Jan Zienau

Jörg Kussmann

Christian Ochsenfeld
email: christian.ochsenfeld@uni-tuebingen.de

Quantum-Chemical Simulation of Solid-State NMR Spectra: The Example of a Molecular Tweezer Host-Guest Complex

Keywords: quantum chemistry, linear scaling, NMR, molecular recognition, molecular tweezer

A systematic quantum-chemical study of the convergence of proton NMR shieldings with the size of solid-state fragments is presented for a host-guest system. The largest system computed at Hartree-Fock and density-functional theory levels comprises a full first shell of complexes surrounding a central unit within an X-ray based structure and a total of 1196 atoms and 13260 basis functions. While the influence of methodological aspects can be considered to be converged within the error bars of experiment and theory, the deviation of one of the protons provides evidence for the possibility of a dynamic rotation process of the guest within the host complex.

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important experimental methods for gaining insights not only into the atomistic structure of molecular systems, but also into some aspects of their dynamical behavior [1,2]. Despite this tremendous success, the lack of a direct relationship between the measured NMR signals and the structure of a molecule raises the need for reliable assignments of the experimental spectra. Here, quantum-chemical calculations can provide important insights (see e.g. Refs. [3][START_REF]Calculation of NMR and EPR Parameters[END_REF][START_REF] Gauss | Modern Methods and Algorithms of Quantum Chemistry NIC Series[END_REF]).

While quantum chemistry has evolved over the last decades to become a very valuable tool for computing molecular properties including NMR chemical shifts [START_REF] Gauss | Modern Methods and Algorithms of Quantum Chemistry NIC Series[END_REF], the applicability to larger molecular systems has been hampered by the strong, at least cubic, increase of the computational cost with molecular size. To overcome these limitations, methods were introduced whose cost scales only linearly with molecular size (see e.g. Ref. [START_REF] Ochsenfeld | [END_REF] and references therein), so that systems in the range of 1000 atoms are computable even on today's oneprocessor computers.

For the ab-initio calculation of NMR chemical shieldings this scaling wall was overcome only recently [7][8][9], so that important new possibilities for studying molecular NMR spectra for large systems with 1000 and more atoms open up. This has not only interesting implications for the study of NMR spectra of large molecules, but also for describing the 'environment' of a molecule in solution or the solid state.

In our present work, we focus on studying the influence of the solid-state environment on the NMR chemical shifts of a host-guest complex. By means of our linear-scaling gaugeincluding atomic-orbital Hartree-Fock (GIAO-HF) and GIAO-density functional theory (GIAO-DFT) methods [7,8], we are for the first time able to systematically increase the fragment size of the solid-state structure and to account for all the neighboring complexes of a chosen host-guest complex. Here, we focus on a molecular tweezer system synthesized in the Klärner group [10] which binds a dicyanobenzene guest molecule and can be employed as useful model system for molecular recognition processes. Since an X-ray structure is available for this system [10], it is ideally suited for studying the possibilities of assigning NMR spectra by means of quantum-chemical approaches. In order to account for the full neighboring sphere of a host-guest complex, we consider as largest fragment a system with 1196 atoms and 13260 basis functions without molecular symmetry.

Computational Details

For all calculations a development version of the Q-Chem program package [START_REF]Development version of the Q-Chem program package[END_REF] was used. Structures of the solid-state fragments of the dicyanobenzene-tweezer complex were obtained by optimizing the monomer at the HF/6-31G* level with constraints from the X-ray structure [10] and subsequently projecting the monomer units onto the experimentally maintained positions in the solid-state [START_REF] Ochsenfeld | [END_REF]. SCF calculations were carried out employing linear-scaling methods for calculating the Fock matrix: continuous fast multipole method (CFMM) [13] and linear exchange (LinK) method [14,15]. For the DFT calculations we employed the BP86(VWN) functional [16][17][18] with the SG-1 grid [19] for the numerical integrations [START_REF] Johnson | Recent Developments in Density Functional Theory[END_REF]. NMR calculations were performed using the 6-31G * * [START_REF] Hehre | [END_REF]22] basis with our linear-scaling method [7,8] at the GIAO-HF [23][24][25][26][27] and GIAO-DFT [28][29][30][31][32][33][34] levels, respectively. Relative NMR shifts are given, unless noted otherwise, with respect to those of a TMS molecule calculated at the same level of theory. For experimental details concerning the X-ray structure and the magic-angle spinning (MAS) experiment see Ref. [10]. It should be mentioned that the crystallographic structure data were obtained at a temperature of 298 K whereas the NMR spectrum was recorded at 321 K. The reliable simulation of solid-state NMR spectra by quantum-chemical methods poses three major challenges: (1) Structure determination of building blocks (monomers) and their arrangement in the solid phase must be followed by (2) convergence studies of the NMR data with respect to fragment size, where it is also necessary (3) to estimate error bars caused by the chosen quantum-chemical method and basis set (see as well discussion in Refs. [START_REF] Ochsenfeld | [END_REF]35]).

While we were able to gain useful information by quantum-chemical simulation of NMR spectra for a variety of similar systems [START_REF] Ochsenfeld | [END_REF]10,[START_REF] Ochsenfeld | [END_REF][35][36][37][38][39][40][41][42], we focus in our present work on the study of a dicyanobenzene (DCNB) tweezer host-guest complex (see Fig. 1) and compare the experimentally observed MAS-NMR proton shieldings to quantum-chemically calculated shieldings for different fragment sizes of the solid-state structure. The DCNB system has already been subject to earlier studies by us [10,[START_REF] Ochsenfeld | [END_REF]35], where we were constrained to rather small fragments such as a trimer at most. Due to the availability of our linear-scaling code for the calculation of NMR shifts we are now able to perform full DFT and HF calculations for fragment sizes of up to a tridecamer, i.e., a DCNB tweezer monomer with the full first sphere of neighboring complexes, without having to resort to an incremental scheme [START_REF] Ochsenfeld | [END_REF] or other additional approximations. In this way, we study the convergence of calculated proton NMR chemical shieldings at DFT and HF levels, where we expect that the major effects of neighboring groups are sufficiently accounted for by the tridecamer. This corresponds to the second challenge mentioned above, whereas the first and third challenges for the present system have been discussed earlier [START_REF] Ochsenfeld | [END_REF]35] and will be briefly re-examined below.

