-CG coarse-graining procedure. The dynamic properties of the CG water model closely match those obtained from the reference atomistic system. The general application of this approach to any existing coarse-graining methods is discussed.

Molecular simulation studies of self-assembly for a chromonic perylene dye: All-atom studies and new approaches to coarse-graining

Perylene tetracarboxylic acid bisimides are compounds that show intense visible light absorption and exhibit excellent chemical, photochemical and thermal stability. As such, they have been widely used as dyes and have a range of industrial applications. These dyes have also been investigated for various applications in aqueous media as chromonic liquid crystals: lyotropic systems characterised by the association of aromatic mesogenic cores into stacked structures. In this study, we focus on one perylene dye bis-(N,N-diethylaminoethyl) perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride, PER, and study its self-assembly in aqueous solution through both atomistic and coarse-grained molecular models. All-atom molecular dynamics simulations demonstrate spontaneous self-assembly into chromonic H-aggregate stacks with an interparticle twist between molecules. The coarse-graining of complex chromonic mesogens introduces a wealth of subtle complexities that presents a significant challenge to overcome. Consequently, we developed coarse-grained (CG) models using both bottom-up and top-down approaches: the multiscale coarse-graining method (MS-CG) in the form of hybrid force matching (FM) and the MARTINI 3 force field, respectively. We discuss the successes/deficiencies of these approaches and introduce changes to improve upon their performance and representability. For the MARTINI 3 model, careful optimisation of parameters allows it to exactly reproduce the atomistic self-assembly behaviour including the relevant thermodynamic properties in solution. The bottom-up CG model, produced using a conventional MS-CG treatment, fails to reproduce most of the target properties, but the implementation of the potentials into a combined FM-MARTINI 3 framework allows the recovery of the correct self-assembly behaviour in solution.

Analysis of local density potentials.

Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.

Quantum theory of multiscale coarse-graining.

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Refining amino acid hydrophobicity for dynamics simulation of membrane proteins.

Coarse-grained (CG) models have been successful in simulating the chemical properties of lipid bilayers, but accurate treatment of membrane proteins and lipid-protein molecular interactions remains a challenge. The CgProt force field, original developed with the multiscale coarse graining method, is assessed by comparing the potentials of mean force for sidechain insertion in a DOPC bilayer to results reported for atomistic molecular dynamics simulations. Reassignment of select CG sidechain sites from the apolar to polar site type was found to improve the attractive interfacial behavior of tyrosine, phenylalanine and asparagine as well as charged lysine and arginine residues. The solvation energy at membrane depths of 0, 1.3 and 1.7 nm correlates with experimental partition coefficients in aqueous mixtures of cyclohexane, octanol and POPC, respectively, for sidechain analogs and Wimley-White peptides. These experimental values serve as important anchor points in choosing between alternate CG models based on their observed permeation profiles, particularly for Arg, Lys and Gln residues where the all-atom OPLS solvation energy does not agree well with experiment. Available partitioning data was also used to reparameterize the representation of the peptide backbone, which needed to be made less attractive for the bilayer hydrophobic core region. The newly developed force field, CgProt 2.4, correctly predicts the global energy minimum in the potentials of mean force for insertion of the uncharged membrane-associated peptides LS3 and WALP23. CgProt will find application in studies of lipid-protein interactions and the conformational properties of diverse membrane protein systems.

Procedure for Transferable Coarse-Grained Models of Aqueous Polysaccharides.

We present a procedure to obtain Coarse-Grained (CG) models for aqueous polysaccharide solutions that are transferable over different degrees of polymerization and different polysaccharide concentrations based on atomistic Molecular Dynamics (MD) simulations. This is achieved by a hybrid procedure combining Boltzmann Inversion (BI) and the Multiscale Coarse-Graining (MS-CG) method. In order to overcome problems that have been previously reported with this approach, namely differences in the aggregation behavior and the end to end distance between the atomistic reference simulation and the coarse-grained simulation, we employ a separation-ansatz and explicit 1-3 and 1-4 nonbonded intramolecular interactions. This allows the use of the model for long polysaccharides. We demonstrate the transferability over both concentration and degrees of polymerization, evaluate the scope for which the coarse-grained model can be applied, and then present a scheme to extend the concentration transferability. In addition, we show that the procedure can be applied to generate a transferable implicit solvent model and demonstrate that it can be used for different atomistic force fields (FFs) as well. The procedure is then applied to derive a coarse-grained model of different hemicellulose polysaccharides. The resulting model is used to demonstrate that branching with monomer side-chains significantly increases the water uptake capacity of the molecules in comparison to linear polysaccharides which is consistent with experimental results.

Multiscale Coarse-Graining of Polarizable Models through Force-Matched Dipole Fluctuations.

