The role of atomic level steric effects and attractive forces in protein folding

Protein folding into tertiary structures is controlled by an interplay of attractive contact interactions and steric effects. We investigate the balance between these contributions using structure‐based models using an all‐atom representation of the structure combined with a coarse‐grained contact potential. Tertiary contact interactions between atoms are collected into a single broad attractive well between the C^β atoms between each residue pair in a native contact. Through the width of these contact potentials we control their tolerance for deviations from the ideal structure and the spatial range of attractive interactions. In the compact native state dominant packing constraints limit the effects of a coarse‐grained contact potential. During folding, however, the broad attractive potentials allow an early collapse that starts before the native local structure is completely adopted. As a consequence the folding transition is broadened and the free energy barrier is decreased. Eventually two‐state folding behavior is lost completely for systems with very broad attractive potentials. The stabilization of native‐like residue interactions in non‐perfect geometries early in the folding process frequently leads to structural traps. Global mirror images are a notable example. These traps are penalized by the details of the repulsive interactions only after further collapse. Successful folding to the native state requires simultaneous guidance from both attractive and repulsive interactions. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Designing cooperativity into the designed protein Top7

The topology of the designed protein Top7 is not found in natural proteins. Top7 shows signatures of non‐cooperative folding in both experimental studies and computer simulations. In particular, molecular dynamics of coarse‐grained structure‐based models of Top7 show a well‐populated C‐terminal folding‐intermediate. Since most similarly sized globular proteins are cooperative folders, the non‐natural topology of Top7 has been suggested as a reason for its non‐cooperative folding. Here, we computationally examine the folding of Top7 with the intent of making it cooperative. We find that its folding cooperativity can be increased in two ways: (a) Optimization of packing interactions in the N‐terminal half of the protein enables further folding of the C‐terminal intermediate. (b) Reduction in the packing density of the C‐terminal region destabilizes the intermediate. In practice, these strategies are implemented in our Top7 model through modifications to the contact‐map. These modifications do not alter the topology of Top7 but result in cooperative folding. Amino‐acid mutations that mimic these modifications also lead to a significant increase in folding cooperativity. Finally, we devise a method to randomize the sizes of amino‐acids within the same topology, and confirm that the structure of Top7 makes its folding sensitive to packing interactions. In contrast, the ribosomal protein S6, which has secondary structure similar to Top7, has folding which is much less sensitive to packing perturbations. Thus, it should be possible to make a sequence fold cooperatively to the structure of Top7, but to do so its side‐chain packing needs to be carefully designed. Proteins 2014; 82:364–374. © 2013 Wiley Periodicals, Inc.     

Analyses of the folding properties of ferredoxin‐like fold proteins by means of a coarse‐grained Gō model: Relationship between the free energy profiles and folding cores

The folding mechanisms of proteins with multi‐state transitions, the role of the intermediate states, and the precise mechanism how each transition occurs are significant on‐going research issues. In this study, we investigate ferredoxin‐like fold proteins which have a simple topology and multi‐state transitions. We analyze the folding processes by means of a coarse‐grained Gō model. We are able to reproduce the differences in the folding mechanisms between U1A, which has a high‐free‐energy intermediate state, and ADA2h and S6, which fold into the native structure through two‐state transitions. The folding pathways of U1A, ADA2h, S6, and the S6 circular permutant, S6_p54‐55, are reproduced and compared with experimental observations. We show that the ferredoxin‐like fold contains two common regions consisting folding cores as predicted in other studies and that U1A produces an intermediate state due to the distinct cooperative folding of each core. However, because one of the cores of S6 loses its cooperativity and the two cores of ADA2h are tightly coupled, these proteins fold into the native structure through a two‐state mechanism. Proteins 2014; 82:954–965. © 2013 Wiley Periodicals, Inc.     

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C_α structure‐based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well‐separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non‐native contact interactions in different folding scenarios. These findings strongly correlate with the protein free‐energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.Proteins 2013; 81:1727–1737. © 2013 Wiley Periodicals, Inc.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Folding of tandem-linked domains

One of the factors, which influences protein folding in vivo, is a linkage of protein domains into multidomain tandems. However, relatively little is known about the impact of domain connectivity on protein folding mechanisms. In this article, we use coarse grained models of proteins to explore folding of tandem-linked domains (TLD). We found TLD folding to follow two scenarios. In the first, the tandem connectivity produces relatively minor impact on folding and the mechanisms of folding of tandem-linked and single domains remain similar. The second scenario involves qualitative changes in folding mechanism because of tandem linkage. As a result, protein domains, which fold via two-state mechanism as single isolated domains, may form new stable intermediates when inserted into tandems. The new intermediates are created by topological constraints imposed by the linkers between domains. In both cases tandem linkage slows down folding. We propose that the impact of tandem connectivity can be minimized, if the terminal secondary structure elements (SSEs) are flexible. In particular, two factors appear to facilitate TLD folding: (1) the interactions between terminal SSE are poorly ordered in the folding transition state, whereas nonterminal SSE are better structured, (2) the interactions between terminal SSE are weak in the native state. We apply these findings to wild-type proteins by examining experimental phi-value data and by performing all-atom molecular dynamics simulations. We show that immunoglobulin-like domains appear to utilize the factors, which minimize the impact of tandem connectivity on their folding. Several single domain proteins, which are likely to misfold in tandems, are also identified.     

