Dynamic Formation and Breaking of Disulfide Bonds in Molecular Dynamics Simulations with the UNRES Force Field

Integrating Explicit and Implicit Fullerene Models into UNRES Force Field for Protein Interaction Studies

Fullerenes, particularly C60, exhibit unique properties that make them promising candidates for various applications, including drug delivery and nanomedicine. However, their interactions with biomolecules, especially proteins, remain not fully understood. This study implements both explicit and implicit C60 models into the UNRES coarse-grained force field, enabling the investigation of fullerene-protein interactions without the need for restraints to stabilize protein structures. The UNRES force field offers computational efficiency, allowing for longer timescale simulations while maintaining accuracy. Five model proteins were studied: FK506 binding protein, HIV-1 protease, intestinal fatty acid binding protein, PCB-binding protein, and hen egg-white lysozyme. Molecular dynamics simulations were performed with and without C60 to assess protein stability and investigate the impact of fullerene interactions. Analysis of contact probabilities reveals distinct interaction patterns for each protein. FK506 binding protein (1FKF) shows specific binding sites, while intestinal fatty acid binding protein (1ICN) and uteroglobin (1UTR) exhibit more generalized interactions. The explicit C60 model shows good agreement with all-atom simulations in predicting protein flexibility, the position of C60 in the binding pocket, and the estimation of effective binding energies. The integration of explicit and implicit C60 models into the UNRES force field, coupled with recent advances in coarse-grained modeling and multiscale approaches, provides a powerful framework for investigating protein-nanoparticle interactions at biologically relevant scales without the need to use restraints stabilizing the protein, thus allowing for large conformational changes to occur. These computational tools, in synergy with experimental techniques, can aid in understanding the mechanisms and consequences of nanoparticle-biomolecule interactions, guiding the design of nanomaterials for biomedical applications.

Free-Docking and Template-Based Docking: Physics Versus Knowledge-Based Docking

Docking methods can be used to predict the orientations of two or more molecules with respect of each other using a plethora of various algorithms, which can be based on the physics of interactions or can use information from databases and templates. The usability of these approaches depends on the type and size of the molecules, whose relative orientation will be estimated. The two most important limitations are (i) the computational cost of the prediction and (ii) the availability of the structural information for similar complexes. In general, if there is enough information about similar systems, knowledge-based and template-based methods can significantly reduce the computational cost while providing high accuracy of the prediction. However, if the information about the system topology and interactions between its partners is scarce, physics-based methods are more reliable or even the only choice. In this chapter, knowledge-, template-, and physics-based methods will be compared and briefly discussed providing examples of their usability with a special emphasis on physics-based protein-protein, protein-peptide, and protein-fullerene docking in the UNRES coarse-grained model.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.

Cyclic cystine knot and its strong implication on the structure and dynamics of cyclotides

The archetypal Viola odorata cyclotide cycloviolacin-O1 and its seven analogs, created by partial or total reduction of the three native S-S linkages belonging to the "cyclic cystine knot" (CCK) motif are studied for their structural and dynamical diversities using molecular dynamics simulations. The results indicate interesting interplay between the constraints imposed by the S-S bonds on the dynamical modes and the corresponding structure of the model peptide. Principal component analysis brings out the variation in the extent of dynamical freedom along the peptide backbone for each model. The motions are characterized by low amplitude diffusive modes in the peptides retaining most of the native S-S linkages in contrast to the large amplitude discrete jumps where at least two or all of the three S-S linkages are reduced. Simulation results further indicate that the disulfide bond between Cys1-18 is formed at a much faster pace compared with its two other peers Cys5-20 and Cys10-25 as found in the native peptide. This gives insight as to why the S-S linkages appear in the native peptide in a particular combination. Model therapeutics and drug delivery engines can potentially utilize this information to customize the engineered S-S bonds and gauge its impact on the dynamic flexibility of a model macrocyclic peptide.

