Department of Chemistry, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland
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Abstract |
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Keywords: free energy/folding/molecular dynamics/peptide/type VIII turn
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Introduction |
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The intrinsic tendency of sequences to form a reverse turn conformation have been studied extensively experimentally and computationally (Dyson et al., 1988; Lazaridis et al., 1991
; Tobias et al., 1991
; Yao et al., 1994
; Yang et al., 1996
; Bashford et al., 1997
; Demchuk et al., 1997
; Santa et al. 1999
). Although some oligopeptides have been found to form reverse turns in aqueous solution, indicating that turns are at least marginally stable in aqueous solutions, free energy calculations have proposed that most of the turns are less stable than the extended structures. For example, the type I turn has been predicted to be significantly less stable than the corresponding extended structure (Tobias et al., 1990
; Lazaridis et al., 1991
; Yang et al., 1996
). Yang et al. estimated that regardless of sequence, the turn types I, I', II and II' are always less stable than the corresponding extended structures by 6.732.2 kJ/mol (Yang et al., 1996
). Bashford et al. studied the Ac-APGD-NHMe peptide and found that its free energy of folding is 0.0 ± 1.3 kJ/mol (Bashford et al., 1997
). Dyson et al. proposed on the basis of NMR data that population of type II turn of the same peptide is about 50% (Dyson et al., 1988
). Also the molecular dynamics simulations (Bashford et al., 1997
) are in fair agreement with the results: the 4
1 hydrogen bond existed during 20% of the total time of 7.7 ns. The proline containing sequence XY(cis-P)YD is a rare example of a peptide forming an exceptionally stable turn (of uncommon type VI), which has been estimated to be 8.4 kJ/mol more stable than the extended structure (Dyson et al., 1988
; Yao et al., 1994
). We have previously concluded that the segment SALN (Santa et al., 1999
) has a tendency to form an
rß turn (type VIII turn): the population of the
rß turn in SALN was estimated by NMR to be 50% at 278 K (Santa et al., 1999
) and, in MD simulations, the central SALN segment of the hexapeptide MSALNT and the octapeptide NMSALNTL folded into the
rß conformation.
The aim of this study was to characterize the formation and energetics of peptide rß conformations, in general and especially in some peptides derived from the sequence SALN which was originally found in the conserved N-terminal sequence of flagellin (Hakalehto et al., 1997
). In this work we applied free energy calculations based on the MM-PBSA (Molecular Mechanics PoissonBolzmann Surface Area) method (Vorobjev et al., 1998
; Jayaram, et al., 1998
; Kollman et al., 2000
). To avoid complete analysis of conformational space we computed the energetics between the ßßßß (extended) and ß
rßß conformations (type VIII turn). The relative free energies of the ß
r
rß conformations (type I turn) in a few selected sequences were also calculated. In order to draw a general picture about the occurence and statistics of the
rß stuctures and the sequences related to SALN, we analysed protein X-ray structures for the existence of XAXN sequences in turn conformations and report revised positional potentials for the type VIII turn (Hutchinson and Thornton, 1994
).
In this work we calculated the energetics of the conformations of 14 tetrapeptides. The first 11 peptides in Table I are the parent SALN and 10 peptides derived from it by one and two amino acid mutations. The two peptides EANL and MSHV were found to exist in a type VIII turn in protein X-ray structures. The sequence LSLI was included because it has been found in a conserved N-terminal sequence of flagellin (Hakalehto et al., 1997
).
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Materials and methods |
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There are two different nomenclatures for turn types. In the Ramachandran nomenclature the reverse turn name describes the regions of the Ramachandran plot (like rß) occupied by the turn residues i +1 and i + 2 (Wilmot and Thornton, 1990
). There are 16 different turn types in this nomenclature. In the conventional naming system turns are classified using four standard values for the
and
angles of the turn residues i +1 and i + 2 (Wilmot and Thornton, 1988
, 1990
). Normally deviations of ±30° are allowed for the angles. The most common turn types of this nomenclature are I, I', II, II', VIa, VIb and VIII. The type VIII turn studied here corresponds to the
rß turn in the Ramachandran nomenclature. However, in the Ramachandran nomenclature larger than ±30° deviations are allowed for the turns. In our protein databank analyses we used the conventional nomenclature with ±30° deviations, whereas the criteria of the Ramachandran nomenclature were used to classify turn structures of the MD simulations. To stress this difference, the two naming conventions are applied.
