Identifying the Minimal Copper- and Zinc-binding Site Sequence in Amyloid-β Peptides*

With a combination of complementary experimental techniques, namely sedimentation assay, Fourier transform infrared spectroscopy, and x-ray absorption spectroscopy, we are able to determine the atomic structure around the metal-binding site in samples where amyloid-β (Aβ) peptides are complexed with either Cu(II) or Zn(II). Exploiting information obtained on a selected set of fragments of the Aβ peptide, we identify along the sequence the histidine residues coordinated to the metal in the various peptides we have studied (Aβ1-40, Aβ1-16, Aβ1-28, Aβ5-23, and Aβ17-40). Our data can be consistently interpreted assuming that all of the peptides encompassing the minimal 1-16 amino acidic sequence display a copper coordination mode that involves three histidines (His6, His13, and His14). In zinc-Aβ complexes, despite the fact that the metal coordination appears to be more sensitive to solution condition and shows a less rigid geometry around the binding site, a four-histidine coordination mode is seen to be preferred. Lacking a fourth histidine along the Aβ peptide sequence, this geometrical arrangement hints at a Zn(II)-promoted interpeptide aggregation mode.

The term amyloidosis refers to a family of pathologies in which endogenous proteins and peptides switch from the physiological soluble configuration to a pathological fibrillar insoluble state. They comprise a heterogeneous group of diseases (more than 20) that are characterized by plaque formation (1,2). Senile plaques in Alzheimer disease patients have been generally found (Refs. 3 and 4 and references therein) to display an increased concentration of transition metals like copper, iron, and zinc (the last one being the most abundant) whose role is not yet fully understood. There is evidence, however, that a breakdown in metal trafficking regulation has a significant impact in the development of age-related neurodegenerative diseases (5,6). The interest of elucidating the role of metals in amyloidosis development strongly increased after noticing that Cu(II) and Zn(II) chelators can be used to solubilize the amyloid-␤ (A␤) 3,4 aggregates (8,9) that appear to make up the fibrillar material associated with Alzheimer disease.
The main proteinaceous component of the amyloid brain deposition, detected in Alzheimer disease patients, is the socalled A␤ peptide, which originates from the cleavage (10) of a 770-amino acid-long transmembrane protein called A␤ protein precursor.
There is experimental evidence that Cu(II) and Zn(II), in complex with A␤ peptides, may play opposite functions, with Cu(II) having an inhibitory effect on the Zn(II)-induced aggregation propensity (11).
In this context it is worth mentioning the special role played by the Raman microscopy study of Ref 15, because, to our knowledge, this is the only place where the natural A␤ peptides have been investigated. In the paper a careful analysis comparing the A␤ 1-42 synthetic peptide and the major components of senile plaque cores has been carried out. Two are the main results of the work. On the one hand it was shown that A␤ in vivo is a metalloprotein, and on the other it was proved that the secondary structure of the core major component strongly resembles that of synthetic A␤ fibrils.
As for the specific question of metal coordination, recent NMR studies of the Cu(II)-A␤ 1-16 complex (14) have suggested that the aromatic ring of a tyrosine residue (Tyr 10 ) and the imidazole groups of the His residues, His 6 , His 13 , and His 14 , are likely to be involved in the coordination of the peptide with the metal. This model is well compatible with the XAS study performed on the Cu(II)-A␤ 1-40 complex in Ref. 17. Similarly, * This work was supported in part by INFN and MIUR (under the PRIN05 contract). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 1  analysis of CD, EPR, and NMR data (12) of the Cu(II)-A␤ [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and Cu(II)-A␤ 1-28 samples hint at a geometrical structure where Cu(II) is coordinated to the N-terminal nitrogen and the three His 6 , His 13 , and His 14 imidazole rings. The situation appears to be more complicated for Zn(II) complexes, and several Zn(II) coordination modes have been proposed. In particular, NMR investigations (13) have suggested a variety of intermolecular Zn(II) binding modes involving different numbers of histidines as well as the peptide N terminus. The existence of these peculiar intermolecular binding modes was confirmed by a XAS study (16) of the Zn(II)-A␤ [13][14][15][16][17][18][19][20][21] complex in which pairs of peptides appear to be crosslinked by a Zn(II) bridge binding two histidines, one from each of the peptides of the pair. In recent NMR studies also intrapeptide coordination modes in which Zn(II) binds three histidines and either the N terminus (18) or Glu 11 (19) have been proposed. The variability of Zn(II) coordination mode according to circumstances (concentration, sample preparation mode, etc.) has also been confirmed by XAS results on the Zn(II)-A␤ 1-40 complex (17).
In this paper we present a thorough XAS study of a selected set of synthetic fragments of the A␤ peptide complexed with either Cu(II) or Zn(II), exploiting the ability of this spectroscopy in determining the structure of the metal coordination environment (20 -24). In addition to confirming the general results of Ref. 17 concerning the existence of important structural differences between Cu(II) and Zn(II) coordination modes, we are able to elucidate the special role played by the N-terminal region in binding the metals. In particular, we find that only two (instead of three) histidines are coordinated to Cu(II) when the first four amino acids are cut out. We argue that it is the His 6 -metal bond that is lost because of the strain induced by steric hindrance effects resulting when the first four amino acids are missing. Differently, Zn(II)-A␤ complexes are in all cases coordinated with four histidines, indicating that each metal ion is shared by two A␤ peptides. Furthermore, we observe that the local geometry around the Zn(II) absorber is strongly affected depending on whether the first four amino acids are present or not.