Improvements and new functionalities of UNRES server for coarse-grained modeling of protein structure, dynamics, and interactions

In this paper we report the improvements and extensions of the UNRES server (https://unres-server.chem.ug.edu.pl) for physics-based simulations with the coarse-grained UNRES model of polypeptide chains. The improvements include the replacement of the old code with the recently optimized one and adding the recent scale-consistent variant of the UNRES force field, which performs better in the modeling of proteins with the β and the α+β structures. The scope of applications of the package was extended to data-assisted simulations with restraints from nuclear magnetic resonance (NMR) and chemical crosslink mass-spectroscopy (XL-MS) measurements. NMR restraints can be input in the NMR Exchange Format (NEF), which has become a standard. Ambiguous NMR restraints are handled without expert intervention owing to a specially designed penalty function. The server can be used to run smaller jobs directly or to prepare input data to run larger production jobs by using standalone installations of UNRES.

Prediction of Aggregation of Biologically-Active Peptides with the UNRES Coarse-Grained Model

The UNited RESidue (UNRES) model of polypeptide chains was applied to study the association of 20 peptides with sizes ranging from 6 to 32 amino-acid residues. Twelve of those were potentially aggregating hexa- or heptapeptides excised from larger proteins, while the remaining eight contained potentially aggregating sequences, functionalized by attaching larger ends rich in charged residues. For 13 peptides, the experimental data of aggregation were used. The remaining seven were synthesized, and their properties were measured in this work. Multiplexed replica-exchange simulations of eight-chain systems were conducted at 12 temperatures from 260 to 370 K at concentrations from 0.421 to 5.78 mM, corresponding to the experimental conditions. The temperature profiles of the fractions of monomers and octamers showed a clear transition corresponding to aggregate dissociation. Low simulated transition temperatures were obtained for the peptides, which did not precipitate after incubation, as well as for the H-GNNQQNY-NH2 prion-protein fragment, which forms small fibrils. A substantial amount of inter-strand β-sheets was found in most of the systems. The results suggest that UNRES simulations can be used to assess peptide aggregation except for glutamine- and asparagine-rich peptides, for which a revision of the UNRES sidechain-sidechain interaction potentials appears necessary.

Mechanical Stability of Ribonuclease A Heavily Depends on the Redox Environment

Disulfide bonds are covalent bonds that connect nonlocal fragments of proteins, and they are unique post-translational modifications of proteins. They require the oxidizing environment to be stable, which occurs for example during oxidative stress; however, in a cell the reductive environment is maintained, lowering their stability. Despite many years of research on disulfide bonds, their role in the protein life cycle is not fully understood and seems to strictly depend on a system or process in which they are involved. In this article, coarse-grained UNited RESidue (UNRES), and all-atom Assisted Model Building with Energy Refinement (AMBER) force fields were applied to run a series of steered molecular dynamics (SMD) simulations of one of the most studied, but still not fully understood, proteins─ribonuclease A (RNase A). SMD simulations were performed to study the mechanical stability of RNase A in different oxidative-reductive environments. As disulfide bonds (and any other covalent bonds) cannot break/form in any classical all-atom force field, we applied additional restraints between sulfur atoms of reduced cysteines which were able to mimic the breaking of the disulfide bonds. On the other hand, the coarse-grained UNRES force field enables us to study the breaking/formation of the disulfide bonds and control the reducing/oxidizing environment owing to the presence of the designed distance/orientation-dependent potential. This study reveals that disulfide bonds have a strong influence on the mechanical stability of RNase A only in a highly oxidative environment. However, the local stability of the secondary structure seems to play a major factor in the overall stability of the protein. Both our thermal unfolding and mechanical stretching studies show that the most stable disulfide bond is Cys65-Cys72. The breaking of disulfide bonds Cys26-Cys84 and Cys58-Cys110 is associated with large force peaks. They are structural bridges, which are mostly responsible for stabilizing the RNase A conformation, while the presence of the remaining two bonds (Cys65-Cys72 and Cys40-Cys95) is most likely connected with the enzymatic activity rather than the structural stability of RNase A in the cytoplasm. Our results prove that disulfide bonds are indeed stabilizing fragments of the proteins, but their role is strongly redox environment-dependent.

