Similar folds with different stabilization mechanisms: the cases of prion and doppel proteins
© Colacino et al; licensee BioMed Central Ltd. 2006
Received: 23 February 2006
Accepted: 21 July 2006
Published: 21 July 2006
Protein misfolding is the main cause of a group of fatal neurodegenerative diseases in humans and animals. In particular, in Prion-related diseases the normal cellular form of the Prion Protein PrP (PrP C ) is converted into the infectious PrP Sc through a conformational process during which it acquires a high β-sheet content. Doppel is a protein that shares a similar native fold, but lacks the scrapie isoform. Understanding the molecular determinants of these different behaviours is important both for biomedical and biophysical research.
In this paper, the dynamical and energetic properties of the two proteins in solution is comparatively analyzed by means of long time scale explicit solvent, all-atom molecular dynamics in different temperature conditions. The trajectories are analyzed by means of a recently introduced energy decomposition approach (Tiana et al, Prot. Sci. 2004) aimed at identifying the key residues for the stabilization and folding of the protein. Our analysis shows that Prion and Doppel have two different cores stabilizing the native state and that the relative contribution of the nucleus to the global stability of the protein for Doppel is sensitively higher than for PrP. Moreover, under misfolding conditions the Doppel core is conserved, while the energy stabilization network of PrP is disrupted.
These observations suggest that different sequences can share similar native topology with different stabilizing interactions and that the sequences of the Prion and Doppel proteins may have diverged under different evolutionary constraints resulting in different folding and stabilization mechanisms.
The molecular determinants of neurodegenerative diseases have been the subject of very intense research over recent years [1, 2]. Particular attention in this field has been devoted to Prion proteins (PrP) due to their fundamental role as infective agents in diseases generally known as Transmissible Spongiform Encephalopathies (TSE) that affect humans and animals, including Creuzfeld-Jakob disease, fatal familial insomnia and Gerstmann-Straussler-Scheinker disease in humans, scrapie in sheep and mad-cow disease in cattle. The distinctive trait of Prion-related diseases is that PrP proteins seem to act as the only infectious agents, with no intervention of genetic material, by causing self-propagating conformational changes [3–5]. Experimental evidences unveiled that in all these cases the normal and benign form of the Prion Protein (PrP C ) can undergo a conformational change of the native state leading to a new isoform designated PrP Sc which is insoluble, characterized by an increased content in β-structure and with a high tendency to form amyloid aggregates [5, 6]. Misfolding to the pathological species occurs through the unfolding of the α-helical-rich conformation and refolding to a β-sheet rich one [6, 7]. Once formed, PrP Sc can interact with other monomeric PrPs, acting as a template to speed up the conversion of the normal form to the scrapie one. Interestingly, more than 20 mutations distributed throughout the sequence of PrP have been shown to lead to neurological disorders: their role has been suggested to be connected with either the lowering of the free-energy barrier in the conformational conversion favoring the formation of PrP Sc , or with an increase in the oligomerization rate of the insoluble isoforms .
These observations suggest that, despite the structural similarities, there may be fundamental differences in the stabilization and unfolding/misfolding mechanisms of PrP and Dpl, which may be strictly connected to the interactions among residues in the native state.
In this paper we make use of long-timescale, explicit-solvent, all-atom simulations of the structured part of the human PrP protein (residues 125 to 229, pdb code 1qlz) , and of the Doppel protein (Dpl, pdb code 1i17)  (see Fig. 1a and 1b). These simulations are used as a basis to perform an analysis of the stabilization energy of the two proteins, in order to obtain direct information on the determinants of their (de)stabilization and indirect information on the associated folding properties. MD simulations for both proteins were thus run at 310 K for 50 ns with protonation conditions of the titratable groups consistent with pH 7 (see the Methods section). The final structures of each simulation at room temperature were used as starting points for two more simulations at 350 K for 20 ns at pH 7, and after this time span the temperature was raised to 450 K for 20 more nanoseconds to speed up the complete unfolding of the proteins and to investigate possible pathways to the formation of infectious species.