MATERIALS AND METHODS
The general strategy we followed in this investigation was to exploit information coming from complementary experimental techniques. To this end we have subjected to sedimentation, FTIR, and XAS measurements the following five fragments of the A␤ peptide, A␤ 1-16 , A␤ 1-28 , A␤ 5-23 , A␤  , and A␤ 1-40 .

Sample Preparation
A␤ 1-16 , A␤ 1-28 , A␤  , and A␤ 1-40 peptides were obtained from AnaSpec Inc. (purity index, Ͼ95%). A␤ 5-23 was produced by solid phase synthesis using a ResPep synthesizer (Intavis) with Fmoc (N-(9-fluorenyl)methoxycarbonyl) chemistry, further purified by reverse phase high pressure liquid chromatography on a C18 column (Phenomenex), and checked for its molecular mass by electrospray ionization-mass spectrometry. All of the peptides were solubilized in hexafluoroisopropanol (Riedel de Haen) to obtain stock solutions at the concentration of 2 mg/ml. The latter were then frozen and stored at Ϫ20°C.
Aliquots of stocks were dried under nitrogen flux and resuspended in the proper buffer just before use.

Sedimentation Assay
The effect of different metals on A␤ peptide aggregation was assessed using a sedimentation assay based on optical density (OD) readings, according to Refs. 25 and 26. A␤ peptides stock solutions were first diluted in 20 mM Tris-HCl, pH 7.4, and centrifuged at 4°C at 10,000 ϫ g for 15 min (using a fixed angle rotor in an Optima TL100 Beckman Centrifuge) with the purpose of purifying the solution from pre-existing aggregates. The resulting supernatant was collected for use in aggregation experiments. The concentration of the peptide in the supernatant was estimated by measuring the absorption line at 214 nm characteristic of the peptide bond. The supernatant containing soluble A␤ peptide was mixed with Tris buffer alone or buffer containing 3.5-fold molar excess metal (CuSO 4 or ZnCl 2 ). The final concentration of peptide in each test sample was about 20 M (27,28). At this point each sample was divided in four aliquots of equal volume. The OD of one aliquot sample, OD f , was quickly read at 220 nm with a V-550 Jasco spectrophotometer and thereafter kept on ice. The other three aliquot samples were incubated for 30 min at 37°C and then separately ultracentrifuged at 4°C at 100,000 ϫ g for 15 min. Supernatants were collected and diluted 10 times with buffer, and the OD at (the nearby line of) 220 nm was measured (OD i ) as described above. The percentage of aggregation, A, is evaluated through the simple formula, A ϭ 100 ϫ (OD i Ϫ OD f )/OD i . The error on A is the standard deviation taken on at least three independent measures.
The OD of the sample that was kept refrigerated on ice was successively measured to estimate the amount of aggregation occurring at 0°C and was found to be totally negligible (data not shown).