Modeling and dynamical analysis of the full-length structure of factor XII with zinc

Zinc (II), the second most abundant transition metal in blood, binds to the initiator of the contact pathway, factor XII (FXII). This binding induces conformational changes in the structure of FXII eventually leading to its activation. Despite many in vitro and in vivo studies on zinc-mediated activation of FXII, its molecular mechanism remains elusive mainly due to absence of a full-length structural model of FXII. To this end, this study investigated the role of zinc in the structure and dynamics of the full-length structure FXII that was obtained through molecular modeling. We have used four structural templates covering more than 70% of the FXII sequence and the remaining interconnecting regions were built by loop modeling. The resulting full-length structure of FXII contained disordered regions, but in comparison to the AlphaFold (AF) prediction, our full-length model represented a more realistic structure because of the disordered regions which were modeled to yield a more compact full-length structure in our model than the AF structure. Other than the disordered regions, our model and AF prediction were highly similar. The resulting full-length FXII structure was used to generate different systems representing the zinc-bound form (holo). Further to assess the contribution of the disulfide bridges, we also analyzed the apo and holo FXII structures with oxidized or reduced cysteine side-chains. Simulations suggested zinc binding conferred rigidity to the structure, particularly to the light chain of FXII. Zinc binding alone was sufficient to limit the backbone flexibility while 15 disulfide bonds, which were scattered throughout the structure, made a less significant contribution to the backbone rigidity. Altogether our results provide insights into the first realistic full-length structure of FXII focusing on the impact of structural zinc and disulfide bridges in the dynamics of this structure.

Modeling the Structure, Dynamics, and Transformations of Proteins with the UNRES Force Field

The physics-based united-residue (UNRES) model of proteins ( www.unres.pl ) has been designed to carry out large-scale simulations of protein folding. The force field has been derived and parameterized based on the principles of statistical-mechanics, which makes it independent of structural databases and applicable to treat nonstandard situations such as, proteins that contain D-amino-acid residues. Powered by Langevin dynamics and its replica-exchange extensions, UNRES has found a variety of applications, including ab initio and database-assisted protein-structure prediction, simulating protein-folding pathways, exploring protein free-energy landscapes, and solving biological problems. This chapter provides a summary of UNRES and a guide for potential users regarding the application of the UNRES package in a variety of research tasks.

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

Extended disorder at the cell surface: The conformational landscape of the ectodomains of syndecans

Syndecans are membrane proteoglycans regulating extracellular matrix assembly, cell adhesion and signaling. Their ectodomains can be shed from the cell surface, and act as paracrine and autocrine effectors or as competitors of full-length syndecans. We report the first biophysical characterization of the recombinant ectodomains of the four human syndecans using biophysical techniques, and show that they behave like flexible random-coil intrinsically disordered proteins, and adopt several conformation ensembles in solution. We have characterized their conformational landscapes using native mass spectrometry (MS) and ion-mobility MS, and demonstrated that the syndecan ectodomains explore the majority of their conformational landscape, from minor compact, globular-like, conformations to extended ones. We also report that the ectodomain of syndecan-4, corresponding to a natural isoform, is able to dimerize via a disulfide bond. We have generated a three-dimensional model of the C-terminus of this dimer, which supports the dimerization via a disulfide bond. Furthermore, we have mapped the NXIP adhesion motif of syndecans and their sequences involved in the formation of ternary complexes with integrins and growth factor receptors on the major conformations of their ectodomains, and shown that these sequences are not accessible in all the conformations, suggesting that only some of them are biologically active. Lastly, although the syndecan ectodomains have a far lower number of amino acid residues than their membrane partners, their intrinsic disorder and flexibility allow them to adopt extended conformations, which have roughly the same size as the cell surface receptors (e.g., integrins and growth factor receptors) they bind to.

