PRIMO/PRIMONA: a coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy

Global Optimization of Large Molecular Systems Using Rigid-Body Chain Stochastic Surface Walking

The global potential energy surface (PES) search of large molecular systems remains a significant challenge in chemistry due to "the curse of dimensionality". To address this, here we develop a rigid-body chain method in the framework of a stochastic surface walking (SSW) global optimization method, termed rigid-body chain SSW (RC-SSW). Based on the angle-axis representation for a single rigid body, our algorithm realizes the cooperative motion of connected rigid bodies and achieves the coupling between rigid-body chain movement and lattice variation in the generalized coordinate. By exploiting the numerical energy second derivative information on rigid bodies, RC-SSW can optimize the global PES of large molecular systems with an unprecedentedly high efficiency. We show that RC-SSW is more than 10 times faster in locating the model protein global minimum while revealing many more low energy conformations than molecular dynamics and can identify low energy phases of molecular crystals up to 172 atoms missed in the sixth CCDC blind test.

FlowBack: A Generalized Flow-Matching Approach for Biomolecular Backmapping

Coarse-grained models have become ubiquitous in biomolecular modeling tasks aimed at studying slow dynamical processes such as protein folding and DNA hybridization. These models can considerably accelerate sampling but it remains challenging to accurately and efficiently restore all-atom detail to the coarse-grained trajectory, which can be vital for detailed understanding of molecular mechanisms and calculation of observables contingent on all-atom coordinates. In this work, we introduce FlowBack as a deep generative model employing a flow-matching objective to map samples from a coarse-grained prior distribution to an all-atom data distribution. We construct our prior distribution to be agnostic to the coarse-grained map and molecular type. A protein-specific model trained on ∼65k structures from the Protein Data Bank achieves state-of-the-art performance on structural metrics compared to previous generative and rules-based approaches in applications to static PDB structures, all-atom simulations of fast-folding proteins, and coarse-grained trajectories generated by a machine-learned force field. A DNA-protein model trained on ∼1.5k DNA-protein complexes achieves excellent reconstruction and generative capabilities on static DNA-protein complexes from the Protein Data Bank as well as on out-of-distribution coarse-grained dynamical simulations of DNA-protein complexation. FlowBack offers an accurate, efficient, and easy-to-use tool to recover all-atom structures from coarse-grained molecular simulations with higher robustness and fewer steric clashes than previous approaches. We make FlowBack freely available to the community as an open source Python package.

AMARO: All Heavy-Atom Transferable Neural Network Potentials of Protein Thermodynamics

All-atom molecular simulations offer detailed insights into macromolecular phenomena, but their substantial computational cost hinders the exploration of complex biological processes. We introduce Advanced Machine-learning Atomic Representation Omni-force-field (AMARO), a new neural network potential (NNP) that combines an O(3)-equivariant message-passing neural network architecture, TensorNet, with a coarse-graining map that excludes hydrogen atoms. AMARO demonstrates the feasibility of training coarser NNP, without prior energy terms, to run stable protein dynamics with scalability and generalization capabilities.

A coarse-grained model for disordered and multi-domain proteins

Many proteins contain more than one folded domain, and such modular multi-domain proteins help expand the functional repertoire of proteins. Because of their larger size and often substantial dynamics, it may be difficult to characterize the conformational ensembles of multi-domain proteins by simulations. Here, we present a coarse-grained model for multi-domain proteins that is both fast and provides an accurate description of the global conformational properties in solution. We show that the accuracy of a one-bead-per-residue coarse-grained model depends on how the interaction sites in the folded domains are represented. Specifically, we find excessive domain-domain interactions if the interaction sites are located at the position of the Cα atoms. We also show that if the interaction sites are located at the center of mass of the residue, we obtain good agreement between simulations and experiments across a wide range of proteins. We then optimize our previously described CALVADOS model using this center-of-mass representation, and validate the resulting model using independent data. Finally, we use our revised model to simulate phase separation of both disordered and multi-domain proteins, and to examine how the stability of folded domains may differ between the dilute and dense phases. Our results provide a starting point for understanding interactions between folded and disordered regions in proteins, and how these regions affect the propensity of proteins to self-associate and undergo phase separation.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Reverse Mapping of Coarse Grained Polyglutamine Conformations from PRIME20 Sampling