FTIR Spectroscopy
FTIR spectra were collected on a Bio-Rad FTS 185. The secondary structure of the peptides is determined as described in Ref. 29. Typically 64 interferograms were collected for each measurement, Fourier transformed, and averaged. Absorption spectra in the region between 1690 and 1600 cm Ϫ1 , at a resolution of one data point every 0.25 cm Ϫ1 , were obtained using a clean crystal as background. 100 g of peptide in hexafluoroisopropanol, dried under nitrogen flux and then resuspended in 10 mM Hepes, pH 7.4, were deposited and gently dried again under nitrogen in a thin layer on one side of the crystal. After collecting spectra in a water saturated environment, the crystal was flushed with D 2 O-saturated nitrogen for 30 -40 min to allow deuteration of the quickly exchangeable amide hydrogen ions (30,31), and new, deuterated spectra were collected. ric metal concentrations (required in XAS measurements to avoid free metal in solution) are prepared starting from CuSO 4 and ZnCl 2 salt, respectively. The solutions obtained in this way are directly transferred in a 1-mm-thick plastic holder closed by two Kapton windows, rapidly frozen in liquid nitrogen, and kept at 20 K throughout the whole measurement session.
Data Collection-XAS data have been collected at the D2 bending magnet beam line of the EMBL Outstation Hamburg at DESY. The synchrotron was operating at 4.5 GeV with ring currents ranging from 90 to 150 mA. XAS spectra were recorded in fluorescence mode using a 13-element Germanium solid state detector (Canberra, Meriden, CT).
Data Analysis Strategy-In each run several (from 16 to 27) spectra were collected and averaged. After background subtraction, the resulting spectrum was normalized, and the extended x-ray absorption fine structure (EXAFS) signal, (k) (see Appendix), was extracted using the Kemp software (32) with E 0,Zn ϭ 9662 eV and E 0,Cu ϭ 8979 eV. The EXAFS data have been analyzed and fitted employing the EXCURV98 package (33). The theoretical absorption coefficient is calculated by taking into account single and multiple scattering contributions (34). A detailed description of the data analysis procedure is given in Ref. 35

(and references therein).
Model Building-Because of the lack of detailed structural information (no x-ray crystallographic data are available for A␤ peptides), we decided to follow the strategy advocated in Ref. 17, where it was suggested to extract the possible geometries needed to start the fitting procedure from structures contained in the Metalloprotein Data Base and Browser (36). Further-more, the constrained refinement strategy proposed in Ref. 37 was followed, in which the His imidazole and the Tyr phenyl rings are treated as rigid bodies. In the rest of the paper we will refer to the N imidazole and O hydroxyl atoms, through which His and Tyr are respectively bound to the absorber, as "leading" atoms. It is important to note here that, even if generally one cannot distinguish among light scatterers (like N, O, and C) only on the basis of their individual contribution to the EXAFS signal, when they act as leading atoms they can be most often unambiguously identified.

RESULTS AND DISCUSSION
For the sake of comparing different physicochemical situations, we decided to study the five peptides whose sequences are   Table 1 in complex with either Cu(II) (left panel) or Zn(II) (right panel), the FTIR spectrum at a concentration ratio [metal]/[peptide] equal to 2 (black line) or in the absence of metal (gray line) is shown. In the lowest part of each panel the difference spectrum is also drawn. The peak at k ϭ ϳ1630 cm Ϫ1 (k ϭ ϳ1654 cm Ϫ1 ) is typical of a ␤-sheet (␣-helix) secondary structure. Zn(II) is seen to have essentially no influence on peptide conformation, whereas in the presence of Cu(II) a conformational change from ␤-sheet to ␣-helix is observed in the case of A␤ 1-40 and A␤ 1-28 .