The main goal is to shed light on the different role that structural motifs and specific residues play in the (de)stabilization of native structures of the two proteins. In particular, we have used a simple energy-analysis approach developed in our group to obtain a detailed picture of the sites mostly responsible for the stability of the native state of each protein in selected environments . The energy analysis is based on an eigenvalue-decomposition of the symmetric interaction energy matrix obtained by the calculation of all the interactions between non consecutive residues along an MD trajectory. The analysis of the components of the eigenvector associated with the lowest eigenvalue has proven useful to identify those sites mostly responsible for protein stabilization in a series of uncorrelated test proteins and in a family of proteins sharing the same 3D fold with low sequence identity [15–17]. One can thus investigate and highlight the main differences in the dynamics and in the energy distribution in the native states of PrP and Dpl, and correlate them with the impact that topological and sequence differences may ultimately have on the presence or absence of the structural rearrangements which are at the basis of neurodegenerative diseases.
Results and discussion
The structural properties of PrP were already discussed elsewhere , so that in this paper we will concentrate on the structural properties of Dpl and on their comparison with those of PrP at pH 7.
To gain a deeper understanding of the molecular interactions responsible for the differential behavior of the two molecules, we analyzed directly the distribution of stabilization energy among the residues of the two proteins, as described in the Methods. In brief, it was shown that single domain proteins usually display a core of few residues stabilizing collectively the whole protein . The lowest eigenvalue λ1 of the residue-residue interaction matrix obtained by the simulated trajectory is, for core-stabilized proteins, consistently lower than the other eigenvalues. The elements of the associated eigenvectors indicate to which extent each amino acid participates to the core (for details on the application of the method to small single-domain proteins see references [15–17]). The details of eigenvectors corresponding to higher eigenvalues are reported in the supplementary material [see Additional file 1].
The results of the energy analysis show quite substantial differences among the two proteins. First of all, the ratio of the separation between the first two eigenvalues Δλ12 and the average spacing between all the others is much higher for Dpl than for PrP in all conditions. This ratio quantifies to which extent the stabilization energy of the protein is concentrated in a few, mutually interacting residues and, consequently, to which extent the overall stabilization energy is well accounted for by the first eigenvector μ1. In particular, at pH 7 the Δλ12/Δλ ratio for the Dpl protein is 10.53 at 310 K and 9.17 at 350 K, while for the PrP these values decrease to 3.03 and 2.33 respectively.
Correlation coefficients between and component values of the principal eigenvectors for PrP and Dpl at different temperatures
PrP 350 K
PrP 450 K
Dpl 350 K
Dpl 450 K
PrP 310 K
PrP 350 K
Dpl 310 K
Dpl 350 K
The situation is different for Dpl. The profile of the principal eigenvector reporting the most stabilizing interactions in the native state is not changed when raising the temperature at pH7: the spectra of the first Dpl eigenvectors are almost superimposable at pH7 for the situations at 310 K and 350 K, their correlation coefficient being 0.93, a value consistently higher than that observed for the analogous PrP simulations. The different characteristics of the two main eigenvector profiles can be considered as an indication of the changes in the free-energy profiles of Dpl and PrP when raising the temperature from 310 to 350 K, differences which are highly dependent upon the sequences. As we noticed in ref. , in fact, the energy decomposition analysis described should be considered to yield an approximation of the free energy of the state around which the simulation is being carried out. The free energy landscape around one state of a protein can actually change with temperature, without substantial changes in conformational properties.
It is interesting to observe at this point that also in Dpl the two Cys residues constituting the additional S-S bridge are not part of the folding nucleus of the protein. In this context, White and coworkers  noticed that while removal of the second disulphide bond from Dpl causes the melting temperature to decrease as expected from ~50°C to ~40°C, it does not affect the unfolding mechanism: no intermediate formation and no transition to β-rich structures is in fact observed. The fact that neither Dpl nor its mutant exhibited the α-β transformation typical of the prion protein suggest that this conversion property may actually be strictly dependent on the sequence differences in the folding nuclei of the two proteins.
Moreover, these observations show that similar topological organizations can be obtained by two significantly different sequences (25% homology) by a different distribution and organization of the stabilizing interactions. Strictly connected to the sequence-topology properties, the significant variation in the principal eigenvector profile upon temperature variation suggests possible different mechanisms for the unfolding/misfolding reactions of the two proteins. Interestingly, the most significant energy redistribution at 350 K characterizes PrP, which is known experimentally to undergo a transition to an intermediate structure.
