Peptide Folding Using Multiscale Coarse-Grained Models

Dissipative Particle Dynamics Simulation of Protein Folding in Explicit and Implicit Solvents: Coarse-Grained Model for Atomic Resolution

Advancements have been made to dissipative particle dynamics (DPD), a robust coarse-grained (CG) simulation method, to study the folded structures of four miniproteins (1L2Y, 1WN8, 1YRF, and 2I9M) in explicit and implicit solvents. In this endeavor, we aim to establish model parametrization and enhance computational efficiency. Unlike traditional CG models that use empirical force parameters, ex-force parameters (r0(ex), a ~ , δd, δp) of DPD particles constructed for specific research purposes can be obtained from atomistic molecular dynamics simulations. On the other hand, im-force parameters (r0(im), c, σ) can be derived from ex-DPD simulations, according to the underlying thermodynamic theory. Based on a mapping scheme proposed for the modeling of amino acids, all-atom proteins can be converted into a CG model. Both ex-/im-DPDs are then carried out to investigate the folding pathways of the four mini-proteins. Structural analysis of the RMSDs shows that the im-simulated proteins have greater structural similarity to native proteins than the ex-simulated ones. The constructed CG models achieve a resolution of Angstrom (Å), a level normally associated with atomic models. Additionally, speed tests reveal that im-DPD accelerates the simulation process and significantly improves simulation efficiency.

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Bottom-up coarse-grained models for external fields and interfaces

Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.

Multiconfigurational Coarse-Grained Molecular Dynamics

Standard low resolution coarse-grained modeling techniques have difficulty capturing multiple configurations of protein systems. Here, we present a method for creating accurate coarse-grained (CG) models with multiple configurations using a linear combination of functions or “states”. Individual CG models are created to capture the individual states, and the approximate coupling between the two states is determined from an all-atom potential of mean force. We show that the resulting multiconfiguration coarse-graining (MCCG) method accurately captures the transition state as well as the free energy between the two states. We have tested this method on the folding of dodecaalanine, as well as the amphipathic helix of endophilin.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initiopotential-energysurface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of β-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

Single molecule translocation in smectics illustrates the challenge for time-mapping in simulations on multiple scales

Understanding the connections between the characteristic dynamical time scales associated with a coarse-grained (CG) and a detailed representation is central to the applicability of the coarse-graining methods to understand molecular processes. The process of coarse graining leads to an accelerated dynamics, owing to the smoothening of the underlying free-energy landscapes. Often a single time-mapping factor is used to relate the time scales associated with the two representations. We critically examine this idea using a model system ideally suited for this purpose. Single molecular transport properties are studied via molecular dynamics simulations of the CG and atomistic representations of a liquid crystalline, azobenzene containing mesogen, simulated in the smectic and the isotropic phases. The out-of-plane dynamics in the smectic phase occurs via molecular hops from one smectic layer to the next. Hopping can occur via two mechanisms, with and without significant reorientation. The out-of-plane transport can be understood as a superposition of two (one associated with each mode of transport) independent continuous time random walks for which a single time-mapping factor would be rather inadequate. A comparison of the free-energy surfaces, relevant to the out-of-plane transport, qualitatively supports the above observations. Thus, this work underlines the need for building CG models that exhibit both structural and dynamical consistency to the underlying atomistic model.

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.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

Biomembranes in atomistic and coarse-grained simulations

The architecture of biological membranes is tightly coupled to the localization, organization, and function of membrane proteins. The organelle-specific distribution of lipids allows for the formation of functional microdomains (also called rafts) that facilitate the segregation and aggregation of membrane proteins and thus shape their function. Molecular dynamics simulations enable to directly access the formation, structure, and dynamics of membrane microdomains at the molecular scale and the specific interactions among lipids and proteins on timescales from picoseconds to microseconds. This review focuses on the latest developments of biomembrane force fields for both atomistic and coarse-grained molecular dynamics (MD) simulations, and the different levels of coarsening of biomolecular structures. It also briefly introduces scale-bridging methods applicable to biomembrane studies, and highlights selected recent applications.