Structures of the Investigated Fragments

The structures employed for the NMR calculations of the solid-state fragments (first challenge discussed above) are based on an X-ray structure [START_REF] Ochsenfeld | [END_REF]. Since proton positions were not determined in the experimental structure, the structure of the monomer unit was optimized at the HF/6-31G* level, while several constraints were imposed as described in Ref. [START_REF] Ochsenfeld | [END_REF] in order to account for the lack of dispersion forces at the HF level and for missing influences occurring in the solid-state environment. The (partially) optimized monomer structure was afterwards projected onto the corresponding positions in the solid-state structure.

Just as a side note, it is clear that a theoretically more satisfying alternative to this pragmatic approach would be a full geometry optimization of a unit cell of the solid-phase crystal employing a sufficiently accurate method that accounts for dispersion-type effects. In the past, this was prevented due to the prohibitive scaling properties of conventional post-HF methods and the failure of traditional DFT functionals to handle dispersive interactions. Here, recent developments in particular in the field of low-order scaling Møller-Plesset perturbation theory for the calculation of energies and gradients [43][44][45][46][47][48], but also the design of dispersioncorrected DFT functionals (see e.g. Refs. [49,50] and Refs. [51,52] for applications) seem to offer promising perspectives. However, as these methodologies are mostly still topics of active developments, the structures used in this study were all obtained using the pragmatic approach described above, which also ensures comparability to earlier studies [10,[START_REF] Ochsenfeld | [END_REF]35].

In our present work, we focus on the second aspect discussed above for simulating a solidstate NMR spectrum, namely to study the convergence with respect to the fragment size employed for modeling the solid phase. It is worthwhile to note, that besides this 'cluster approach' an alternative approach for simulating solid-state NMR spectra would be the use of periodic boundary conditions for describing the solid phase [53][54][55][56]. While we have currently not explored this approach so far, there has been some success described in the literature for smaller systems in other context (see e.g. Ref. [57]).

Monomer Host-Guest Complex and Methodological Accuracies

The host-guest complex of the naphthalene-spaced tweezer host and the dicyanobenzene guest, which represents the monomer unit, is schematically depicted in Fig. 1. In terms of the accuracy of the chosen method and basis set (third challenge mentioned above) we have found in earlier quantum-chemical studies that for a given molecular structure of the isolated dicyanobenzene its proton shieldings computed at the GIAO-HF/6-31G** and the GIAO-BP86(VWN)/6-31G** levels agree within 0.0 and 0.3 ppm, respectively, with our most reliable GIAO-MP2/QZ2P data [35]. Upon binding the dicyanobenzene molecule within the tweezer host, the ring-currents of the aromatic units of the tweezer influence the proton shieldings of the guest by up to 5-6 ppm [35]. Using a model consisting of the DCNB and one benzene molecule of the central sidewall of the tweezer host, we compared our most reliable GIAO-MP2/SVP data for this system with the GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G** results and found deviations of 0.0 and 0.5 ppm for proton H b facing the benzene unit, respectively [35]. The underestimation of ring-current influences using small basis sets such as 6-31G** at the DFT level is found as well for other functionals and reduces only for larger basis sets (and hybrid functionals which include more HF exchange; see discussion in Ref. [35]). Despite these disadvantages compared to Hartree-Fock, the GIAO-BP86(VWN)/6-31G** method has the important benefit of being computationally significantly less demanding than the GIAO-HF/6-31G** method, since no iterative solution of the CPSCF equations is required. We therefore consider it reasonable to further estimate the usefulness of the BP86(VWN) method in the context of the present study, so that we computed the NMR shifts mostly at both GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G** levels of theory (see Table 1 and Fig. 1 for numbering). As a side note, it would also be interesting to explore, in the present context, the performance of other DFT functionals developed specifically for the calculation of NMR chemical shifts, such as the ones of Keal and Tozer [58,59]. While we plan to carry out such investigations in the future, they are, however, not in focus of the present work. Prior to the present work, we have performed studies on monomer, dimer, and trimer units of the host-guest complex using the HF method with a variety of basis sets [10,[START_REF] Ochsenfeld | [END_REF]. At that time no linear-scaling NMR code [7] had been developed, so that we were constrained to using small basis sets for the dimer and trimer fragments. We therefore employed an incremental scheme based on our ab-initio data, by adding the influences of neighboring units onto the monomer values (see Ref. [START_REF] Ochsenfeld | [END_REF] for a detailed discussion). This approach did not only allow to estimate environmental influences, but as well was expected to profit from an error cancellation for the rather small basis sets employed. The accuracy of this incremental approach was recently discussed for a fragment of five tweezer units with a tetracyano-pquinodimethane (TCNQ) guest [7,35].

In Table 1 we list the computed 1 H-NMR chemical shifts (GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G**) for monomer, dimer, trimer, heptamer, and tridecamer units in comparison to the experimental solid state MAS-NMR data. Here, we analyze the shieldings calculated at the HF level first, before discussing the BP86(VWN) results. If we consider initially the relative chemical shifts of the monomer, the comparison to the experiment shows already a good agreement for the guest protons (deviations of 0.1 and 0.2 ppm), while it should be kept in mind that the error bars in both experiment and theory are expected to be in the order of 0.2-0.4 ppm [START_REF] Ochsenfeld | [END_REF] for the present systems. The only protons which are clearly outside the error bars of experiment and theory are those at the tip of the tweezer (H 2/3/14/15 , see Fig. 1) with a deviation of 1.7 ppm. As discussed earlier by us [10,[START_REF] Ochsenfeld | [END_REF]60] the reason is obvious if a larger fragment of the solid state is considered: The corresponding protons are located directly above the naphthalene system of the neighboring host-guest complex so that strong ring-current influences are expected. Therefore, the major part can already be accounted for by employing a dimer fragment (Table 1): The chemical shifts of the corresponding protons in unit A of the dimer (which corresponds to just the units A and B of the trimer shown in Fig. 4) change by 1.4-1.5 ppm as compared to the monomer values and then agree within 0.2-0.3 ppm with the experimental value. These values do not change much (0.2 ppm at most) in proceeding from the dimer to the trimer system (Tab. 1 and Fig. 4), which shows that unit C in this fragment has only a minor influence on the corresponding shieldings of A.