An extension of the multiscale coarse-graining method (MS-CG) to polarizable coarse-grain (CG) models is presented. In the extension, force matching is used to derive charged dimers that mimic the dipole behavior, including electronic polarizability, of fine resolution systems. The extended MS-CG method separates short-range and electrostatic forces and treats the polarization interactions by representing dipole fluctuations with a harmonic bond reminiscent of the Drude oscillator. The new method is first tested on several flexible alcohols, where the transferable head groups in the atomistic field lead to transferable electrostatics in the CG field. The method is then applied to a polarizable methanol model, where the CG dimer is able to match the atomistic dipole distribution. Force fields are benchmarked with radial distribution functions and dielectric constants. The static dielectric constants agree well with atomistic models, but the faster dynamics in the CG ensembles leads to significant deviations in the frequency-dependent permittivity. Model transferability is checked by measuring response to static external fields through a dipole coupling order parameter. Effective polarizabilities are inferred from the dimer harmonic bonds, and an ad hoc correction is used to improve one CG force field's dipole magnitude response to electric fields. Broader applicability is explored through a small set of amines, and several multibead models are tested where CG dipole orientations are restricted through intramolecular forces, capturing constructive and destructive dipole interactions within single molecules.

Bottom-up coarse-grained models that accurately describe the structure, pressure, and compressibility of molecular liquids.

The present work investigates the capability of bottom-up coarse-graining (CG) methods for accurately modeling both structural and thermodynamic properties of all-atom (AA) models for molecular liquids. In particular, we consider 1, 2, and 3-site CG models for heptane, as well as 1 and 3-site CG models for toluene. For each model, we employ the multiscale coarse-graining method to determine interaction potentials that optimally approximate the configuration dependence of the many-body potential of mean force (PMF). We employ a previously developed "pressure-matching" variational principle to determine a volume-dependent contribution to the potential, UV(V), that approximates the volume-dependence of the PMF. We demonstrate that the resulting CG models describe AA density fluctuations with qualitative, but not quantitative, accuracy. Accordingly, we develop a self-consistent approach for further optimizing UV, such that the CG models accurately reproduce the equilibrium density, compressibility, and average pressure of the AA models, although the CG models still significantly underestimate the atomic pressure fluctuations. Additionally, by comparing this array of models that accurately describe the structure and thermodynamic pressure of heptane and toluene at a range of different resolutions, we investigate the impact of bottom-up coarse-graining upon thermodynamic properties. In particular, we demonstrate that UV accounts for the reduced cohesion in the CG models. Finally, we observe that bottom-up coarse-graining introduces subtle correlations between the resolution, the cohesive energy density, and the "simplicity" of the model.

The multiscale coarse-graining method. XI. Accurate interactions based on the centers of charge of coarse-grained sites.

It is essential to be able to systematically construct coarse-grained (CG) models that can efficiently and accurately reproduce key properties of higher-resolution models such as all-atom. To fulfill this goal, a mapping operator is needed to transform the higher-resolution configuration to a CG configuration. Certain mapping operators, however, may lose information related to the underlying electrostatic properties. In this paper, a new mapping operator based on the centers of charge of CG sites is proposed to address this issue. Four example systems are chosen to demonstrate this concept. Within the multiscale coarse-graining framework, CG models that use this mapping operator are found to better reproduce the structural correlations of atomistic models. The present work also demonstrates the flexibility of the mapping operator and the robustness of the force matching method. For instance, important functional groups can be isolated and emphasized in the CG model.

Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence.

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

Bottom-Up Coarse-Graining of Peptide Ensembles and Helix-Coil Transitions.

This work investigates the capability of bottom-up methods for parametrizing minimal coarse-grained (CG) models of disordered and helical peptides. We consider four high-resolution peptide ensembles that demonstrate varying degrees of complexity. For each high-resolution ensemble, we parametrize a CG model via the multiscale coarse-graining (MS-CG) method, which employs a generalized Yvon-Born-Green (g-YBG) relation to determine potentials directly (i.e., without iteration) from the high-resolution ensemble. The MS-CG method accurately describes high-resolution models that fluctuate about a single conformation. However, given the minimal resolution and simple molecular mechanics potential, the MS-CG method provides a less accurate description for a high-resolution peptide model that samples a disordered ensemble with multiple distinct conformations. We employ an iterative g-YBG method to develop a CG model that more accurately describes the relevant distribution functions and free energy surfaces for this disordered ensemble. Nevertheless, this more accurate model does not reproduce the cooperative helix-coil transition that is sampled by the high resolution model. By comparing the different models, we demonstrate that the errors in the MS-CG model primarily stem from the lack of cooperative interactions afforded by the minimal representation and molecular mechanics potential. This work demonstrates the potential of the MS-CG method for accurately modeling complex biomolecular structures, but also highlights the importance of more complex potentials for modeling cooperative transitions with a minimal CG representation.

Solvent-Free, Highly Coarse-Grained Models for Charged Lipid Systems.

We present a methodology to develop coarse-grained lipid models such that electrostatic interactions between the coarse-grained sites can be derived accurately from an all-atom molecular dynamics trajectory and expressed as an effective pairwise electrostatic potential with appropriate screening functions. The reference nonbonded forces from the all-atom trajectory are decomposed into separate electrostatic and van der Waals (vdW) forces, based on the multiscale coarse-graining method. The coarse-grained electrostatic potential is assumed to be a general function of unknown variables and the final site–site interactions are obtained variationally, where the residual of the electrostatic forces from the assumed field is minimized. The resulting electrostatic interactions are fitted to screened electrostatics functions, with a special treatment for distance-dependent dielectrics and screened dipole–dipole interactions. The vdW interactions are derived separately. The resulting charged hybrid coarse-graining method is applied to various solvent-free three-site models of anionic lipid systems.

