Simple Method for Simulating the Mixture of Atomistic and Coarse-Grained Molecular Systems

A Robust Induced Fit Docking Approach with the Combination of the Hybrid All-Atom/United-Atom/Coarse-Grained Model and Simulated Annealing

Molecular docking remains an indispensable tool in computational biology and structure-based drug discovery. However, the correct prediction of binding poses remains a major challenge for molecular docking, especially for target proteins where a substrate binding induces significant reorganization of the active site. Here, we introduce an Induced Fit Docking (IFD) approach named AA/UA/CG-SA-IFD, which combines a hybrid All-Atom/United-Atom/Coarse-Grained model with Simulated Annealing. In this approach, the core region is represented by the All-Atom(AA) model, while the protein environment beyond the core region and the solvent are treated with either the United-Atom (UA) or the Coarse-Grained (CG) model. By combining the Elastic Network Model (ENM) for the CG region, the hybrid model ensures a reasonable description of ligand binding and the environmental effects of the protein, facilitating highly efficient and reliable sampling of ligand binding through Simulated Annealing (SA) at a high temperature. Upon validation with two testing sets, the AA/UA/CG-SA-IFD approach demonstrates remarkable accuracy and efficiency in induced fit docking, even for challenging cases where the docked poses significantly deviate from crystal structures.

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.

Machine Learning-Guided Adaptive Parametrization for Coupling Terms in a Mixed United-Atom/Coarse-Grained Model for Diphenylalanine Self-Assembly in Aqueous Ionic Liquids

Precise regulation of the peptide self-assembly into ordered nanostructures with intriguing properties has attracted intense attention. However, predicting peptide assembly at atomic resolution is a challenge due to both the structural flexibility of peptides and the associated huge computational costs. A machine learning-guided adaptive parametrization method was proposed for developing a mixed atomic and coarse-grained (CG) model through a multiobjective optimization strategy. Our model incorporates the united-atom (UA) model for diphenylalanine (P) and the polarizable electrostatic-variable coarse-grained (VaCG) model for aqueous ionic liquid [BMIM]+[BF4]- solution. In this mixed model, the coupling van der Waals (vdW) interaction is addressed by introducing virtual sites (VS) in the UA model to interact with solvent CG beads. The coupling parameters, including the electrostatic parameter and vdW parameters, are automatically optimized through ML-guided adaptive parametrization. The performance of this model was tested by some microstructural properties, e.g., the average number of P-P intermolecular hydrogen bonds (HBs) and radius distribution functions (RDFs) between P and different fragments of IL, in comparison with all-atom (AA) simulations. The computational cost is significantly reduced using such a parametrization scheme, which could search tens of thousands of force-field parameter sets, while needing only a small fraction of them to be assessed with molecular dynamics (MD) simulations. We used such a mixed resolution model to investigate the self-assembly in IL-water mixtures with variants of IL concentration (X). The long-range-ordered fibril structure is formed in a pure water system (X = 0). With an increase of IL concentrations, the formation of an ordered self-assembly nanostructure is prohibited, instead forming branched fibril at X = 2 mol % or amorphous aggregates when X > 10 mol %, resulting from the interplay between π-stacking and HB interactions between P and IL. The qualitative agreement between the simulated structures and the observed morphologies in experiments indicates the applicability of ML-guided parametrization strategy in the study of complex systems, such as polymers, lipid bilayers, and polysaccharides.

Toward a Mobility-Preserving Coarse-Grained Model: A Data-Driven Approach

Coarse-grained molecular dynamics (MD) simulation is a promising alternative to all-atom MD simulation for the fast calculation of system properties, which is imperative in designing materials with a specific target property. There have been several coarse-graining strategies developed over the past few years that provide accurate structural properties of the system. However, these coarse-grained models share a major drawback in that they introduce an artificial acceleration in molecular mobility. In this paper, we report a data-driven approach to generate coarse-grained models that preserve the all-atom molecular mobility. We designed a machine learning model in the form of an artificial neural network, which directly predicts the simulation-ready mobility-preserving coarse-grained potential as an output given the all-atom force field (FF) parameters as inputs. As a proof of principle, we took 2,3,4-trimethylpentane as a model system and described the development of machine learning models in detail. We quantify the artificial acceleration in molecular mobility by defining the acceleration factor as the ratio of the coarse-grained and the all-atom diffusion coefficient. The predicted coarse-grained potential generated by the best machine learning model can bring down the acceleration factor to a value of ∼2, which could be otherwise as large as 7 for a typical value of 3 × 10^-9 m² s^-1 for the all-atom diffusion coefficient. We believe our method will be of interest in the community as a route to generating coarse-grained potentials with accurate dynamics.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level N_G (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, N_G = s³ is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s³ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Back-mapping augmented adaptive resolution simulation