An inverse coarse-graining protocol is presented for generating and validating atomistic structures of large (bio-) molecules from conformations obtained via a coarse-grained sampling method. Specifically, the protocol is implemented and tested based on the (coarse-grained) PRIME20 protein model (P20/SAMC), and the resulting all-atom conformations are simulated using conventional biomolecular force fields. The phase space sampling at the coarse-grained level is performed with a stochastical approximation Monte Carlo approach. The method is applied to a series of polypeptides, specifically dimers of polyglutamine with varying chain length in aqueous solution. The majority (>70 %) of the conformations obtained from the coarse-grained peptide model can successfully be mapped back to atomistic structures that remain conformationally stable during 10 ns of molecular dynamics simulations. This work can be seen as the first step towards the overarching goal of improving our understanding of protein aggregation phenomena through simulation methods.

GENESIS CGDYN: large-scale coarse-grained MD simulation with dynamic load balancing for heterogeneous biomolecular systems

Residue-level coarse-grained (CG) molecular dynamics (MD) simulation is widely used to investigate slow biological processes that involve multiple proteins, nucleic acids, and their complexes. Biomolecules in a large simulation system are distributed non-uniformly, limiting computational efficiency with conventional methods. Here, we develop a hierarchical domain decomposition scheme with dynamic load balancing for heterogeneous biomolecular systems to keep computational efficiency even after drastic changes in particle distribution. These schemes are applied to the dynamics of intrinsically disordered protein (IDP) droplets. During the fusion of two droplets, we find that the changes in droplet shape correlate with the mixing of IDP chains. Additionally, we simulate large systems with multiple IDP droplets, achieving simulation sizes comparable to those observed in microscopy. In our MD simulations, we directly observe Ostwald ripening, a phenomenon where small droplets dissolve and their molecules redeposit into larger droplets. These methods have been implemented in CGDYN of the GENESIS software, offering a tool for investigating mesoscopic biological processes using the residue-level CG models.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Simulations of Functional Motions of Super Large Biomolecules with a Mixed-Resolution Model

Many large protein machines function through an interplay between large-scale movements and intricate conformational changes. Understanding functional motions of these proteins through simulations becomes challenging for both all-atom and coarse-grained (CG) modeling techniques because neither approach alone can readily capture the full details of these motions. In this study, we develop a multiscale model by employing the popular MARTINI CG model to represent a heterogeneous environment and structurally stable proteins and using the united-atom (UA) model PACE to describe proteins undergoing subtle conformational changes. PACE was previously developed to be compatible with the MARTINI solvent and membrane. Here, we couple the protein descriptions of the two models by directly mixing UA and CG interaction parameters to greatly simplify parameter determination. Through extensive validations with diverse protein systems in solution or membrane, we demonstrate that only additional parameter rescaling is needed to enable the resulting model to recover the stability of native structures of proteins under mixed representation. Moreover, we identify the optimal scaling factors that can be applied to various protein systems, rendering the model potentially transferable. To further demonstrate its applicability for realistic systems, we apply the model to a mechanosensitive ion channel Piezo1 that has peripheral arms for sensing membrane tension and a central pore for ion conductance. The model can reproduce the coupling between Piezo1's large-scale arm movement and subtle pore opening in response to membrane stress while consuming much less computational costs than all-atom models. Therefore, our model shows promise for studying functional motions of large protein machines.

From simple to complex: Reconstructing all-atom structures from coarse-grained models using cg2all

In this issue of Structure, Heo and Feig present cg2all, a novel deep-learning model capable of efficiently predicting all-atom protein structures from coarse-grained (CG) representations. The model maintains high accuracy, even when the CG model is simplified to a single bead per residue, and has a number of promising applications.

One bead per residue can describe all-atom protein structures

Atomistic resolution is the standard for high-resolution biomolecular structures, but experimental structural data are often at lower resolution. Coarse-grained models are also used extensively in computational studies to reach biologically relevant spatial and temporal scales. This study explores the use of advanced machine learning networks for reconstructing atomistic models from reduced representations. The main finding is that a single bead per amino acid residue allows construction of accurate and stereochemically realistic all-atom structures with minimal loss of information. This suggests that lower resolution representations of proteins may be sufficient for many applications when combined with a machine learning framework that encodes knowledge from known structures. Practical applications include the rapid addition of atomistic detail to low-resolution structures from experiment or computational coarse-grained models. The application of rapid, deterministic all-atom reconstruction within multi-scale frameworks is further demonstrated with a rapid protocol for the generation of accurate models from cryo-EM densities close to experimental structures.

