- Research article
- Open Access
Similar folds with different stabilization mechanisms: the cases of prion and doppel proteins
BMC Structural Biology volume 6, Article number: 17 (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 (PrPC) is converted into the infectious PrPScthrough 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 (PrPC) can undergo a conformational change of the native state leading to a new isoform designated PrPScwhich 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, PrPSccan 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 PrPSc, or with an increase in the oligomerization rate of the insoluble isoforms .
Despite the vast amount of research carried out on the Prion Protein, its physiological function is still unknown. Recent results have shown that the N-terminal unstructured region of the protein binds Cu(II) ions suggesting that it should be implicated in copper transport and regulation [9, 10]. Other studies suggested that PrPCmay function in signal transduction through a pathway involving Fyn Kinase . In this context, it was hoped that the study of mice animal models in which the Prnp gene was deleted could provide clues on the function of PrP. Deletion of the Prnp gene actually eliminated susceptibility to prion infection with PrPSc. However, this caused the degeneration of Purkinje neurons, causing a different type of neurological disease . The cause for this behavior was associated with a paralog of the Prnp gene, termed Prnd, with about 25% sequence identity to the PrP gene. In particular, Prnd encoded for a different protein named Doppel (Dpl) which has a 3D structure and native topology almost identical to PrPC, in spite of the low sequence similarity (25%) (Figure 1) . Most interestingly, Dpl does not convert to a different conformation, i.e. it seems to cause neurodegeneration without a transition to an analogous of the Scrapie form of Prion Protein .
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.
Both proteins tend to conserve their overall tertiary and secondary structural arrangements at both 310 K (first 50 ns of the simulations) and 350 K (interval between 50 and 70 ns of the simulations) (Fig. 2a and 2b), indicating the absence of major conformational changes or sub-global unfolding processes at these temperatures, as expected when considering that the Tm is about 60°C for PrP and about 50°C for Dpl, and that the characteristic time for unfolding is known to exceed 20 ns at 350 K. This is also evident in the two RMSD plots for the same simulations (Fig. 3a and 3b). Interestingly, the ordered secondary structure of the C-terminal part of helix H2' (after the helix kink) and the N-terminal part of helix H3 in Dpl appear to be unstable and undergo transitions to disordered conformations. The comparison of the flexibility properties of the two proteins, calculated as the Root Mean Square Fluctuation (RMSF) per residue over the whole simulation length, already highlights a difference between them. In the case of PrP at pH 7, a substantial increase in the flexibility can be noticed in the N-terminal part of the molecule when raising the temperature from 310 to 350 K. PrP helix H1 fluctuates as a rigid body conserving its secondary structure. In contrast, the flexibility properties of Dpl appear to be much less sensitive to variations in external conditions (Fig. 4), except for the disordered N-terminal region which displays high fluctuations at 310 K. However, in the last 5 ns of the 310 K simulation a stabilizing interaction between the N-terminal R51 and Q85 is established and not broken in the subsequent part of the simulation at 350 K. Interestingly, the regions encompassing the two β-strands and most of the H1 α-helix are of low flexibility at both temperature conditions. In contrast, higher values are observed for the loop connecting the second β-strand and the N-terminal part of helix H2, and for the terminal part of helix H2 after the kink (labeled H2'), despite the presence of a well defined secondary structure. These data are consistent with experimentally derived flexibility measures based on heteronuclear NOE determinations . These first characterizations of the dynamical properties suggest that the two proteins, despite sharing the same global 3D topology, differ in their finely detailed flexibility properties and fluctuations around the native conformation.
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.
This calculation indicates that Dpl possesses a core of amino acids whose interactions concentrate a fraction of the stabilization energy for the protein (about 30% of the overall stabilization energy) much higher than that concentrated in the PrP nucleus (about 20%) . The relative contribution of the stabilization core is calculated by determining the relative contribution to the total energy due to the interaction of residues corresponding to peaks over the threshold calculated using Eq. (2) in the Methods section (see ref.  for details). More interesting differences appear if one compares the variation of the energy spectrum of the first eigenvector for Dpl and PrP when the temperature is raised from 310 K to 350 K. In order to provide a quantitative estimate of the differences among the different profiles, we calculated the correlation coefficients between the corresponding components of the different eigenvectors. The results of the calculations are reported in Table 1. As noticed previously, the profile of the principal eigenvector of PrP at 350 K, pH 7 changes with respect to the situation at 310 K, their correlation coefficient being 0.71, and the distribution of peaks appears to become very similar to that of the first eigenvector for the trajectory calculated at 310 K or 350 K at pH 2 conditions, known to induce fibril formation in vitro (Fig. 5) (see  for the eigenvalue decomposition at low pH and ref.  for the experimental data). The main point here is that in all the cases where PrP is known to be in denaturing or misfolding conditions (high temperature at pH 7, or low pH), the profile of the principal eigenvector is characterized by the disappearance of the well defined stabilizing core of residues, with a general spreading of the stabilization energy along the whole sequence and a well defined difference with respect to the situation where the protein is known to be in native conditions (Fig. 5; Table 1).