TABLE 1 Peptide sequences
The amino acid sequences of the five A␤ peptides considered in the paper are given. Table 1 (the XAS data of the Cu(II)-A␤ 1-40 peptides are taken from Ref. 17). The four fragments of A␤  have been selected for specific reasons. A␤ 1-16 is the minimal fragment containing all the three histidines, His 6 , His 13 , and His 14 , that are supposed to be involved in metal binding, and A␤ 17-40 is the complementary sequence where none of these histidines is present. In the A␤ 1-28 fragment, besides the presence of the above three histidines, a long hydrophobic region that is believed to be relevant in the aggregation processes is present (38). Finally the A␤ 5-23 fragment was included in the analysis to try to answer the question on whether the N-terminal region of the A␤ peptide can play any role as metal ligands.

Sedimentation Assay
In Fig. 1 the measured percentages of aggregation, A, for the five samples of Table 1 are reported. As a general feature we see that in the absence of metal none of the samples shows any sign of aggregation.
When metal (either Zn(II) or Cu) is added, we notice that, within the large error bars attributed to the data, only the 1-40 sample, both in the presence of Zn(II) and Cu(II), and, although to a much less extent, the 1-28 sample, in the presence of Zn(II), show a significant level of aggregation.

FTIR Spectroscopy
In the absence of metals, the FTIR spectra collected at the amide IЈ band of A␤ 1-28 , A␤ 5-23 , A␤ 1-40 , and A␤ 17-40 show a peak (Fig. 2) at a wave number (k ϭ ϳ1630 cm Ϫ1 ) typical of a ␤-sheet secondary structure, whereas for the A␤ 1-16 sample the peak is at a wave-number (k ϭ ϳ1654 cm Ϫ1 ) typical of an ␣-helix structure.
Despite its stronger aggregating activity, Zn(II) has almost no influence (with perhaps the exception of a fairly small effect in the case of the A␤ 1-28 fragment) on peptide conformation. This is consistent with the hypothesis (13) according to which Cu(II) is mainly involved in intrapeptide binding (accompanied by conformational change), whereas Zn(II) promotes interpeptide binding, hence possibly aggregation, but not significant conformational changes. In this respect it is interesting to remark that indeed, in the presence of Zn(II), A␤ 1-40 retains its ␤-sheet secondary structure, which may favor peptide aggregation, as also indicated by our sedimentation assay results (see Fig. 1 and above).
XAS Spectroscopy-XAS spectra are normally analyzed by separating the near edge region, the so-called x-ray absorption near edge structure (XANES) region, from the EXAFS region that extends from about 50 eV above the edge onward.
In fact, the difficulty of getting a reliable theoretical description of the very complicated electronic processes affecting the XANES part of the spectrum makes its quantitative interpretation especially problematic (33, 35, 39 -42). At the same time, however, the shape of the edge region of the spectrum is very sensitive to the electronic structure of the absorber and the symmetry of the local environment around it (see, for instance, Ref. 43 and the systematic study of Zn(II) XANES spectra in Ref. 44) and can yield valuable information on similarities and differences when relative local geometries of structurally similar samples are compared (34).
A general comparison of the XANES and EXAFS portions of the spectra among the 10 samples (five fragments complexed with either Cu(II) or Zn(II)) that we have subjected to XAS measurements reveals an interesting pattern of similarities and differences that are summarized below, where the equality