Molecular dynamics simulations
For the simulations of the extended conformations the values of and
angles were set to 113 and 119°, respectively. For the simulations of the
rß conformations the
angles of residues i + 1 and i + 2 were set to 54 and 140°, respectively, and the
angles to 65 and 85°, respectively. For the
simulations the respective values were set to 60, 30, 90 and 0° (Wilmot and Thornton, 1988
). To relax the structures, MD simulations of 10 ps at 300 K in vacuum were performed. The geometries of the peptides were then minimized and the peptides were embedded into the water box with dimensions of 43.5x34.1x34.1 Å. The water box was equilibrated by heating the system to 300 K in 20 ps followed by another 20 ps of MD at that temperature. The simulations were performed at a constant pressure of 1 atm using the Berendsen temperature coupling algorithm (Berendsen et al., 1984
) to keep the temperature at 300 K. This protocol was found to produce simulation systems with the desired density of 1 g/cm3. The constraints were then removed and the systems minimized. In the following constant volume simulations we used the NOSE method (Nose, 1984
; Hoover, 1985
) to keep the simulation system at 300 K. The CHARMM force field (Brooks et al., 1983
) and the TIP3 water model (Jorgensen et al., 1983
) were used. The equations of motion were solved using the velocityVerlet algorithm (Verlet, 1967
) and a time step of 1.0 fs. The calculations were carried out using a non-bonded cut-off value of 9 Å. The non-bonded energies and forces were smoothly truncated using the van der Waals switching function and an electrostatic shifting function. The non-bonded energies were updated at every 20 steps. The SHAKE algorithm (Ryckaert et al., 1977
) was used to constrain the positions of hydrogens with the tolerance of 109 Å. The CHARMM version 23.2 and the all-atom PARMM22 force field were used in the simulations.
Free energy calculations
In the MM-PBSA method, the snapshot structures of the solute are taken from the MD simulation in explicit water and molecular mechanical gas-phase energies, solvation free energies and entropies are calculated for each structure. The total free energy (Gtot) of a conformation is the average of all the snapshot energies. The total free energy difference between two conformations is calculated from the equation
![]() | (1) |
GPB is the difference in the average electrostatic solvation free energies of two conformations calculated with a numerical solution to the PoissonBolzmann equation using the PBEQ module of the CHARMM program (Nina et al., 1997
). In the calculations we used
= 1 for the solute and
= 80 for the solvent water. The size of the grid was 25.2x25.2x25.2 Å with 2.5 points/Å. The set of atomic radii of Nina et al. and the all-atom PARMM22 force field of CHARMM were used.
The non-polar solvation free energies (Gnp) were calculated with the following equation (Wesson and Eisenberg, 1992
) using the Asp values of Kyte and Doolittle (1982):
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For the vibrational entropy term (TS) the solute structures, saved every 1 ps, were first energy minimized with the steepest descent method followed by minimization with the adopted-basis NewtonRaphson method to reach the local minimum. The mass-weighted second-derivative matrix was then calculated and diagonalized for each structure to give normal modes and, thereby, vibrational entropy correction.
Databank analysis
The June 2000 issue of the PDB SELECT representative set (Hobohm and Sander, 1994) of PDB structures (Bernstein et al., 1977
) with 95% identity cutoff (6548 chains) was scanned for sequences matching for the motives AAIN, AALN, AAMN, DALN, EANL, LSLI, MSHV, PAIN, PALI, PALN, PAMN, SAFN, SAIN, SALN, SAMN, SATN, SAVN, SMLN, SPLN, SSIN, TAIN, TALN and TAMN by an in-house written computer program. The dihedrals
and
of the residues i + 1 and i + 2 and the distance between C
(i) and C
(i + 3) atoms of all sequences found were calculated. The sequences with C
(i)C
(i + 3) distances of <7 Å were considered to be in a turn conformation. A further databank analysis was done to find out amino acid preferences for type VIII turn. In the analysis the February 2000 issue of the PDB SELECT (Hobohm and Sander, 1994
) with 25% identity cutoff (1289 chains) was combined with the PROMOTIF summary of the PDBsum database (Laskowski et al., 1997
) and searched for type VIII turns. The total number of type VIII turns found was 1337. The positional potentials of amino acid residues at each position i, i + 1, i + 2 and i + 3 of type VIII turn were then calculated with the following equation (Hutchinson and Thornton, 1994
):
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Results and discussion |
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To study the convergence of the calculated energies we carried out 500 ps MD simulations for the ßßßß (Figure 1a) and ß
rßß (Figure 1b
) conformations of SALN. On the basis of these simulations we concluded that 250 ps simulations produce average energies accurate enough for our purposes. However, convergence of the energy of the simulations was monitored and if needed, longer simulations were performed. An additional 500 ps simulation was performed for the extended structure of SALN. In the simulation the conformations of the terminal groups did not stay in the ß region but visited also other regions of the conformational space. However, the total free energy of this simulation stayed within 1.3 kJ/mol from the first simulation. One of the cases in which the energy did not converge in 250 ps was the extended structure of SATN. In this case the reported
Gtot was calculated from the last 368 ps of the total simulation time of 668 ps. It seems that the unsymmetrical ß-branched side chain prevented the peptide from adopting the most stable conformation during the first 250 ps of the MD simulation.