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.
This implies that the stabilization pattern of Dpl is conserved also in conditions which are known to trigger misfolding and aggregation in the far-related homologous PrP. In particular, the peaks with the highest intensity over the flat t value are always located in the H2' and H3 helices of Dpl and correspond to residues E120, Q132 and W136. To compare the role in protein stabilization of the physico-chemical properties of these residues with those on analogous secondary structure motifs on PrP, a structural alignment of the two proteins was necessary. The structural alignment was carried out on the representatives of the most populated structural clusters obtained from the two 50 ns simulations at 310 K, as described in Methods. This alignment strategy objectively identifies which substructures of PrP can be correlated with those of Dpl. After this operation is completed, the components of the principal eigenvector of each of the two proteins are compared simply by superimposing the peaks corresponding to residues belonging to the superimposed secondary structures in the aligned structures. This should allow an objective comparison of the profiles (Fig. 6a and 6b), independent of the simple sequence alignment which may be flawed by the low homology degree. As shown in Fig. 6b, the common part of the stabilizing cores is located in the N-terminal part of helix H3. A large difference can be noticed for the region of helix H1, showing high value components for the first eigenvector of PrP and low values for the corresponding first eigenvector of Dpl. These differences reflect the higher helical propensity of the sequence of PrP helix H1 compared to that of Dpl: helix H1 from the Prion protein was in fact observed to be structured in solution in isolation with NMR and other spectroscopic tools . Moreover, Kuznetsov and Rackowsky  showed with comparative computational analysis that while several algorithms could correctly predict a helical conformation for PrP H1 sequence, this was not the case for the corresponding Dpl H1 sequence, which in most cases was predicted to have low helical propensity. This latter sequence, moreover, contains one chameleon sequence, which is not found in PrP. The other main significant difference is found in correspondence of helix H2' of Dpl, which is the part of the second helix following the kink, the only small but substantial structural difference between the two proteins (See Figs. 6 and 7). The comparison of the identities of residues corresponding to the highest peaks in Dpl with those in corresponding positions on PrP after the structural alignment shows that charged or highly polar residues in the former (E120, Q132) correspond to uncharged or hydrophobic residues on the latter (T190, V203), while the aromatic residue W136 on Dpl corresponds to a negatively charged moiety E207 on PrP, showing that the chemical properties of the residues belonging to the common cores are highly different. These three positions in the Prion Protein are all associated directly or are within one residue from sites whose mutations have been shown to induce disease or misfolding. Moreover, three residues conserved in Dpl and PrP, i.e. T113 (T183 in PrP), R133 (R208) and V184 (V210), which are part of the stabilizing core of Dpl are connected to genetic mutations related to increased probabilities of developing familial forms of TSE . The presence of conserved residues, important for stability and implied in the onset of the misfolding diseases in one of two far related proteins, may be indicative of the common origin of a part of the folding nucleus. W136 in Dpl, in particular, is located at the center of the large hydrophobic cleft which differentiates the surfaces of Dpl and Prp. The role of the large Trp side chain in this case is to stabilize this particular hydrophobic surface. Luhrs and coworkers  noticed that the hydrophobic residues forming this surface are highly conserved in doppel proteins from different species, and might represent a binding site for unidentified, functionally important factors. Since this surface is absent in PrP, this view might also support a function that is unique to doppel proteins. A second important structural difference between the two proteins is the presence in Dpl of an additional S-S bridge between residues 94 and 143 connecting the loop between β2 and α2 with the C-terminal segment of the protein. This second S-S bridge is absent in PrP. Luhrs and coworkers showed  that this second S-S contributes to the aforementioned hydrophobic cleft on the one hand, while on the other it causes a rather dramatic structural difference when compared to the analogous region of PrP. Since this loop in PrP was suggested to be part of the "Protein X" recognition epitope, which seems to be involved in transmission and propagation of TSEs, this conformational difference was considered as a possible basis for the functional differences between the two proteins. Experimental NMR structural determinations on a double mutant of PrP with an additional disulfide bridge in the "protein X" binding site showed that the double mutation (M166C/E221C) could be accommodated with slight and strictly localized conformational changes . The residues corresponding to the possible locations of the additional S-S bridge in PrP do not correspond to high peaks in the profile of the principal eigenvector (Fig. 5). This is consistent with the observations by Zahn et al. who showed that the insertion of a second disulfide bridge in the "protein X" epitope could be highly compatible with the structure of PrP.
