Toward a Coarse-Grained Protein Model Coupled with a Coarse-Grained Solvent Model: Solvation Free Energies of Amino Acid Side Chains

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.

Development, Validation, and Applications of Nonbonded Interaction Parameters between Coarse-Grained Amino Acid and Water Models

Interactions between amino acids and water play an important role in determining the stability and folding/unfolding, in aqueous solution, of many biological macromolecules, which affects their function. Thus, understanding the molecular-level interactions between water and amino acids is crucial to tune their function in aqueous solutions. Herein, we have developed nonbonded interaction parameters between the coarse-grained (CG) models of 20 amino acids and the one-site CG water model. The nonbonded parameters, represented using the 12-6 Lennard Jones (LJ) potential form, have been optimized using an artificial neural network (ANN)-assisted particle swarm optimization (PSO) (ANN-assisted PSO) method. All-atom (AA) molecular dynamics (MD) simulations of dipeptides in TIP3P water molecules were performed to calculate the Gibbs hydration free energies. The nonbonded force-field (FF) parameters between CG amino acids and the one-site CG water model were developed to accurately reproduce these energies. Furthermore, to test the transferability of these newly developed parameters, we calculated the hydration free energies of the analogues of the amino acid side chains, which showed good agreement with reported experimental data. Additionally, we show the applicability of these models by performing self-assembly simulations of peptide amphiphiles. Overall, these models are transferable and can be used to study the self-assembly of various biomaterials and biomolecules to develop a mechanistic understanding of these processes.

Effect of Slp4-a on Membrane Bending During Prefusion of Vesicles in Blood-Brain Barrier

Vesicle exocytosis is a promising pathway for brain drug delivery through the blood-brain barrier to treat neurodegenerative diseases. In vesicle exocytosis, the membrane fusion process is initiated by the calcium sensor protein named synaptotagmin-like protein4-a (Slp4-a). Understanding conformational changes of Slp4-a during the prefusion stage of exocytosis will help to develop vesicle-based drug delivery to the brain. In this work, we use molecular dynamics (MD) simulations with a hybrid force field coupling united-atom protein model with MARTINI coarse-grained (CG) solvent to capture the conformational changes of Slp4-a during the prefusion stage. These hybrid coarse-grained simulations are more efficient than all-atom MD simulations and can capture protein interactions and conformational changes. Our simulation results show that the calcium ions play critical roles during the prefusion stage. Only one calcium ion can remain in each calcium-binding pocket of Slp4-a C2 domains. The C2B domain of calcium-unbound Slp4-a remains parallel to the endothelial membrane, while the C2B domain of calcium-bound Slp4-a rotates perpendicular to the endothelial membrane to approach the vesicular membrane. For the calcium-bound case, three Slp4-a proteins can effectively bend lipid membranes at the prefusion stage, which could later trigger lipid stalk between membranes. This work provides a better understanding how C2 domains of Slp4-a operate during vesicle exocytosis from an endothelial cell.

Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions

Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ_16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ_16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.

Substrate-dependent transport mechanism in AcrB of multidrug resistant bacteria

The multidrug resistance (MDR) system effectively expels antibiotics out of bacteria causing serious issues during bacterial infection. In addition to drug, indole, a common metabolic waste of bacteria, is expelled by MDR system of gram-negative bacteria for their survival. Experimental results suggest that AcrB, one of the key components of MDR system, undergoes large scale conformation changes during the pumping due to proton-motive process. However, due to extremely short time scale, it is difficult to observe (experimentally) those changes in the AcrB, which might facilitate the pumping process. Molecular simulations can shed light to understand the conformational changes for transport of indole in AcrB. Examination of conformational changes using all-atom simulation is, however, impractical. Here, we develop a hybrid coarse-grained force field to study the conformational changes of AcrB in presence of indole in the porter domain of monomer II. Using the coarse-grained force field, we investigated the conformational changes of AcrB for a number of model systems considering the effect of protonation in aspartic acid (Asp) residues Asp407 and Asp408 in the transmembrane domain of monomer II. Our results show that in the presence of indole, protonation of Asp408 or Asp407 residue causes conformational changes from binding state to extrusion state in monomer II, while remaining two monomers (I and III) approach access state in AcrB protein. We also observed that all three AcrB monomers prefer to go back to access state in the absence of indole. Steered molecular dynamics simulations were performed to demonstrate the feasibility of indole transport mechanism for protonated systems. Identification of indole transport pathway through AcrB can be very helpful in understanding the drug efflux mechanism used by the MDR bacteria.