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C(i)C
(i + 3) distance distribution analysis
The distribution of the C(i)C
(i + 3) distance during the 250 ps MD simulations of the
ß turn conformations of all our peptides are shown in Figure 2
. The common criterion for a turn has been that the distance between the C
(i) and C
(i + 3) atoms is <7 Å (Wilmot and Thornton, 1988
). However, for a type ß
r turn a distance of 7.3 Å has been accepted (Ashish et al., 2000
). In the case of SALN 79% of the conformations have distances <7.0 Å and the highest population density is located at
6.5 Å. In addition, 92% of the conformations have distances <7.4 Å. Similar conformational behaviour applies for the rest of the peptides. In the cases of SAVN, SATN, AALN, LSLI and EANL more than 80% of the conformations have a C
(i)C
(i + 3) distance <7.0 Å. SAIN and SSIN have distance distributions with the highest population density located >7.0 Å. In the case of SAIN the maximum is at 7.3 Å and 63% of the structures have the C
(i)C
(i + 3) distance <7.4 Å. In the case of SSIN there are two maxima. The first maximum is located at 6.3 Å and these structures are clearly classified as turns, whereas the second one is located at 7.7 Å, being outside any turn criterion.
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The free energies of the tetrapeptide conformations in Table I show that
rß conformations of SALN, SAIN, SAVN, SATN, SSIN and MSHV are of comparable stability to their extended conformations. This is in agreement with the experimental NMR data on the SALN (Santa et al., 1999
) and SATN (unpublished data) tetrapeptides. These two peptides have equal populations of extended and type VIII turn conformations in aqueous solution. The free energy calculations show that the
conformations are at least 12 kJ/mol less stable, as expected, than the extended conformations. On the basis of the calculated free energies, the assumption that the ßßßß and ß
rßß structures are the main solution conformations seems to be a good approximation at least for SALN and SATN.
The stability order of rß turns of the SAXN series of peptides is SATN
SALN > SAIN, SAVN > SAMN, SAFN (Table I
). SATN has the most stable
rß turn of these peptides, being 4 kJ/mol more stable than the extended conformation. Although we have a limited number of peptides in this comparison, it seems that residues with small branched side chains (Thr, Ile, Leu and Val) at position i + 2 stabilize the ß conformation of the residue i + 1. Note also, that with the exception of MSHV, the peptides having the most stable
rß conformations have Ser at position i. In SALN the hydroxyl oxygen of Ser interacts with the backbone amide proton of Leu, which presumably stabilizes the turn. Because the two tetrapeptides with the most stable
rß turn, SSIN and MSHV, have Ser at position i + 1, Ser seems to stabilize the
rß turn also at position i + 1. The stability of the
rß conformation of SSIN and MSHV can be partly explained by the ability of Ser at position i + 1 to make a hydrogen bond with its own backbone amide proton. It has been proposed (Wilmot and Thornton, 1990
), based on protein structure analysis, that His at position i + 2 stabilizes the ß conformation of that position. This occurs probably via an interaction between the side-chain NH and the backbone carbonyl oxygen of residue i + 3. The interaction was observed also in the MD simulations.
Energetic factors stabilizing the rß turn
The EvdW and
GPB,elect terms play key roles in the stabilities of the different peptide conformations. The SAXN peptides having the most stable
rß conformations have a negative
EvdW term for the turn formation. In the cases of SALN, AALN and DALN, the
EvdW terms for the turn formation are similar, 4.6, 4.6 and 5.9 kJ/mol, respectively. Thus, the order of stability of these three peptides (SALN > AALN > DALN) is determined by the other energy terms. The
Gnp term destabilizes the
rß turn of DALN (destabilization is 13 kJ/mol) and AALN (8.4 kJ/mol) more than that of SALN (4.2 kJ/mol). This order is the reverse of the preferences of these residues towards position i observed in protein X-ray structures (Table III
). In addition to
EvdW, also the
GPB,elect term and the entropy contribution are important for the stability of the turn conformation. For example, the
GPB,elect term is the most favourable for AALN and most unfavourable for DALN among the three peptides. In the cases of SSIN and MSHV, which form the most stable turns of the peptides studied, they have
EvdW,
GPB,elect and the entropy contribution which all are favourable for the turn formation. The entropy contribution is calculated to be unfavourable for the
conformation on average by 5.5 kJ/mol compared with the ßß and 2.2 kJ/mol as compared with the
rß conformation (Table I
). This agrees with the idea that in the
conformation both the side chain and backbone motions are restricted in comparison with the other conformations. The
conformation is favoured by the
EvdW and
GPB term relative to the ßß conformation. The more compact
structure is the probable reason for the favourable
EVdW term. Since the
Eelec term more than compensates the
GPB term, the electrostatic energies (
GPB,elec) in total are unfavourable for the
in comparison with the ßß conformation.