XANES
Before concentrating on the more informative EXAFS region of the spectra, some comments on XANES data, although of a qualitative nature, are useful.
In Fig. 3 the XANES spectra of Zn(II) (left panel) and Cu(II) complexes (right panel) are shown. In the figure only the XANES spectra of the complexes that display visibly different features are reported.
For Zn(II) complexes, appreciable differences can be detected by looking at the shape of the main peak (see the blow-up in the left panel of Fig. 3). More in detail one can notice that the symmetry around the maximum is progressively lost when we go from the Zn(II)-A␤ 1-40 sample to Zn(II)-A␤ 5-23 , passing through Zn(II)-A␤ 1-16 . 5 The loss of peak symmetry is known to be an indication of a decrease in the degree of geometrical symmetry of the metal-binding site (45,46). In other words the XANES spectral differences visible among these three complexes should be interpreted as solely caused by small geometrical dissimilarities in the atomic arrangement around the metal and not to differences in the number or the nature of the amino acidic residues primarily bound to the absorber. Indeed any such difference would markedly affect the shape of the EXAFS region of the spectrum, something that we do not see in our data ( Fig. 4 and the synopsis of XAS data above).
For Cu(II) complexes, looking at the right panel of Fig. 3, one clearly sees that differences in the shape of the main peak of the various Cu(II) complexes are definitely much less pronounced than in the case of Zn(II) complexes, confirming the lower flexibility of the Cu(II) binding mode with respect to that of Zn(II).