Parametrization of Backbone Flexibility in a Coarse-Grained Force Field for Proteins (COFFDROP) Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of All Possible Two-Residue Peptides

Recently, we reported the parametrization of a set of coarse-grained (CG) nonbonded potential functions, derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acid pairs and designed for use in (implicit-solvent) Brownian dynamics (BD) simulations of proteins; this force field was named COFFDROP (COarse-grained Force Field for Dynamic Representations Of Proteins). Here, we describe the extension of COFFDROP to include bonded backbone terms derived from fitting to results of explicit-solvent MD simulations of all possible two-residue peptides containing the 20 standard amino acids, with histidine modeled in both its protonated and neutral forms. The iterative Boltzmann inversion (IBI) method was used to optimize new CG potential functions for backbone-related terms by attempting to reproduce angle, dihedral, and distance probability distributions generated by the MD simulations. In a simple test of the transferability of the extended force field, the angle, dihedral, and distance probability distributions obtained from BD simulations of 56 three-residue peptides were compared to results from corresponding explicit-solvent MD simulations. In a more challenging test of the COFFDROP force field, it was used to simulate eight intrinsically disordered proteins and was shown to quite accurately reproduce the experimental hydrodynamic radii (Rhydro), provided that the favorable nonbonded interactions of the force field were uniformly scaled downward in magnitude. Overall, the results indicate that the COFFDROP force field is likely to find use in modeling the conformational behavior of intrinsically disordered proteins and multidomain proteins connected by flexible linkers.

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecond-timescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed. The folding mechanisms obtained from the simulated folding kinetics are in agreement with experimental results, with a few discrepancies for which we have accounted. The origins of single- and double-exponential kinetics and their correlations with two- and three-state folding scenarios are shown to be related to the relative barrier heights between the various states. The rate constants obtained from time profiles of the fractions of the native, intermediate, and unfolded structures, and the kinetic equations fitted to them, correlate with the experimental values; however, they are about three orders of magnitude larger than the experimental ones for most of the systems. These differences are in agreement with the timescale extension derived by scaling down the friction of water and averaging out the fast degrees of freedom when passing from all-atom to a coarse-grained representation. Our results indicate that the UNRES force field can provide accurate predictions of folding kinetics of these WW domains, often used as models for the study of the mechanisms of proein folding.

COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids

We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions—which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)—quantitatively reproduced all of the “target” MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol.2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP’s nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

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.

A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions

A unified coarse-grained model of three major classes of biological molecules—proteins, nucleic acids, and polysaccharides—has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site–site interactions as mean-field dipole–dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo’s cluster-cumulant series leads to the appearance of mean-field dipole–dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

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Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Mesoscopic coarse-grained simulations of lysozyme adsorption

Coarse-grained simulations are adopted to study the adsorption behavior of lysozyme on different (hydrophobic, neutral hydrophilic, zwitterionic, negatively charged, and positively charged) surfaces at the mesoscopic microsecond time scale (1.2 μs). Simulation results indicate the following: (i) the conformation change of lysozyme on the hydrophobic surface is bigger than any other studied surfaces; (ii) the active sites of lysozyme are faced to the hydrophobic surface with a "top end-on" orientation, while they are exposed to the liquid phase on the hydrophilic surface with a "back-on" orientation; (iii) the neutral hydrophilic surface can induce the adsorption of lysozyme, while the nonspecific protein adsorption can be resisted by the zwitterionic surface; (iv) when the solution ionic strength is low, lysozyme can anchor on the negatively charged surface easily but cannot adsorb on the positively charged surface; (v) when the solution ionic strength is high, the positively charged lysozyme can also adsorb on the like-charged surface; (vi) the major positive potential center of lysozyme, especially the residue ARG128, plays a vital role in leading the adsorption of lysozyme on charged surfaces; (vii) when the ionic strength is high, a counterion layer is formed above the positively charged surface, which is the key factor why lysozyme can adsorb on a like-charged surface. The coarse-grained method based on the MARTINI force field for proteins and the BMW water model could provide an efficient way to understand protein interfacial adsorption behavior at a greater length scale and time scale.

PRIMO: A Transferable Coarse-grained Force Field for Proteins

We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.