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.
PrP, whose network of stabilization contacts is looser than that for Dpl, can form different sets of interactions on the folding pathway and end up folding to a different energy minimum, the PrPScisoform. It is worth noting, at this point, that the profile of peaks for the first eigenvector after complete unfolding of Dpl at 450 K is totally different from the native one, in contrast to what happens for PrP (Fig. 5). In particular, the interaction spectrum for denatured Dpl does not show any particularly ordered patterns of interaction with intense peaks appearing all along the sequence. The correlation coefficient between the components of the principal eigenvectors at 310 and 450 K, 0.44, is significantly lower than that between the components of the principal eigenvectors at 310 and 350 K, 0.93. The PrP case is different: after 20 ns at 450 K, where the structure is denatured and rapidly refolded to a β-sheet rich conformation, the clusters of strong interactions are formed by the same residues as those present in the native state, although in a different 3D structural arrangement. In this case the correlation coefficient between the principal components for 310 and 450 K is 0.84, significantly higher than in the case of Dpl. This value for PrP significantly higher than the overlap between the principal components for 310 K and all the other eigenvectors at 450 K. In order to ensure that the above reported observations are not random, the superposition between the first eigenvector at 310 K and all the eigenvectors at 450 K were calculated and the distributions of the correlations coefficient are reported in Fig. 8a) and 8b). For both cases the distributions are highly peaked at values corresponding to correlation coefficients of 0.08 substantially showing that, except for the case first eigenvectors at 310 and 450 K of the PrP protein, no correlation is present between the components of the first eigenvector at 310 K and all the other eigenvectors at 450 K.
The picture that emerges from these results suggests that the PrP sequence can access multiple conformations all compatible with a similar energy distribution, while the Dpl sequence cannot. Clearly, at this stage of simulation and analysis, this model only represents a possible rationalization of experimental observations on two closely correlated proteins, and should not be considered as a diagnostic tool to predict in advance whether a certain sequence is able to misfold to different intermediates or not. A second important caveat that one should consider is that the set of conformations on which the analysis is carried out is highly heterogeneous at 450 K, where large conformational transitions occur and highly diverse sets of interactions may be present. To address this point, the components of the principal eigenvector of the residue-residue interaction matrices were calculated for the first 10 most populated conformational clusters for the simulations of PrP and Dpl at 450 K, Fig 9a and 9b. In the case of Prion the components of the first eigenvector calculated for each cluster are more correlated to one another and to the components of the first eigenvector of the native simulation. The distribution of correlation coefficients between all the pairs of eigenvectors belonging to different conformational clusters was also calculated (Fig 10a and 10b). The distribution for PrP, Fig 10a, displays two superclusters. Within each supercluster the eigenvectors are highly correlated (cf. the peak centered around 1), while pairs belonging to two different superclusters are not. The presence of these superclusters reflects the conformational variability actually present at 450 K. It is anyway interesting to note that this new set of conformations, despite being structurally dissimilar, displays remarkably similar energy distributions, thus being very different from a random collection of unfolded states. In the case of Dpl, in contrast, a sensitively higher degree of heterogeneity is observed also for the distribution of the components of the first eigenvector for each cluster (see Figs. 9b and 10b.). Clearly, in the case of high temperature simulations, and for Dpl in particular, one should be careful in drawing conclusions based on sets of highly heterogeneous conformations. However, the fact that in the case for PrP similar interaction profiles, superimposable to the native one, are conserved for a highly diverse set of conformations is suggestive of the chamaleontic properties of the prion sequence, able to access different states thorough a similar set of interactions.
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.
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SC carried out the molecular dynamics studies and analysis and developed analysis software and drafted a first version of the manuscript. GT participated in the design of the study and in the development of the energy analysis method. GC conceived of the study, participated in its design and coordination and wrote the manuscript.
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Colacino, S., Tiana, G. & Colombo, G. Similar folds with different stabilization mechanisms: the cases of prion and doppel proteins. BMC Struct Biol 6, 17 (2006). https://doi.org/10.1186/1472-6807-6-17
- Prion Protein
- Stabilization Energy
- Stabilization Core
- Principal Eigenvector