Hydrophobic hydration and pairwise hydrophobic interaction of Lennard-Jones and Mie particles in different water models

The study provides a deep computational analysis of the thermodynamic and structural features associated with the hydration of xenon, Xe, and its pairwise hydrophobic interaction (i.e., the potential of mean force, PMF), over a large temperature range. Xe is described both as a Lennard-Jones particle, LJ-Xe, and as a Mie particle, Mie-Xe (pseudo hard sphere). Three different water models are used: TIP3P-Ew, SPCE and TIP4P-2005. Mie-Xe is more hydrophobic than LJ-Xe due to the lack of the attractive energetic interactions with water molecules; its hydration, around room temperature, is opposed by a large and negative entropy change and a positive enthalpy change. The PMF of Mie-Xe is characterized by a deep minimum at contact distance whose depth increases with temperature, and whose magnitude is significantly larger than that obtained for LJ-Xe. The contact minimum configuration of Mie-Xe is favoured by a large positive entropy change and contrasted by a positive enthalpy change. These results are qualitatively the same regardless of the water model used. There is no clear connection between the values determined for the thermodynamic functions and the structural features of the hydration shells surrounding the single Mie-Xe and the couple of Mie-Xe particles in the contact minimum configuration. This confirms that the structural reorganization of water associated with such processes is characterized by an almost complete enthalpy-entropy compensation.

Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers

In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.

Improved Consensus-Fragment Selection in Template-Assisted Prediction of Protein Structures with the UNRES Force Field in CASP13

The method for protein-structure prediction, which combines the physics-based coarse-grained UNRES force field with knowledge-based modeling, has been developed further and tested in the 13th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP13). The method implements restraints from the consensus fragments common to server models. In this work, the server models to derive fragments have been chosen on the basis of quality assessment; a fully automatic fragment-selection procedure has been introduced, and Dynamic Fragment Assembly pseudopotentials have been fully implemented. The Global Distance Test Score (GDT_TS), averaged over our “Model 1” predictions, increased by over 10 units with respect to CASP12 for the free-modeling category to reach 40.82. Our “Model 1” predictions ranked 20 and 14 for all and free-modeling targets, respectively (upper 20.2% and 14.3% of all models submitted to CASP13 in these categories, respectively), compared to 27 (upper 21.1%) and 24 (upper 18.9%) in CASP12, respectively. For oligomeric targets, the Interface Patch Similarity (IPS) and Interface Contact Similarity (ICS) averaged over our best oligomer models increased from 0.28 to 0.36 and from 12.4 to 17.8, respectively, from CASP12 to CASP13, and top-ranking models of 2 targets (H0968 and T0997o) were obtained (none in CASP12). The improvement of our method in CASP13 over CASP12 was ascribed to the combined effect of the overall enhancement of server-model quality, our success in selecting server models and fragments to derive restraints, and improvements of the restraint and potential-energy functions.

Blind prediction of homo- and hetero-protein complexes: The CASP13-CAPRI experiment

We present the results for CAPRI Round 46, the third joint CASP-CAPRI protein assembly prediction challenge. The Round comprised a total of 20 targets including 14 homo-oligomers and 6 heterocomplexes. Eight of the homo-oligomer targets and one heterodimer comprised proteins that could be readily modeled using templates from the Protein Data Bank, often available for the full assembly. The remaining 11 targets comprised 5 homodimers, 3 heterodimers, and two higher-order assemblies. These were more difficult to model, as their prediction mainly involved "ab-initio" docking of subunit models derived from distantly related templates. A total of ~30 CAPRI groups, including 9 automatic servers, submitted on average ~2000 models per target. About 17 groups participated in the CAPRI scoring rounds, offered for most targets, submitting ~170 models per target. The prediction performance, measured by the fraction of models of acceptable quality or higher submitted across all predictors groups, was very good to excellent for the nine easy targets. Poorer performance was achieved by predictors for the 11 difficult targets, with medium and high quality models submitted for only 3 of these targets. A similar performance "gap" was displayed by scorer groups, highlighting yet again the unmet challenge of modeling the conformational changes of the protein components that occur upon binding or that must be accounted for in template-based modeling. Our analysis also indicates that residues in binding interfaces were less well predicted in this set of targets than in previous Rounds, providing useful insights for directions of future improvements.

