Dynamic folding pathway models of the villin headpiece subdomain (HP‐36) structure

We have investigated the folding pathway of the 36‐residue villin headpiece subdomain (HP‐36) by action‐derived molecular dynamics simulations. The folding is initiated by hydrophobic collapse, after which the concurrent formation of full tertiary structure and α‐helical secondary structure is observed. The collapse is observed to be associated with a couple of specific native contacts contrary to the conventional nonspecific hydrophobic collapse model. Stable secondary structure formation after the collapse suggests that the folding of HP‐36 follows neither the framework model nor the diffusion‐collision model. The C‐terminal helix forms first, followed by the N‐terminal helix positioned in its native orientation. The short middle helix is shown to form last. Signs for multiple folding pathways are also observed. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Dynamic NMR line-shape analysis demonstrates that the villin headpiece subdomain folds on the microsecond time scale

There is considerable interest in small proteins that fold very rapidly. These proteins have become attractive targets for both theoretical and computational studies. The independently folded 36-residue villin headpiece subdomain has been the subject of a number of such studies and is predicted to fold quickly. We demonstrate using dynamic NMR line-shape analysis that the protein folds on the time scale of 10 mus. Folding rates were directly estimated between 56 and 78 degrees C using resolved protein resonances from three different residues at both 500 and 700 MHz. The rates estimated using different residues and different field strengths agree well with each other. The estimated folding rate lies between 0.5 and 2.0 x 105 s-1 over this temperature range. The folding rate depends only weakly on temperature.     

Using massively parallel simulation and Markovian models to study protein folding: examining the dynamics of the villin headpiece

We report on the use of large-scale distributed computing simulation and novel analysis techniques for examining the dynamics of a small protein. Matters addressed include folding rate, very long time scale kinetics, ensemble properties, and interaction with water. The target system for the study, the villin headpiece, has been of great interest to experimentalists and theorists both. Sampling totaled nearly 500 mus-the most extensive published to date for a system of villin's size in explicit solvent with all atom detail-and was in the form of tens of thousands of independent molecular dynamics trajectories, each several tens of nanoseconds in length. We report on kinetics sensitivity analyses that, using a set of short simulations, probed the role of water in villin's folding and sensitivity to the simulation's electrostatics treatment. By constructing Markovian state models (MSMs) from the collected data, we were able to propagate dynamics to times far beyond those directly simulated and to rapidly compute mean first passage times, long time kinetics (tens of microseconds), and evolution of ensemble property distributions over long times, otherwise currently impossible. We also tested our MSM by using it to predict the structure of villin de novo.     

The earliest events in protein folding: a structural requirement for ultrafast folding in cytochrome C

The folding dynamics of reduced cytochrome c (redcyt c) obtained from tuna heart, which contains a tryptophan residue at the site occupied by His33 in horse heart cytochrome c, was studied using nanosecond time-resolved optical rotatory dispersion spectroscopy. As observed previously for horse heart redcyt c, two time regimes were observed for secondary structure formation in tuna redcyt c: a fast (microseconds) and a slow (milliseconds) phase. However, the fast phase of tuna redcyt c folding was much slower and smaller in amplitude than the same phase in horse. The differences in the fast folding phases suggest that for horse heart redcyt c, the conformers that undergo the fastest observed folding have the His18-Fe-His33 heme configuration, which appears to be necessary, but not sufficient, to poise an unfolded chain conformation for fastest folding in redcyt c.     

Expanding the realm of ultrafast protein folding: gpW, a midsize natural single-domain with alpha+beta topology that folds downhill

All ultrafast folding proteins known to date are either very small in size (less than 45 residues), have an alpha-helix bundle topology, or have been artificially engineered. In fact, many of them share two or even all three features. Here we show that gpW, a natural 62-residue alpha+beta protein expected to fold slowly in a two-state fashion, folds in microseconds (i.e., from tau = 33 micros at 310 K to tau = 1.7 micros at 355 K). Thermodynamic analyses of gpW reveal probe dependent thermal denaturation, complex coupling between two denaturing agents, and differential scanning calorimetry (DSC) thermogram characteristic of folding over a negligible thermodynamic folding barrier. The free energy surface analysis of gpW folding kinetics also produces a marginal folding barrier of about thermal energy ( RT) at the denaturation midpoint. From these results we conclude that gpW folds in the downhill regime and is close to the global downhill limit. This protein seems to be poised toward downhill folding by a loosely packed hydrophobic core with low aromatic content, large stabilizing contributions from local interactions, and abundance of positive charges on the native surface. These special features, together with a complex functional role in bacteriophage lambda assembly, suggest that gpW has been engineered to fold downhill by natural selection.     