A molecular dynamics study of protein denaturation induced by sulfonate-based surfactants

Microsecond timescale explicit-solvent atomistic simulations were carried out to investigate how anionic surfactants modulate protein structure and dynamics. We found that lysozyme undergoes near-complete denaturation at the high concentration (> 0.1 M) of sodium pentadecyl sulfonate (SPDS), while only partial denaturation occurs at the concentration slightly below 0.1 M. In large part, protein denaturation is structurally manifested by disappearance of helical segments and loss of tertiary interactions. The computational prediction of the extent of burial of cysteine residues was experimentally validated by measuring the accessibility of the respective sulfhydryl groups. Overall, our work indicates an interesting synergy between electrostatic and hydrophobic contributions to lysozyme's denaturation process by anionic surfactants. In fact, first disulfide bridges and hydrogen bonds from protein surface to SPDS head groups loosen the protein globule followed by fuller denaturation via insertion of the surfactant's hydrophobic tails into the protein core.

Synthesis and Guest-Binding Properties of pH/Reduction Dual-Responsive Cyclophane Dimer

A water-soluble cyclophane dimer having two disulfide groups as a reduction-responsive cleavable bond as well as several acidic and basic functional groups as a pH-responsive ionizable group 1 was successfully synthesized. It was found that 1 showed pH-dependent guest-binding behavior. That is, 1 strongly bound an anionic guest, 6-p-toluidinonaphthalene-2-sulfonate (TNS) with binding constant (K/M⁻¹) for 1:1 host-guest complexes of 9.6 × 10⁴ M⁻¹ at pH 3.8, which was larger than those at pH 7.4 and 10.7 (6.0 × 10⁴ and 2.4 × 10⁴ M⁻¹, respectively), indicating a favorable electrostatic interaction between anionic guest and net cationic 1. What is more, release of the entrapped guest molecules by 1 was easily controlled by pH stimulus. Large favorable enthalpies (ΔH) for formation of host-guest complexes were obtained under the pH conditions employed, suggesting that electrostatic interaction between anionic TNS and 1 was the most important driving force for host-guest complexation. Such contributions of ΔH for formation of host-guest complexes decreased along with increased pH values from acidic to basic solutions. Upon addition of dithiothreitol (DTT) as a reducing reagent to an aqueous PBS buffer (pH 7.4) containing 1 and TNS, the fluorescence intensity originating from the bound guest molecules decreased gradually. A treatment of 1 with DTT gave 2, having less guest-binding affinity by the cleavage of disulfide bonds of 1. Consequently, almost all entrapped guest molecules by 1 were released from the host. Moreover, such reduction-responsive cleavage of 1 and release of bound guest molecules was performed more rapidly in aqueous buffer at pH 10.7.

Stimuli-Responsive Supramolecular Coaggregation and Disaggregation of Host-Guest Conjugates Having a Disulfide Linkage

Water-soluble cationic and anionic cyclophanes (1a and 2a, respectively) having a dabsyl group with a cleavable disulfide linkage were synthesized as a host-guest conjugate covalently bound with both host and guest components. Self-inclusion phenomena but not self-aggregation behaviors were observed for each cyclophane in aqueous media. Each cyclophane includes its own dabsyl moiety (guest component) in its macrocyclic cavity (host component) through hydrophobic interaction. When 1 equiv. of cationic 1a was added to an aqueous solution of anionic 2a, however, supramolecular coaggregates formed spontaneously through host-guest complexation. As regard the supramolecular coaggregates, the existence of larger particles was confirmed by DLS measurements and TEM observation. The hydrophobic interaction between the dabsyl moiety and macrocyclic cavity and electrostatic interactions between 1a and 2a play important roles in the supramolecular coaggregate formation. Each cyclophane having a cleavable disulfide linkage was easily transformed to the corresponding thiols by reducing reagents such as DTT, which was confirmed by MALDI-TOF MS. Disaggregation of the supramolecular coaggregates composed of 1a and 2a was successfully performed upon addition of DTT, with release of the thiol derivative of dabsyl. Such disaggregation of the coaggregates was also conducted by other external stimuli such as salts and competitive guests.

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.

