Multiscale Coarse-Graining via Normal Mode Analysis

Persistent Dirac for molecular representation

Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design and materials discovery have been greatly contributed by molecular representation models. In this paper, we present a computational framework for molecular representation that is mathematically rigorous and based on the persistent Dirac operator. The properties of the discrete weighted and unweighted Dirac matrix are systematically discussed, and the biological meanings of both homological and non-homological eigenvectors are studied. We also evaluate the impact of various weighting schemes on the weighted Dirac matrix. Additionally, a set of physical persistent attributes that characterize the persistence and variation of spectrum properties of Dirac matrices during a filtration process is proposed to be molecular fingerprints. Our persistent attributes are used to classify molecular configurations of nine different types of organic-inorganic halide perovskites. The combination of persistent attributes with gradient boosting tree model has achieved great success in molecular solvation free energy prediction. The results show that our model is effective in characterizing the molecular structures, demonstrating the power of our molecular representation and featurization approach.

Coarse-Grained Models for Vault Normal Model Analysis

Recent experiments have shown that the molecular complex of vault has large conformational changes at its shoulder and cap regions in solution. From the comparison of two configuration structures, it has been found that the shoulder region can twist and move outward, while the cap region will rotate and push upward correspondingly. To further understand these experimental results, in this paper, we study the vault dynamics for the first time. Since vault has an extremely large-sized structure with around 63,336 Cα atoms, traditional normal mode method with the Cα coarse-grained representation will fall short. We employ a newly invented multiscale virtual particle-based anisotropic network model (MVP-ANM). To reduce the complexity, the 39-folder vault structure is coarse-grained to about 6000 virtual particles, which significantly reduces the computational cost while still maintaining the basic structure information. Among the 14 low frequency eigenmodes from Mode 7 to Mode 20, two eigenmodes, i.e., Mode 9 and Mode 20, are found to be directly associated with the experimental observations. In Mode 9, shoulder region undergoes a significant expansion while the cap part is lifted upward. In Mode 20, a clear rotation of both shoulder and cap regions is well observed. Our results are consistent with the experimental observations. More importantly, these low frequency eigenmodes indicate that the vault waist, shoulder and lower cap regions are the most likely regions for the opening of the vault particle. And the opening mechanism is highly likely to be rotation and expansion at these regions. As far as we know, this is the first work to provide the normal mode analysis for the vault complex.

Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.

Atomistic detailed free-energy landscape of intrinsically disordered protein studied by multi-scale divide-and-conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α-helix form in the presence Ca²⁺ -loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺ -loaded CaM must be simultaneously treated. However, it is time-consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi-scale divide-and-conquer MD (MSDC-MD), which combines AAM-MD and coarse-grained model MD (CGM-MD). To speed up the conformation sampling, MSDC-MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM-MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC-MD; the root-mean-square distance (RMSD) with respect to the experimental structure was 2.23 Å.

Double-Well Ultra-Coarse-Grained Model to Describe Protein Conformational Transitions

The double-well model is usually used to describe the conformational transition between two states of a protein. Since conformational changes usually occur within a relatively large time scale, coarse-grained models are often used to accelerate the dynamic process due to their inexpensive computational cost. In this work, we develop a double-well ultra-coarse-grained (DW-UCG) model to describe the conformational transitions of the adenylate kinase, glutamine-binding protein, and lactoferrin. The coarse-grained simulation results show that the DW-UCG model of adenylate kinase captures the crucial intermediate states in the LID-closing and NMP-closing pathways, reflecting the key secondary structural changes in the conformational transition. A comparison of the different DW-UCG models of adenylate kinase indicates that an appropriate choice of bead resolution could generate the free energy landscape that is comparable to that from the residue-based model. The coarse-grained simulations for the glutamine-binding protein and lactoferrin also demonstrate that the DW-UCG model is valid in reproducing the correct two-state behavior for their functional study, which indicates the potential application of the DW-UCG model in investigating the mechanism of conformational changes of large proteins.

A new method for the construction of coarse-grained models of large biomolecules from low-resolution cryo-electron microscopy data

The rapid development of cryo-electron microscopy (cryo-EM) has led to the generation of significant low-resolution electron density data of biomolecules. However, the atomistic details of huge biomolecules usually cannot be obtained because it is very difficult to construct all-atom models for MD simulations. Thus, it is still a challenge to make use of the rich low-resolution cryo-EM data for computer simulation and functional study. In this study, we proposed a new method called Convolutional and K-means Coarse-Graining (CK-CG) for the efficient coarse-graining of large biological systems. Using the CK-CG method, we could directly map the cryo-EM data into coarse-grained (CG) beads. Furthermore, the CG beads were parameterized with an empirical harmonic potential to construct a new CG model. We subjected the CK-CG models of the fibrillar protein assemblies F-actin and collagen to external forces in pulling dynamic simulations to assess their mechanical response. The agreement between the estimated tensile stiffness between CG models and experiments demonstrates the validity of the CK-CG method. Thus, our method provides a practical strategy for the direct construction of a structural model from low-resolution data for biological function studies.