Assessment of chemical-crosslink-assisted protein structure modeling in CASP13

With the advance of experimental procedures obtaining chemical crosslinking information is becoming a fast and routine practice. Information on crosslinks can greatly enhance the accuracy of protein structure modeling. Here, we review the current state of the art in modeling protein structures with the assistance of experimentally determined chemical crosslinks within the framework of the 13th meeting of Critical Assessment of Structure Prediction approaches. This largest-to-date blind assessment reveals benefits of using data assistance in difficult to model protein structure prediction cases. However, in a broader context, it also suggests that with the unprecedented advance in accuracy to predict contacts in recent years, experimental crosslinks will be useful only if their specificity and accuracy further improved and they are better integrated into computational workflows.

Extension of the UNRES Coarse-Grained Force Field to Membrane Proteins in the Lipid Bilayer

The physics-based UNRES coarse-grained force field for the simulations of protein structure and dynamics has been extended to treat membrane proteins. The lipid bilayer has been modeled by introducing a continuous nonpolar phase with the water-interface region of appropriate thickness. The potentials for average electrostatic and correlation interactions of the peptide groups have been rescaled to account for the reduction of the dielectric permittivity compared to the water phase and new potentials for protein side-chain-side-chain interactions inside and across the lipid phase have been introduced. The model was implemented in the UNRES package for coarse-grained simulations of proteins, and the package with the new functionality was tested for total energy conservation and thermostat behavior in microcanonical and canonical molecular dynamics simulations runs, respectively. The method was validated by running unrestricted ab initio blind-prediction tests of 10 short α-helical membrane proteins, all runs started from the extended structures. The modified UNRES force field was able to predict correctly the overall folds of the membrane proteins studied.

Evaluation of the scale-consistent UNRES force field in template-free prediction of protein structures in the CASP13 experiment

The recent NEWCT-9P version of the coarse-grained UNRES force field for proteins, with scale-consistent formulas for the local and correlation terms, has been tested in the CASP13 experiment of the blind-prediction of protein structure, in the ab initio, contact-assisted, and data-assisted modes. Significant improvement of the performance has been observed with respect to the CASP11 and CASP12 experiments (by over 10 GDT_TS units for the ab initio mode predictions and by over 15 GDT_TS units for the contact-assisted prediction, respectively), which is a result of introducing scale-consistent terms and improved handling of contact-distance restraints. As in previous CASP exercises, UNRES ranked higher in the free modeling category than in the general category that included template based modeling targets. Use of distance restraints from the predicted contacts, albeit many of them were wrong, resulted in the increase of GDT_TS by over 8 units on average and introducing sparse restraints from small-angle X-ray/neutron scattering and chemical cross-link-mass-spectrometry experiments, and ambiguous restraints from nuclear magnetic resonance experiments has also improved the predictions by 8.6, 9.7, and 10.7 GDT_TS units on average, respectively.

Introduction of Phosphorylated Residues into the UNRES Coarse-Grained Model: Toward Modeling of Signaling Processes

Phosphorylated proteins take part in many signaling pathways and play a key role in homeostasis regulation. The all-atom force fields enable us to study the systems containing phosphorylated proteins, but they are limited to short time scales. In this paper, we report the extension of the physics-based coarse-grained UNRES force field to treat systems with phosphorylated amino-acid residues. To derive the respective potentials, appropriate physics-based analytical expressions were fitted to the potentials of mean force of systems modeling phosphorylated amino-acid residues computed in our previous work and implemented in UNRES. The extended UNRES performed well in ab initio simulations of two miniproteins containing phosphorylated residues, strongly suggesting that realistic large-scale simulations of processes involving phosphorylated proteins, especially signaling processes, are now possible.

Introduction of a bounded penalty function in contact-assisted simulations of protein structures to omit false restraints

Contact-assisted simulations, the contacts being predicted or determined experimentally, have become very important in the determination of the structures of proteins and other biological macromolecules. In this work, the effect of contact-distance restraints on the simulated structures was investigated with the use of multiplexed replica exchange simulations with the coarse-grained UNRES force field. A modified bounded flat-bottom restraint function that does not generate a gradient when a restraint cannot be satisfied was implemented. Calculations were run with (i) a set of four small proteins, with contact restraints derived from experimental structures, and (ii) selected CASP11 and CASP12 targets, with restraints as used at prediction time. The bounded penalty function largely omitted false contacts, which were usually inconsistent. It was found that at least 20% of correct contacts must be present in the restraint set to improve model quality with respect to unrestrained simulations. © 2019 Wiley Periodicals, Inc.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. III. Determination of scale-consistent backbone-local and correlation potentials in the UNRES force field and force-field calibration and validation

The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures.