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.

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.

Insights into the Folding of Disulfide-Rich μ-Conotoxins

The study of protein conformations using molecular dynamics (MD) simulations has been in place for decades. A major contribution to the structural stability and native conformation of a protein is made by the primary sequence and disulfide bonds formed during the folding process. Here, we investigated μ-conotoxins GIIIA, KIIIA, PIIIA, SIIIA, and SmIIIA as model peptides possessing three disulfide bonds. Their NMR structures were used for MD simulations in a novel approach studying the conformations between the folded and the unfolded states by systematically breaking the distinct disulfide bonds and monitoring the conformational stability of the peptides. As an outcome, the use of a combination of the existing knowledge and results from the simulations to classify the studied peptides within the extreme models of disulfide folding pathways, namely the bovine pancreatic trypsin inhibitor pathway and the hirudin pathway, is demonstrated. Recommendations for the design and synthesis of cysteine-rich peptides with a reduced number of disulfide bonds conclude the study.

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.

Simple MD-based model for oxidative folding of peptides and proteins

Significant strides have been recently made to fold peptides and small proteins in silico using MD simulations. However, facilities are currently lacking to include disulfide bonding in the MD models of protein folding. To address this problem, we have developed a simple empirical protocol to model formation of disulfides, which is perturbation-free, retains the same speed as conventional MD simulations and allows one to control the reaction rate. The new protocol has been tested on 15-aminoacid peptide guanylin containing four cysteine residues; the net simulation time using Amber ff14SB force field was 61 μs. The resulting isomer distribution is in qualitative agreement with experiment, suggesting that oxidative folding of guanylin in vitro occurs under kinetic control. The highly stable conformation of the so-called isomer 2(B) has been obtained for full-length guanylin, which is significantly different from the poorly ordered structure of the truncated peptide PDB ID 1GNB. In addition, we have simulated oxidative folding of guanylin within the 94-aminoacid prohormone proguanylin. The obtained structure is in good agreement with the NMR coordinates 1O8R. The proposed modeling strategy can help to explore certain fundamental aspects of protein folding and is potentially relevant for manufacturing of synthetic peptides and recombinant proteins.

Different dynamics and pathway of disulfide bonds reduction of two human defensins, a molecular dynamics simulation study

Human defensins are a class of antimicrobial peptides that are crucial components of the innate immune system. Both human α defensin type 5 (HD5) and human β defensin type 3 (hBD-3) have 6 cysteine residues which form 3 pairs of disulfide bonds in oxidizing condition. Disulfide bond linking is important to the protein structure stabilization, and the disulfide bond linking and breaking order have been shown to influence protein function. In this project, microsecond long molecular dynamics simulations were performed to study the structure and dynamics of HD5 and hBD-3 wildtype and analogs which have all 3 disulfide bonds released in reducing condition. The structure of hBD-3 was found to be more dynamic and flexible than HD5, based on RMSD, RMSF, and radius of gyration calculations. The disulfide bridge breaking order of HD5 and hBD-3 in reducing condition was predicted by two kinds of methods, which gave consistent results. It was found that the disulfide bonds breaking pathways for HD5 and hBD-3 are very different. The breaking of disulfide bonds can influence the dimer interface by making the dimer structure less stable for both kinds of defensin. In order to understand the difference in dynamics and disulfide bond breaking pathway, hydrophilic and hydrophobic accessible surface areas (ASA), buried surface area between cysteine pairs, entropy of cysteine pairs, and internal energy were calculated. Comparing to the wildtype, hBD-3 analog is more hydrophobic, while HD5 is more hydrophilic. For hBD-3, the disulfide breaking is mainly entropy driven, while other factors such as the solvation effects may take the major role in controlling HD5 disulfide breaking pathway. Proteins 2017; 85:665-681. © 2016 Wiley Periodicals, Inc.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