Probing the bottom of a folding funnel using conformationally gated electron transfer reactions

The effect of global stability on the kinetics of interconversion between the native (N) and a compact, partially unfolded form (I) of iso-1-cytochrome c stabilized by His73-heme ligation is investigated using a novel conformationally gated ET method. For the K73H variant and the 2-fold less stable AcH73 variant, the N and I conformers are of nearly equal stability at pH 7.5. The pH jump kinetic data yield kobs = kNI + kIN of 35-40 s-1 at final pH values from 6 to 8 for the AcH73 variant, about 3-fold faster than for the more stable K73H variant. Gated ET measurements give kNI = 28 s-1 and kIN = 13 s-1 for the AcH73 variant, 10- and 2-fold greater than that for the more stable K73H variant. Thus, funneled landscapes have evolved such that loss of global stability lowers barriers at the bottom of a folding funnel, still allowing for efficient folding.     

Contact pair dynamics during folding of two small proteins: chicken villin head piece and the Alzheimer protein beta-amyloid

The folding of an extended protein to its unique native state requires establishment of specific, predetermined, often distant, contacts between amino acid residue pairs. The dynamics of contact pair formation between various hydrophobic residues during folding of two different small proteins, the chicken villin head piece (HP-36) and the Alzheimer protein beta-amyloid (betaA-40), are investigated by Brownian dynamics (BD) simulations. These two proteins represent two very different classes-HP-36 being globular while betaA-40 is nonglobular, stringlike. Hydropathy scale and nonlocal helix propensity of amino acids are used to model the complex interaction potential among the various amino acid residues. The minimalistic model we use here employs a connected backbone chain of atoms of equal size while an amino acid is attached to each backbone atom as an additional atom of differing sizes and interaction parameters, determined by the characteristics of each amino acid. Even for such simple models, we find that the low-energy structures obtained by BD simulations of both the model proteins mimic the native state of the real protein rather well, with a best root-mean-square deviation of 4.5 A for HP-36. For betaA-40 (where a single well-defined structure is not available), the simulated structures resemble the reported ensemble rather well, with the well-known beta-bend correctly reproduced. We introduce and calculate a contact pair distance time correlation function, C(P) (ij)(t), to quantify the dynamical evolution of the pair contact formation between the amino acid residue pairs i and j. The contact pair time correlation function exhibits multistage dynamics, including a two stage fast collapse, followed by a slow (microsecond long) late stage dynamics for several specific pairs. The slow late stage dynamics is in accordance with the findings of Sali et al. Analysis of the individual trajectories shows that the slow decay is due to the attempt of the protein to form energetically more favorable pair contacts to replace the less favorable ones. This late stage contact formation is a highly cooperative process, involving participation of several pairs and thus entropically unfavorable and expected to face a large free energy barrier. This is because any new pair contact formation among hydrophobic pairs will require breaking of several contacts, before the favorable ones can be formed. This aspect of protein folding dynamics is similar to relaxation in glassy liquids, where also alpha relaxation requires highly cooperative process of hopping. The present analysis suggests that waiting time for the necessary pair contact formation may obey the Poissonian distribution. We also study the dynamics of Forster energy transfer during folding between two tagged amino acid pairs. This dynamics can be studied by fluorescence resonance energy transfer (FRET). It is found that suitably placed donor-acceptor pairs can capture the slow dynamics during folding. The dynamics probed by FRET is predicted to be nonexponential.     