Investigation of Coarse-Grained Mappings via an Iterative Generalized Yvon–Born–Green Method

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

Multi-scale coarse-graining of non-conservative interactions in molecular liquids

A new bottom-up procedure for constructing non-conservative (dissipative and stochastic) interactions for dissipative particle dynamics (DPD) models is described and applied to perform hierarchical coarse-graining of a polar molecular liquid (nitromethane). The distant-dependent radial and shear frictions in functional-free form are derived consistently with a chosen form for conservative interactions by matching two-body force-velocity and three-body velocity-velocity correlations along the microscopic trajectories of the centroids of Voronoi cells (clusters), which represent the dissipative particles within the DPD description. The Voronoi tessellation is achieved by application of the K-means clustering algorithm at regular time intervals. Consistently with a notion of many-body DPD, the conservative interactions are determined through the multi-scale coarse-graining (MS-CG) method, which naturally implements a pairwise decomposition of the microscopic free energy. A hierarchy of MS-CG/DPD models starting with one molecule per Voronoi cell and up to 64 molecules per cell is derived. The radial contribution to the friction appears to be dominant for all models. As the Voronoi cell sizes increase, the dissipative forces rapidly become confined to the first coordination shell. For Voronoi cells of two and more molecules the time dependence of the velocity autocorrelation function becomes monotonic and well reproduced by the respective MS-CG/DPD models. A comparative analysis of force and velocity correlations in the atomistic and CG ensembles indicates Markovian behavior with as low as two molecules per dissipative particle. The models with one and two molecules per Voronoi cell yield transport properties (diffusion and shear viscosity) that are in good agreement with the atomistic data. The coarser models produce slower dynamics that can be appreciably attributed to unaccounted dissipation introduced by regular Voronoi re-partitioning as well as by larger numerical errors in mapping out the dissipative forces. The framework presented herein can be used to develop computational models of real liquids which are capable of bridging the atomistic and mesoscopic scales.

Solvent Free Ionic Solution Models from Multiscale Coarse-Graining.

Solvent free models for aqueous ionic solutions are derived using the multiscale coarse-graining (MS-CG) method to obtain many-body potentials of mean force and generalized Langevin equations to propagate the model in time. The resulting models are compared to other implicit solvent models for aqueous NaCl in terms of both sampling efficiency and accuracy. First, the equilibrium structural properties of the models are compared, and then the temperature dependence of the interion potentials of mean force are determined to obtain the pairwise entropy associated with the effective ionic interactions. After validating the equilibrium behavior of the new models, the dynamical properties are investigated using generalized Langevin equation dynamics simulations. The dynamical properties can be put into better agreement with the original atomistic models by introducing an exponential memory kernel to account for the strong coupling between the ions and their water solvation shells.

A Hybrid Approach for Highly Coarse-grained Lipid Bilayer Models.

We present a systematic methodology to develop highly coarse-grained (CG) lipid models for large scale bio-membrane simulations, in which we derive CG interactions using a powerful combination of the multiscale coarse-graining (MS-CG) method, and an analytical form of the CG potential to model interactions at short range. The resulting hybrid coarse-graining (HCG) methodology is used to develop a three-site solvent-free model for 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and a 1:1 mixture of 1,2-dioleoyl-sn-glycero-3-phospho-L-serine (DOPS) and DOPC. In addition, we developed a four-site model of DOPC, demonstrating the capability of the HCG methodology in designing model lipid systems of a desired resolution. We carried out microsecond-scale molecular dynamics (MD) simulations of large vesicles, highlighting the ability of the model to study systems at mesoscopic length and time scales. The models of DLPC, DOPC and DOPC-DOPS have elastic properties consistent with experiment and structural properties such as the radial distribution functions (RDF), bond and angle distributions, and the z-density distributions that compare well with reference all-atom systems.

Multiscale Coarse-Graining via Normal Mode Analysis.

A multiscale coarse-graining method called the normal-mode analysis based fluctuation matching (NMA-FM) is developed for constructing coarse-grained models of biomolecular systems. In the framework of normal-mode analysis, an arbitrary fine-grained model can be systematically converted to a more coarse-grained model, while the crucial low-frequency motions of the fine-grained system are able to be reproduced in the coarse-grained modeling. The method relies on the technique of fluctuation matching that has been devised earlier for parametrizing heterogeneous elastic network models based on data from atomistic molecular dynamics simulations. The new approach is quite efficient since it avoids expensive atomistic molecular dynamics simulations and can start from already coarse-grained elastic network models. In the practical aspect, the method is suitable for conformational analyses of large biomacromolecules and calculations of mechanical properties of biomaterials, which is demonstrated by the studied systems including an amyloid dimer, lysozyme and adenylate kinase proteins, and the S2 subdomain of myosin.