Protein folding guides disulfide bond formation

The Anfinsen principle that the protein sequence uniquely determines its structure is based on experiments on oxidative refolding of a protein with disulfide bonds. The problem of how protein folding drives disulfide bond formation is poorly understood. Here, we have solved this long-standing problem by creating a general method for implementing the chemistry of disulfide bond formation and rupture in coarse-grained molecular simulations. As a case study, we investigate the oxidative folding of bovine pancreatic trypsin inhibitor (BPTI). After confirming the experimental findings that the multiple routes to the folded state contain a network of states dominated by native disulfides, we show that the entropically unfavorable native single disulfide [14-38] between Cys14 and Cys38 forms only after polypeptide chain collapse and complete structuring of the central core of the protein containing an antiparallel β-sheet. Subsequent assembly, resulting in native two-disulfide bonds and the folded state, involves substantial unfolding of the protein and transient population of nonnative structures. The rate of [14-38] formation increases as the β-sheet stability increases. The flux to the native state, through a network of kinetically connected native-like intermediates, changes dramatically by altering the redox conditions. Disulfide bond formation between Cys residues not present in the native state are relevant only on the time scale of collapse of BPTI. The finding that formation of specific collapsed native-like structures guides efficient folding is applicable to a broad class of single-domain proteins, including enzyme-catalyzed disulfide proteins.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some 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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MOLECULAR DYNAMICS SIMULATIONS OF HELIX BUNDLE PROTEINS USING UNRES FORCE FIELD AND ALL-ATOM FORCE FIELD

We have investigated the folding of two helix-bundle proteins, 36-residue Villin headpiece and 56-residue E-domain of Staphylococcal protein A, by combining molecular dynamics (MD) simulations with Coarse-Grained United-Residue (UNRES) Force Field and all-atom force field. Starting from extended structures, each of the proteins was folded to a stable structure within a short time frame using the UNRES model. However, the secondary structures of helices were not well formed. Further refinement using MD simulations with the all-atom force field was able to fold the protein structure into the native-like state with the smallest main-chain root-mean-square deviation of around 3 Å. Detailed analysis of the folding trajectories was presented and the performance of GPU-based MD simulations was also discussed.

Detailed structural and assembly model of the type II secretion pilus from sparse data

Many gram-negative bacteria secrete specific proteins via the type II secretion systems (T2SS). These complex machineries share with the related archaeal flagella and type IV pilus (T4P) biogenesis systems the ability to assemble thin, flexible filaments composed of small, initially inner membrane-localized proteins called "pilins." In the T2SS from Klebsiella oxytoca, periplasmic pseudopili that are essential for pullulanase (PulA) secretion extend beyond the bacterial surface and form pili when the major pilin PulG is overproduced. Here, we describe the detailed, experimentally validated structure of the PulG pilus generated from crystallographic and electron microscopy data by a molecular modeling approach. Two intermolecular salt bridges crucial for function were demonstrated using single and complementary charge inversions. Double-cysteine substitutions in the transmembrane segment of PulG led to position-specific cross-linking of protomers in assembled pili. These biochemical data provided information on residue distances in the filament that were used to derive a refined model of the T2SS pilus at pseudoatomic resolution. PulG is organized as a right-handed helix of subunits, consistent with protomer organization in gonococcal T4P. The conserved character of residues involved in key hydrophobic and electrostatic interactions within the major pseudopilin family supports the general relevance of this model for T2SS pseudopilus structure.

Determination of side-chain-rotamer and side-chain and backbone virtual-bond-stretching potentials of mean force from AM1 energy surfaces of terminally-blocked amino-acid residues, for coarse-grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics-based side-chain-rotamer and virtual-bond-deformation potentials which now replace the respective statistical potentials used so far in our physics-based united-reside UNRES force field for large-scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally-blocked amino-acid residues calculated with the AM1 quantum-mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles lambda for rotation of the peptide groups about the C(alpha)...C(alpha) virtual bonds, and for fixed values of the side-chain dihedral angles chi, which formed a multidimensional grid. A harmonic-approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC-calculated surfaces but the harmonic-approximation- and MC-calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force-field optimization for foldability.

Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field

Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .

