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Oligomerization of Amyloid Aß_16–22 Peptides Using Hydrogen Bonds and Hydrophobicity Forces

Complex Systems Division, Department of Theoretical Physics, Lund University, Lund, Sweden

Correspondence: Address reprint requests to A. Irbäck, Tel: 46-46-222-3493; Fax: 46-46-222-9686; E-mail: anders{at}thep.lu.se.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The 16–22 amino-acid fragment of the ß-amyloid peptide associated with the Alzheimer's disease, Aß, is capable of forming amyloid fibrils. Here we study the aggregation mechanism of Aß_16–22 peptides by unbiased thermodynamic simulations at the atomic level for systems of one, three, and six Aß_16–22 peptides. We find that the isolated Aß_16–22 peptide is mainly a random coil in the sense that both the -helix and ß-strand contents are low, whereas the three- and six-chain systems form aggregated structures with a high ß-sheet content. Furthermore, in agreement with experiments on Aß_16–22 fibrils, we find that large parallel ß-sheets are unlikely to form. For the six-chain system, the aggregated structures can have many different shapes, but certain particularly stable shapes can be identified.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The fibrillar aggregates that characterize amyloid diseases, such as the Alzheimer's disease, are formed by specific peptides or proteins. However, it is known that several non-disease-related proteins are capable of forming similar amyloid structures (Rochet and Lansbury, 2000; Dobson, 2003), and that the aggregation of such proteins can be cytotoxic (Bucciantini et al., 2002). This suggests, first, that polypeptide chains have a general tendency to form amyloid structures and, second, that natural proteins should have evolved mechanisms to avoid this tendency. Such mechanisms have indeed been proposed (Otzen et al., 2000; Broome and Hecht, 2000; Richardson and Richardson, 2002). The propensity of a given polypeptide chain to form amyloid fibrils depends, nevertheless, on its amino-acid sequence (West et al., 1999; Villegas et al., 2000; Hammarström et al., 2002; López de la Paz et al., 2002; Chiti et al., 2003), and short sequence stretches promoting amyloid formation have been identified (López de la Paz and Serrano, 2004; Ventura et al., 2004).

Although the structure of amyloid fibrils is not known in atomic detail, there is ample evidence from x-ray fiber diffraction studies that the core of the typical amyloid fibril is composed of ß-sheets whose strands run perpendicular to the fibril axis (Sunde and Blake, 1997). More detailed information is available, for example, for fibrils made from different fragments of the Alzheimer's Aß peptide. In particular, there is evidence from solid-state NMR studies for a parallel organization of the ß-strands in Aß_10–35 (Burkoth et al., 2000) and Aß_1–40 (Petkova et al., 2002) fibrils, and for an antiparallel organization in Aß_34–42 (Lansbury et al., 1995), Aß_11–25 (Petkova et al., 2004), and Aß_16–22 fibrils (Balbach et al., 2000; Gordon et al., 2004). Most of these fragments contain the hydrophobic Aß_16–20 segment (KLVFF), which is known to be important in the Aß–Aß interaction (Tjernberg et al., 1996).

Small peptides like Aß_16–22 are well suited as model systems for probing the mechanisms of aggregation and fibril formation, and are being studied not only in vitro but also in silico. Computer simulations of simplified (Bratko and Blanch, 2001; Harrison et al., 2001; Dima and Thirumalai, 2002; Jang et al., 2004; Friedel and Shea, 2004) and atomic (Ma and Nussinov, 2002a,b; Klimov and Thirumalai, 2003; Gsponer et al., 2003; Paci et al., 2004) models have provided useful insights into the aggregation behavior of some peptide systems. To properly explore the free-energy landscape of aggregation at the atomic level is, nevertheless, a computational challenge.

Here we investigate the formation and properties of Aß_16–22 oligomers by unbiased Monte Carlo (MC) simulations of systems with up to six chains, using a sequence-based atomic model with an effective potential based on hydrogen bonds and hydrophobic attraction (no explicit water molecules). The same model has previously been used to study the folding of individual peptides (Irbäck et al., 2003; Irbäck and Sjunnesson, 2004; A. Irbäck and S. Mohanty, unpublished). It was shown that this model is able to fold several different peptides, both -helical and ß-sheet peptides, for one and the same choice of parameters. The calculated melting behaviors were, moreover, in good agreement with experimental data for all these peptides.