Electrostatic-Consistent Coarse-Grained Potentials for Molecular Simulations of Proteins

We present a new generation of coarse-grained (CG) potentials that account for a simplified electrostatic description of soluble proteins. The treatment of permanent electrostatic dipoles of the backbone and polar side-chains allows to simulate proteins, preserving an excellent structural and dynamic agreement with respective reference structures and all-atom molecular dynamics simulations. Moreover, multiprotein complexes can be well described maintaining their molecular interfaces thanks to the ability of this scheme to better describe the actual electrostatics at a CG level of resolution. An efficient and robust heuristic algorithm based on particle swarm optimization is used for the derivation of CG parameters via a force-matching procedure. The ability of this protocol to deal with high dimensional search spaces suggests that the extension of this optimization procedure to larger data sets may lead to the generation of a fully transferable CG force field. At the present stage, these electrostatic-consistent CG potentials are easily and efficiently parametrized, show a good degree of transferability, and can be used to simulate soluble proteins or, more interestingly, large macromolecular assemblies for which long all-atom simulations may not be easily affordable.

Combining coarse-grained protein models with replica-exchange all-atom molecular dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.

Coarse-grained models for protein folding and aggregation

Coarse-grained models for protein folding and aggregation are used to explore large dimension scales and timescales that are inaccessible to all-atom models in explicit aqueous solution. Combined with enhanced configuration search methods, these simplified models with various levels of granularity offer the possibility to determine equilibrium structures, compare folding kinetics and thermodynamics with experiments for single proteins and understand the dynamic assembly of amyloid proteins leading to neurodegenerative diseases. I shall describe recent progress in developing such models, and discuss their potentials and limitations in probing the folding and misfolding of proteins with computer simulations.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

From coarse-grained to atomic-level characterization of protein dynamics: transition state for the folding of B domain of protein A

Atomic-level molecular dynamics simulations are widely used for the characterization of the structural dynamics of proteins; however, they are limited to shorter time scales than the duration of most of the relevant biological processes. Properly designed coarse-grained models that trade atomic resolution for efficient sampling allow access to much longer time-scales. In-depth understanding of the structural dynamics, however, must involve atomic details. In this study, we tested a method for the rapid reconstruction of all-atom models from α carbon atom positions in the application to convert a coarse-grained folding trajectory of a well described model system: the B domain of protein A. The results show that the method and the spatial resolution of the resulting coarse-grained models enable computationally inexpensive reconstruction of realistic all-atom models. Additionally, by means of structural clustering, we determined the most persistent ensembles of the key folding step, the transition state. Importantly, the analysis of the overall structural topologies suggests a dominant folding pathway. This, together with the all-atom characterization of the obtained ensembles, in the form of contact maps, matches the experimental results well.

Structural modelling and dynamics of proteins for insights into drug interactions

Proteins are the workhorses of biomolecules and their function is affected by their structure and their structural rearrangements during ligand entry, ligand binding and protein-protein interactions. Hence, the knowledge of protein structure and, importantly, the dynamic behaviour of the structure are critical for understanding how the protein performs its function. The predictions of the structure and the dynamic behaviour can be performed by combinations of structure modelling and molecular dynamics simulations. The simulations also need to be sensitive to the constraints of the environment in which the protein resides. Standard computational methods now exist in this field to support the experimental effort of solving protein structures. This review presents a comprehensive overview of the basis of the calculations and the well-established computational methods used to generate and understand protein structure and function and the study of their dynamic behaviour with the reference to lung-related targets.

Computational model for protein unfolding simulation

The protein folding problem is one of the fundamental and important questions in molecular biology. However, the all-atom molecular dynamics studies of protein folding and unfolding are still computationally expensive and severely limited by the time scale of simulation. In this paper, a simple and fast protein unfolding method is proposed based on the conformational stability analyses and structure modeling. In this method, two structure-based conditions are considered to identify the unstable regions of proteins during the unfolding processes. The protein unfolding trajectories are mimicked through iterative structure modeling according to conformational stability analyses. Two proteins, chymotrypsin inhibitor 2 (CI2) and α -spectrin SH3 domain (SH3) were simulated by this method. Their unfolding pathways are consistent with the previous molecular dynamics simulations. Furthermore, the transition states of the two proteins were identified in unfolding processes and the theoretical Φ values of these transition states showed significant correlations with the experimental data (the correlation coefficients are >0.8). The results indicate that this method is effective in studying protein unfolding. Moreover, we analyzed and discussed the influence of parameters on the unfolding simulation. This simple coarse-grained model may provide a general and fast approach for the mechanism studies of protein folding.