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The PDB SELECT set (Hobohm and Sander, 1994) of PDB structures with 95% identity cutoff was searched for the occurrence of the selected 23 sequences with four residues in a type VIII turn and in structures with the C
(i)C
(i + 3) distance of <7 Å (Table II
). The latter structures were further divided into
conformations and the rest of the structures. There were 930 tetrapeptides matching the sequences searched and 613 (66%) of those were in a turn conformation. However, most of them (579) were in an
conformation, only 24 were in a type VIII turn and the other 10 structures belong to other turn types. Note that there were only 42 tetrapeptides matching the sequences searched when the set with 25% identity cutoff was searched (Table II
).
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The positional potentials of the amino acid residues for positions i, i + 1, i + 2 and i + 3 of type VIII turn are shown in Table III. In this analysis the protein data set with 25% identity cutoff was used. The potentials indicate the preference of a residue to be in a specified position of the type VIII turn. The values of Table III
that are statistically significant at the 5% level (d
1.97) are indicated with asterisk and those significant at the 0.01% level (d
3.35) are in bold. Hutchinson and Thornton (1994) have analysed previously the type VIII turns. Here we have updated this analysis with larger number of turns (1337 vs 325 turns) and more stringent criteria for the inclusion of homologous proteins (25 vs 35%). The results of the present analysis confirm the main lines of the earlier analyses but also reveals several new strong positional preferences, especially for positions i + 1 and i + 2.
The present analysis confirms the preferences of Gly and Pro for position i and reveals Cys (at the 0.01% level) and Ser (at the 5% level ) as new residues with preference for this position in type VIII turn. The unfavourable potential (<1.0) of Asp at this position is in agreement with the free energy calculations (Table I). Calculations showed that this is due to the unfavourable
GPB and
Gnb energy terms for the turn formation. Pro and Asp were found in the previous analysis to favour position i + 1. The preference of Pro has been explained as being due to the correct
and
angles of this position and that of Asp to the interaction of the side chain with the main chain amide (Hutchinson and Thornton,1994
). The new residue found to favour i + 1 position is Lys. On the other hand, Cys, Met, Phe, Ile, Val, Leu, Trp and Gly are significantly unfavoured for the i + 1 position, at which the main chain is in the
conformation. Thus, the unfavourable potentials of most of these residues is explained by their tendency for a ß conformation (Fersht, 1998
). This analysis confirms the earlier found preferences of Val, Asn and Asp towards position i + 2. In the earlier analysis there were indications that also Ile and Phe would favour this position. In agreement with this, Ile and Phe, as well as Tyr, now have significant preference for position i + 2. Asn and Asp are known to form a classic Asx turn (Rees et al., 1983
). Hutchinson and Thornton suggested that Ile and Phe favour this position because they prefer to adopt the ß conformation (Hutchinson and Thornton, 1994
). That also the new i + 2-favouring amino acids, Phe and Tyr, prefer the ß conformation (Fersht, 1998
) confirms that it is likely a reason for the observed amino acid preference of this position. The present analysis shows that Pro prefers the i + 3 position, in agreement with the previous analysis, but disagrees with it by indicating that Thr is not preferred. Furthermore, this analysis reveals that Ile, Lys and Val significantly favour the i + 3 position. There is no clear explanation for these potentials. Hutchinson and Thornton suggested that these peptides are favoured at this position because the i + 3 position is often followed by a ß strand (Hutchinson and Thornton, 1994
).
Implications for the structure of unfolded proteins
That the rß turn (type VIII turn) is energetically accessible for several peptide sequences is in contrast to the stabilities of other types of turns. For example, turns of the types I, I', II and II' have been reported to be energetically less stable than their extended structures and there are only a few examples of sequences with stable turns. Since in the
rß turn there is no backbone hydrogen bond, as in several other types of turns, the detection of this turn type is not straightforward. This is probably one of the reasons why
rß turns have been detected and studied less than the other types of turns. The indications of this work, that there exist a large number of sequences capable of forming stable
rß turns, suggests that in the random coil (or unfolded) structure of a protein there may be a large number turns present. If the protein backbone is in a ß conformation, the
rß conformation is also kinetically favoured because only one torsional barrier must be crossed. Such turns may act as initiation points of secondary structure or hydrophobic cluster formation in the early stages of protein folding. As suggested recently (Pappu et al., 2000
), turns of the unfolded protein significantly reduce the number of possible conformations and in this way enhance protein folding.
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Notes |
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Acknowledgments |
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References |
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Received January 31, 2001; revised February 8, 2002; accepted April 18, 2002.