The native ensemble and folding of a protein molten-globule: functional consequence of downhill folding

The continually emerging functional significance of intrinsic disorder and conformational flexibility in proteins has challenged the long-standing dogma of a well-defined structure contributing to a specific function. Molten-globular states, a class of proteins with significant secondary-structure but a fluid hydrophobic core, is one such example. They have however been difficult to characterize due to the complexity of experimental data and lack of computational avenues. Here, we dissect the folding mechanism of the α-helical molten-globular protein NCBD from three fundamentally different approaches: statistical-mechanical variable barrier model, C(α)-based Gō-model and explicit water all-atom molecular dynamics (MD) simulations. We find that NCBD displays the characteristics of a one-state globally downhill folder but is significantly destabilized. Using simulation techniques, we generate a highly constrained but a heterogeneous native ensemble of the molten-globule for the first time that is consistent with experimental data including small angle X-ray scattering (SAXS), circular dichroism (CD), and nuclear magnetic resonance (NMR). The resulting native ensemble populates conformations reported in other bound-forms providing direct evidence to the mechanism of conformational selection for binding multiple partners in this domain. Importantly, our simulations reveal a connection between downhill folding and large conformational flexibility in this domain that has been evolutionarily selected and functionally exploited resulting in large binding promiscuity. Finally, the multimodel approach we employ here serves as a powerful methodology to study mechanisms and suggests that the thermodynamic features of molten-globules fall within the array of folding mechanisms available to small single-domain proteins.     

Sampling of states for estimating the folding funnel entropy and energy landscape of a model alpha-helical hairpin peptide

Protein folding times are many orders of magnitude shorter than would occur if the peptide chain randomly sampled possible configurations, which implies that protein folding is a directed process. The detailed shape of protein's energy landscape determines the rate and reliability of folding to the native state, but the large number of structural degrees of freedom generates an energy landscape that is hard to visualize because of its high dimensionality. A commonly used picture is that of an energy funnel leading from high energy random coil state down to the low energy native state. As lattice computer models of protein dynamics become more realistic, the number of possible configurations becomes too large to count directly. Statistical mechanic and thermodynamic approaches allow us to count states in an approximate manner to quantify the entropy and energy of the energy landscape within a folding funnel for an alpha-helical protein. We also discuss the problems that arise in attempting to count the huge number of individual states of the random coil at the top of the funnel.     

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.     

The simulation of the three-dimensional lattice hydrophobic-polar protein folding

One of the most prominent problems in computational biology is to predict the natural conformation of a protein from its amino acid sequence. This paper focuses on the three-dimensional hydrophobic-polar (HP) lattice model of this problem. The modified elastic net (EN) algorithm is applied to solve this nonlinear programming hard problem. The lattice partition strategy and two local search methods (LS(1) and LS(2)) are proposed to improve the performance of the modified EN algorithm. The computation and analysis of 12 HP standard benchmark instances are also involved in this paper. The results indicate that the hybrid of modified EN algorithm, lattice partition strategy, and local search methods has a greater tendency to form a globular state than genetic algorithm does. The results of noncompact model are more natural in comparison with that of compact model.     

Synthesis and evaluation of coumermycin A1 analogues that inhibit the Hsp90 protein folding machinery

[structure: see text] The coumarin antibiotics are not only potent inhibitors of DNA gyrase but also represent the most effective C-terminal inhibitors of 90 kDa heat shock proteins (Hsp90) reported thus far. In contrast to the N-terminal ATP-binding site, little is known about the Hsp90 C-terminus. In addition, very limited structure-activity relationships exist between this class of natural products and Hsp90. In this letter, the syntheses of dimeric coumarin analogues are presented along with their inhibitory values in breast cancer cell lines.     