Refining amino acid hydrophobicity for dynamics simulation of membrane proteins

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

Coarse-grained simulations of conformational changes in the multidrug efflux transporter AcrB

The multidrug resistance (MDR) system actively pumps antibiotics out of cells causing serious health problems. During the pumping, AcrB (one of the key components of MDR) undergoes a series of large-scale and proton-motive conformational changes. Capturing the conformational changes through all-atom simulations is challenging. Here, we implement a hybrid coarse-grained force field to investigate the conformational changes of AcrB in the porter domain under different protonation states of Asp407/Asp408 in the trans-membrane domain. Our results show that protonation of Asp408 in monomer III (extrusion) stabilizes the asymmetric structure of AcrB; deprotonation of Asp408 induces clear opening of the entrance and closing of the exit leading to the transition from extrusion to access state. The structural changes in the porter domain of AcrB are strongly coupled with the proton translocation stoichiometry in the trans-membrane domain. Moreover, our simulations support the postulation that AcrB should adopt the symmetric resting state in a substrate-free situation.

Exploration of conformational changes in lactose permease upon sugar binding and proton transfer through coarse-grained simulations

Escherichia coli lactose permease (LacY) actively transports lactose and other galactosides across cell membranes through lactose/H⁺ symport process. Lactose/H⁺ symport is a highly complex process that involves sugar translocation, H⁺ transfer, and large-scale protein conformational changes. The complete picture of lactose/H⁺ symport is largely unclear due to the complexity and multiscale nature of the process. In this work, we develop the force field for sugar molecules compatible with PACE, a hybrid and coarse-grained force field that couples the united-atom protein models with the coarse-grained MARTINI water/lipid. After validation, we implement the new force field to investigate the binding of a β-d-galactopyranosyl-1-thio- β-d-galactopyranoside (TDG) molecule to a wild-type LacY. Results show that the local interactions between TDG and LacY at the binding pocket are consistent with the X-ray experiment. Transitions from inward-facing to outward-facing conformations upon TDG binding and protonation of Glu269 have been achieved from ∼5.5 µs simulations. Both the opening of the periplasmic side and closure of the cytoplasmic side of LacY are consistent with double electron-electron resonance and thiol cross-linking experiments. Our analysis suggests that the conformational changes of LacY are a cumulative consequence of interdomain H-bonds breaking at the periplasmic side, interdomain salt-bridge formation at the cytoplasmic side, and the TDG orientational changes during the transition.

Coarse-grained simulations of proton-dependent conformational changes in lactose permease

During lactose/H(+) symport, the Escherichia coli lactose permease (LacY) undergoes a series of global conformational transitions between inward-facing (open to cytoplasmic side) and outward-facing (open to periplasmic side) states. However, the exact local interactions and molecular mechanisms dictating those large-scale structural changes are not well understood. All-atom molecular dynamics simulations have been performed to investigate the molecular interactions involved in conformational transitions of LacY, but the simulations can only explore early or partial global structural changes because of the computational limits (< 100 ns). In this work, we implement a hybrid force field that couples the united-atom protein models with the coarse-grained MARTINI water/lipid, to investigate the proton-dependent dynamics and conformational changes of LacY. The effects of the protonation states on two key glutamate residues (Glu325 and Glu269) have been studied. Our results on the salt-bridge dynamics agreed with all-atom simulations at early short time period, validating our simulations. From our microsecond simulations, we were able to observe the complete transition from inward-facing to outward-facing conformations of LacY. Our results showed that all helices have participated during the global conformational transitions and helical movements of LacY. The inter-helical distances measured in our simulations were consistent with the double electron-electron resonance experiments at both cytoplasmic and periplasmic sides. Our simulations indicated that the deprotonation of Glu325 induced the opening of the periplasmics side and partial closure of the cytoplasmic side of LacY, while protonation of the Glu269 caused a stable cross-domain salt-bridge (Glu130-Arg344) and completely closed the cytoplasmic side. Proteins 2016; 84:1067-1074. © 2016 Wiley Periodicals, Inc.

