Hierarchy of folding and unfolding events of protein G, CI2, and ACBP from explicit-solvent simulations

The study of the mechanism which is at the basis of the phenomenon of protein folding requires the knowledge of multiple folding trajectories under biological conditions. Using a biasing molecular-dynamics algorithm based on the physics of the ratchet-and-pawl system, we carry out all-atom, explicit solvent simulations of the sequence of folding events which proteins G, CI2, and ACBP undergo in evolving from the denatured to the folded state. Starting from highly disordered conformations, the algorithm allows the proteins to reach, at the price of a modest computational effort, nativelike conformations, within a root mean square deviation (RMSD) of approximately 1 A?. A scheme is developed to extract, from the myriad of events, information concerning the sequence of native contact formation and of their eventual correlation. Such an analysis indicates that all the studied proteins fold hierarchically, through pathways which, although not deterministic, are well-defined with respect to the order of contact formation. The algorithm also allows one to study unfolding, a process which looks, to a large extent, like the reverse of the major folding pathway. This is also true in situations in which many pathways contribute to the folding process, like in the case of protein G.     

The protein folding transition state: insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4相似文献   

Slow Unfolded-State Structuring in Acyl-CoA Binding Protein Folding Revealed by Simulation and Experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ～10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (～100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.     

Ligand-biased ensemble receptor docking (LigBEnD): a hybrid ligand/receptor structure-based approach

Ligand docking to flexible protein molecules can be efficiently carried out through ensemble docking to multiple protein conformations, either from experimental X-ray structures or from in silico simulations. The success of ensemble docking often requires the careful selection of complementary protein conformations, through docking and scoring of known co-crystallized ligands. False positives, in which a ligand in a wrong pose achieves a better docking score than that of native pose, arise as additional protein conformations are added. In the current study, we developed a new ligand-biased ensemble receptor docking method and composite scoring function which combine the use of ligand-based atomic property field (APF) method with receptor structure-based docking. This method helps us to correctly dock 30 out of 36 ligands presented by the D3R docking challenge. For the six mis-docked ligands, the cognate receptor structures prove to be too different from the 40 available experimental Pocketome conformations used for docking and could be identified only by receptor sampling beyond experimentally explored conformational subspace.     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Exploring experimental sources of multiple protein conformations in structure-based drug design

Receptor flexibility must be incorporated into structure-based drug design in order to portray a more accurate representation of a protein in solution. Our approach is to generate pharmacophore models based on multiple conformations of a protein and is very similar to solvent mapping of hot spots. Previously, we had success using computer-generated conformations of apo human immunodeficiency virus-1 protease (HIV-1p). Here, we examine the use of an NMR ensemble versus a collection of crystal structures, and we compare back to our previous study based on computer-generated conformations. To our knowledge, this is the first direct comparison of an NMR ensemble and a collection of crystal structures to incorporate protein flexibility in structure-based drug design. To provide an accurate comparison between the experimental sources, we used bound structures for our multiple protein structure (MPS) pharmacophore models. The models from an NMR ensemble and a collection of crystal structures were both able to discriminate known HIV-1p inhibitors from decoy molecules and displayed superior performance over models created from single conformations of the protein. Although the active-site conformations were already predefined by bound ligands, the use of MPS allows us to overcome the cross-docking problem and generate a model that does not simply reproduce the chemical characteristics of a specific ligand class. We show that there is more structural variation between 28 structures in an NMR ensemble than 90 crystal structures bound to a variety of ligands. MPS models from both sources performed well, but the model determined using the NMR ensemble appeared to be the most general yet accurate representation of the active site. This work encourages the use of NMR models in structure-based design.     

Simulation studies of the fidelity of biomolecular structure ensemble recreation

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.     

A Carboxylate to Amide Substitution That Switches Protein Folds

Metamorphic proteins are biomolecules prone to adopting alternative conformations. Because of this feature, they represent ideal systems to investigate the general rules allowing primary structure to dictate protein topology. A comparative molecular dynamics study was performed on the denatured states of two proteins, sharing nearly identical amino‐acid sequences (88 %) but different topologies, namely an all‐α‐helical bundle protein named G_A88 and an α+β‐protein named G_B88. The analysis allowed successful design of and experimental validation of a site‐directed mutant that promotes, at least in part, the switch in folding from G_B88 to G_A88. The mutated position, in which a glutamic acid was replaced by a glutamine, does not make any intramolecular interactions in the native state of G_A88, such that its stabilization can be explained by considering the effects on the denatured state. The results represent a direct demonstration of the role of the denatured state in sculpting native structure.     