EXAFS
We now turn to the study of the EXAFS spectra. After identifying the sample spectra we want to analyze, we discuss our fitting strategy and present the structural results we get.
No fitting of the Cu(II)-A␤  and Zn(II)-A␤ 17-40 data were carried out because of the reasons explained in note 4. Concerning the initial configurations used to start off the fitting procedure, we have proceeded, exploiting indications found in the literature (13,14,(17)(18)(19), by trying various initial geometrical models differing in the number of histidines involved in the metal coordination (see "Model Building " under "Material and Methods"). Of course, our use of known crystallographic data were simply of help to not start from some chemically unreasonable structure. No special meaning related to any biological or structural homology between the deposited Metalloprotein Data Base and Browser structures and our samples should be attached to this procedure.
As for the quality of the fits, we see that in all cases experimental data can be rather well reproduced with values of the r, N, and 2 DW parameters that are fairly accurate and physically very reasonable. This consistency is confirmed by the nice correspondence between the location and the height of the peaks of the FT of the experimental and theoretical signal. 5 We remark that the peak shape of the Zn(II)-A␤  complex is also rather different from that of the other three samples and even more symmetric. This complex, however, is not of much interest to us in this work because, as we have recalled above, it does not appear to be able to bind the metal.  Table 2. Fitted and experimental signals agree rather well. This is confirmed by the nice correspondence between the location and the height of the peaks of the FT of experimental and theoretical signals.
Concerning Cu(II) complexes, in Fig. 5 we show the results for Cu(II)-A␤ 1-16 sample. The best fit displayed in the figure corresponds to a site configuration in which three histidines and one tyrosine are included in the Cu(II) coordination sphere, plus an oxygen possibly belonging to a water molecule or to an amino acid other than His or Tyr. This structure, sketched in the left-most panel of Fig. 8, is the one already proposed in Ref. 17 for the Cu(II)-A␤ 1-40 peptide.
We would like to point out that in the case of the Cu(II)-A␤ 1-16 complex, the model in which the Tyr oxygen is replaced by the nitrogen of the N terminus, gives rise to a fit only marginally worse than the one whose structural parameters are reported in Table 2 (data not shown). Consequently we cannot completely rule out the possibility of a Cu(II) coordination with the N-terminal nitrogen. 6 Moving now to Cu(II)-A␤ 5-23 , we remark that, if we let the coordinated residues be the same as for Cu(II)-A␤ 1-16 and only modify their geometrical parameters, a satisfactory fit cannot be obtained. A good fit (Fig. 6) is instead found starting from a configuration, inspired by Ref. 48, in which His 6 is replaced by the N-terminal amino group. In this model Cu(II) is coordinated with two histidines, one tyrosine, the nitrogen belonging to the N-terminal amino group, and one oxygen. As already mentioned in the Introduction, the fact that, by cutting out the first four amino acids, the number of coordinated histidines passes from three to two, is a strong indication that His 6 is the third residue normally bound to the metal. We will momentarily show how this conclusion is indirectly supported by the results on Zn(II)-A␤ complexes.
Concerning Zn(II) complexes, although no appreciable difference of the whole XAS spectrum of Cu(II)-A␤ 1-40 is visible when comparing the data of Ref. 17, obtained in a Tris buffer, with the present ones, taken in a N-ethylmorpholine buffer, the situation is different for the Zn(II)-A␤ 1-40 complex. The newly collected data, where Zn(II)-A␤ 1-40 is dissolved in a N-ethylmorpholine buffer, are definitely different from those presented in Ref. 17, thus confirming the high flexibility of the Zn(II)-A␤ coordination mode and its dependence on the details of the Zn(II) physicochemical environment. For the present comparative study we then used the newly collected Zn(II)-A␤ 1-40 data.
Just like in the case of Cu(II) complexes, the Zn(II)-A␤ 17-40 spectrum is almost identical to that of Zn(II) in buffer (data not shown). This identity confirms that the absence of the first 16 amino acids prevents metal binding. However, at variance with Cu(II) complexes, here it turns out that also the EXAFS spectrum of Zn(II)-A␤ 5-23 is very similar to the spectrum of the three other Zn(II) samples (i.e. Zn(II)-A␤ 1-16 , Zn(II)-A␤ 1-28 , and Zn(II)-A␤ 1-40 ) comprising the first four amino acids of the A␤ peptide sequence (Fig. 4). As a prototype of the above four (almost) identical Zn(II) complex spectra, we chose to subject to a quantitative analysis the Zn(II)-A␤ 1-16 EXAFS data. 6 We are at the moment performing ab initio simulations of the Car-Parrinello type aimed at clarifying this and other issues related to the understanding of the phenomenology of A␤ peptide metal binding (47).  The best fit to the data, shown in Fig. 7, is obtained by including four histidines and one oxygen in the Zn(II) coordination sphere. This structure is of particular relevance, and it is perhaps the most interesting result of the present paper. Recalling, in fact, that each A␤ peptide only contains three histidines, our finding means that for the metal to be coordinated to four histidines, at least two different peptides must be involved in the Zn(II) binding mode.
A Comment-We end this section with an observation on the peculiar role played by His 6 in metal coordination we alluded to above. With reference to the Cu(II)-A␤ 5-23 sample, we recall that we have attributed the difference of its EXAFS spectrum compared with that of all the other Cu(II) complexes to the absence of the Cu(II)-His 6 coordination bond. Because, instead, all Zn(II) complexes display very similar EXAFS spectral features, we are led to conclude that in none of the Zn(II) samples His 6 is involved in metal coordination. These two results are very consistent with the indications coming from our FTIR measurements and suggest that His 6 must play a role in the secondary structure switch induced by Cu(II). We have seen, in fact, that although Zn(II) is unable to induce secondary conformational changes, Cu(II) is effective in the cases of Cu(II)-A␤ 1-28 and Cu(II)-A␤ 1-40 samples, where the metal-His 6 bond is present, but not in the case of Cu(II)-A␤ 5-23 , where hindrance effects prevent the formation of such a bond. We conclude from this analysis that, if His 6 is not bound to the metal, the effectiveness of the latter in inducing the ␤-sheet 3 ␣-helix peptide conformational switch is strongly reduced.