As we have pointed out in Ref. [START_REF] Ochsenfeld | [END_REF] it is clear that in order to truly account for all influences in the solid state, we need to include at least the first shell of host-guest complexes around a specific complex, which leads to the tridecamer (13 host-guest complexes, 1196 atoms) depicted in Fig. 6. The NMR chemical shifts computed at the GIAO-HF level are listed in Tab. 1. All protons in the tridecamer except H a deviate only by 0.2 ppm at most when comparing them to the trimer fragment, so that these protons can be considered to be converged with respect to the fragment size already for the trimer. For guest proton H a , however, the data show a large effect onto the chemical shieldings by 0.9 ppm in the tridecamer as compared to the monomer, while the corresponding influences for proton H a within the dimer and trimer models studied so far are only small in the order of 0.3 ppm.

The reason for this large effect onto the guest proton H a is obvious if one considers the large tridecamer fragment: It is due to the relatively close position of two neighboring guest systems (within the guest plane). Although the dimer/trimer models which we have studied in Ref. [START_REF] Ochsenfeld | [END_REF] allow to reliably account for the major ring current effects influencing the neighboring complexes, this guest-guest interaction has not been accounted for so far. As compared to the intramolecular ring current effects within the host-guest complex influencing the guest protons H a and H b by 2.4 and 5.7 ppm, respectively (GIAO-HF/6-31G**; compare Tables 1 and 3 of Ref. [35]), the present effect of 0.9 ppm is smaller but nevertheless very important for the description.

In order to study this influence on the guest proton H a in more detail, we performed calculations focusing only onto the guest molecules of the three central 'face-on' complexes within the tridecamer. The interaction of three guest molecules without the tweezers (structures and structural positions of the guests are kept unchanged) leads to a change of the H a chemical shift by 1.4 ppm at the GIAO-HF/6-31G** level compared to the isolated guest, while H b is influenced by 0.1 ppm at most. The same values hold if the calculations are performed at the GIAO-BP86(VWN)/6-31G** level. These values remain virtually unchanged (0.1 ppm) if just two guest molecules are considered instead of three. If the tweezer hosts are also included in the above mentioned 'face-on' trimer, which leads to the 'face-on' trimer host-guest complex fragment depicted in Fig. 3, the influence on proton H a of the guest of the central complex is very similar (1.5 ppm as compared to the monomer host-guest complex), whereas the influence on H b is slightly larger (0.4 ppm) as when considering the guest molecules only.

The larger influence onto the guest proton H a of 1.4/1.5 ppm in considering the 'face-on' structures (without/with the tweezer hosts) instead of 0.9 ppm for the entire tridecamer has to be due to compensation effects of the tweezer complexes neglected in the 'face-on' systems. These effects are also illustrated by comparing the monomer data to the corresponding data for complex A of the heptamer (see Fig. 5 and Tab. 1). Here, no guest 'face-on' effects are included, so that the difference in the chemical shift for H a when comparing monomer and heptamer should be solely due to the compensation effects mentioned above. As can be seen from Tab. 1, the chemical shift of the proton H a changes from the monomer value of 5.5 ppm to 5.0 ppm in the heptamer, yielding a shift change of 0.5 ppm which is similar to the difference of the influences discussed above (1.4/1.5 ppm vs. 0.9 ppm). The consideration of the heptamer therefore explains the partial compensation of the guest 'face-on' influence in the tridecamer.

While we have so far focused on NMR shieldings computed at the GIAO-HF/6-31G** level, it is worthwhile to discuss the corresponding GIAO-BP86(VWN)/6-31G** shifts as listed in Tab. 1. Here, the difference in the relative shieldings compared to HF is 0.3 ppm at most for all given protons except for H b , where the deviation is significantly larger with 0.5 to 0.6 ppm. As already reported earlier [35], the BP86(VWN) functional shows for smaller basis sets such as 6-31G** an inferior description of the (non-local) ring-current effects influencing this proton as compared to HF. Therefore the GIAO-HF/6-31G** method is expected to be more reliable than the GIAO-BP86(VWN)/6-31G** method for the present systems.

Tridecamer Fragment

So far we have discussed the convergence behavior of the computed NMR data with respect to increasing fragment size, so that it remains to compare the chemical shifts of our best model for the solid-state, the tridecamer, to those of the experiment. The GIAO-HF/6-31G** and the GIAO-BP86(VWN)/6-31G** methods yield an agreement with the MAS-NMR data within 0.5 ppm and 0.6 ppm, respectively, for all protons except H a , where the deviation is in the order of 0.9 ppm for both methods and therefore outside the estimated experimental and theoretical error bars (see above).

As a first attempt to explain this disagreement, one may assume problems associated with the chosen TMS reference, that can occur for both the quantum-chemical calculation and the solid-state MAS-NMR experiment: The quantum-chemical difficulty is related to the often strongly different electronic structure of TMS as compared to the one of the molecular system of interest. This is well known to be a problem, in particular if 13 C-NMR chemical shifts are considered (see e.g. Ref. [START_REF] Ochsenfeld | [END_REF]). For the latter the use of intermediate reference systems has proven to be quite successful [START_REF] Ochsenfeld | [END_REF]. Also in the MAS experiment several difficulties may arise, since TMS cannot be used as internal standard, but instead often adamantane or other compounds [61]. This has been discussed, e.g., in Ref.

[61] as possible source of difficulties. As a consequence, it often proves useful to entirely avoid the external TMS standard, but instead to compare just the pattern of the NMR spectrum in employing an internal standard for comparing experiment and theory.

If one selects, e.g., H b as internal reference, we obtain the values shown in Tab. 2. Although the corresponding GIAO-BP86(VWN)/6-31G** results are in good agreement with the experimental solid-state NMR data with deviations of 0.6 ppm at most (H Bridgehead ), this good agreement is in large parts fortuitious, since the GIAO-BP86(VWN)/6-31G** approach is known to underestimate ring-current influences (see Ref. [35]). For the more reliable GIAO-HF/6-31G** method such a nice agreement as observed at the BP86 level is not found: At the HF level, the tridecamer data computed with respect to H b as internal reference shows a strong maximum difference to the experiment (0.9 ppm, similar to the data obtained without internal standard). This means that the maximum deviation between theory and experiment in the order of 0.9 ppm persists, independently whether the internal or the external TMS reference is employed.

