A topological order parameter for describing folding free energy landscapes of proteins.

We studied the refolding free energy landscape of 26 proteins using the Go-like model. The distance between the denaturated state and the transition state, X F, was calculated using the Bell theory and the nonlinear Dudko-Hummer-Szabo theory, and its relation to the geometrical properties of the native state was considered in detail. We showed that none of the structural parameters, such as the contact order, protein length, and radius of cross section, correlate with X F for all classes of proteins. To overcome this problem, we have introduced the nematic order parameter P 02, which describes the ordering of the structured elements of the native state. Due to its topologically global nature, P 02 is better than other structural parameters in describing the folding free energy landscape. In particular, P 02 displays a good correlation with X F extracted from the nonlinear theory for all three classes of proteins. Therefore, this parameter can be used to predict X F for any protein, if its native structure is known.

Kinetics and mechanical stability of the fibril state control fibril formation time of polypeptide chains: A computational study.

Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Despite much progress in the understanding of the protein aggregation process, the factors governing fibril formation rates and fibril stability have not been fully understood. Using lattice models, we have shown that the fibril formation time is controlled by the kinetic stability of the fibril state but not by its energy. Having performed all-atom explicit solvent molecular dynamics simulations with the GROMOS43a1 force field for full-length amyloid beta peptides Aß40 and Aß42 and truncated peptides, we demonstrated that kinetic stability can be accessed via mechanical stability in such a way that the higher the mechanical stability or the kinetic stability, the faster the fibril formation. This result opens up a new way for predicting fibril formation rates based on mechanical stability that may be easily estimated by steered molecular dynamics.

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models.

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

Role of Resultant Dipole Moment in Mechanical Dissociation of Biological Complexes.

Protein-peptide interactions play essential roles in many cellular processes and their structural characterization is the major focus of current experimental and theoretical research. Two decades ago, it was proposed to employ the steered molecular dynamics (SMD) to assess the strength of protein-peptide interactions. The idea behind using SMD simulations is that the mechanical stability can be used as a promising and an efficient alternative to computationally highly demanding estimation of binding affinity. However, mechanical stability defined as a peak in force-extension profile depends on the choice of the pulling direction. Here we propose an uncommon choice of the pulling direction along resultant dipole moment (RDM) vector, which has not been explored in SMD simulations so far. Using explicit solvent all-atom MD simulations, we apply SMD technique to probe mechanical resistance of ligand-receptor system pulled along two different vectors. A novel pulling direction-when ligand unbinds along the RDM vector-results in stronger forces compared to commonly used ligand unbinding along center of masses vector. Our observation that RDM is one of the factors influencing the mechanical stability of protein-peptide complex can be used to improve the ranking of binding affinities by using mechanical stability as an effective scoring function.

Modeling of protein-peptide interactions using the CABS-dock web server for binding site search and flexible docking.

Protein-peptide interactions play essential functional roles in living organisms and their structural characterization is a hot subject of current experimental and theoretical research. Computational modeling of the structure of protein-peptide interactions is usually divided into two stages: prediction of the binding site at a protein receptor surface, and then docking (and modeling) the peptide structure into the known binding site. This paper presents a comprehensive CABS-dock method for the simultaneous search of binding sites and flexible protein-peptide docking, available as a user's friendly web server. We present example CABS-dock results obtained in the default CABS-dock mode and using its advanced options that enable the user to increase the range of flexibility for chosen receptor fragments or to exclude user-selected binding modes from docking search. Furthermore, we demonstrate a strategy to improve CABS-dock performance by assessing the quality of models with classical molecular dynamics. Finally, we discuss the promising extensions and applications of the CABS-dock method and provide a tutorial appendix for the convenient analysis and visualization of CABS-dock results. The CABS-dock web server is freely available at http://biocomp.chem.uw.edu.pl/CABSdock/.

Switch from thermal to force-driven pathways of protein refolding.

The impact of the quenched force on protein folding pathways and free energy landscape was studied in detail. Using the coarse-grain Go model, we have obtained the low, middle, and high force regimes for protein refolding under the quenched force. The folding pathways in the low force regime coincide with the thermal ones. A clear switch from thermal folding pathways to force-driven pathways in the middle force regime was observed. The distance between the denatured state and transition state xf in the temperature-driven regime is smaller than in the force-driven one. The distance xf obtained in the middle force regime is consistent with the available experimental data suggesting that atomic force microscopy experiments deal with the force-regime which is just above the thermal one.

Preformed template fluctuations promote fibril formation: insights from lattice and all-atom models.

Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleus size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in slowing down fibril elongation in vivo.

A structure-based model fails to probe the mechanical unfolding pathways of the titin I27 domain.