The molecular mechanism of structural changes in the antimicrobial peptide CM15 upon complex formation with drug molecule suramin: a computational analysis

Stabilization of helical conformations of CM15 upon interactions with suramin.

Reoptimized UNRES Potential for Protein Model Quality Assessment

Ranking protein structure models is an elusive problem in bioinformatics. These models are evaluated on both the degree of similarity to the native structure and the folding pathway. Here, we simulated the use of the coarse-grained UNited RESidue (UNRES) force field as a tool to choose the best protein structure models for a given protein sequence among a pool of candidate models, using server data from the CASP11 experiment. Because the original UNRES was optimized for Molecular Dynamics simulations, we reoptimized UNRES using a deep feed-forward neural network, and we show that introducing additional descriptive features can produce better results. Overall, we found that the reoptimized UNRES performs better in selecting the best structures and tracking protein unwinding from its native state. We also found a relatively poor correlation between UNRES values and the model’s Template Modeling Score (TMS). This is remedied by reoptimization. We discuss some cases where our reoptimization procedure is useful.

A new protein nucleic-acid coarse-grained force field based on the UNRES and NARES-2P force fields

Based on the coarse-grained UNRES and NARES-2P models of proteins and nucleic acids, respectively, developed in our laboratory, in this work we have developed a coarse-grained model of systems containing proteins and nucleic acids. The UNRES and NARES-2P effective energy functions have been applied to the protein and nucleic-acid components of a system, respectively, while protein-nucleic-acid interactions have been described by the respective coarse-grained potentials developed in our recent work (Yin et al., J. Chem Theory Comput. 2015, 11, 1792). The Debye-Hückel screening has been applied to the electrostatic-interaction energy between the phosphate groups and charged amino-acid side chains. The model has been integrated into the UNRES package for coarse-grained molecular dynamics simulations of proteins and the implementation has been tested for energy conservation in microcanonical molecular dynamics runs and for temperature conservation in canonical molecular dynamics runs. Two case studies were performed: (i) the dynamics of the Ku protein heterodimer bound to DNA, for which it was found that the Ku70/Ku80 protein complex plays an active role in DNA repairing and (ii) conformational changes of the multiple antibiotic resistance (MarA) protein occurring during DNA binding, for which the functionally important motions occurring during this process were identified. © 2018 Wiley Periodicals, Inc.

Protein-Ligand Interaction Energy-Based Entropy Calculations: Fundamental Challenges For Flexible Systems

Entropy calculations represent one of the most challenging steps in obtaining the binding free energy in biomolecular systems. A novel computationally effective approach (IE) was recently proposed to calculate the entropy based on the computation of protein-ligand interaction energy directly from molecular dynamics (MD) simulations. We present a study focused on the application of this method to flexible molecular systems and compare its performance with well-established normal mode (NM) and quasiharmonic (QH) entropy calculation approaches. Our results demonstrated that the IE method is intended for calculating entropy change for binding partners in fixed conformations, as by the original definition of IE, and is not applicable to the molecular complexes in which the interacting partners undergo significant conformational changes during the binding process.

Insights into the structure and dynamics of lysyl oxidase propeptide, a flexible protein with numerous partners

Lysyl oxidase (LOX) catalyzes the oxidative deamination of lysine and hydroxylysine residues in collagens and elastin, which is the first step of the cross-linking of these extracellular matrix proteins. It is secreted as a proenzyme activated by bone morphogenetic protein-1, which releases the LOX catalytic domain and its bioactive N-terminal propeptide. We characterized the recombinant human propeptide by circular dichroism, dynamic light scattering, and small-angle X-ray scattering (SAXS), and showed that it is elongated, monomeric, disordered and flexible (D_max: 11.7 nm, R_g: 3.7 nm). We generated 3D models of the propeptide by coarse-grained molecular dynamics simulations restrained by SAXS data, which were used for docking experiments. Furthermore, we have identified 17 new binding partners of the propeptide by label-free assays. They include four glycosaminoglycans (hyaluronan, chondroitin, dermatan and heparan sulfate), collagen I, cross-linking and proteolytic enzymes (lysyl oxidase-like 2, transglutaminase-2, matrix metalloproteinase-2), a proteoglycan (fibromodulin), one growth factor (Epidermal Growth Factor, EGF), and one membrane protein (tumor endothelial marker-8). This suggests new roles for the propeptide in EGF signaling pathway.