DiAMoNDBack: Diffusion-Denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces

Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long time scales, such as aggregation and folding. The reduced resolution realizes computational accelerations, but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side-chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side-chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from the Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side-chain clashes, and the diversity of the generated side-chain configurational states. We make the DiAMoNDBack model publicly available as a free and open-source Python package.

RNA origami: design, simulation and application

Design strategies for DNA and RNA nanostructures have developed along parallel lines for the past 30 years, from small structural motifs derived from biology to large 'origami' structures with thousands to tens of thousands of bases. With the recent publication of numerous RNA origami structures and improved design methods-even permitting co-transcriptional folding of kilobase-sized structures - the RNA nanotechnolgy field is at an inflection point. Here, we review the key achievements which inspired and enabled RNA origami design and draw comparisons with the development and applications of DNA origami structures. We further present the available computational tools for the design and the simulation, which will be key to the growth of the RNA origami community. Finally, we portray the transition from RNA origami structure to function. Several functional RNA origami structures exist already, their expression in cells has been demonstrated and first applications in cell biology have already been realized. Overall, we foresee that the fast-paced RNA origami field will provide new molecular hardware for biophysics, synthetic biology and biomedicine, complementing the DNA origami toolbox.

NARall: a novel tool for reconstruction of the all-atom structure of nucleic acids from heavily coarse-grained model

Nucleic acids are one of the most important cellular components. These molecules have been studied both experimentally and theoretically. As all-atom simulations are still limited to short time scales, coarse-grain modeling allows to study of those molecules on a longer time scale. Nucleic-Acid united RESidue (NARES-2P) is a low-resolution coarse-grained model with two centers of interaction per repeating unit. It has been successfully applied to study DNA self-assembly and telomeric properties. This force field enables the study of nucleic acids Behavior on a long time scale but lacks atomistic details. In this article, we present new software to reconstruct atomistic details from the NARES-2P model. It has been applied to RNA pseudoknot, nucleic acid four-way junction, G-quadruplex and DNA duplex converted to NARES-2P model and back. Moreover, it was applied to DNA structure folded and self-assembled with NARES-2P.

Accurate and Efficient Estimation of Lennard-Jones Interactions for Coarse-Grained Particles via a Potential Matching Method

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

Implementation of residue-level coarse-grained models in GENESIS for large-scale molecular dynamics simulations

Residue-level coarse-grained (CG) models have become one of the most popular tools in biomolecular simulations in the trade-off between modeling accuracy and computational efficiency. To investigate large-scale biological phenomena in molecular dynamics (MD) simulations with CG models, unified treatments of proteins and nucleic acids, as well as efficient parallel computations, are indispensable. In the GENESIS MD software, we implement several residue-level CG models, covering structure-based and context-based potentials for both well-folded biomolecules and intrinsically disordered regions. An amino acid residue in protein is represented as a single CG particle centered at the Cα atom position, while a nucleotide in RNA or DNA is modeled with three beads. Then, a single CG particle represents around ten heavy atoms in both proteins and nucleic acids. The input data in CG MD simulations are treated as GROMACS-style input files generated from a newly developed toolbox, GENESIS-CG-tool. To optimize the performance in CG MD simulations, we utilize multiple neighbor lists, each of which is attached to a different nonbonded interaction potential in the cell-linked list method. We found that random number generations for Gaussian distributions in the Langevin thermostat are one of the bottlenecks in CG MD simulations. Therefore, we parallelize the computations with message-passing-interface (MPI) to improve the performance on PC clusters or supercomputers. We simulate Herpes simplex virus (HSV) type 2 B-capsid and chromatin models containing more than 1,000 nucleosomes in GENESIS as examples of large-scale biomolecular simulations with residue-level CG models. This framework extends accessible spatial and temporal scales by multi-scale simulations to study biologically relevant phenomena, such as genome-scale chromatin folding or phase-separated membrane-less condensations.