An improved functional form for the temperature scaling factors of the components of the mesoscopic UNRES force field for simulations of protein structure and dynamics

Coarse-grained or mesoscopic models of proteins and the corresponding force fields are of great importance because they enable us to reduce the folding simulation time by several orders of magnitude compared to the all-atom approach and, consequently, reach the millisecond time scale of simulations. In the coarse-grained UNRES model for simulations of protein structure and dynamics, developed by our group, each amino acid residue is represented by a united side chain and a united peptide group located in the middle between the two neighboring alpha-carbon atoms, which assist only in the definition of the geometry. The prototype of the UNRES force field has been defined as a potential of mean force or restricted free-energy function corresponding to averaging out the degrees of freedom not present in the coarse-grained representation, which has further been approximated by a truncated Kubo cumulant series to enable us to derive analytical expressions for the corresponding terms. This force field should depend on temperature, and in its simplest form, a term corresponding to the cumulant of order n should be multiplied by f(n) = 1/T(n-1). The temperature dependence has been introduced in recent work ( J. Phys. Chem. B , 2007 , 111 , 260 - 285 ), and in order to prevent too steep a variation with temperature, the factors at the nth order cumulant terms were assumed to have a form f(n) = ln[exp(1) + exp(-1)]/ln{exp[(T/T(0))(n-1)] + exp[-(T/T(0))(n-1)]}, where T(0) = 300 K is the reference temperature. In this work, we have introduced a modified scaling factor f(n) = ln[exp(c) + exp(-c)]/ln{exp[c(T/T(0))(n-1)] + exp[-c(T/T(0))(n-1)]}, where c is an adjustable parameter, and determined c by fitting the analytical approximation of the temperature dependence of the virtual bond torsional term corresponding to rotation about the C(alpha)...C(alpha) virtual bond in terminally blocked dialanine to the respective potential of mean force calculated from the MP2/6-31G(d, p) ab initio energy surfaces of terminally blocked alanine (Ac-Ala-NHMe) and, independently, by optimizing it to obtain a sharp heat capacity curve and the lowest ensemble-averaged root-mean-square deviation over the C(alpha) atoms of 1GAB used as a training protein. Both approaches gave consistent results, and c = 1.4 has been selected as the optimal value of this parameter. The force field with the new temperature scaling factors has been optimized using 1GAB as the training protein. The new force field has been tested on a series of medium size alpha-helical proteins and found to perform better than that with the original temperature scaling factors.

Dynamic redox environment-intensified disulfide bond shuffling for protein refolding in vitro: molecular simulation and experimental validation

One challenge in protein refolding is to dissociate the non-native disulfide bonds and promote the formation of native ones. In this study, we present a coarse-grained off-lattice model protein containing disulfide bonds and simulate disulfide bond shuffling during the folding of this model protein. Introduction of disulfide bonds in the model protein led to enhanced conformational stability but reduced foldability in comparison to counterpart protein without disulfide bonds. The folding trajectory suggested that the model protein retained the two-step folding mechanism in terms of hydrophobic collapse and structural rearrangement. The disulfide bonds located in the hydrophobic core were formed before the collapsing step, while the bonds located on the protein surface were formed during the rearrangement step. While a reductive environment at the initial stage of folding favored the formation of native disulfide bonds in the hydrophobic core, an oxidative environment at a later stage of folding was required for the formation of disulfide bonds at protein surface. Appling a dynamic redox environment, that is, one that changes from reductive to oxidative, intensified disulfide bond shuffling and thus resulted in improved recovery of the native conformation. The above-mentioned simulation was experimentally validated by refolding hen-egg lysozyme at different urea concentrations and oxidized glutathione/reduced glutathione (GSSG/GSH) ratios, and an optimal redox environment, in terms of the GSSG to GSH ratio, was identified. The implementation of a dynamic redox environment by tuning the GSSG/GSH ratio further improved the refolding yield of lysozyme, as predicted by molecular simulation.