In order to analyze this discrepancy between theory and experiment in more detail, it is important to reconsider the accuracies expected at this stage of the investigation: (1) the GIAO-HF/6-31G** method was shown earlier to provide a good description of proton chemical shifts in the present systems [35], (2) choosing an internal standard does not alter the observed 3) choosing an even larger fragment, i.e. incorporating the second shell, is expected to have only minor influences on the shifts of the central host-guest complex as compared to those of the 13-mer. Therefore it seems that methodological reasons for the observed discrepancy of 0.9 ppm between theory and experiment can be excluded.

A possible explanation for the discrepancy of the H a shieldings could be the static description of the guest position in the X-ray structure employed as the basis for the quantumchemical NMR calculations. As observed earlier by means of MAS-NMR measurements at higher temperatures (coalescence of H a and H b signals at 410 K) [10], a rotation of the DCNB guest within the tweezer cavity can occur. In principle, two rotation modes are possible: Either a rotation around the C 2 axis perpendicular to the benzene plane of DCNB denoted as 'in-plane-rotation' in the following, or a rotation around the axis through the CN units of DCNB denoted as 'CN-rotation' (see also Fig. 2 for an illustration of the rotations). While a full (60 degrees) in-plane-rotation can be excluded within the solid-state due to space constraints (collision of neighboring CN groups during the rotation process; see discussion in Ref. [START_REF] Ochsenfeld | [END_REF]), a small oscillation is always possible. Even though the MAS-NMR data discussed in our present work were recorded at a lower temperature (321 K) than the coalescence temperature mentioned above, a slight rotation by a few degrees around the crystallographically determined positions at 298 K is conceivable for both modes.

In order to evaluate the influence of such rotations on the calculated NMR shieldings, we chose as a model system the 'face-on' trimer host-guest complex fragment depicted in Fig. 3, which represents a cutout of the central unit of the three 'face-on' complexes in the tridecamer. We subsequently estimated the changes in chemical shifts when rotating the guest molecules starting from their crystallographically determined positions around both axes by angles ϑ and ϕ, respectively (for definition of angles see Fig. 2). Here, all three guest molecules were rotated in the same manner, i.e., 'synchronously'. The in-plane-rotation was performed so that the N-N distances of neighboring guest molecules were enlarged during rotation (i.e., clockwise in the projection of Fig. 6 (b)); the CN-rotation is quasi symmetric concerning the rotation direction. The resulting shift changes for the central tweezer of the 'face-on' trimer fragment were computed at the GIAO-HF/6-31G** level for two/three different angles (see Tab. 3).

For all the considered rotation angles an upfield-shifting influence on the NMR shielding of H a is observed. Table 3 shows that both a CN-rotation of 22 • or an in-plane-rotation of only 5 • causes upfield changes of about 0.4 ppm for H a . The chemical shifts of the other given protons remain virtually unaffected by the 5 • in-plane-rotation, whereas they are mostly less influenced than H a for the other listed cases, and are, if at all, shifted slightly downfield (0.3 ppm at maximum) when the average values are considered.

We note in passing that analogous calculations at the GIAO-BP86(VWN)/6-31G** level for the example of an in-plane-rotation angle of 5 • yield the same behavior. We also tested the influence of the 5 • in-plane-rotation on all other protons except H a of the central tweezer (not only the ones given in Tab. 3) and found only negligible effects (0.1 ppm at most).

As can be seen from Table 3 and already discussed above, rotations around both axes lead to an upfield-shifting influence on the shielding of H a , whereas the other protons are less influenced and show in part slight down-field shifts. Although at higher temperatures with larger rotation angles the CN-rotation process should be favored over the in-plane-rotation due to space constraints within the solid state (see Ref. [START_REF] Ochsenfeld | [END_REF] where '180 • rotation' refers to the full 180 degrees CN-rotation and '60 • rotation' refers to the full 60 degrees in-plane rotation process), this statement is not necessarily true for small values of rotation angles which we expect at lower temperatures. However, solely on the basis of our computed NMR values a distinction of both processes is not possible.

In order to illustrate the influence of the rotation upon the total shieldings of the 13-mer, we added the shift changes upon the guest in-plane-rotation of 5 • (∆ rot (5 • )) computed for the 'face-on' trimer to the computed shieldings of the tridecamer. This seems justified since we do not expect the additional complexes within the 13-mer, as compared to the 'face-on' trimer, to exert a significant influence on these shift changes. The resulting incremented tridecamer chemical shifts are displayed in the penultimate column of Table 1. These 'rotationally corrected' values show a much better overall agreement between theory and experiment within 0.5 ppm at the HF and 0.6 ppm at the DFT level for all protons, which is within the experimental and theoretical error bars. The good agreement suggests that such rotational processes might be expected to be of importance for describing the MAS-NMR spectrum recorded at 321 K, while the two rotation processes cannot be distinguished within our present study.

Conclusion

In this work, we have performed quantum-chemical NMR calculations to simulate a solidstate MAS-NMR spectrum of a host-guest system by systematically studying the convergence of proton chemical shifts upon increasing the size of solid-state fragments. As model system a dicyanobenzene tweezer host-guest complex is considered for which an X-ray structure is available. The largest fragment computed at the GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G** levels comprises a full shell of neighboring complexes around a central host-guest unit and a total of 13 tweezer complexes with 1196 atoms and 13260 basis functions.

Although the shieldings of the central host-guest unit are expected to be largely converged, it is only one guest proton (H a ) which shows a larger deviation of about 0.9 ppm as compared to the experiment. The agreement of theory and experiment for the shieldings of the remaining protons is within 0.5/0.6 ppm and in this way well within the error bars of both experiment and theory estimated to be in the order of 0.2-0.4 ppm, respectively. Since the computed data is expected to be widely independent of methodological deficiencies, our detailed study suggests that the discrepancy for the H a guest proton can be attributed to the static nature of the X-ray structure employed for the quantum-chemical calculation of the NMR shieldings. Taking into account some degree of guest dynamical processes, some of which were already observed earlier in different context for higher temperatures [10], we observe that a slight rotatory distortion can explain the deviation between theory and experiment. In this way, the NMR results obtained upon taking into account a rotation process lead to a satisfactory accordance of theory and experiment for all considered protons. Therefore, we conclude that such guest dynamics may indeed play a role already at the temperature where the MAS-NMR measurements were made. 4, Fig. 5, and Fig. 6. For the tridecamer all presented shifts are those calculated for the central tweezer complex. Here, ∆ rot (5 • ) means the increment of the chemical shift as obtained due to the in-plane-rotation of the guest molecule by ϕ = 5 degrees in the 'face-on' trimer fragment (see Fig. 3 and Table 3).