	MODEL AND METHODS

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The main object of study in this article is the peptide Aß_16–22, given by acetyl-Lys-Leu-Val-Phe-Phe-Ala-Glu-NH₂. We consider systems of one, three, and six Aß_16–22 peptides. The multichain systems are contained in periodic boxes. All the interactions are short range, which makes the implementation of the periodic boundary conditions straightforward. The box sizes are (35 Å)³ and (44 Å)³ for three and six chains, respectively, corresponding to a constant peptide concentration. For computational efficiency, the peptide concentration is taken to be high.

Our model (Irbäck et al., 2003; Irbäck and Sjunnesson, 2004; A. Irbäck and S. Mohanty, unpublished) contains all atoms of the peptide chains, including hydrogen atoms. The model assumes fixed bond lengths, bond angles, and peptide torsion angles (180°), so that each amino acid only has the Ramachandran torsion angles , , and a number of side-chain torsion angles as its degrees of freedom. Numerical values of the geometrical parameters held constant can be found elsewhere (Irbäck et al., 2003).

The interaction potential

(1)

is composed of four terms, which we describe next. Energy parameters are given on a scale (A. Irbäck and S. Mohanty, unpublished) such that a temperature of T = 300 K corresponds to kT 0.447 (k is Boltzmann's constant).

The first term in Eq. 1, E_ev, represents excluded-volume effects and has the form

(2)

where the summation is over pairs of atoms (i,j), _ev = 0.10, and _i = 1.77, 1.75, 1.55, 1.42, and 1.00 Å for S, C, N, O, and H atoms, respectively. The parameter _ij has the value 0.75 for all pairs except those connected by three covalent bonds, for which _ij = 1. When the two atoms belong to different chains, we always use _ij = 0.75. To speed up the calculations, Eq. 2 is evaluated using a cutoff of and pairs with fixed separation are omitted.

The second energy term, E _loc, is a local intrachain potential. It has the form

(3)

where the inner sum represents the interactions between the partial charges of the backbone NH and C'O groups in one amino acid, I. This potential is not used for Gly and Pro amino acids which have very different , distributions, but is the same for all other amino acids. The inner sum has four terms (NC', NO, HC', and HO) which depend only on the - and -angles for amino acid I. The partial charges are taken as q_i = ±0.20 for H and N and q_i = ±0.42 for C' and O (Brändén and Tooze, 1991), and we put _loc = 100, corresponding to a dielectric constant of _r 2.5.

The third term of the energy function is the hydrogen-bond energy E_hb, which has the form

(4)

where the two functions u(r) and v(,ß) are given by

(5)

(6)

We consider only hydrogen bonds between NH and CO groups, and r_ij denotes the HO distance, _ij the NHO angle, and ß_ij the HOC angle. The parameters and _hb are taken as 3.1, 2.0, and 2.0 Å, respectively. The function u(r) is calculated using a cutoff of r^c = 4.5 Å. The first sum in Eq. 4 contains backbone-backbone interactions, whereas the second sum contains interactions between charged side chains (Asp, Glu, Lys, and Arg) and the backbones. For intrachain hydrogen bonds we make two restrictions. First, we disallow backbone NH (C'O) groups to make hydrogen bonds with the two nearest backbone C'O (NH) groups on each side of them. Second, we forbid hydrogen bonds between the side chain of one amino acid with the nearest donor or acceptor on either side of its C. For interchain hydrogen bonds, we make no such restrictions. As a simple form of context dependence, we assign a reduced strength to hydrogen bonds involving chain ends, which tend to be exposed to water. Following the experimental studies of the Aß_16–22 peptide (Balbach et al., 2000; Gordon et al., 2004), we have used acetyl and amide capping groups at the ends. A hydrogen bond involving one or two such groups is reduced in strength by factors of 2 and 4, respectively.