Searching for Low Probability Opening Events in a DNA Sliding Clamp

The β subunit of E. coli DNA polymererase III is a DNA sliding clamp associated with increasing the processivity of DNA synthesis. In its free form, it is a circular homodimer structure that can accomodate double-stranded DNA in a nonspecific manner. An open state of the clamp must be accessible before loading the DNA. The opening mechanism is still a matter of debate, as is the effect of bound DNA on opening/closing kinetics. We use a combination of atomistic, coarse-grained, and enhanced sampling strategies in both explicit and implicit solvents to identify opening events in the sliding clamp. Such simulations of large nucleic acid and their complexes are becoming available and are being driven by improvements in force fields and the creation of faster computers. Different models support alternative opening mechanisms, either through an in-plane or out-of-plane opening event. We further note some of the current limitations, despite advances, in modeling these highly charged systems with implicit solvent.

Martini 3 Model of Cellulose Microfibrils: On the Route to Capture Large Conformational Changes of Polysaccharides

High resolution data from all-atom molecular simulations is used to parameterize a Martini 3 coarse-grained (CG) model of cellulose I allomorphs and cellulose type-II fibrils. In this case, elementary molecules are represented by four effective beads centred in the positions of O2, O3, C6, and O6 atoms in the D-glucose cellulose subunit. Non-bonded interactions between CG beads are tuned according to a low statistical criterion of structural deviation using the Martini 3 type of interactions and are capable of being indistinguishable for all studied cases. To maintain the crystalline structure of each single cellulose chain in the microfibrils, elastic potentials are employed to retain the ribbon-like structure in each chain. We find that our model is capable of describing different fibril-twist angles associated with each type of cellulose fibril in close agreement with atomistic simulation. Furthermore, our CG model poses a very small deviation from the native-like structure, making it appropriate to capture large conformational changes such as those that occur during the self-assembly process. We expect to provide a computational model suitable for several new applications such as cellulose self-assembly in different aqueous solutions and the thermal treatment of fibrils of great importance in bioindustrial applications.

Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures

Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structures, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail—an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This “neural upscaling” procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 μs atomistic molecular dynamics trajectory of Aβ1–40, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs.

Biomolecular response to hour-long ultralow field microwave radiation: An effective coarse-grained model simulation

Various electronic devices, which we commonly use, radiate microwaves. Such external perturbation influences the functionality of biomolecules. In an ultralow field, the cumulative response of a molecule is expected only over a time scale of hours. To study the structural dynamics of biomolecules over hours, we adopt a simple methodology for constructing the coarse-grained structure of the protein molecule and solve the Langevin equation under different working potentials. In this approach, each amino acid residue of a biomolecule is mapped onto a number of beads, a few for the backbone, and few for the side chain, depending on the complexity of its chemical structure. We choose the force field in such a way that the dynamics of the protein molecule in the presence of ultralow radiation field of microvolt/nm could be followed over the time frame of 2 h. We apply the model to describe a biomolecule, hen egg white lysozyme, and simulate its structural evolution under ultralow strength electromagnetic radiation. The simulation revealed the finer structural details, like the extent of exposure of bioactive residues and the state of the secondary structures of the molecule, further confirmed from spectroscopic measurements [details are available in Phys. Rev. E 97, 052416 (2018)10.1103/PhysRevE.97.052416 and briefly described here]. Though tested for a specific system, the model is quite general. We believe that it harnesses the potential in studying the structural dynamics of any biopolymer under external perturbation over an extended time scale.

Using normal mode analysis on protein structural models. How far can we go on our predictions?

Normal mode analysis (NMA) is a fast and inexpensive approach that is largely used to gain insight into functional protein motions, and more recently to create conformations for further computational studies. However, when the protein structure is unknown, the use of computational models is necessary. Here, we analyze the capacity of NMA in internal coordinate space to predict protein motion, its intrinsic flexibility, and atomic displacements, using protein models instead of native structures, and the possibility to use it for model refinement. Our results show that NMA is quite insensitive to modeling errors, but that calculations are strictly reliable only for very accurate models. Our study also suggests that internal NMA is a more suitable tool for the improvement of structural models, and for integrating them with experimental data or in other computational techniques, such as protein docking or more refined molecular dynamics simulations.