Conclusions
XAS measurements on fragments of various length of the A␤ 1-40 peptide in complex with either Cu(II) or Zn(II) have been collected with the aim of determining the precise location and structure of the metal-binding site. A comparison of Cu(II) and Zn(II) XAS spectra and a detailed analysis of the results of our fits allows us to come up with rather precise conclusions about metal coordination geometry. In the case of Cu(II)-A␤ complexes, we find evidence for an intrapeptide coordination mode with the metal bound to three histidines (His 6 , His 13 , and His 14 ) and, most probably, one tyrosine plus a water molecule. This bonding geometry gives rise to a rather rigid and stable peptide structure (Fig. 8). Results for Zn(I) complexes indicate, instead, in agreement with suggestions coming from the work of Ref. 13, that in the presence of Zn(II) a network of A␤ peptides is formed with the metal stabilizing the structure by binding histidines (see also Ref. 49) belonging to adjacent peptides. This structural arrangement may be interpreted as due to a more pronounced propensity of Zn(II) to form flexible and open coordination geometries. All of these results are supported by complementary sedimentation and FTIR measurements, which show that the differences in metal coordination are correlated with the different abilities of Zn(II) and Cu(II) in promoting aggregation (Fig. 1) and secondary structure switching (Fig. 2).
Finally we find that, by cutting out the first four amino acids, only two (of three) histidines remain coordinated to Cu(II), because His 6 is lost as a third ligand. At variance, the number of histidines in Zn(II)-A␤ complexes does not change, and only the local geometry around the metal is affected depending on whether the first four amino acids are present or not.

Acknowledgment-We are very grateful to G. C. Rossi for discussions and a careful reading of the manuscript.
APPENDIX EXAFS Signal-The EXAFS signal, (k), is defined through the measured total absorption coefficient, (k), and the absorption coefficient of the isolated absorber, 0 (k), by the formula, where k is the wave vector of the extracted electron that is related to the incident photon energy, E, and the ionization energy, E 0 , by the obvious relation with m as the electron mass and h as the (reduced) Planck constant. For completeness and to fix our notations, we recall how the parameters introduced in the text enter the theoretical formula representing the measured EXAFS signal. For simplicity we report equations valid in the single scattering approximation. In this case the EXAFS signal has the simple expression, ͑k͒ ϭ S 0 2 l N l kr l 2 ͉f l ͑k,͉͒ ⅐ sin͑2kr l ϩ l ͑k͒͒e Ϫ2 l 2 k 2 e Ϫ2rl/͑k͒ (Eq. 3) where the sum runs over the different coordination shells around the absorber. N l is the number of scatterers in the l th FIGURE 8. Schematic of the structures around the metal absorber. Protein Data Bank files directly produced at the end of EXCURVE fit step are used for ball-and-stick drawings. The green ribbon is to suggest some kind of peptide folding around the metal coordination structure we have determined. The structure of the Cu(II) coordination mode in Cu(II)-A␤ [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and Cu(II)-A␤ [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] complexes are shown in the first two panels, respectively. In the third panel the interesting Zn(II) coordination mode where the metal is bound to two ϩ two histidine residues coming from two adjacent A␤ peptides is sketched.
shell, located at an average distance r l from the absorber and l 2 is the associated Debye-Waller factor. ͉f l (k,)͉ is the modulus of the back-scattering amplitude, and l (k) is the total scattering phase. Finally, S 0 2 is an empirical quantity that accounts for all the many-body losses in photo-absorption processes, and (k) is the photo-electron mean free path. For multiple scattering processes a formally similar expression can be derived, in which r l represents the length of the full multiple scattering path. Modulus and phase functions are now more complicated expressions that depend on all the individual scattering events occurring along the multiple scattering path (35, 39 -42).
Fourier Transform-An alternative method to separate contributions coming from different "coordination shells" (i.e. from each set of scatterers located at approximately the same distance from the absorber having essentially the same backscattering amplitude and phase) can be that of Fourier transforming in real space the (k) signal (50). A suitable kind of Fourier transform, technically termed "Fourier filtering," must be used for this purpose. A description of this technique, together with detailed information on other standard data analysis procedures can be found in (35).
R Quality Factor-The R quality factor of the fit is computed as follows, where exp and fit are the experimental and theoretical data, respectively, and the sum is over the number, P, of the k values at which data were collected. The "weighting" parameter w i is defined by the formula, where the integer n is selected in such a way that the amplitude of the EXAFS oscillations in k n exp (k) does not die away at large values of k. In this paper we took n ϭ 3. It is a consolidated experience that for complex biological molecules a fit can be considered adequately good for values of R in the interval between 20 and 40% (33).