The fourth energy term, E_hp, represents an effective hydrophobic attraction between nonpolar side chains. It has the pairwise additive form

(7)

where C_IJ is a measure of the degree of contact between side chains I and J, and M_IJ sets the energy that a pair in full contact gets. The matrix M_IJ is defined in Table 1. To calculate C_IJ we use a predetermined set of atoms, A_I, for each side chain I. We define C_IJ as

(8)

where the function f(x) is given by f(x) = 1 if x < A, f(x) = 0 if x > B, and f(x) = (B–x)/(B–A) if A < x < B [A = (3.5 Å)² and B = (4.5 Å)²]. Roughly speaking, C_IJ is the fraction of atoms in A_I or A_J that are in contact with some atom from the other side chain. For Pro, the set A_I consists of the C_ß, C, and C atoms. The definition of A_I for the other hydrophobic side chains has been given elsewhere (Irbäck et al., 2003). For pairs that are nearest or next-nearest neighbors along the same chain, we use a reduced strength for the hydrophobic attraction; M_IJ is reduced by a factor of 2 for next-nearest neighbors, and taken to be 0 for nearest neighbors.

Our simulations are carried out using two different elementary moves for the backbone degrees of freedom: first, the highly nonlocal pivot move in which a single backbone torsion angle is turned; and second, a semilocal method (Favrin et al., 2001) that works with up to eight adjacent backbone degrees of freedom, which are turned in a coordinated manner. Side-chain angles are updated one by one. In addition to these updates, we also use rigid-body translations and rotations of whole chains. Every update involves a Metropolis accept/reject step, thus ensuring detailed balance. All our simulations are started from random configurations. All statistical errors quoted are 1 errors obtained from the variation between independent runs. We performed nine runs with 10⁸ elementary MC steps for N_c = 1, 11 runs with 10⁹ MC steps for N_c = 3, and 18 runs with 2 x 10⁹ MC steps for N_c = 6. Each of the N_c = 6 runs required 12 CPU days on a 1.6-GHz computer.

To characterize the behavior of these systems, we first determine the secondary structure. For a chain with N amino acids, we define the -helix and ß-strand contents as the fractions of the N–2 inner amino acids with their (,) pair in the -helix and ß-strand regions of the Ramachandran space. We assume that -helix corresponds to –90° < < –30°, –77° < < –17° and that ß-strand corresponds to –150° < < –90°, 90° < < 150°. The average -helix and ß-strand contents, over all the chains of the system, are denoted by H and S, respectively.

To distinguish between parallel and antiparallel ß-sheet structure, we examine the orientation of end-to-end vectors. For a given multichain configuration, we first determine all pairs of chains such that 1), their interchain hydrogen bond energy is (roughly corresponding to 2–3 hydrogen bonds), and 2), both chains have a ß-strand content >0.5. For each such pair of chains, we then calculate the scalar product of their normalized end-to-end unit vectors. If this scalar product is >0.7 (<–0.7), we say that the two chains are parallel (antiparallel). We denote the numbers of parallel and antiparallel pairs of chains by n₊ and n_–, respectively. Fig. 1 illustrates the hydrogen-bond patterns in parallel and antiparallel ß-sheets.

View larger version (24K): [in this window] [in a new window]   FIGURE 1  Schematic illustrations of the hydrogen-bond patterns for in-register, parallel ß-strands (left) and in-register, antiparallel ß-strands (right).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

View larger version (44K): [in this window] [in a new window]   FIGURE 2  Monte Carlo evolution in a simulated-tempering run for Nc = 6 Aß16–22 peptides. (a) The total energy E (solid line) and the hydrogen-bond energy Ehb (dashed line), both in kcal/mol. (b) The temperature index k. There are seven allowed temperatures Tk, satisfying T0 = 287 K < T1 < ... < T6 = 369 K. Measurements are taken every 106 MC steps.

View larger version (10K): [in this window] [in a new window]   FIGURE 3  (a) The -helix content H against temperature T for Aß16–22 for Nc = 1 (), Nc = 3 (•), and Nc = 6 (). Lines joining data points are only a guide for the eye. (b) Same for the ß-strand content S; note, however, that the scales in a and b are different.