Application of Multiplexed Replica Exchange Molecular Dynamics to the UNRES Force Field: Tests with alpha and alpha+beta Proteins

The replica exchange (RE) method is increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. Recently, we implemented the united-residue UNRES force field for mesoscopic MD. Initial results from UNRES MD simulations show that we are able to simulate folding events that take place in a microsecond or even a millisecond time scale. To speed up the search further, we applied the multiplexing replica exchange molecular dynamics (MREMD) method. The multiplexed variant (MREMD) of the RE method, developed by Rhee and Pande, differs from the original RE method in that several trajectories are run at a given temperature. Each set of trajectories run at a different temperature constitutes a layer. Exchanges are attempted not only within a single layer but also between layers. The code has been parallelized and scales up to 4000 processors. We present a comparison of canonical MD, REMD, and MREMD simulations of protein folding with the UNRES force-field. We demonstrate that the multiplexed procedure increases the power of replica exchange MD considerably and convergence of the thermodynamic quantities is achieved much faster.

Implementations of Nosé-Hoover and Nosé-Poincaré thermostats in mesoscopic dynamic simulations with the united-residue model of a polypeptide chain

Molecular dynamics (MD) simulations generate a canonical ensemble only when integration of the equations of motion is coupled to a thermostat. Three extended phase space thermostats, one version of Nose-Hoover and two versions of Nose-Poincare, are compared with each other and with the Berendsen thermostat and Langevin stochastic dynamics. Implementation of extended phase space thermostats was first tested on a model Lennard-Jones fluid system; subsequently, they were implemented with our physics-based protein united-residue (UNRES) force field MD. The thermostats were also implemented and tested for the multiple-time-step reversible reference system propagator (RESPA). The velocity and temperature distributions were analyzed to confirm that the proper canonical distribution is generated by each simulation. The value of the artificial mass constant, Q, of the thermostat has a large influence on the distribution of the temperatures sampled during UNRES simulations (the velocity distributions were affected only slightly). The numerical stabilities of all three algorithms were compared with each other and with that of microcanonical MD. Both Nose-Poincare thermostats, which are symplectic, were not very stable for both the Lennard-Jones fluid and UNRES MD simulations started from nonequilibrated structures which implies major changes of the potential energy throughout a trajectory. Even though the Nose-Hoover thermostat does not have a canonical symplectic structure, it is the most stable algorithm for UNRES MD simulations. For UNRES with RESPA, the "extended system inside-reference system propagator algorithm" of the RESPA implementation of the Nose-Hoover thermostat was the only stable algorithm, and enabled us to increase the integration time step.

Implementation of a Serial Replica Exchange Method in a Physics-Based United-Residue (UNRES) Force Field

The kinetic-trapping problem in simulating protein folding can be overcome by using a Replica Exchange Method (REM). However, in implementing REM in molecular dynamics simulations, synchronization between processors on parallel computers is required, and communication between processors limits its ability to sample conformational space in a complex system efficiently. To minimize communication between processors during the simulation, a Serial Replica Exchange Method (SREM) has been proposed recently by Hagan et al. (J. Phys. Chem. B2007, 111, 1416-1423). Here, we report the implementation of this new SREM algorithm with our physics-based united-residue (UNRES) force field. The method has been tested on the protein 1E0L with a temperature-independent UNRES force field and on terminally blocked deca-alanine (Ala(10)) and 1GAB with the recently introduced temperature-dependent UNRES force field. With the temperature-independent force field, SREM reproduces the results of REM but is more efficient in terms of wall-clock time and scales better on distributed-memory machines. However, exact application of SREM to the temperature-dependent UNRES algorithm requires the determination of a four-dimensional distribution of UNRES energy components instead of a one-dimensional energy distribution for each temperature, which is prohibitively expensive. Hence, we assumed that the temperature dependence of the force field can be ignored for neighboring temperatures. This version of SREM worked for Ala(10) which is a simple system but failed to reproduce the thermodynamic results as well as regular REM on the more complex 1GAB protein. Hence, SREM can be applied to the temperature-independent but not to the temperature-dependent UNRES force field.