Summing up, the results of the structural and energy decomposition analysis of the two proteins sharing the same topological organization show important differences in the stabilization mechanism of their native states and provide a possible rationale to explain the different unfolding-misfolding behaviors of the two molecules observed experimentally, which in turn has important pathological consequences. First of all, the nucleus of Dpl concentrates a much higher fraction of the global stabilization energy compared to PrP. Moreover, the distribution of stabilization energy in the former does not change with temperature, at variance with the latter.
These observations indicate that a different and more "solid" set of interactions have to be broken to unfold Dpl. In order to unfold Dpl, one has to break a network of interactions whose weight on stabilization is much higher than in the case of PrP. Once the more stable native interaction network of Dpl is broken, the protein can simply unfold to random coil or molten globule structures. The observation of Fig. 3 actually shows that the unfolding of Dpl is early and more cooperative than in the case of PrP, which undergoes a gradual unfolding without a single cooperative event. If one considers the reverse process, the folding of Dpl would require the formation of a more stable and extended folding nucleus, which would restrict the protein from exploring pathways alternative to the one leading to the native state, making this state energetically more accessible than alternative ones leading to different 3D structures.
These observations are consistent with the results obtained by other authors using a different approach to study the folding dynamics of Dpl and PrP. Settanni and coworkers, in particular, using a simplified potential biased towards the native topology, could show that while Dpl folds by crossing one main free energy barrier, PrP has two alternative folding pathways available .
Using a different approach, Fernandez and coworkers proposed a measure of amyloidogenic propensity relying on the analysis of the density of backbone hydrogen bonds exposed to water attack in monomeric structure . On this basis, the authors proposed a diagnostic tool based on the identification of hydrogen bonds with a paucity of intramolecular dehydration or "wrapping", and used this predictor to successfully identify potentially pathogenic mutations that foster amyloidogenic propensity in human prions. When the same analysis was applied to Dpl, the wrapping measurements yielded a dramatically different level of amyloidogenic propensity. The authors suggested that that the packing within the fold, and not the fold itself, contains the signal for aggregation.
These observations are also consistent with what we observe herein. The higher number of stabilizing interactions in the nucleus of Dpl determine a tighter packing, and a lower tendency of water to disrupt intramolecular interactions favouring conformational transitions to the β-sheet rich structures characteristic of amyloids.
The results of our comparative analysis of PrP and Dpl, sharing the same native topology despite a very low sequence homology, have provided valuable information on several aspects of the stabilization and (mis)-folding mechanisms of the two proteins. In particular, we could show that:
1) the stabilization core of Dpl provides a higher relative contribution to the overall stabilization energy compared to that of PrP.
2) the stabilization core of Dpl is stable and conserved also at 350 K. At this temperature, which is known to trigger misfolding and aggregation in PrP, the stabilization core of this latter protein is not conserved, and the whole stabilization energy is spread over the whole sequence favoring conformational interconversions to other structures.
3) As a consequence, PrP can misfold to different aggregation prone conformations, while Dpl cannot.
We think that our results are consistent and supportive of the experimental findings that Doppel lacks the scrapie isoform and that such remarkably different behavior is due to the presence of a different stabilization core, which in turn determines a different folding mechanism when compared to PrP.
From the practical point of view, we think that this type of analysis can be extended to other sequences which fold (or can be modeled) into the 3D structure typical of PrP as a relatively rapid diagnostic tool to predict mis-folding properties. This approach can also overcome the current limitations of all-atom MD simulations, which are still too computationally demanding to provide directly thermodynamical information about the folding and misfolding of a protein of the size of the two studied here. We have shown in fact that the shape of the principal eigenvector, which can be obtained with simulations accessible with present day computational power, can clearly distinguish the conditions which promote misfolding from those which do not.
Structures, simulation set-up and analysis
The starting structures for the all-atom MD simulations of the Doppel Protein (Dpl, fragment 51–157) and for the human Prion Protein (PrP, fragment 125–229) were taken from the protein data bank, with codes 1I17.pdb  and 1QLZ.pdb .
To mimic the solution conditions at pH 7, Lysin amino groups were considered protonated, while the carboxyl groups were considered to bear a negative charge. In the case of Dpl, the total formal charge on the protein resulted to be +1 and one Chloride counterion was added to ensure electroneutrality of the simulation box; in the case of PrP The total charge on the protein was -3 and three Sodium ions were added to ensure electroneutrality of the system.