3

  Simulation of Solid-State NMR Spectra

3

 3 Convergence of NMR Shifts with Respect to Fragment Size

  and GIAO-HF/6-31G** data, and (

Figure 1 :Figure 2 :

 12 Figure 1: Schematic structure and numbering of the dicyanobenzene-tweezer complex. The label H Bridgehead as used in tables and text refers to protons No. 5, 7, 10, 12, 17, 19, 22, and 24.

Figure 3 :Figure 4 :

 34 Figure 3: 'Face-on' trimer fragment.

Figure 5 :Figure 6 :

 56 Figure 5: Heptamer fragment with unit A for which the shieldings are analyzed.

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  [61] C.R. Morcombe and K.W. Zilm; J. Mag.Res. 162, 479 (2003).

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Table 1 :

 1 Relative isotropic NMR chemical shifts of selected protons for various fragment sizes up to a 13-mer (with 1196 atoms) with respect to TMS as obtained at the GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G** levels. Structures of the trimer, heptamer, and tridecamer are shown in Fig.

Table 2 :

 2 Relative isotropic NMR chemical shifts of selected protons for various fragment sizes up to a 13-mer (with 1196 atoms) with respect to proton H b as obtained at the GIAO-HF/6-31G** and GIAO-BP86(VWN)/6-31G** levels. Structures of the trimer, heptamer, and tridecamer are shown in Fig.4, Fig.5, and Fig.6. For the tridecamer all presented shifts are those calculated for the central tweezer complex.

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				Monomer Dimer Trimer Heptamer Tridecamer Exp.
		Method	Proton		A	A	A
	21	HF	H a	3.3	3.3	3.3	3.4	4.5	3.6
			H b	0.0	0.0	0.0	0.0-0.1	0.0-0.1	0.0
			H 2/3/14/15	4.4	3.2-3.3 3.2-3.4	3.5-3.6	3.4-3.5	2.9
			H Bridgehead	1.7-1.9	1.9-2.1 1.7-2.2	1.4-2.3	1.6-2.4	1.8
		BP86(VWN) H a	2.7	2.8	2.7-2.8	2.8	4.0	3.6
			H b	0.0	0.0	0.0	0.0	0.0	0.0
			H 2/3/14/15	3.7-3.8	2.9-3.0 2.8-3.0	3.1	3.0	2.9
			H Bridgehead	1.2-1.4	1.4-1.6 1.3-1.6	1.0-1.8	1.2-1.8	1.8

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Table 3 :

 3 Relative isotropic NMR chemical shifts (δ) of selected protons for the central tweezer of the 'face-on' trimer fragment (see Fig.3) with respect to TMS and corresponding changes ∆δ of NMR chemical shifts upon rotation of the guest molecule around the CN axis (angle ϑ) and the perpendicular C 2 axis (angle ϕ) (see Fig.2). All shifts were obtained at the GIAO-HF/6-31G** level.

	δ		∆δ (ϑ)			∆δ (ϕ)
	Proton	5 •	11 •	22 •	5 •	11 •

Acknowledgments

The authors thank Dr. F. Koziol for preparing the projected fragment structures during his graduate studies in our group. Furthermore, we thank Prof. Dr. F.-G. Klärner (Universität Duisburg-Essen, Germany), Prof. Dr. H.W. Spiess (MPIP Mainz, Germany), and Dr. S.P. Brown (University of Warwick, England) for fruitful collaborations on the DCNB complex. C.O. acknowledges financial support by an Emmy Noether research grant of the DFG ("Deutsche Forschungsgemeinschaft"). J.Z. thanks the 'Landesgraduiertenförderung' (LGFG) for a graduate fellowship.


Josefina Pernille

Deborah Olesen

Michela Gustafson

Leonardo Simoni

Svante Pantoni

Xinxin Östling

Ingmar Guo

Skoog

Dr Pernille J Olesen
email: pernille.olesen@neuro.gu.se.

PhD Deborah R Gustafson

PhD Michela Simoni

PhD Leonardo Pantoni

PhD Svante Östling

PhD Xinxin Guo

PhD Ingmar Skoog

PJ Olesen

Temporal Lobe Atrophy and White Matter Lesions are Related to Major Depression Over 5 Years in the Elderly

Keywords: depression, elderly, brain atrophy, white matter lesions, population, longitudinal

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INTRODUCTION

Depression is one of the most common mental disorders in the elderly and has a significant impact on quality of life, mortality, and cognitive function [START_REF] Palsson | The epidemiology of affective disorders in the elderly: a review[END_REF]. It is therefore important to learn more about its risk factors. Reported risk factors include female gender, adverse life events, other psychosocial factors, and somatic disorders, such as stroke and cardiovascular disorders [START_REF] Djernes | Prevalence and predictors of depression in populations of elderly: a review[END_REF][START_REF] Palsson | The epidemiology of affective disorders in the elderly: a review[END_REF]. In addition, it has been suggested that organic brain changes, such as neurodegeneration and cerebrovascular disease, may be important in the etiology of geriatric depression.

Most studies on the association between brain atrophy and depression in the elderly have been cross-sectional and performed in clinical samples. The most consistent findings from crosssectional studies are that depression in the elderly is associated with atrophy in the frontal and temporal lobes, especially hippocampal atrophy and ventricular enlargement [START_REF] Schweitzer | Structural neuroimaging studies in latelife depression: a review[END_REF]. Only one longitudinal population-based study examined the association between brain atrophy and occurrence of depressive symptoms or syndromes during follow-up [START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF]. This study reported a cross-sectional association between temporal and parietal lobe atrophy at baseline and concurrent depressive symptoms, and no association with depression occurring during follow-up. Another longitudinal study in elderly without dementia examined the association between mean depressive symptom scores over time and change in brain atrophy on magnetic resonance imaging (MRI) over nine years [START_REF] Dotson | Depressive symptoms and brain volumes in older adults: a longitudinal magnetic resonance imaging study[END_REF]. Cross-sectional associations between temporal and frontal lobe atrophy and depressive symptoms, and a longitudinal association between volume decline in frontal white matter and depressive symptom score over time were reported [START_REF] Dotson | Depressive symptoms and brain volumes in older adults: a longitudinal magnetic resonance imaging study[END_REF]. This study did not Olesen,PJ 4 examine baseline brain atrophy in relation to incidence of depressive symptoms during follow-up.