PACE Force Field for Protein Simulations. 2. Folding Simulations of Peptides

We present the application of our recently developed PACE force field to the folding of peptides. These peptides include α-helical (AK17 and Fs), β-sheet (GB1m2 and Trpzip2), and mixed helical/coil (Trp-cage) peptides. With replica exchange molecular dynamics (REMD), our force field can fold the five peptides into their native structures while maintaining their stabilities reasonably well. Our force field is also able to capture important thermodynamic features of the five peptides that have been observed in previous experimental and computational studies, such as different preferences for a helix-turn-helix topology for AK17 and Fs, the relative contribution of four hydrophobic side chains of GB1p to the stability of β-hairpin, and the distinct role of a hydrogen bond involving Trp-Hε and a D9/R16 salt bridge in stabilizing the Trp-cage native structure. Furthermore, multiple folding and unfolding events are observed in our microsecond-long normal MD simulations of AK17, Trpzip2, and Trp-cage. These simulations provide mechanistic information such as a "zip-out" pathway of the folding mechanism of Trpzip2 and the folding times of AK17 and Trp-cage, which are estimated to be about 51 ± 43 ns and 270 ± 110 ns, respectively. A 600 ns simulation of the peptides can be completed within one day. These features of our force field are potentially applicable to the study of thermodynamics and kinetics of real protein systems.

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.

Characterization of folding mechanisms of Trp-cage and WW-domain by network analysis of simulations with a hybrid-resolution model

In this study, we apply a hybrid-resolution model, namely, PACE, to characterize the free energy surfaces (FESs) of Trp-cage and a WW-domain variant along with the respective folding mechanisms. Unbiased, independent simulations with PACE are found to achieve together multiple folding and unfolding events for both proteins, allowing us to perform network analysis of the FESs to identify folding pathways. PACE reproduces for both proteins expected complexity hidden in the folding FESs, in particular metastable non-native intermediates. Pathway analysis shows that some of these intermediates are, actually, on-pathway folding intermediates and that intermediates kinetically closest to the native states can be either critical on-pathway or off-pathway intermediates, depending on the protein. Apart from general insights into folding, specific folding mechanisms of the proteins are resolved. We find that Trp-cage folds via a dominant pathway in which hydrophobic collapse occurs before the N-terminal helix forms; full incorporation of Trp6 into the hydrophobic core takes place as the last step of folding, which, however, may not be the rate-limiting step. For the WW-domain variant studied, we observe two main folding pathways with opposite orders of formation of the two hairpins involved in the structure; for either pathway, formation of hairpin 1 is more likely to be the rate-limiting step. Altogether, our results suggest that PACE combined with network analysis is a computationally efficient and valuable tool for the study of protein folding.

Coarse-Grained Models for Protein-Cell Membrane Interactions

The physiological properties of biological soft matter are the product of collective interactions, which span many time and length scales. Recent computational modeling efforts have helped illuminate experiments that characterize the ways in which proteins modulate membrane physics. Linking these models across time and length scales in a multiscale model explains how atomistic information propagates to larger scales. This paper reviews continuum modeling and coarse-grained molecular dynamics methods, which connect atomistic simulations and single-molecule experiments with the observed microscopic or mesoscale properties of soft-matter systems essential to our understanding of cells, particularly those involved in sculpting and remodeling cell membranes.