We discuss the use of a structure based Cα-Go model and Langevin dynamics to study in detail the mechanical properties and unfolding pathway of the titin I27 domain. We show that a simple Go-model does detect correctly the origin of the mechanical stability of this domain. The unfolding free energy landscape parameters x(u) and ΔG(‡), extracted from dependencies of unfolding forces on pulling speeds, are found to agree reasonably well with experiments. We predict that above v = 10(4) nm/s the additional force-induced intermediate state is populated at an end-to-end extension of about 75 Å. The force-induced switch in the unfolding pathway occurs at the critical pulling speed v(crit) ≈ 10(6)-10(7) nm/s. We argue that this critical pulling speed is an upper limit of the interval where Bell's theory works. However, our results suggest that the Go-model fails to reproduce the experimentally observed mechanical unfolding pathway properly, yielding an incomplete picture of the free energy landscape. Surprisingly, the experimentally observed intermediate state with the A strand detached is not populated in Go-model simulations over a wide range of pulling speeds. The discrepancy between simulation and experiment is clearly seen from the early stage of the unfolding process which shows the limitation of the Go model in reproducing unfolding pathways and deciphering the complete picture of the free energy landscape.

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

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

Final Remarks.

Aggregation of biomolecules is responsible for a number of neurodegenerative diseases, but it is also behind the formation of membraneless organelles that are vital to life. There are many novel experimental tools to investigate the phenomenon. There is also a rapid progress in its computational studies, as evidenced by the chapters in this volume.

Velocity scaling for optimizing replica exchange molecular dynamics.

We discuss the use of velocity rescaling for generating rejection-free exchange moves in replica exchange molecular dynamics. We test the efficiency of this approach for a common test case, the trp-cage protein. Advantages and limitations of the approach are discussed and possible extensions outlined.

Mechanical unfolding of acylphosphatase studied by single-molecule force spectroscopy and MD simulations.

Single-molecule manipulation methods provide a powerful means to study protein transitions. Here we combined single-molecule force spectroscopy and steered molecular-dynamics simulations to study the mechanical properties and unfolding behavior of the small enzyme acylphosphatase (AcP). We find that mechanical unfolding of AcP occurs at relatively low forces in an all-or-none fashion and is decelerated in the presence of a ligand, as observed in solution measurements. The prominent energy barrier for the transition is separated from the native state by a distance that is unusually long for alpha/beta proteins. Unfolding is initiated at the C-terminal strand (beta(T)) that lies at one edge of the beta-sheet of AcP, followed by unraveling of the strand located at the other. The central strand of the sheet and the two helices in the protein unfold last. Ligand binding counteracts unfolding by stabilizing contacts between an arginine residue (Arg-23) and the catalytic loop, as well as with beta(T) of AcP, which renders the force-bearing units of the protein resistant to force. This stabilizing effect may also account for the decelerated unfolding of ligand-bound AcP in the absence of force.

A numerical investigation into possible mechanisms by that the A629P mutant of ATP7A causes Menkes Disease.

We study in silico possible mechanisms by that the A629P mutant of ATP7A causes Menkes Disease. Our results indicate that the mutation does not have appreciable affects on the stability of copper-bound states but rather destabilizes the characteristic end-to-end ß-sheet. In this way, the mutation presumably increases the probability for aggregation and/or degradation leading to decreased concentration of the monomer.

Relationship between population of the fibril-prone conformation in the monomeric state and oligomer formation times of peptides: insights from all-atom simulations.

Despite much progress in understanding the aggregation process of biomolecules, the factors that govern its rates have not been fully understood. This problem is of particular importance since many conformational diseases such as Alzheimer, Parkinson, and type-II diabetes are associated with the protein oligomerization. Having performed all-atom simulations with explicit water and various force fields for two short peptides KFFE and NNQQ, we show that their oligomer formation times are strongly correlated with the population of the fibril-prone conformation in the monomeric state. The larger the population the faster the aggregation process. Our result not only suggests that this quantity plays a key role in the self-assembly of polypeptide chains but also opens a new way to understand the fibrillogenesis of biomolecules at the monomeric level. The nature of oligomer ordering of NNQQ is studied in detail.

Rapid self-association of highly amyloidogenic H-fragments of insulin: Experiment and molecular dynamics simulations.