View larger version (16K): [in this window] [in a new window]   FIGURE 4  Specific heat Cv against temperature T for Nc = 1, 3, and 6 Aß16–22 peptides, as obtained using histogram reweighting techniques (Ferrenberg and Swendsen, 1988). The bands are centered around the expected values and show statistical 1 errors. Cv is defined as Cv = (NcN)–1dE/dT = (NcNkT2)–1(E2–E2), where Nc is the number of chains, N is the number of amino acids per chain, and O denotes a Boltzmann average of variable O.

For the N_c = 3 system, Klimov and Thirumalai (2003) furthermore found evidence for an obligatory -helical intermediate. To see whether or not such an intermediate exists in our model, we divided the energy axis into bins and calculated the average -helix and ß-strand contents for each bin, at a fixed temperature near the specific heat maximum. Fig. 5 shows the resulting -helix and ß-strand profiles H(E) and S(E). We see that the ß-strand content S(E) increases steadily with decreasing energy. The -helix content H(E), on the other hand, has its global maximum at E 130 kcal/mol. However, the maximum value of H(E) is very small. Hence, we find no sign of an obligatory -helical intermediate in our model. Most of the amino acids in a typical configuration at intermediate energies are either random coils or ß-strands.

View larger version (13K): [in this window] [in a new window]   FIGURE 5  The -helix () and ß-strand (•) profiles H(E) and S(E) (see the text) for the six-chain Aß16–22 system at T = 325 K.

Table 2 shows this distribution for the N_c = 3 system at T = 275 K. For this system, the most probable combination of (n₊,n_–) is (1,1), corresponding to a mixed ß-sheet. At the same time, the distribution shows a clear asymmetry. The frequency of occurrence for antiparallel ß-sheets with (n₊,n_–) = (0,2) is a factor of 7 higher than that for parallel ß-sheets with (n₊,n_–) = (2,0).

Although the statistical uncertainties are somewhat large, the results in Tables 2 and 3 show some clear trends. The most striking one is that large n₊ values are strongly suppressed, which means that large parallel ß-sheets are very unlikely to form. The probability of having large antiparallel ß-sheets is much higher. Compared to purely antiparallel ß-sheet structures, it is possible that mixed ß-sheet structures are more difficult to extend to large stable structures. To be able to check whether or not this is the case, simulations of larger systems are required.

Why are antiparallel ß-sheets favored over parallel ones? Klimov and Thirumalai (2003) concluded that Aß_16–22 peptides make antiparallel ß-sheets because of Coulomb interactions between charged side chains; the two end side chains of the Aß_16–22 peptide carry opposite charges, which indeed should make the antiparallel orientation electrostatically favorable. However, our model completely ignores Coulomb interactions between side-chain charges and still strongly favors the antiparallel organization. Other mechanisms than Coulomb interactions between side-chain charges might therefore play a significant role, such as the geometry of backbone-backbone hydrogen bonds (see Fig. 1), steric effects, and the precise distribution of hydrophobicity along the chains. A recent experimental study (Gordon et al., 2004) highlights the importance of the hydrophobicity distribution. This study showed that the ß-sheet structure of Aß_16–22 fibrils can be changed from antiparallel to parallel by adding an octanyl end group to the peptide which increases its amphiphilicity.

To probe the registry of the ß-sheets, we monitored backbone-backbone hydrogen bond patterns (see Fig. 1). Fig. 6 illustrates three possible antiparallel registries: 17 + k 20 – k (Fig. 6 a), 17 + k 21 – k (Fig. 6 b), and 17 + k 22 – k (Fig. 6 c). The 17 + k 21 – k registry is the one found in experiments on Aß_16–22 fibrils (Balbach et al., 2000; Gordon et al., 2004), whereas experiments on fibrils made from the slightly larger segment Aß_11–25 found evidence for the 17 + k 20 – k registry at pH 7.4 and for the 17 + k 22 – k registry at pH 2.4 (Petkova et al., 2004). In our calculations, the 17 + k 20 – k and 17 + k 21 – k registries occur with high and comparable frequencies. The 17 + k 22 – k registry is, by contrast, strongly suppressed, which probably is due to hydrophobic effects, although steric clashes between the large Phe side chains could play a role, too. As to the 17 + k 20 – k and 17 + k 21 – k registries, it would be very interesting to see whether their relative frequencies of occurrence depend on (n₊,n_–), but that will require higher statistics than those provided by the present calculations.