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.

Further optimization of a hybrid united-atom and coarse-grained force field for folding simulations: Improved backbone hydration and interactions between charged side chains

PACE, a hybrid force field which couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve itse ciency for folding simulations. Backbone hydration parameters have been re-optimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE in order to provide a more realistic description of interactions between charged groups. Using replica exchange molecular dynamics (REMD), ab initio folding using the new PACE has been achieved for seven small proteins (16 - 23 residues) with different structural motifs. Experimental data about folded states, such as their stability at room temperature, melting point and NMR NOE constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temperature has been made with experiments, through standard MD simulations, showing that the new PACE may speed up the actual folding kinetics 5-10 times. Together with the computational speedup benefited from coarse-graining, the force field provides opportunities to study folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, 3D, in multiple 10 - 30 μs simulations, to its native states (C(α) RMSD ~ 0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins.

A generic force field for protein coarse-grained molecular dynamics simulation

Coarse-grained (CG) force fields have become promising tools for studies of protein behavior, but the balance of speed and accuracy is still a challenge in the research of protein coarse graining methodology. In this work, 20 CG beads have been designed based on the structures of amino acid residues, with which an amino acid can be represented by one or two beads, and a CG solvent model with five water molecules was adopted to ensure the consistence with the protein CG beads. The internal interactions in protein were classified according to the types of the interacting CG beads, and adequate potential functions were chosen and systematically parameterized to fit the energy distributions. The proposed CG force field has been tested on eight proteins, and each protein was simulated for 1000 ns. Even without any extra structure knowledge of the simulated proteins, the Cα root mean square deviations (RMSDs) with respect to their experimental structures are close to those of relatively short time all atom molecular dynamics simulations. However, our coarse grained force field will require further refinement to improve agreement with and persistence of native-like structures. In addition, the root mean square fluctuations (RMSFs) relative to the average structures derived from the simulations show that the conformational fluctuations of the proteins can be sampled.

Multiscale coarse-graining of the protein energy landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.

A Transferable Coarse Grain Non-bonded Interaction Model For Amino Acids

The large quantity of protein sequences being generated from genomic data has greatly outpaced the throughput of experimental protein structure determining methods and consequently brought urgency to the need for accurate protein structure prediction tools. Reduced resolution, or coarse grained (CG) models, have become a mainstay in computational protein structure prediction perfoming among the best tools available. The quest for high quality generalized CG models presents an extremely challenging yet popular endeavor. To this point, a CG based interaction potential is presented here for the naturally occurring amino acids. In the present approach, three to four heavy atoms and associated hydrogens are condensed into a single CG site. The parameterization of the site-site interaction potential relies on experimental data thus providing a novel approach that is neither based on all-atom (AA) simulations nor experimental protein structural data. Specifically, intermolecular potentials, which are based on Lennard-Jones (LJ) style functional forms, are parameterized using thermodynamic data including surface tension and density. Using this approach, an amino acid potential dataset has been developed for use in modeling peptides and proteins. The potential is evaluated here by comparing the solvent accessible surface area (SASA) to AA representations and ranking of protein decoy data sets provided by Decoys 'R' Us. The model is shown to perform very well compared to other existing prediction models for these properties.

Monte Carlo, harmonic approximation, and coarse-graining approaches for enhanced sampling of biomolecular structure

The rugged energy landscape of biomolecules and associated large-scale conformational changes have triggered the development of many innovative enhanced sampling methods, either based or not based on molecular dynamics (MD) simulations. Surveyed here are methods in the latter class - including Monte Carlo methods, harmonic approximations, and coarse graining - many of which yield valuable conformational insights into biomolecular structure and flexibility, despite altered kinetics. MD-based methods are surveyed in an upcoming issue of F1000 Biology Reports.

Insights from coarse-grained Gō models for protein folding and dynamics

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.