Regarding cerebrovascular disease, cross-sectional studies, often from patient samples, consistently show associations between white matter lesions (WMLs) and depression [START_REF] Kramer-Ginsberg | Neuroanatomic localization of magnetic resonance imaging signal hyperintensities in geriatric depression[END_REF][START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF][START_REF] Kumar | Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression[END_REF][START_REF] Kumar | Autonomous neurobiological pathways to late-life major depressive disorder: clinical and pathophysiological implications[END_REF]. The results from longitudinal population-based studies are conflicting. Three studies using MRI reported that WMLs increased the risk of subsequent depression [START_REF] Godin | White matter lesions as a predictor of depression in the elderly: the 3C-Dijon study[END_REF][START_REF] Steffens | Cerebrovascular disease and evolution of depressive symptoms in the cardiovascular health study[END_REF][START_REF] Teodorczuk | White matter changes and late-life depressive symptoms: longitudinal study[END_REF] while two could not confirm these findings [START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF][START_REF] Versluis | Progression of cerebral white matter lesions is not associated with development of depressive symptoms in elderly subjects at risk of cardiovascular disease: The PROSPER Study[END_REF].

It has been suggested that cortical atrophy and WMLs represent two relatively independent pathways to major depression in the elderly [START_REF] Kumar | Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression[END_REF][START_REF] Kumar | Autonomous neurobiological pathways to late-life major depressive disorder: clinical and pathophysiological implications[END_REF]. This hypothesis was based on a cross-sectional clinical study, and has not been tested in longitudinal population-based studies. We examined brain atrophy and WMLs on computed tomography (CT) in a population-based sample of elderly without depression or dementia who were followed for five years for the occurrence of major and minor depression.

MATERIALS AND METHODS

Participants

The study sample has been described in detail [START_REF] Simoni | Prevalence of CT-detected cerebral abnormalities in an elderly Swedish population sample[END_REF], and was derived from the Prospective Population Study of Women (PPSW) [START_REF] Bengtsson | The study of women in Gothenburg 1968 -1969 -a population study. General design, purpose and sampling results[END_REF] and the Gerontological and Geriatric Population Studies (H70) [START_REF] Skoog | Psychiatric epidemiology of old age: the H70 study--the NAPE lecture 2003[END_REF] in Gothenburg, Olesen,PJ 5 Sweden. The participants were obtained from the Swedish Population Register based on birth date and were born in 1908, 1914, 1918, 1922 and 1930. Persons living in private households and institutions were included. In total, there were 1495 eligible individuals in 2000-2001, and 1051 accepted to participate (response rate 70.3%). Of the 1051, 1018 participated in a psychiatric examination and were invited for a CT scan. Of these, 642 (63.1%) accepted to have a CT scan. The 642 individuals who participated in the CT examination were younger (mean age 74 versus 77 years, p<0.001), less often women (71.3% versus 88.0%, p<0.001), and had a lower mortality rate from baseline to November 2003 (3.1% versus 11.5%, p<0.001) compared to the 376 non-participants [START_REF] Simoni | Prevalence of CT-detected cerebral abnormalities in an elderly Swedish population sample[END_REF]. According to the Swedish Hospital Discharge Register, participants in CT experienced a lower frequency of dementia (0.8% versus 7.7%, p<0.001), any psychiatric diagnosis (5.9% versus 13.9%, p<0.001) and stroke (5.6% versus 12.3%, p<0.001) compared to non-participants. There was no difference in the prevalence of major (3.0% versus 3.5%, p=0.66) or minor (9.7% versus 9.6%, p=0.97) depression between participants and non-participants.

A follow-up was performed in 2005-2006. Among those surviving, 459 accepted a new psychiatric examination (response rate 84.7%). Those lost to follow-up (83 refusals and 21 who died) were traced for dementia, major and minor depression in the Swedish Hospital Discharge Register. Thus, the sample comprised 563 individuals.

Individuals with dementia (n=16; 2.5%), major depression (n=19; 3.0%) or a score on the Mini-Mental State Examination (MMSE) less than 26 (n=44; 6.9%) at baseline were excluded. Those who developed dementia during follow-up (n=38) were also excluded from further analyses, leaving 525 individuals.

Olesen, PJ 6

Informed consent was obtained from all participants and/or their relatives. The study was approved by the Ethics Committee for Medical Research at the University of Gothenburg.

Neuropsychiatric Examinations and Interviews

Both in 2000-2001 and in 2005-2006, trained psychiatric research nurses performed the semi-structured neuropsychiatric examinations that included ratings of the past month's psychiatric signs and symptoms according to Comprehensive Psychopathological Rating Scale [START_REF] Asberg | A comprehensive psychopathological rating scale[END_REF], which is valid and reliable in elderly populations (van der [START_REF] Van Der Laan | The applicability and the inter-rater reliability of the Comprehensive Psychopathological Rating Scale in an elderly clinical population[END_REF], and Mini-International Neuropsychiatric Interview [START_REF] Sheehan | The Mini-International Neuropsychiatric Interview (M.I.N.I.): the development and validation of a structured diagnostic psychiatric interview for DSM-IV and ICD-10[END_REF], history of depression and assessment of current medications. Ratings of common signs and symptoms of dementia were also done (e.g. assessments of memory, orientation, general knowledge, apraxia, visuospatial function, understanding proverbs, following commands, naming ability and language) and has been described in detail [START_REF] Guo | Midlife respiratory function and Incidence of Alzheimer's disease: a 29-year longitudinal study in women[END_REF][START_REF] Skoog | A population-based study of dementia in 85-year-olds[END_REF].