View larger version (9K): [in this window] [in a new window]   FIGURE 6  (a–c) Schematic representations of three different registries for an antiparallel pair of Aß16–22 peptides.

As an example of a peptide with a significant hydrophobicity but an uneven distribution of it, we studied the peptide acetyl-Lys-Phe-Phe-Ala-Ala-Ala-Glu-NH₂, in which the two strongly hydrophobic Phe amino acids are asymmetrically placed. For this peptide, we obtained aggregated ß-sheet structures with a predominantly parallel ß-strand organization, which in particular confirms that our model is capable of generating stable parallel ß-sheets.

Examples of low-energy structures
It is known that relatively small assemblies formed early in the aggregation of full-length Aß (Lambert et al., 1998; Walsh et al., 1999, 2002), as well as non-disease-related proteins (Bucciantini et al., 2002), can be toxic—which makes it very interesting to study possible oligomer shapes. In addition, such structures represent potential seeds for the fibril formation.

From our simulations, we find that the six-chain Aß_16–22 system does not exhibit a single dominating free-energy minimum, but rather a number of more or less degenerate local minima. Fig. 7 shows two snapshots of such minima. The ß-strand content is, as noted earlier, high, and the structures shown in Fig. 7 illustrate this property.

View larger version (27K): [in this window] [in a new window]   FIGURE 7  Two typical low-energy structures from our simulations of six Aß16–22 peptides: a five-stranded ß-sheet (left), and two three-stranded ß-sheets "sandwiching" several of their hydrophobic side chains between them (right). Drawn with RasMol (Sayle and Milner-White, 1995).

In none of our simulations did we find any indication of a free-energy minimum in which the ß-strands are joined end-to-end to form the so-called ß-helix (Wetzel, 2002). In our model, stability is enhanced by increasing the number of hydrogen bonds or by increasing hydrophobic contacts. For system sizes as small as those we examined, the ß-helix is inferior to many competing structures in both of these respects, and hence its absence is expected.

	CONCLUSION

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Using a sequence-based atomic model which was originally developed for folding studies of single peptides (Irbäck et al., 2003; Irbäck and Sjunnesson, 2004; A. Irbäck and S. Mohanty, unpublished), we studied the aggregation properties of Aß_16–22 peptides. In this model, we found that Aß_16–22 peptides have a high propensity to self-assemble into aggregated structures with a high ß-strand content, whereas the isolated Aß_16–22 peptide is mainly a random coil. Both parallel and antiparallel arrangements of the ß-strands occur in the model, with a definite preference for the antiparallel arrangement.

It is important to note that we find this preference for the antiparallel ß-strand orientation despite ignoring the Coulomb interactions between the two charged side chains at the ends of the peptide. It has been suggested (Klimov and Thirumalai, 2003) that such Coulomb interactions are the main determinant for the antiparallel orientation. Although these Coulomb interactions might enhance the tendency for Aß_16–22 peptides to form ß-sheets with an antiparallel organization, our results strongly suggest that other factors play a significant role, too. It is worth noting that the orientation is not necessarily determined solely by sequence-specific side-chain interactions, as antiparallel ß-sheets are widely held to be intrinsically more stable than parallel ones. For the Aß_16–22 peptide, which in particular lacks a clear amphiphilicity, there is no obvious mechanism to overcome this tendency.

In our simulations, we did not observe an absolute free-energy minimum, but rather several nearly degenerate minima corresponding to different supramolecular structures, all consisting of arrangements of ß-strands. Apart from single ß-sheets, laminated multisheet structures were found near free-energy minima for the six-chain system. It should be pointed out that the six-chain system is still too small to permit the formation of, for example, a barrel-type structure. It will therefore be very interesting to try to extend these calculations to larger system sizes.

	SUPPLEMENTARY MATERIAL

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
An online supplement to this article can be found by visiting BJ Online at http://www.biophysj.org.

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION MODEL AND METHODS RESULTS AND DISCUSSION CONCLUSION SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
This work was in part supported by the Swedish Research Council and the Knut and Alice Wallenberg Foundation through the Swegene consortium.

Submitted on June 1, 2004; accepted for publication August 25, 2004.

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