The proteins were solvated with water in a octahedral box large enough to contain 1.2 nm of solvent around the peptide. The simple point charge (SPC) water model was used  to solvate each protein in the simulation box. Each system was subsequently energy minimized with a steepest descent method for 1000 steps. The calculation of electrostatic forces utilized the PME implementation of the Ewald summation method. The LINCS  algorithm was used to constrain all bond lengths. For the water molecules the SETTLE algorithm  was used. A dielectric permittivity, ε = 1, and a time step of 2 fs were used. All atoms were given an initial velocity obtained from a Maxwellian distribution at the desired initial temperature of 300 K. The density of the system was adjusted performing the first equilibration runs at NPT condition by weak coupling to a bath of constant pressure (P0 = 1 bar, coupling time τ P = 0.5 ps) . In all simulations the temperature was maintained close to the intended values by weak coupling to an external temperature bath  with a coupling constant of 0.1 ps. The peptide and the rest of the system were coupled separately to the temperature bath.
In both cases, the protein was simulated at 310 K for 50 ns, then the temperature was raised at 350 K for the next 20 ns and finally, after this period, each system was heated up to 450 K for 20 more ns, resulting in a total simulation time of 90 ns for each of the two studied systems. All simulations were run at NPT conditions.
All simulations and analysis were carried out using the GROMACS package (version 3.2) [30–32], using the GROMOS96 43A1 force field . All calculations were performed on clusters of PCs, with Linux operating system. Graphical display of structures was done using the PyMOL software. Structural alignments were carried out with the Sofist algorithm  on the representatives of the most populated clusters for the 50 ns 310 K simulations. Structural Clusters were defined using the structural clustering algorithm proposed by Daura and coworkers .
Energy decomposition analysis
The basic idea behind the energy decomposition analysis is to extract energetic information on the protein from molecular dynamics (MD) simulations, and from it to gain insight into the determinants of the stability of the native protein conformation, and their influence on the folding process [15, 36]. The main information needed to achieve this goal is the interaction matrix M ij , calculated averaging the corresponding interaction energies, comprising all the non-bonded inter-residue energy components (e.g. van der Waals and Electrostatic), over a MD trajectory starting from the native conformation. The matrix M ij can be decomposed in eigenvalues, in the form
where N is the number of amino acids in the protein, λα is an eigenvalue and are the components of the associated eigenvector. We assume that the eigenvectors are normalized to unity and, since M ij is symmetrical, all the eigenvalues are real.
For the sake of simplicity, we label the N eigenvalues in increasing order, so that λ1 is the most negative. Accordingly, the different terms in the sum in Eq. (1) approximate the real interaction energy M ij to an increasing extent, the first term containing the largest contribution to the stabilization of the native conformation. The components of the associated eigenvector indicate to which extent each amino acid participates to the stabilization. In other words, each term in Eq. (1) accounts for an amount of energy λα which is shared among the different residues according to the corresponding eigenvector
If the second eigenvalue λ2 is much higher than λ1, one can approximate the whole interaction matrix as
reducing the information needed to specify the interaction from N2 to N numbers.
The network of interactions containing most of the information on the stabilization energy is then determined by analyzing the first eigenvector and identifying those sites whose component is higher than a threshold value t. This is calculated as the value corresponding to a normalized vector whose components provide the same contribution for each site (flat eigenvector). This corresponds, to a first approximation, to a situation in which each residue contributes with the same weight to structural stability. In this approximation the threshold value depends only on the number N of residues in the protein and is calculated as:
In the case of Dpl the value of t is 0.097, while in the case of PrP this value equals 0.098.