Cognitive function was also measured with the MMSE [START_REF] Folstein | Mini-mental state". A practical method for grading the cognitive state of patients for the clinician[END_REF]. The psychiatric nurses who performed the examinations were supervised and trained by psychiatrists. In training sessions, nurses and psychiatrists rated symptoms and signs among both participants without dementia and those with dementia. Inter-rater reliability between psychiatrists and nurses was studied in 50 individuals. Kappa values for the presence versus absence of signs and symptoms necessary to diagnose depression were between 0.62 and 1.00 indicating "good" (reference range kappa=0.61-0.80) or "excellent" (kappa=0.81-1.00) agreement.

Measurements of Covariates

At baseline, participants underwent a physical examination and blood tests. Body mass index (BMI) was calculated as kg/m 2 . Systolic and diastolic blood pressure (SBP and DBP) was measured in the right arm in the seated position after 5 minutes' rest using a mercury

Diagnosis of Dementia and Depression

Dementia was diagnosed by geriatric psychiatrists according to the Diagnostic and Statistical Manual of Mental Disorders (DSM), third edition, revised (American Psychiatric Association, 1987) based on symptoms rated by the examiners during detailed neuropsychiatric examinations and close informant interviews, as described [START_REF] Skoog | A population-based study of dementia in 85-year-olds[END_REF]. Diagnoses of major and minor depression according to DSM-IV (American Psychiatric Association, 1994) were determined from algorithms based on symptoms rated by the examiners during the psychiatric examinations. Depression was only diagnosed in the absence of dementia. Major depression excluded a diagnosis of minor depression. According to DSM-IV, major depression includes ≥5 symptoms of depression during the same 2-week period while minor depression includes 2-4 symptoms during the same 2-week period. The symptoms "depressed mood" or "loss of interest" is required for diagnoses.

The diagnosis of depression for individuals lost to follow-up was based on information from the Swedish Hospital Discharge Register. In Sweden, doctors registers primary and secondary Olesen, PJ 8 diagnoses according to the International Classification of Diseases, version 10 (ICD-10) (World Health Organization, 1993) on all patients discharged from hospitals. ICD-10 codes for major depression were F31.4-5/32.2-3/33.2-3 and for minor depression F31.3/32.0-1/32.8- 9/33.0-1/33.8-9/34.1/34.8-9/38.0-1/41.2.

CT Scan Rating Methods

The same CT scanner and scanning procedure were used for all scans. Ten millimetre continuous slices were obtained. No contrast enhancement was used. The scans were evaluated by a neurologist (MS) experienced in CT and MRI ratings of WMLs and other cerebral lesions. The neurologist was blind to all clinical data.

The Gothenburg scale was used to rate WMLs [START_REF] Skoog | The prevalence of white-matter lesions on computed tomography of the brain in demented and nondemented 85-year-olds[END_REF]. According to this scale, WMLs are defined as periventricular or subcortical areas of decreased attenuation below that expected for normal white matter. The changes were always diffusely distributed within the white matter. The scale gives a global measure of WMLs in the brain, and has been used in our epidemiological studies since 1986 [START_REF] Skoog | The prevalence of white-matter lesions on computed tomography of the brain in demented and nondemented 85-year-olds[END_REF]. It is a 0-3 point scale which takes into account the severity of the hypodensity of WMLs, including 0 (absence of any attenuation), 1 (mild signal attenuation), 2 (moderate signal attenuation), and 3 (severe signal attenuation).

A subjective scale with three grades (absent, mild or moderate and severe) was used to evaluate cortical atrophy. Location of atrophy was categorized as frontal, temporal, parietal or occipital regions, according to the anatomical subdivision [START_REF] Gustafson | A 24-year follow-up of body mass index and cerebral atrophy[END_REF], and severity was scored according to the extent of sulcal widening (De [START_REF] Leon | Computed tomography evaluations of brain-behavior relationships in senile dementia of the Alzheimer's type[END_REF].

Olesen, PJ 9

The intra-rater Kappa values for the CT assessment were between "fair" (kappa = 0.21-0.40) and "good" (kappa = 0.61-0.80) for both WMLs and atrophy [START_REF] Simoni | Prevalence of CT-detected cerebral abnormalities in an elderly Swedish population sample[END_REF]. Interobserver agreement between the rater and a neuroradiologist was "fair" (kappa = 0.30) for WMLs, "moderate" for temporal lobe atrophy (kappa = 0.43) and "fair" for the other cortical regions (kappa = 0.29-0.36).

Statistical Analysis

The statistical analyses on the outcome major depression were based on participants without major depression or dementia at baseline, and who did not develop dementia during followup. In the analyses on minor depression, also those with minor depression at baseline and those who developed major depression at follow-up were excluded. WMLs were dichotomized as none or mild versus moderate or severe lesions. Cortical atrophy was dichotomized as absence versus presence of atrophy in each brain region. The comparison group was free from both depression and dementia during follow-up. Sex and age-category (70 versus >70 years) were preselected covariates. Additional covariates that were evaluated included level of education (0-7, 8-10 or ≥11 years), baseline stroke, myocardial infarction, angina pectoris, claudicatio intermittens, hypertension and diabetes mellitus, and levels of plasma glucose, serum cholesterol, BMI, SBP and DBP.

The statistical analyses were performed with logistic regression models in two steps: First, we selected the covariates to be included in the final models by analysing the association of each covariate with major depression adjusting for gender. Factors were included in the final models if they were associated at a level of p≤0.10. This resulted in hypertension and serum cholesterol being included as covariates. Second, multivariate logistic regression analyses were performed estimating the odds of major or minor depression during follow-up in relation Olesen, PJ 10 to cortical atrophy or WMLs at baseline and including age, sex, and the covariates selected in step one. Odds ratios (ORs) and 95% confidence intervals (CI) were calculated.

We present the results for three models: Model I without adjustments, Model II adjusting for age, sex and the covariates selected in step one; and Model III including both cortical atrophy and WMLs in the same regression model. As a secondary analysis, we also present the results for Model III performed on a subsample of individuals with MMSE above 25 at both baseline and follow-up.

Statistical analyses were performed using SPSS version 16.0. Results were considered statistically significant at a level of p<0.05.

RESULTS

Baseline characteristics are given in Table 1. Of the 525 participants who were free from major depression and dementia at baseline, 20 developed major depression (19 were diagnosed at the follow-up examination and one from the hospital discharge register). In the analyses on minor depression we also excluded 46 participants with minor depression at baseline as well as those who developed major depression, leaving 471 individuals. Among these, 63 developed minor depression (58 were diagnosed at the follow-up examination and 5 from the hospital discharge register). Results are presented for unadjusted ( There was no association between brain atrophy or WMLs and development of minor depression.