Coarse‐ and fine‐grained models for proteins: Evaluation by decoy discrimination

Coarse‐grained models for protein structure are increasingly used in simulations and structural bioinformatics. In this study, we evaluated the effectiveness of three granularities of protein representation based on their ability to discriminate between correctly folded native structures and incorrectly folded decoy structures. The three levels of representation used one bead per amino acid (coarse), two beads per amino acid (medium), and all atoms (fine). Multiple structure features were compared at each representation level including two‐body interactions, three‐body interactions, solvent exposure, contact numbers, and angle bending. In most cases, the all‐atom level was most successful at discriminating decoys, but the two‐bead level provided a good compromise between the number of model parameters which must be estimated and the accuracy achieved. The most effective feature type appeared to be two‐body interactions. Considering three‐body interactions increased accuracy only marginally when all atoms were used and not at all in medium and coarse representations. Though two‐body interactions were most effective for the coarse representations, the accuracy loss for using only solvent exposure or contact number was proportionally less at these levels than in the all‐atom representation. We propose an optimization method capable of selecting bead types of different granularities to create a mixed representation of the protein. We illustrate its behavior on decoy discrimination and discuss implications for data‐driven protein model selection. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

A comparative analysis of the equilibrium dynamics of a designed protein inferred from NMR,X‐ray,and computations

A detailed analysis of high‐resolution structural data and computationally predicted dynamics was carried out for a designed sugar‐binding protein. The mean‐square deviations in the positions of residues derived from nuclear magnetic resonance (NMR) models and those inferred from X‐ray crystallographic B‐factors for two different crystal forms were compared with the predictions based on the Gaussian Network Model (GNM) and the results from molecular dynamics (MD) simulations. GNM systematically yielded a higher correlation than MD, with experimental data, suggesting that the lack of atomistic details in the coarse‐grained GNM is more than compensated for by the mathematically exact evaluation of fluctuations using the native contacts topology. Evidence is provided that particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments. Interestingly, the information conveyed by X‐ray crystallography becomes more consistent with NMR models and computational predictions when ensembles of X‐ray models are considered. Less precise (broadly distributed) ensembles indeed appear to describe the accessible conformational space under native state conditions better than B‐factors. Our results highlight the importance of using multiple conformations obtained by alternative experimental methods, and analyzing results from both coarse‐grained models and atomic simulations, for accurate assessment of motions accessible to proteins under native state conditions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Protein folding pathways and kinetics: molecular dynamics simulations of beta-strand motifs

The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R(2)(g), the fraction of native contacts within the protein as a whole Q, and between specific strands Q(ab). In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the beta-strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.     

Non-native interactions play an effective role in protein folding dynamics

Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non‐native contacts. Furthermore, strong evidence for a positive role played by non‐native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two‐state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.     

Incorporating into a Cα Go model the effects of geometrical restriction on Cα atoms caused by side chain orientations

Coarse‐grained Go models have been widely used for studying protein‐folding mechanisms. Despite the simplicity of the model, these can reproduce the essential features of the folding process of a protein. However, it is also known that side chains significantly contribute to the folding mechanism. Hence, it is desirable to incorporate the side chain effects into a coarse‐grained Go model. In this study, to distinguish the effects of side chain orientation and to understand how these effects contribute to folding mechanisms, we incorporate into a Cα Go model not only heterogeneous contact energies but also geometrical restraints around two Cα atoms in contact with each other. We confirm that the heterogeneity of contact energies governs the folding pathway of a protein and that the geometric constraints attributed to side chains reproduce cooperative transitions in folding. Proteins 2013; 81:1434–1445. © 2013 Wiley Periodicals, Inc.     

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.     

Simulating protein folding initiation sites using an alpha‐carbon‐only knowledge‐based force field