- Dobson CM: Protein folding and its link to human disease. Biochem Soc Symp 2001, 1–26.Google Scholar
- Conway K, Harper J, Lansbury P: Fibrils formed from alpha-synuclein and two mutant forms linked to Parkinson's diesease are typical amyloid. Biochemistry 2000, 39: 2552–2563. 10.1021/bi991447rView ArticlePubMedGoogle Scholar
- Prusiner S: Molecular biology of prion diseases. Science 1991, 252: 1515–1522.View ArticlePubMedGoogle Scholar
- Prusiner S: Prions. Proc Natl Acad Sci USA 1998, 95: 13363–13383. 10.1073/pnas.95.23.13363PubMed CentralView ArticlePubMedGoogle Scholar
- Prusiner S, Scott M, DeArmond S, Cohen F: Prion protein biology. Cell 1998, 93: 337–348. 10.1016/S0092-8674(00)81163-0View ArticlePubMedGoogle Scholar
- Pan K, Baldwin M, Nguyen J, Gasset M, Serban A, Groth D, Mehlhorn I, Huang Z, Fletterick R, Cohen F, et al.: Conversion of alpha-helices into beta-sheets features in the formation of the scrapie prion proteins. Proc Natl Acad Sci USA 1993, 90: 10962–10966. 10.1073/pnas.90.23.10962PubMed CentralView ArticlePubMedGoogle Scholar
- Wille H, Michelitsch M, Guenebaut V, Supattapone S, Serban A, Cohen F, Agard D, Prusiner S: Structural Studies of the scrapie prion protein by electron crystallography. Proc Natl Acad Sci USA 2002, 99: 3563–3568. 10.1073/pnas.052703499PubMed CentralView ArticlePubMedGoogle Scholar
- Kovacs GG, Trabattoni G, Hainfellner JA, Ironside JW, Knight RS, Budka H: Mutations of the prion protein gene phenotypic spectrum. J Neurol 2002, 249: 1567–1582. 10.1007/s00415-002-0896-9View ArticlePubMedGoogle Scholar
- Hornshaw MP, McDermott JR, Candy JM: Copper-binding to the N-Terminal tandem repeat regions of mammalian and avian prion protein. Biochem Biophys Res Commun 1995, 207(2):621–629. 10.1006/bbrc.1995.1233View ArticlePubMedGoogle Scholar
- Viles JH, Cohen FE, Prusiner SB, Goodin DB, Wright PE, Dyson HJ: Copper binding to the prion protein: Structural implications of four identical cooperative binding sites. Proc Natl Acad Sci USA 1999, 96(5):2042–2047. 10.1073/pnas.96.5.2042PubMed CentralView ArticlePubMedGoogle Scholar
- Mouillet-Richard S, Ermonval M, Chebassier C, Laplanche JL, Lehmann S, Launay JM, Kellermann O: Signal transduction through prion protein. Science 2000, 289: 1925–1928. 10.1126/science.289.5486.1925View ArticlePubMedGoogle Scholar
- Sakaguchi S, Katamine S, Nishida N, Moriuchi R, Shigematsu K, Sugimoto T, Nakatani A, Kataoka Y, Houtani T, Shirabe S, et al.: Loss of cerebellar Purkinje cells in aged mice homozygous for a disrupted Prp gene. Nature 1996, 380: 528–531. 10.1038/380528a0View ArticlePubMedGoogle Scholar
- Mo H, Moore RC, Cohen FE, Westaway D, Prusiner SB, Wright PE, Dyson HJ: Two different neurodegenerative diseases caused by proteins with similar structures. Proc Natl Acad Sci USA 2001.Google Scholar
- Zahn R, Liu A, Luhrs T, Riek R, Schroetter CV, Garcia FL, Billeter M, Calzolai L, Wider G, Wuthrich K: NMR solution Structure of the human prion protein. Proc Natl Acad Sci USA 2000, 97: 145–150. 10.1073/pnas.97.1.145PubMed CentralView ArticlePubMedGoogle Scholar
- Tiana G, Simona F, Mori GMSD, Broglia RA, Colombo G: Understanding the determinants of stability and folding of small globular proteins from their energetics. Protein Science 2004, 13(1):113–124. 10.1110/ps.03223804PubMed CentralView ArticlePubMedGoogle Scholar
- Colacino S, Tiana G, Broglia RA, Colombo G: The determinants of stability in the human prion protein: insights into the folding and misfolding from the analysis of the change in the stabilization energy distribution in different condition. Proteins: Structure, Function and Bioinformatics 2006, 62(3):698–707. 10.1002/prot.20804View ArticleGoogle Scholar
- Ragona L, Colombo G, Catalano M, Molinari H: Determinants of protein stability and folding: Comparative analysis of beta-lactoglobulins and liver basic fatty acid binding protein. Proteins: Structure, Function and Bioinformatics 2005, 61(2):366–376. 10.1002/prot.20493View ArticleGoogle Scholar