Order through disorder: hyper-mobile C-terminal residues stabilize the folded state of a helical peptide. a molecular dynamics study

Conventional wisdom has it that the presence of disordered regions in the three-dimensional structures of polypeptides not only does not contribute significantly to the thermodynamic stability of their folded state, but, on the contrary, that the presence of disorder leads to a decrease of the corresponding proteins' stability. We have performed extensive 3.4 µs long folding simulations (in explicit solvent and with full electrostatics) of an undecamer peptide of experimentally known helical structure, both with and without its disordered (four residue long) C-terminal tail. Our simulations clearly indicate that the presence of the apparently disordered (in structural terms) C-terminal tail, increases the thermodynamic stability of the peptide's folded (helical) state. These results show that at least for the case of relatively short peptides, the interplay between thermodynamic stability and the apparent structural stability can be rather subtle, with even disordered regions contributing significantly to the stability of the folded state. Our results have clear implications for the understanding of peptide energetics and the design of foldable peptides.

Characterizing protein energy landscape by self-learning multiscale simulations: application to a designed β-hairpin

Characterizing the energy landscape of proteins at atomic resolution is still a very challenging problem, since it simultaneously requires high accuracy in estimating specific interactions and high efficiency in conformational sampling. Here, for these two requirements to meet, we extended the self-learning multiscale simulation (SLMS) method developed recently and applied it to the designed β-hairpin CLN025. The SLMS integrates all-atom and coarse-grained (CG) models in an iterative way such that the conformational sampling is performed by the CG model, the AA energy is used to calibrate the energy landscape, and the CG model is improved by the calibrated energy landscape. We extended the SLMS in two aspects, use of the energy decomposition for self-learning of the CG potential and a two-bead/residue CG model. The results show that the self-learning greatly improved the CG potential, and with the derived CG potential, the β-hairpin CLN025 robustly folded to the native structure. The self-learning iteration progressively enhanced the context dependence in the CG potential and increased the energy gap between the native and the denatured states of the CG model, leading to a funnel-like energy landscape. By using the SLMS method, without prior knowledge of the native structure but with the help of the AA energy, we can obtain a tailor-made CG potential specific to the target protein. The method can be useful for de novo structure prediction as well.

Molecular dynamics simulations of polyglutamine aggregation using solvent-free multiscale coarse-grained models

The multiscale coarse-graining (MS-CG) method is used to construct solvent-free CG models for polyglutamine peptides having various repeat lengths. Because the resulting CG models have fewer degrees of freedom than a corresponding all-atom simulations, they make it possible to study the self-assembly of polyglutamines at high concentrations for the first time by allowing for better equilibration and statistical sampling that is well beyond the range achievable by all-atom models. Molecular dynamics (MD) simulations performed with these models show that polyglutamine monomers with repeat lengths < or = 28 fluctuate between their folded and unfolded states. Monomers with 32 or more residues are stable and form alpha-helix solid structures. The degree of monomer compactness increases with chain length in both cases. CG MD simulations of equilibrium polyglutamine aggregates show that even at high concentrations, the system statistically fluctuates between heterogeneous and homogeneous configurations, rather than simply aggregates. The degree of aggregation and fluctuation increases with concentration and chain length. All of these phenomena are consistent with the experimental observations and may be explained by a mechanism that the collective nonbonded interactions between polyglutamine molecules in water solution are only weakly attractive. Finally, this work demonstrates that computer simulation of polypeptides self-assembly and aggregation, which is presently beyond the reach of all-atom MD simulations, is attainable using solvent-free MS-CG models.

Mimicking coarse-grained simulations without coarse-graining: enhanced sampling by damping short-range interactions

The damped-short-range-interaction (DSRI) method is proposed to mimic coarse-grained simulations by propagating an atomistic scale system on a smoothed potential energy surface. The DSRI method has the benefit of enhanced sampling provided by a typical coarse-grained simulation without the need to perform coarse-graining. Our method was used to simulate liquid water, alanine dipeptide folding, and the self-assembly of dimyristoylphosphatidylcholine lipid. In each case, our method appreciably accelerated the dynamics without significantly changing the free energy surface. Additional insights from DSRI simulations and the promise of coupling our DSRI method with Hamiltonian replica-exchange molecular dynamics are discussed.

Minimalist models for proteins: a comparative analysis

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