Coarse-grained (hybrid) integrative modeling of biomolecular interactions

The computational modeling field has vastly evolved over the past decades. The early developments of simplified protein systems represented a stepping stone towards establishing more efficient approaches to sample intricated conformational landscapes. Downscaling the level of resolution of biomolecules to coarser representations allows for studying protein structure, dynamics and interactions that are not accessible by classical atomistic approaches. The combination of different resolutions, namely hybrid modeling, has also been proved as an alternative when mixed levels of details are required. In this review, we provide an overview of coarse-grained/hybrid models focusing on their applicability in the modeling of biomolecular interactions. We give a detailed list of ready-to-use modeling software for studying biomolecular interactions allowing various levels of coarse-graining and provide examples of complexes determined by integrative coarse-grained/hybrid approaches in combination with experimental information.

Computational reconstruction of atomistic protein structures from coarse-grained models

Three-dimensional protein structures, whether determined experimentally or theoretically, are often too low resolution. In this mini-review, we outline the computational methods for protein structure reconstruction from incomplete coarse-grained to all atomistic models. Typical reconstruction schemes can be divided into four major steps. Usually, the first step is reconstruction of the protein backbone chain starting from the C-alpha trace. This is followed by side-chains rebuilding based on protein backbone geometry. Subsequently, hydrogen atoms can be reconstructed. Finally, the resulting all-atom models may require structure optimization. Many methods are available to perform each of these tasks. We discuss the available tools and their potential applications in integrative modeling pipelines that can transfer coarse-grained information from computational predictions, or experiment, to all atomistic structures.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Recent Advances in Coarse-Grained Models for Biomolecules and Their Applications

Molecular dynamics simulations have emerged as a powerful tool to study biological systems at varied length and timescales. The conventional all-atom molecular dynamics simulations are being used by the wider scientific community in routine to capture the conformational dynamics and local motions. In addition, recent developments in coarse-grained models have opened the way to study the macromolecular complexes for time scales up to milliseconds. In this review, we have discussed the principle, applicability and recent development in coarse-grained models for biological systems. The potential of coarse-grained simulation has been reviewed through state-of-the-art examples of protein folding and structure prediction, self-assembly of complexes, membrane systems and carbohydrates fiber models. The multiscale simulation approaches have also been discussed in the context of their emerging role in unravelling hierarchical level information of biosystems. We conclude this review with the future scope of coarse-grained simulations as a constantly evolving tool to capture the dynamics of biosystems.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Backmapping from Multiresolution Coarse-Grained Models to Atomic Structures of Large Biomolecules by Restrained Molecular Dynamics Simulations Using Bayesian Inference

Coarse-grained (CG) simulations have allowed access to larger length scales and longer time scales in the study of the dynamic processes of large biomolecules than all-atom (AA) molecular dynamics (MD) simulations. Backmapping from CG models to AA structures has long been studied because it enables us to gain detailed structure insights from CG simulations. Many methods first construct an AA structure from the CG model by fragments, random placement, or geometrical rules and subsequently optimize the solution via energy minimization, simulated annealing or position-restrained simulations. However, such methods may only work well on residue-level CG models and cannot consider the deviations of CG models. In this work, we describe, to the best of our knowledge, a new backmapping method based on Bayesian inference and restrained MD simulations. Restraints with log harmonic energy terms are defined according to the target CG model using the Bayesian inference in which the CG deviations can be estimated. From an initial AA structure obtained from either high-resolution experiments or homology modeling, a MD simulation with the aforementioned restraints is performed to obtain a final AA structure that is a backmapping of the target CG model. The method was validated using multiresolution CG models of the soluble extracellular region of the human epidermal growth factor receptor and was further applied to construct AA structures from CG simulations of the nucleosome core particle. The results demonstrate that our method can generate accurate AA structures of different types of biomolecules from multiple CG models with either residue-level resolution or much lower resolution than one-site-per-residue.

Reconstruction of Atomistic Structures from Coarse-Grained Models for Protein-DNA Complexes

While coarse-grained (CG) simulations have widely been used to accelerate structure sampling of large biomolecular complexes, they are unavoidably less accurate and thus the reconstruction of all-atom (AA) structures and the subsequent refinement is desirable. In this study we developed an efficient method to reconstruct AA structures from sampled CG protein-DNA complex models, which attempts to model the protein-DNA interface accurately. First we developed a method to reconstruct atomic details of DNA structures from a three-site per nucleotide CG model, which uses a DNA fragment library. Next, for the protein-DNA interface, we referred to the side chain orientations in the known structure of the target interface when available. The other parts are modeled by existing tools. We confirmed the accuracy of the protocol in various aspects including the structure deviation in the self-reproduction, the base pair reproducibility, atomic contacts at the protein-DNA interface, and feasibility of the posterior AA simulations.