Concurrent multiscale techniques such as Adaptive Resolution Scheme (AdResS) can offer ample computational advantages over conventional atomistic (AT) molecular dynamics simulations. However, they typically rely on aphysical hybrid regions to maintain numerical stability when high-resolution degrees of freedom (DOFs) are randomly re-inserted at the resolution interface. We propose an Energy Minimized AT (DOF) Insertion (EMATI) method that uses an informed rather than random AT DOF insertion to tackle the root cause of the issue, i.e., overlapping AT potentials. EMATI enables us to directly couple AT and coarse-grained resolutions without any modifications of the interaction potentials. We exemplify AdResS-EMATI in a system of liquid butane and show that it yields improved structural and thermodynamic properties at the interface compared to competing AdResS approaches. Furthermore, our approach extends the applicability of the AdResS without a hybrid region to systems for which force capping is inadequate.

Dual Resolution Membrane Simulations Using Virtual Sites

All-atomistic (AA) and coarse-grain (CG) simulations have been successfully applied to investigate a broad range of biomolecular processes. However, the accessible time and length scales of AA simulation are limited and the specific molecular details of CG simulation are simplified. Here, we propose a virtual site (VS) based hybrid scheme that can concurrently couple AA and CG resolutions in a single membrane simulation, mitigating the shortcomings of either representation. With some adjustments to make the AA and CG force fields compatible, we demonstrate that lipid bilayer properties are well kept in our hybrid approach. Our VS hybrid method was also applied to simulate a small lipid vesicle, with the inner leaflet and interior solvent represented in AA, and the outer leaflet together with exterior solvent at the CG level. Our multiscale method opens the way to investigate biomembrane properties at increased computational efficiency, in particular applications involving large solvent filled regions.

From quantum to subcellular scales: multi-scale simulation approaches and the SIRAH force field

Modern molecular and cellular biology profits from astonishing resolution structural methods, currently even reaching the whole cell level. This is encompassed by the development of computational methods providing a deep view into the structure and dynamics of molecular processes happening at very different scales in time and space. Linking such scales is of paramount importance when aiming at far-reaching biological questions. Computational methods at the interface between classical and coarse-grained resolutions are gaining momentum with several research groups dedicating important efforts to their development and tuning. An overview of such methods is addressed herein, with special emphasis on the SIRAH force field for coarse-grained and multi-scale simulations. Moreover, we provide proof of concept calculations on the implementation of a multi-scale simulation scheme including quantum calculations on a classical fine-grained/coarse-grained representation of double-stranded DNA. This opens the possibility to include the effect of large conformational fluctuations in chromatin segments on, for instance, the reactivity of particular base pairs within the same simulation framework.

Graph-Based Approach to Systematic Molecular Coarse-Graining

A novel methodology is introduced here to generate coarse-grained (CG) representations of molecular models for simulations. The proposed strategy relies on basic graph-theoretic principles and is referred to as graph-based coarse-graining (GBCG). It treats a given system as a molecular graph and derives a corresponding CG representation by using edge contractions to combine nodes in the graph, which correspond to atoms in the molecule, into CG sites. A key element of this methodology is that the nodes are combined according to well-defined protocols that rank-order nodes based on the underlying chemical connectivity. By iteratively performing these operations, successively coarser representations of the original atomic system can be produced to yield a systematic set of CG mappings with hierarchical resolution in an automated fashion. These capabilities are demonstrated in the context of several test systems, including toluene, pentadecane, a polysaccharide dimer, and a rhodopsin protein. In these examples, GBCG yields multiple, intuitive structures that naturally preserve the chemical topology of the system. Importantly, these representations are rendered from algorithmic implementation rather than an arbitrary ansatz, which, until now, has been the conventional approach for defining CG mapping schemes. Overall, the results presented here indicate that GBCG is efficient, robust, and unambiguous in its application, making it a valuable tool for future CG modeling.