The so-called 'H-fragment' of insulin is an extremely amyloidogenic double chain peptide consisting of the N-terminal parts of A-chain and B-chain linked by a disulfide bond between Cys-7A and Cys-7B. Here, we conduct a detailed investigation of the self-association behavior of H-fragment monomers into amyloid-like fibrils using kinetic assays, infrared spectroscopy, circular dichroism (CD), atomic force microscopy (AFM) and molecular dynamics (MD) simulations. Unlike the intact predominantly α-helical insulin, H-fragment remains in a disordered state in aqueous solutions. Its aggregation accelerates with acidification of the environment leading, at pH 1.9, to the formation of thin and structurally homogenous fibrils with the infrared features typical for parallel ß-sheet conformation. According to time-lapse AFM morphological analysis both secondary nucleation and fragmentation are involved in later stages of H-fibrils' self-assembly. Based on the low nucleation order (two) obtained from the global fitting of kinetic data, realistic all-atom MD simulations of pairs of interacting H-fragment monomers were subsequently carried out. The molecular self-association scenario emerging from these simulations implicates the intrinsic conformational instability of H-monomer in its tendency to aggregate and form intermolecular ß-sheet structure. Our findings provide the new mechanistic context for studies of insulin misfolding and aggregation.

Dependence of protein mechanical unfolding pathways on pulling speeds.

Mechanical unfolding of the fourth domain of Distyostelium discoideum filamin (DDFLN4) was studied in detail using the C(alpha)-Go model. We show that unfolding pathways of this protein depend on the pulling speed. The agreement between theoretical and experimental results on the sequencing of unfolding events is achieved at low loading rates. The unfolding free energy landscape is also constructed using dependencies of unfolding forces on pulling speeds.

Protein mechanical unfolding: Importance of non-native interactions.

Mechanical unfolding of the fourth domain of Distyostelium discoideum filamin (DDFLN4) was studied by all-atom molecular dynamics simulations, using the GROMOS96 force field 43a1 and the simple point charge explicit water solvent. Our study reveals an important role of non-native interactions in the unfolding process. Namely, the existence of a peak centered at the end-to-end extension DeltaR approximately 22 nm in the force-extension curve is associated with breaking of non-native hydrogen bonds. Such a peak has been observed in experiments but not in Go models, where non-native interactions are neglected. We predict that an additional peak occurs at DeltaR approximately 2 nm using not only GROMOS96 force field 43a1 but also Amber 94 and OPLS force fields. This result would stimulate further experimental studies on elastic properties of DDFLN4.

The GOR Method of Protein Secondary Structure Prediction and Its Application as a Protein Aggregation Prediction Tool.

The GOR method of protein secondary structure prediction is described. The original method was published by Garnier, Osguthorpe, and Robson in 1978 and was one of the first successful methods to predict protein secondary structure from amino acid sequence. The method is based on information theory, and an assumption that information function of a protein chain can be approximated by a sum of information from single residues and pairs of residues. The analysis of frequencies of occurrence of secondary structure for singlets and doublets of residues in a protein database enables prediction of secondary structure for new amino acid sequences. Because of these simple physical assumptions the GOR method has a conceptual advantage over other later developed methods such as PHD, PSIPRED, and others that are based on Machine Learning methods (like Neural Networks), give slightly better predictions, but have a "black box" nature. The GOR method has been continuously improved and modified for 30 years with the last GOR V version published in 2002, and the GOR V server developed in 2005. We discuss here the original GOR method and the GOR V program and the web server. Additionally we discuss new highly interesting and important applications of the GOR method to chameleon sequences in protein folding simulations, and for prediction of protein aggregation propensities. Our preliminary studies show that the GOR method is a promising and efficient alternative to other protein aggregation predicting tools. This shows that the GOR method despite being almost 40 years old is still important and has significant potential in application to new scientific problems.

Fast and Accurate Accessible Surface Area Prediction Without a Sequence Profile.

A fast accessible surface area (ASA) predictor is presented. In this new approach no residue mutation profiles generated by multiple sequence alignments are used as inputs. Instead, we use only single sequence information and global features such as single-residue and two-residue compositions of the chain. The resulting predictor is both highly more efficient than sequence alignment based predictors and of comparable accuracy to them. Introduction of the global inputs significantly helps achieve this comparable accuracy. The predictor, termed ASAquick, is found to perform similarly well for so-called easy and hard cases indicating generalizability and possible usability for de-novo protein structure prediction. The source code and a Linux executables for ASAquick are available from Research and Information Systems at http://mamiris.com and from the Battelle Center for Mathematical Medicine at http://mathmed.org .

Folding simulations of the A and B domains of protein G.

We study wild type and mutants of the A and B domain of protein G using all-atom Go-models. Our data substantiate the usefulness of such simulation for probing the folding mechanism of proteins and demonstrate that multifunnel versions of such models also allow probing of more complicated funnel landscapes. In our case, such models reproduce the experimentally observed distributions of the GA98 and GB98 mutants which differ only by one residue but fold into different structures. They also reveal details on the folding mechanism in these two proteins.