Predicting ligand binding poses for low-resolution membrane protein models: Perspectives from multiscale simulations

Membrane receptors constitute major targets for pharmaceutical intervention. Drug design efforts rely on the identification of ligand binding poses. However, the limited experimental structural information available may make this extremely challenging, especially when only low-resolution homology models are accessible. In these cases, the predictions may be improved by molecular dynamics simulation approaches. Here we review recent developments of multiscale, hybrid molecular mechanics/coarse-grained (MM/CG) methods applied to membrane proteins. In particular, we focus on our in-house MM/CG approach. It is especially tailored for G-protein coupled receptors, the largest membrane receptor family in humans. We show that our MM/CG approach is able to capture the atomistic details of the receptor/ligand binding interactions, while keeping the computational cost low by representing the protein frame and the membrane environment in a highly simplified manner. We close this review by discussing ongoing improvements and challenges of the current implementation of our MM/CG code.

SURPASS Low-Resolution Coarse-Grained Protein Modeling

Coarse-grained modeling of biomolecules has a very important role in molecular biology. In this work we present a novel SURPASS (Single United Residue per Pre-Averaged Secondary Structure fragment) model of proteins that can be an interesting alternative for existing coarse-grained models. The design of the model is unique and strongly supported by the statistical analysis of structural regularities characteristic for protein systems. Coarse-graining of protein chain structures assumes a single center of interactions per residue and accounts for preaveraged effects of four adjacent residue fragments. Knowledge-based statistical potentials encode complex interaction patterns of these fragments. Using the Replica Exchange Monte Carlo sampling scheme and a generic version of the SURPASS force field we performed test simulations of a representative set of single-domain globular proteins. The method samples a significant part of conformational space and reproduces protein structures, including native-like, with surprisingly good accuracy. Future extension of the SURPASS model on large biomacromolecular systems is briefly discussed.

Hybrid All-Atom/Coarse-Grained Simulations of Proteins by Direct Coupling of CHARMM and PRIMO Force Fields

Hybrid all-atom/coarse-grained (AA/CG) simulations of proteins offer a computationally efficient compromise where atomistic details are only applied to biologically relevant regions while benefiting from the speedup of treating the remaining parts of a given system at the CG level. The recently developed CG model, PRIMO, allows a direct coupling with an atomistic force field with no additional modifications or coupling terms and the ability to carry out dynamic simulations without any restraints on secondary or tertiary structures. A hybrid AA/CG scheme based on combining all-atom CHARMM and coarse-grained PRIMO representations was validated via molecular dynamics and replica exchange simulations of soluble and membrane proteins. The AA/CG scheme was also tested in the calculation of the free energy profile for the transition from the closed to the open state of adenylate kinase via umbrella sampling molecular dynamics method. The overall finding is that the AA/CG scheme generates dynamics and energetics that are qualitatively and quantitatively comparable to AA simulations while offering the computational advantages of coarse-graining. This model opens the door to challenging applications where high accuracy is required only in parts of large biomolecular complexes.

Adaptive resolution simulations of biomolecular systems

In this review article, we discuss and analyze some recently developed hybrid atomistic-mesoscopic solvent models for multiscale biomolecular simulations. We focus on the biomolecular applications of the adaptive resolution scheme (AdResS), which allows solvent molecules to change their resolution back and forth between atomistic and coarse-grained representations according to their positions in the system. First, we discuss coupling of atomistic and coarse-grained models of salt solution using a 1-to-1 molecular mapping-i.e., one coarse-grained bead represents one water molecule-for development of a multiscale salt solution model. In order to make use of coarse-grained molecular models that are compatible with the MARTINI force field, one has to resort to a supramolecular mapping, in particular to a 4-to-1 mapping, where four water molecules are represented with one coarse-grained bead. To this end, bundled atomistic water models are employed, i.e., the relative movement of water molecules that are mapped to the same coarse-grained bead is restricted by employing harmonic springs. Supramolecular coupling has recently also been extended to polarizable coarse-grained water models with explicit charges. Since these coarse-grained models consist of several interaction sites, orientational degrees of freedom of the atomistic and coarse-grained representations are coupled via a harmonic energy penalty term. The latter aligns the dipole moments of both representations. The reviewed multiscale solvent models are ready to be used in biomolecular simulations, as illustrated in a few examples.