Design of an adenosine analogue that selectively improves the affinity of a mutant U1A protein for RNA

The RNA recognition motif (RRM), one of the most common RNA binding domains, contains three highly conserved aromatic amino acids that participate in stacking interactions with RNA bases. We have investigated the contribution of these highly conserved aromatic amino acids to the affinity of the complex formed between the N-terminal RRM of the U1A protein and stem loop 2 of U1 snRNA. Previously, we found that substitution of one of these conserved aromatic amino acids, Phe56, with Ala resulted in a large destabilization of the complex. Here, we have modified A6, the base in stem loop 2 RNA that stacks with Phe56, to compensate for a portion of the destabilization caused by the Phe56Ala mutation. We have designed two modified adenosines, A-3CPh and A-4CPh, in which a phenyl group is linked to the adenosine such that it may replace the phenyl group that is eliminated by the Phe56Ala mutation in the complex. We have found that incorporation of A-3CPh into stem loop 2 RNA stabilizes the complex formed with Phe56Ala by 0.6 kcal/mol, while incorporation of A-4CPh into stem loop 2 RNA stabilizes this complex by 1.8 kcal/mol. Either base modification destabilizes the wild-type complex by 0.8-0.9 kcal/mol. Experiments with other U1A mutant proteins suggest that the stabilization of the complex between the Phe56Ala U1A protein and stem loop 2 RNA is due to a specific interaction between the Phe56Ala U1A protein and A6-4CPh stem loop 2 RNA.     

Radester, a novel inhibitor of the Hsp90 protein folding machinery

[reaction: see text]. The antitumor antibiotics radicicol and geldanamycin are potent inhibitors of the Hsp90 protein folding machinery. Radester is a hybrid composed of radicicol's resorcinol ring and geldanamycin's quinone through an isopropyl ester. Radester was prepared, and the cytotoxicity of it and the corresponding hydroquinone were determined in MCF-7 breast cancer cells to be 13.9 and 7.1 microM, respectively. Protein degradation assays were performed on Hsp90-dependent client proteins, Her-2 and Raf, to correlate Hsp90 inhibition to cytotoxicity.     

Polypeptide folding on a conformational‐space network: Dependence of network topology on the structural discretization procedure

Mapping the conformational space of a polypeptide onto a network of conformational states involves a number of subjective choices, mostly in relation to the definition of conformation and its discrete nature in a network framework. Here, we evaluate the robustness of the topology of conformational‐space networks derived from Molecular Dynamics (MD) simulations with respect to the use of different discretization (clustering) methods, variation of their parameters, simulation length and analysis time‐step, and removing high‐frequency motions from the coordinate trajectories. In addition, we investigate the extent to which polypeptide dynamics can be reproduced on the resulting networks when assuming Markovian behavior. The analysis is based on eight 500 ns and eight 400 ns MD simulations in explicit water of two 10‐residue peptides. Three clustering algorithms were used, two of them based on the pair‐wise root‐mean‐square difference between structures and one on dihedral‐angle patterns. A short characteristic path length and a power‐law behavior of the probability distribution of the node degree are obtained irrespective of the clustering method or the value of any of the tested parameters. The average cliquishness is consistently one or two orders of magnitude larger than that of a random realization of a network of corresponding size and connectivity. The cliquishness as function of node degree and the kinetic properties of the networks are found to be most dependent on clustering method and/or parameters. Although Markovian simulations on the networks reproduce cluster populations accurately, their kinetic properties most often differ from those observed in the MD simulations. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Transition network based on equilibrium sampling: a new method for extracting kinetic information from Monte Carlo simulations of protein folding

We propose a new type of transition network for modeling of protein dynamics. The nodes of the network correspond to the conformations taken from random sampling of equilibrium ensemble available, e.g., by Monte Carlo simulations. Although this approach does not provide absolute values of folding/unfolding rates, it allows identification of reaction pathways, transition state ensemble, and, eventually, intermediates. The new method is verified by a comparison with direct molecular dynamic simulations performed for a coarse-grained Gō-like model of proteins. As an illustrative example, we analyze kinetics of formation of a small β-hairpin (Trp zipper 1) in the all-atom representation.     

Application of the accelerated molecular dynamics simulations to the folding of a small protein

In this paper, we further explore the applicability of the accelerated molecular dynamics simulation method using a bias potential. The method is applied to both simple model systems and real multidimensional systems. The method is also compared to replica exchange simulations in folding a small protein, Trp cage, using an all atom potential for the protein and an implicit model for the solvent. We show that the bias potential method allows quick searches of folding pathways. We also show that the choice of the bias potential has significant influence on the efficiency of the bias potential method.