Protein folding is a hierarchical process where structure forms locally first, then globally. Some short sequence segments initiate folding through strong structural preferences that are independent of their three‐dimensional context in proteins. We have constructed a knowledge‐based force field in which the energy functions are conditional on local sequence patterns, as expressed in the hidden Markov model for local structure (HMMSTR). Carbon‐alpha force field (CALF) builds sequence specific statistical potentials based on database frequencies for α‐carbon virtual bond opening and dihedral angles, pair‐wise contacts and hydrogen bond donor‐acceptor pairs, and simulates folding via Brownian dynamics. We introduce hydrogen bond donor and acceptor potentials as α‐carbon probability fields that are conditional on the predicted local sequence. Constant temperature simulations were carried out using 27 peptides selected as putative folding initiation sites, each 12 residues in length, representing several different local structure motifs. Each 0.6 μs trajectory was clustered based on structure. Simulation convergence or representativeness was assessed by subdividing trajectories and comparing clusters. For 21 of the 27 sequences, the largest cluster made up more than half of the total trajectory. Of these 21 sequences, 14 had cluster centers that were at most 2.6 Å root mean square deviation (RMSD) from their native structure in the corresponding full‐length protein. To assess the adequacy of the energy function on nonlocal interactions, 11 full length native structures were relaxed using Brownian dynamics simulations. Equilibrated structures deviated from their native states but retained their overall topology and compactness. A simple potential that folds proteins locally and stabilizes proteins globally may enable a more realistic understanding of hierarchical folding pathways. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

All‐atom and coarse‐grained simulations of the forced unfolding pathways of the SNARE complex

The SNARE complex, consisting of three proteins (VAMP2, syntaxin, and SNAP‐25), is thought to drive membrane fusion by assembling into a four‐helix bundle through a zippering process. In support of the above zippering model, a recent single‐molecule optical tweezers experiment by Gao et al. revealed a sequential unzipping of SNARE along VAMP2 in the order of the linker domain → the C‐terminal domain → the N‐terminal domain. To offer detailed structural insights to this unzipping process, we have performed all‐atom and coarse‐grained steered molecular dynamics (sMD) simulations of the forced unfolding pathways of SNARE using different models and force fields. Our findings are summarized as follows: First, the sMD simulations based on either an all‐atom force field (with an implicit solvent model) or a coarse‐grained Go model were unable to capture the forced unfolding pathway of SNARE as observed by Gao et al., which may be attributed to insufficient simulation time and inaccurate force fields. Second, the sMD simulations based on a reparameterized coarse‐grained model (i.e., modified elastic network model) were able to predict a sequential unzipping of SNARE in good agreement with the findings by Gao et al. The key to this success is to reparameterize the intrahelix and interhelix nonbonded force constants against the pair‐wise residue–residue distance fluctuations collected from all‐atom MD simulations of SNARE. Therefore, our finding supports the importance of accurately describing the inherent dynamics/flexibility of SNARE (in the absence of force), in order to correctly simulate its unfolding behaviors under force. This study has established a useful computational framework for future studies of the zippering function of SNARE and its perturbations by point mutations with amino‐acid level of details, and more generally the forced unfolding pathways of other helix bundle proteins. Proteins 2014; 82:1376–1386. © 2014 Wiley Periodicals, Inc.     

A coarse‐grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse‐grained potential for protein simulations and fold ranking is presented. The potential is based on a two‐point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the “Decoys ‘R’ Us” dataset. In the first test, 58% of tested proteins stay within 5 Å from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Effect of guanidine and arginine on protein–ligand interactions in multimodal cation‐exchange chromatography

The addition of fluid phase modifiers provides significant opportunities for increasing the selectivity of multimodal chromatography. In order to optimize this selectivity, it is important to understand the fundamental interactions between proteins and these modifiers. To this end, molecular dynamics (MD) simulations were first performed to study the interactions of guanidine and arginine with three proteins. The simulation results showed that both guanidine and arginine interacted primarily with the negatively charged regions on the proteins and that these regions could be readily predicted using electrostatic potential maps. Protein surface characterization was then carried out using computationally efficient coarse‐grained techniques for a broader set of proteins which exhibited interesting chromatographic retention behavior upon the addition of these modifiers. It was shown that proteins exhibiting an increased retention in the presence of guanidine possessed hydrophobic regions adjacent to negatively charged regions on their surfaces. In contrast, proteins which exhibited a decreased binding in the presence of guanidine did not have hydrophobic regions adjacent to negatively charged patches. These results indicated that the effect of guanidine could be described as a combination of competitive binding, charge neutralization and increased hydrophobic interactions for certain proteins. In contrast, arginine resulted in a significant decrease in protein retention times primarily due to competition for the resin and steric effects, with minimal accompanying increase in hydrophobic interactions. The approach presented in this paper which employs MD simulations to guide the application of coarse‐grained approaches is expected to be extremely useful for methods development in downstream bioprocesses. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:435–447, 2017     

Structure refinement of protein model decoys requires accurate side‐chain placement

In this study, the application of temperature‐based replica‐exchange (T‐ReX) simulations for structure refinement of decoys taken from the I‐TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self‐guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T‐ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T‐ReX simulation model is provided. Additionally, the effect of side‐chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near‐native backbone conformations among the starting decoys, the determinant of their refinement is side‐chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T‐ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I‐TASSER decoy sets and a 25% reduction in values of C_α root‐mean‐square deviation. The hybrid model succeeded in obtaining a sharper funnel to low‐energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near‐native packing of side chains, the T‐ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.