Optimal allosteric stabilization sites using contact stabilization analysis

Proteins can be destabilized by a number of environmental factors such as temperature, pH, and mutation. The ability to subsequently restore function under these conditions by adding small molecule stabilizers, or by introducing disulfide bonds, would be a very powerful tool, but the physical principles that drive this stabilization are not well understood. The first problem lies is in choosing an appropriate binding site or disulfide bond location to best confer stability to the active site and restore function. Here, we present a general framework for predicting which allosteric binding sites correlate with stability in the active site. Using the Karanicolas-Brooks Gō-like model, we examine the dynamics of the enzyme β-glucuronidase using an Umbrella Sampling method to thoroughly sample the conformational landscape. Each intramolecular contact is assigned a score termed a "stabilization factor" that measures its correlation with structural changes in the active site. We have carried out this analysis for three different scaling strengths for the intramolecular contacts, and we examine how the calculated stabilization factors depend on the ensemble of destabilized conformations. We further examine a locally destabilized mutant of β-glucuronidase that has been characterized experimentally, and show that this brings about local changes in the stabilization factors. We find that the proximity to the active site is not sufficient to determine which contacts can confer active site stability. © 2016 Wiley Periodicals, Inc.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Effects of Concentration and Temperature on DNA Hybridization by Two Closely Related Sequences via Large-Scale Coarse-Grained Simulations

A newly developed coarse-grained model called BioModi is utilized to elucidate the effects of temperature and concentration on DNA hybridization in self-assembly. Large-scale simulations demonstrate that complementary strands of either the tetrablock sequence or randomized sequence with equivalent number of cytosine or guanine nucleotides can form completely hybridized double helices. Even though the end states are the same for the two sequences, there exist multiple kinetic pathways that are populated with a wider range of transient aggregates of different sizes in the system of random sequences compared to that of the tetrablock sequence. The ability of these aggregates to undergo the strand displacement mechanism to form only double helices depends upon the temperature and DNA concentration. On one hand, low temperatures and high concentrations drive the formation and enhance stability of large aggregating species. On the other hand, high temperatures destabilize base-pair interactions and large aggregates. There exists an optimal range of moderate temperatures and low concentrations that allow minimization of large aggregate formation and maximization of fully hybridized dimers. Such investigation on structural dynamics of aggregating species by two closely related sequences during the self-assembly process demonstrates the importance of sequence design in avoiding the formation of metastable species. Finally, from kinetic modeling of self-assembly dynamics, the activation energy for the formation of double helices was found to be in agreement with experimental results. The framework developed in this work can be applied to the future design of DNA nanostructures in both fields of structural DNA nanotechnology and dynamic DNA nanotechnology wherein equilibrium end states and nonequilibrium dynamics are equally important requiring investigation in cooperation.

A distance- and orientation-dependent energy function of amino acid key blocks

Blocks are the selected portions of amino acids. They have been used effectively to represent amino acids in distinguishing the native conformation from the decoys. Although many statistical energy functions exist, most of them rely on the distances between two or more amino acids. In this study, the authors have developed a pairwise energy function "DOKB" that is both distance and orientation dependent, and it is based on the key blocks that bias the distal ends of side chains. The results suggest that both the distance and the orientation are needed to distinguish the fine details of the packing geometry. DOKB appears to perform well in recognizing native conformations when compared with six other energy functions. Highly packed clusters play important roles in stabilizing the structure. The investigation about the highly packed clusters at the residue level suggests that certain residue pairs in a low-energy region have lower probability to appear in the highly packed clusters than in the entire protein. The cluster energy term appears to significantly improve the recognition of the native conformations in ig_structal decoy set, in which more highly packed clusters are contained than in other decoy sets.