Multiscale Simulation of Protein Hydration Using the SWINGER Dynamical Clustering Algorithm

To perform computationally efficient concurrent multiscale simulations of biological macromolecules in solution, where the all-atom (AT) models are coupled to supramolecular coarse-grained (SCG) solvent models, previous studies resorted to modified AT water models, such as the bundled-simple point charge (SPC) models, that use semiharmonic springs to restrict the relative movement of water molecules within a cluster. Those models can have a significant impact on the simulated biomolecules and can lead, for example, to a partial unfolding of a protein. In this work, we employ the recently developed alternative approach with a dynamical clustering algorithm, SWINGER, which enables a direct coupling of original unmodified AT and SCG water models. We perform an adaptive resolution molecular dynamics simulation of a Trp-Cage miniprotein in multiscale water, where the standard SPC water model is interfaced with the widely used MARTINI SCG model, and demonstrate that, compared to the corresponding full-blown AT simulations, the structural and dynamic properties of the solvated protein and surrounding solvent are well reproduced by our approach.

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.

Understanding and Designing the Gold-Bio Interface: Insights from Simulations

Gold nanoparticles (AuNPs) are an integral part of many exciting and novel biomedical applications, sparking the urgent need for a thorough understanding of the physicochemical interactions occurring between these inorganic materials, their functional layers, and the biological species they interact with. Computational approaches are instrumental in providing the necessary molecular insight into the structural and dynamic behavior of the Au-bio interface with spatial and temporal resolutions not yet achievable in the laboratory, and are able to facilitate a rational approach to AuNP design for specific applications. A perspective of the current successes and challenges associated with the multiscale computational treatment of Au-bio interfacial systems, from electronic structure calculations to force field methods, is provided to illustrate the links between different approaches and their relationship to experiment and applications.

Flexible Boundaries for Multiresolution Solvation: An Algorithm for Spatial Multiscaling in Molecular Dynamics Simulations

An algorithm is proposed for performing molecular dynamics (MD) simulations of a biomolecular solute represented at atomistic resolution surrounded by a surface layer of atomistic fine-grained (FG) solvent molecules within a bulk represented by coarse-grained (CG) solvent beads. The method, called flexible boundaries for multiresolution solvation (FBMS), is based on: (i) a three-region layering of the solvent around the solute, involving an FG layer surrounded by a mixed FG-CG buffer layer, itself surrounded by a bulk CG region; (ii) a definition of the layer boundary that relies on an effective distance to the solute surface and is thus adapted to the shape of the solute as well as adjusts to its conformational changes. The effective surface distance is defined by inverse-nth power averaging over the distances to all non-hydrogen solute atoms, and the layering is enforced by means of half-harmonic distance restraints, attractive for the FG molecules and repulsive for the CG beads. A restraint-free region at intermediate distances enables the formation of the buffer layer, where the FG and CG solvents can mix freely. The algorithm is tested and validated using the GROMOS force field and the associated FG (SPC) and CG (polarizable CGW) water models. The test systems include pure-water systems, where one FG molecule plays the role of a solute, and a deca-alanine peptide with two widely different solute shapes considered, α-helical and fully extended. In particular, as the peptide unfolds, the number of FG molecules required to fill its close-range solvation layer increases, with the additional molecules being provided by the buffer layer. Further validation involves simulations of four proteins in multiresolution FG/CG mixtures. The resulting structural, energetic, and solvation properties are found to be similar to those observed in corresponding pure FG simulations.

Tunable Coarse Graining for Monte Carlo Simulations of Proteins via Smoothed Energy Tables: Direct and Exchange Simulations

Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (Lettieri S.; Zuckerman D. M.J. Comput. Chem.2012, 33, 268-275) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70-90% of the α-helical structure while providing a factor of 3-10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a "resolution exchange" setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (Lyman E.; Zuckerman D. M.J. Chem. Theory Comput.2006, 2, 656-666).

Recent advances in transferable coarse-grained modeling of proteins

Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.