- Swietnicki W, Petersen R, Gambetti P, Surewics WK: pH-dependent stability and conformation of the recombinant human prion protein PrP(90–231). J Biol Chem 1997, 272: 27517–27520. 10.1074/jbc.272.44.27517View ArticlePubMedGoogle Scholar
- Ziegler J, Sticht H, Marx UC, Muller W, Rosch P, Schwarzinger S: Cd and NMR studies of Prion Protein (PrP) helix 1. J Biol Chem 2003, 278: 50157–50181.Google Scholar
- Kuznetsov IB, Rackovsky S: Comparative computational analyis of prion proteins reveals two fragments with unusual structural properties and a pattern of increase in hydrophobicity associated with disease-promoting mutations. Prot Sci 2004, 13: 3230–3244. 10.1110/ps.04833404View ArticleGoogle Scholar
- Luhrs T, Riek R, Guntert P, Wutrich K: NMR structure of the human doppel protein. J Mol Biol 2003, 326: 1549–1557. 10.1016/S0022-2836(02)01471-7View ArticlePubMedGoogle Scholar
- Zahn R, Guntert P, von Schrotter C, Wutrich K: NMR structure o a variant of human prion protein with two disulfide bridges. J Mol Biol 2003, 326: 225–234. 10.1016/S0022-2836(02)01332-3View ArticlePubMedGoogle Scholar
- Whyte SM, Sylvester ID, Martin SR, Gill AC, Wopfner F, Schatzl HM, Dodson GG, Bayley PM: Stability and conformational properties of doppel, a prion-like protein, and its single-disuphide mutant. Biochem J 2003, 373: 485–494. 10.1042/BJ20021911PubMed CentralView ArticlePubMedGoogle Scholar
- Settanni G, Hoang TX, Micheletti C, Maritan A: Folding Pathways of Prion and Doppel. Biophysical J 2002, 83: 3533–3541.View ArticleGoogle Scholar
- Fernandez A, Kardos J, Scott LR, Goto Y, Berry RS: Structural defects and the diagnosis of amyloidogenic propensity. Proc Natl Acad Sci USA 2003.Google Scholar
- Berendsen HJC, Grigera JR, Straatsma TP: The missing term in effective pair potentials. J Phys Chem 1987, 91: 6269–6271. 10.1021/j100308a038View ArticleGoogle Scholar
- Hess B, Bekker H, Fraaije JGEM, Berendsen HJC: A linear constraint solver for molecular simulations. JCompChem 1997, 18: 1463–1472.Google Scholar
- Miyamoto S, Kollman PA: SETTLE: An analytical version of the SHAKE and RATTLE algorithms for rigid water models. J Comp Chem 1992, 13: 952–962. 10.1002/jcc.540130805View ArticleGoogle Scholar
- Berendsen HJC, Postma JPM, Gunsteren WFv, Nola AD, Haak JR: Molecular dynamics with coupling to an external bath. J Chem Phys 1984, 81: 3684. 10.1063/1.448118View ArticleGoogle Scholar
- Berendsen HJC, Spoel Dvd, Drunen Rv: GROMACS: A message passing parallel molecular dynamics implementation. Comp Phys Comm 1995, 91: 43–56. 10.1016/0010-4655(95)00042-EView ArticleGoogle Scholar
- Lindahl E, Hess B, Spoel Dvd: Gromacs 3.0: A package for molecular simulation and trajectory analysis. J Mol Mod 2001, 7: 306–317.Google Scholar
- Spoel Dvd, Lindahl E, Hess B, Buuren ARv, Apol E, Meulenhoff PJ, Tieleman DP, Sijbers ALTM, Feenstra KA, Drunen Rv, et al.: Gromacs User Manual version 3.2.2004. [http://www.gromacs.org]Google Scholar
- van Gunsteren WF, Daura X, Mark AE: GROMOS Force Field. Encyclopedia of Computational Chemistry 1998, 2: 1211–1216.Google Scholar
- Boutonnet N, Rooman M, Ochagavia M, Richelle J, Wodak S: Optimal protein-structure alignments by multiple linkage clustering, application to distantly related proteins. Prot Eng 1995, 8: 647–662.View ArticleGoogle Scholar
- Daura X, Jaun B, Seebach D, Gunsteren WFv, Mark AE: Reversible Peptide Folding in Solution by Molecular Dynamics Simulation. J Mol Biol 1998, 280: 925–932. 10.1006/jmbi.1998.1885View ArticlePubMedGoogle Scholar
- De Mori GMS, Micheletti C, Colombo G: All-atom folding simulations of the villin headpiece from stochastically selected coarse-grained structures. J Phys Chem B 2004, 108(33):12267–12270. 10.1021/jp0477699View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.