A complex multiscale virtual particle model based elastic network model (CMVP-ENM) for the normal mode analysis of biomolecular complexes

The CMVP-ENM for virus normal mode analysis. With a special ratio parameter, CMVP-ENM can characterize the multi-material properties of biomolecular complexes and systematically enhance or suppress the modes for different components.

Multiscale virtual particle based elastic network model (MVP-ENM) for normal mode analysis of large-sized biomolecules

In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for the normal mode analysis of large-sized biomolecules. The multiscale virtual particle (MVP) model is proposed for the discretization of biomolecular density data. With this model, large-sized biomolecular structures can be coarse-grained into virtual particles such that a balance between model accuracy and computational cost can be achieved. An elastic network is constructed by assuming "connections" between virtual particles. The connection is described by a special harmonic potential function, which considers the influence from both the mass distributions and distance relations of the virtual particles. Two independent models, i.e., the multiscale virtual particle based Gaussian network model (MVP-GNM) and the multiscale virtual particle based anisotropic network model (MVP-ANM), are proposed. It has been found that in the Debye-Waller factor (B-factor) prediction, the results from our MVP-GNM with a high resolution are as good as the ones from GNM. Even with low resolutions, our MVP-GNM can still capture the global behavior of the B-factor very well with mismatches predominantly from the regions with large B-factor values. Further, it has been demonstrated that the low-frequency eigenmodes from our MVP-ANM are highly consistent with the ones from ANM even with very low resolutions and a coarse grid. Finally, the great advantage of MVP-ANM model for large-sized biomolecules has been demonstrated by using two poliovirus virus structures. The paper ends with a conclusion.

Quantum Mechanics/Molecular Mechanics Method Combined with Hybrid All-Atom and Coarse-Grained Model: Theory and Application on Redox Potential Calculations

We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer.

Constructing Optimal Coarse-Grained Sites of Huge Biomolecules by Fluctuation Maximization

Coarse-grained (CG) models are valuable tools for the study of functions of large biomolecules on large length and time scales. The definition of CG representations for huge biomolecules is always a formidable challenge. In this work, we propose a new method called fluctuation maximization coarse-graining (FM-CG) to construct the CG sites of biomolecules. The defined residual in FM-CG converges to a maximal value as the number of CG sites increases, allowing an optimal CG model to be rigorously defined on the basis of the maximum. More importantly, we developed a robust algorithm called stepwise local iterative optimization (SLIO) to accelerate the process of coarse-graining large biomolecules. By means of the efficient SLIO algorithm, the computational cost of coarse-graining large biomolecules is reduced to within the time scale of seconds, which is far lower than that of conventional simulated annealing. The coarse-graining of two huge systems, chaperonin GroEL and lengsin, indicates that our new methods can coarse-grain huge biomolecular systems with up to 10,000 residues within the time scale of minutes. The further parametrization of CG sites derived from FM-CG allows us to construct the corresponding CG models for studies of the functions of huge biomolecular systems.

A new algorithm for construction of coarse-grained sites of large biomolecules

The development of coarse-grained (CG) models for large biomolecules remains a challenge in multiscale simulations, including a rigorous definition of CG representations for them. In this work, we proposed a new stepwise optimization imposed with the boundary-constraint (SOBC) algorithm to construct the CG sites of large biomolecules, based on the s cheme of essential dynamics CG. By means of SOBC, we can rigorously derive the CG representations of biomolecules with less computational cost. The SOBC is particularly efficient for the CG definition of large systems with thousands of residues. The resulted CG sites can be parameterized as a CG model using the normal mode analysis based fluctuation matching method. Through normal mode analysis, the obtained modes of CG model can accurately reflect the functionally related slow motions of biomolecules. The SOBC algorithm can be used for the construction of CG sites of large biomolecules such as F-actin and for the study of mechanical properties of biomaterials.

Robust Heterogeneous Anisotropic Elastic Network Model Precisely Reproduces the Experimental B-factors of Biomolecules

A computational method called the progressive fluctuation matching (PFM) is developed for constructing robust heterogeneous anisotropic network models (HANMs) for biomolecular systems. An HANM derived through the PFM approach consists of harmonic springs with realistic positive force constants, and yields the calculated B-factors that are basically identical to the experimental ones. For the four tested protein systems including crambin, trypsin inhibitor, HIV-1 protease, and lysozyme, the root-mean-square deviations between the experimental and the computed B-factors are only 0.060, 0.095, 0.247, and 0.049 Å(2), respectively, and the correlation coefficients are 0.99 for all. By comparing the HANM/ANM normal modes to their counterparts derived from both an atomistic force field and an NMR structure ensemble, it is found that HANM may provide more accurate results on protein dynamics.