Prediction of DNA and RNA structure with the NARES-2P force field and conformational space annealing

A physics-based method for the prediction of the structures of nucleic acids, which is based on the physics-based 2-bead NARES-2P model of polynucleotides and global-optimization Conformational Space Annealing (CSA) algorithm has been proposed. The target structure is sought as the global-energy-minimum structure, which ignores the entropy component of the free energy but spares expensive multicanonical simulations necessary to find the conformational ensemble with the lowest free energy. The CSA algorithm has been modified to optimize its performance when treating both single and multi-chain nucleic acids. It was shown that the method finds the native fold for simple RNA molecules and DNA duplexes and with limited distance restraints, which can easily be obtained from the secondary-structure-prediction servers, complex RNA folds can be treated with using moderate computer resources.

UNRES server for physics-based coarse-grained simulations and prediction of protein structure, dynamics and thermodynamics

A server implementation of the UNRES package (http://www.unres.pl) for coarse-grained simulations of protein structures with the physics-based UNRES model, coined a name UNRES server, is presented. In contrast to most of the protein coarse-grained models, owing to its physics-based origin, the UNRES force field can be used in simulations, including those aimed at protein-structure prediction, without ancillary information from structural databases; however, the implementation includes the possibility of using restraints. Local energy minimization, canonical molecular dynamics simulations, replica exchange and multiplexed replica exchange molecular dynamics simulations can be run with the current UNRES server; the latter are suitable for protein-structure prediction. The user-supplied input includes protein sequence and, optionally, restraints from secondary-structure prediction or small x-ray scattering data, and simulation type and parameters which are selected or typed in. Oligomeric proteins, as well as those containing D-amino-acid residues and disulfide links can be treated. The output is displayed graphically (minimized structures, trajectories, final models, analysis of trajectory/ensembles); however, all output files can be downloaded by the user. The UNRES server can be freely accessed at http://unres-server.chem.ug.edu.pl.

An analysis and evaluation of the WeFold collaborative for protein structure prediction and its pipelines in CASP11 and CASP12

Every two years groups worldwide participate in the Critical Assessment of Protein Structure Prediction (CASP) experiment to blindly test the strengths and weaknesses of their computational methods. CASP has significantly advanced the field but many hurdles still remain, which may require new ideas and collaborations. In 2012 a web-based effort called WeFold, was initiated to promote collaboration within the CASP community and attract researchers from other fields to contribute new ideas to CASP. Members of the WeFold coopetition (cooperation and competition) participated in CASP as individual teams, but also shared components of their methods to create hybrid pipelines and actively contributed to this effort. We assert that the scale and diversity of integrative prediction pipelines could not have been achieved by any individual lab or even by any collaboration among a few partners. The models contributed by the participating groups and generated by the pipelines are publicly available at the WeFold website providing a wealth of data that remains to be tapped. Here, we analyze the results of the 2014 and 2016 pipelines showing improvements according to the CASP assessment as well as areas that require further adjustments and research.

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°.

Prediction of protein structure with the coarse-grained UNRES force field assisted by small X-ray scattering data and knowledge-based information

A new approach to assisted protein-structure prediction has been proposed, which is based on running multiplexed replica exchange molecular dynamics simulations with the coarse-grained UNRES force field with restraints derived from knowledge-based models and distance distribution from small angle X-ray scattering (SAXS) measurements. The latter restraints are incorporated into the target function as a maximum-likelihood term that guides the shape of the simulated structures towards that defined by SAXS. The approach was first verified with the 1KOY protein, for which the distance distribution was calculated from the experimental structure, and subsequently used to predict the structures of 11 data-assisted targets in the CASP12 experiment. Major improvement of the GDT_TS was obtained for 2 targets, minor improvement for other 2 while, for 6 target GDT_TS deteriorated compared with that calculated for predictions without the SAXS data, partly because of assuming a wrong multimeric state (for Ts866) or because the crystal conformation was more compact than the solution conformation (for Ts942). Particularly good results were obtained for Ts909, in which use of SAXS data resulted in the selection of a correctly packed trimer and, subsequently, increased the GDT_TS of monomer prediction. It was found that running simulations with correct oligomeric state is essential for the success in SAXS-data-assisted prediction.