Coupled folding and binding with 2D Window-Exchange Umbrella Sampling

Intrinsically disordered regions of proteins can gain structure by binding to a partner. This process, of coupled folding and binding (CFaB), is a fundamental part of many important biological processes. Structure-based models have proven themselves capable of revealing fundamental aspects of how CFaB occurs, however, typical methods to enhance the sampling of these transitions, such as replica exchange, do not adequately sample the transition state region of this extremely rare process. Here, we use a variant of Umbrella Sampling to enforce sampling of the transition states of CFaB of HdeA monomers at neutral pH, an extremely rare process that occurs over timescales ranging from seconds to hours. Using high resolution sampling in the transition state region, we cluster states along the principal transition path to obtain a detailed description of coupled binding and folding for the HdeA dimer, revealing new insight into the ensemble of states that are accessible to client recognition. We then demonstrate that exchanges between umbrella sampling windows, as done in previous work, significantly improve relaxation in variables orthogonal to the restraints used. Altogether, these results show that Window-Exchange Umbrella Sampling is a promising approach for systems that exhibit flexible binding, and can reveal transition state ensembles of these systems in high detail. © 2015 Wiley Periodicals, Inc.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

A Nonradial Coarse-Grained Potential for Proteins Produces Naturally Stable Secondary Structure Elements

We introduce a nonradial potential term for coarse-grained (CG) molecular simulations of proteins. This term mimics the backbone dipole-dipole interactions and accounts for the needed directionality to form stable folded secondary structure elements. We show that α-helical and β-sheet peptide chains are correctly described in dynamics without the need of introducing any a priori bias potentials or ad hoc parametrizations, which limit broader applicability of CG simulations for proteins. Moreover, our model is able to catch the formation of supersecondary structural motifs, like transitions from long single α-helices to helix-coil-helix or β-hairpin assemblies. This novel scheme requires the structural information of Cα beads only; it does not introduce any additional degrees of freedom to the system and has a general formulation, which allows it to be used in synergy with various CG protocols, leading to an improved description of the structural and dynamic properties of protein assemblies and networks.

Martini Coarse-Grained Force Field: Extension to DNA

We systematically parameterized a coarse-grained (CG) model for DNA that is compatible with the Martini force field. The model maps each nucleotide into six to seven CG beads and is parameterized following the Martini philosophy. The CG nonbonded interactions are based on partitioning of the nucleobases between polar and nonpolar solvents as well as base-base potential of mean force calculations. The bonded interactions are fit to single-stranded DNA (ssDNA) atomistic simulations and an elastic network is used to retain double-stranded DNA (dsDNA) and other specific DNA conformations. We present the implementation of the Martini DNA model and demonstrate the properties of individual bases, ssDNA as well as dsDNA, and DNA-protein complexes. The model opens up large-scale simulations of DNA interacting with a wide range of other (bio)molecules that are available within the Martini framework.

Chemically specific multiscale modeling of clay-polymer nanocomposites reveals intercalation dynamics, tactoid self-assembly and emergent materials properties

A quantitative description is presented of the dynamical process of polymer intercalation into clay tactoids and the ensuing aggregation of polymer-entangled tactoids into larger structures, obtaining various characteristics of these nanocomposites, including clay-layer spacings, out-of-plane clay-sheet bending energies, X-ray diffractograms, and materials properties. This model of clay-polymer interactions is based on a three-level approach, which uses quantum mechanical and atomistic descriptions to derive a coarse-grained yet chemically specific representation that can resolve processes on hitherto inaccessible length and time scales. The approach is applied to study collections of clay mineral tactoids interacting with two synthetic polymers, poly(ethylene glycol) and poly(vinyl alcohol). The controlled behavior of layered materials in a polymer matrix is centrally important for many engineering and manufacturing applications. This approach opens up a route to computing the properties of complex soft materials based on knowledge of their chemical composition, molecular structure, and processing conditions.

Coarse-grained simulation study of sequence effects on DNA hybridization in a concentrated environment

A novel coarse-grained model is developed to elucidate thermodynamics and kinetic mechanisms of DNA self-assembly. It accounts for sequence and solvent conditions to capture key experimental results such as sequence-dependent thermal property and salt-dependent persistence length of ssDNA and dsDNA. Moreover, constant-temperature simulations on two single strands of a homogeneous sequence show two main mechanisms of hybridization: a slow slithering mechanism and a one-order faster zippering mechanism. Furthermore, large-scale simulations at a high DNA strand concentration demonstrate that DNA self-assembly is a robust and enthalpically driven process in which the formation of double helices is deciphered to occur via multiple self-assembly pathways including the strand displacement mechanism. However, sequence plays an important role in shifting the majority of one pathway over the others and controlling size distribution of self-assembled aggregates. This study yields a complex picture on the role of sequence on programmable self-assembly and demonstrates a promising simulation tool that is suitable for studies in DNA nanotechnology.