Extensive conformational searches of 13 representative dipeptides and an efficient method for dipeptide structure determinations based on amino acid conformers

Conformations of peptides are the basis for their property studies and the predictions of peptide structures are highly important in life science but very complex in practice. Here, thorough searches on the potential energy surfaces of 13 representative dipeptides by considering all possible combinations of the bond rotational degrees of freedom are performed using the density functional theory based methods. Careful analyses of the conformers of the 13 dipeptides and the corresponding amino acids reveal the connections between the structures of dipeptide and amino acids. A method for finding all important dipeptide conformers by optimizing a small number of trial structures generated by suitable superposition of the parent amino acid conformations is thus proposed. Applying the method to another eight dipeptides carefully examined by others shows that the new approach is both highly efficient and reliable by providing the most complete ensembles of dipeptide conformers and much improved agreements between the theoretical and experimental IR spectra. The method opens the door for the determination of the stable structures of all dipeptides with a manageable amount of effort. Preliminary result on the applicability of the method to the tripeptide structure determination is also presented. The results are the first step towards proving Anfinsen's hypothesis by revealing the relationships between the structures of the simplest peptide and its constituting amino acids. It implies that the structures of peptides are not only determined by their amino acid sequences, but also closely linked with the amino acid conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Critical assessment of side-chain conformational space sampling procedures designed for quantifying the effect of side-chain environment

We introduce a family of procedures designed to sample side-chain conformational space at particular locations in protein structures. These procedures (CRSP) use intensive cycles of random assignment of side-chain conformations followed by minimization to determine all the conformations that a group of side-chains can adopt simultaneously. First, we consider a procedure evolving in the dihedral space (dCRSP). Our results suggest that it can accurately map low-energy conformations adopted by clusters of side-chains of a protein. dCRSP is relatively insensitive to various important parameters, and it is sufficiently accurate to capture efficiently the constraint induced by the environment on the conformations a particular side-chain can adopt. Our results show that dCRSP, compared with molecular dynamics (MD), can overcome the problem of the limited set of conformations reached in a reasonable amount of simulations. Next, we introduce procedures (vCRSP) in which valence angles are relaxed, and we assess how efficiently they quantify the conformational entropy of side-chains in the protein native state. For simple peptides, entropies obtained with vCRSP are fully compatible with those obtained with a Monte Carlo procedure. For side-chains in a protein environment, however, vCRSP appears of limited use. Finally, we consider a two-step procedure that combines dCRSP and vCRSP. Our tests suggest that it is able to overcome the limitations of vCRSP. We also note that dCRSP provides a reasonable initial approximation. This family of procedures offers promise in quantifying the contribution of conformational entropy to the energetics of protein structures.     

Protein stability prediction: a Poisson-Boltzmann approach

Most proteins are only marginally stable at physiological temperatures. Thus a common defect due to mutation is the loss of protein stability, resulting in loss of their well-defined structures and functions at their functioning temperatures. Quantification of protein stability change upon mutation has attracted a large number of experimental and theoretical studies. In this work, we have extended the Poisson-Boltzmann theory that is originally used for predicting stability changes of charged mutations to predicting stability changes of all mutations. To achieve this, we have proposed a free energy model covering both electrostatic and hydrophobic interactions. A G?-like model for the denatured state that incorporates both nativeness and randomness of the denatured state has been used to calculate the hydrophobic contribution to protein stability. The new model is computationally simple and fast, and performs well for charged and hydrophobic mutations for all four tested proteins. Future directions for extending the method into pH-dependent effect and more accurate prediction for polar mutations are discussed.     

Peptide loop-closure kinetics from microsecond molecular dynamics simulations in explicit solvent

End-to-end contact formation rates of several peptides were recently measured by tryptophan triplet quenching (Lapidus et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 7220). Motivated by these experiments, we study loop-closure kinetics for two peptides of different lengths, Cys-(Ala-Gly-Gln)n-Trp (n = 1, 2), in multiple all-atom explicit-solvent molecular dynamics simulations with different initial conditions and force fields. In 150 simulations of approximately 20 ns each, we collect data covering 1.0 and 0.8 micros for the penta-peptide simulated with the AMBER and CHARMM force fields, respectively, and about 0.5 micros each with the two force fields for the octa-peptide. These extensive simulations allow us to analyze the dynamics of peptides in the unfolded state with atomic resolution, thus probing early events in protein folding, and to compare molecular dynamics simulations directly with experiment. The calculated lifetimes of the tryptophan triplet state are in the range of 50-100 ns, in agreement with experimental measurements. However, end-to-end contacts form more rapidly, with characteristic times less than 10 ns. The contact formation rates for the two force fields are similar despite differences in the respective ensembles of peptide conformations.     

Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.     

Comparing pharmacophore models derived from crystallography and NMR ensembles

NMR and X-ray crystallography are the two most widely used methods for determining protein structures. Our previous study examining NMR versus X-Ray sources of protein conformations showed improved performance with NMR structures when used in our Multiple Protein Structures (MPS) method for receptor-based pharmacophores (Damm, Carlson, J Am Chem Soc 129:8225–8235, 2007). However, that work was based on a single test case, HIV-1 protease, because of the rich data available for that system. New data for more systems are available now, which calls for further examination of the effect of different sources of protein conformations. The MPS technique was applied to Growth factor receptor bound protein 2 (Grb2), Src SH2 homology domain (Src-SH2), FK506-binding protein 1A (FKBP12), and Peroxisome proliferator-activated receptor-γ (PPAR-γ). Pharmacophore models from both crystal and NMR ensembles were able to discriminate between high-affinity, low-affinity, and decoy molecules. As we found in our original study, NMR models showed optimal performance when all elements were used. The crystal models had more pharmacophore elements compared to their NMR counterparts. The crystal-based models exhibited optimum performance only when pharmacophore elements were dropped. This supports our assertion that the higher flexibility in NMR ensembles helps focus the models on the most essential interactions with the protein. Our studies suggest that the “extra” pharmacophore elements seen at the periphery in X-ray models arise as a result of decreased protein flexibility and make very little contribution to model performance.     

Two-state folding observed in individual protein molecules

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.     

Reproducing the conformations of protein-bound ligands: a critical evaluation of several popular conformational searching tools

Several programs (Catalyst, Confort, Flo99, MacroModel, and Omega) that are commonly used to generate conformational ensembles have been tested for their ability to reproduce bioactive conformations. The ligands from thirty-two different ligand–protein complexes determined by high-resolution (le2.0 Å) X-ray crystallography have been analyzed. The Low-Mode Conformational Search method (with AMBER^* and the GB/SA hydration model), as implemented in MacroModel, was found to perform better than the other algorithms. The rule-based method Omega, which is orders of magnitude faster than the other methods, also gave reasonable results but were found to be dependent on the input structure. The methods supporting diverse sampling (Catalyst, Confort) performed least well. For the seven ligands in the set having eight or more rotatable bonds, none of the bioactive conformations were ever found, save for one exception (Flo99). These ligands do not bind in a local minimum conformation according to AMBER^*\GB/SA. Taking these last two observations together, it is clear that geometrically similar structures should be collected in order to increase the probability of finding the bioactive conformation among the generated ensembles. Factors influencing bioactive conformational retrieval have been identified and are discussed.     

Statistically based reduced representation of amino acid side chains

Preferred conformations of amino acid side chains have been well established through statistically obtained rotamer libraries. Typically, these provide bond torsion angles allowing a side chain to be traced atom by atom. In cases where it is desirable to reduce the complexity of a protein representation or prediction, fixing all side-chain atoms may prove unwieldy. Therefore, we introduce a general parametrization to allow positions of representative atoms (in the present study, these are terminal atoms) to be predicted directly given backbone atom coordinates. Using a large, culled data set of amino acid residues from high-resolution protein crystal structures, anywhere from 1 to 7 preferred conformations were observed for each terminal atom of the non-glycine residues. Side-chain length from the backbone C(alpha) is one of the parameters determined for each conformation, which should itself be useful. Prediction of terminal atoms was then carried out for a second, nonredundant set of protein structures to validate the data set. Using four simple probabilistic approaches, the Monte Carlo style prediction of terminal atom locations given only backbone coordinates produced an average root mean-square deviation (RMSD) of approximately 3 A from the experimentally determined terminal atom positions. With prediction using conditional probabilities based on the side-chain chi(1) rotamer, this average RMSD was improved to 1.74 A. The observed terminal atom conformations therefore provide reasonable and potentially highly accurate representations of side-chain conformation, offering a viable alternative to existing all-atom rotamers for any case where reduction in protein model complexity, or in the amount of data to be handled, is desired. One application of this representation with strong potential is the prediction of charge density in proteins. This would likely be especially valuable on protein surfaces, where side chains are much less likely to be fixed in single rotamers. Prediction of ensembles of structures provides a method to determine the probability density of charge and atom location; such a prediction is demonstrated graphically.