A logistic regression analysis, adjusted for confounders, and including both temporal lobe atrophy and WMLs at baseline showed that presence of temporal lobe atrophy (OR=2.81, 95% CI 1.04-7.62) and moderate to severe WMLs (OR=3.21, 95% CI 1.00-10.26) independently predicted major depression at follow-up (Table 2, Model III). None of the confounders were significantly associated with major depression in this model. Excluding participants with MMSE less than 26 at follow-up (n=35; two with major depression) did not change the main results. Including baseline history of depression (n=143) as confounder in the multivariate models did not change the findings.

DISCUSSION

We found that temporal lobe atrophy and moderate to severe WMLs predicted occurrence of major, but not minor, depression during a 5-year follow-up of a population-based sample of elderly. Our findings support the hypothesis that brain atrophy and WMLs represent relatively independent and complementary pathways to the development of major depression in the Olesen, PJ 12 elderly [START_REF] Kumar | Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression[END_REF][START_REF] Kumar | Autonomous neurobiological pathways to late-life major depressive disorder: clinical and pathophysiological implications[END_REF]. The only previous study that has explored this hypothesis is a clinical cross-sectional study, and depression was related to frontal but not temporal lobe atrophy [START_REF] Kumar | Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression[END_REF]. Our study adds to this previous study by providing longitudinal data from a population-based sample. Both neurodegenerative and cerebrovascular processes may thus be important for the development of major depression in the elderly.

Only one previous longitudinal population-based study has examined the association between brain atrophy at baseline and depressive symptoms or syndromes during follow-up [START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF]. This study reported cross-sectional associations between temporal and parietal lobe atrophy and depressive symptoms, but no association with depressive syndrome or depressive symptoms during follow-up. A longitudinal MRI study on elderly without dementia examined the association between mean depressive symptom scores over time and change in brain atrophy over nine years [START_REF] Dotson | Depressive symptoms and brain volumes in older adults: a longitudinal magnetic resonance imaging study[END_REF]. In that study [START_REF] Dotson | Depressive symptoms and brain volumes in older adults: a longitudinal magnetic resonance imaging study[END_REF], crosssectional analyses indicated associations between temporal and frontal lobe atrophy and depressive symptoms, and longitudinal analyses indicated an association between volume decline in frontal white matter and mean depressive symptom scores over time. However, in contrast to our study, brain atrophy at baseline was not reported in relation to occurrence of depression or depressive symptoms during follow-up. The somewhat inconsistent findings between these previous longitudinal studies and our study may partly be explained by the fact that we report separately on major and minor depression rather than on depressive syndrome or depressive symptoms.

Presence of temporal lobe atrophy, but not atrophy in other brain areas, predicted major depression. Support for the importance of the temporal lobe in major depression is found in Olesen, PJ 13 cross-sectional hospital-based MRI studies reporting that temporal lobe atrophy is associated with major depression in elderly patients [START_REF] Dolan | The cerebral cortical appearance in depressed subjects[END_REF][START_REF] Rabins | Cortical magnetic resonance imaging changes in elderly inpatients with major depression[END_REF][START_REF] Rainer | Data from the VITA Study do not support the concept of vascular depression[END_REF][START_REF] Wurthmann | Brain morphology assessed by computed tomography in patients with geriatric depression, patients with degenerative dementia, and normal control subjects[END_REF]. However, major depression in cross-sectional MRI studies has also been associated with other brain regions [START_REF] Almeida | Depression with late onset is associated with right frontal lobe atrophy[END_REF][START_REF] Dolan | The cerebral cortical appearance in depressed subjects[END_REF][START_REF] Rabins | Cortical magnetic resonance imaging changes in elderly inpatients with major depression[END_REF][START_REF] Rainer | Data from the VITA Study do not support the concept of vascular depression[END_REF][START_REF] Schweitzer | Structural neuroimaging studies in latelife depression: a review[END_REF][START_REF] Wurthmann | Brain morphology assessed by computed tomography in patients with geriatric depression, patients with degenerative dementia, and normal control subjects[END_REF], including atrophy in the frontal and parietal lobes. Differences between these cross-sectional studies and our longitudinal study, which may explain the inconsistent findings include the estimate of atrophy (i.e. measures of sulcal widening, visual rating of cortical atrophy, estimates of CSF volume etc), the severity of atrophy (e.g. any atrophy, severe atrophy), the choice of brain regions studied, the diagnostic criteria for depression, and the age of the samples.

It is well-known that fronto-subcortical circuits are important for depression [START_REF] Drevets | Brain structural and functional abnormalities in mood disorders: implications for neurocircuitry models of depression[END_REF][START_REF] Ressler | Targeting abnormal neural circuits in mood and anxiety disorders: from the laboratory to the clinic[END_REF]. These circuits include limbic structures such as the amygdala which has substantial projections to the temporal cortex [START_REF] Price | Neurocircuitry of mood disorders[END_REF].

Damage to fronto-subcortical circuits may be caused by subcortical lesions or atrophy in cortical structures. Thus, one explanation for the associations between WMLs and temporal lobe atrophy and major depression could be that these alterations in the brain have caused damage to fronto-subcortical circuits.

The cellular mechanisms that underlie the association between brain atrophy and depression in the elderly remain largely unknown. Due to the few post-mortem studies performed, the results should be interpreted cautiously. Nevertheless, in relation to temporal lobe involvement, changes in myelination, axonal growth and synaptic function have been reported in the temporal cortex of patients with major depression [START_REF] Aston | Transcriptional profiling reveals evidence for signaling and oligodendroglial abnormalities in the temporal cortex from patients with major depressive disorder[END_REF]. Atrophy in the temporal lobe may also reflect hippocampal alterations. Post-mortem studies have reported on Olesen, PJ 14 cellular alterations such as neuronal death, neuronal shrinkage, decrease in dendritic and glial density, and cell death in the frontal cortex and hippocampus of those with major depression [START_REF] Hercher | Through the looking glass: examining neuroanatomical evidence for cellular alterations in major depression[END_REF][START_REF] Khundakar | Morphometric changes in early-and late-life major depressive disorder: evidence from postmortem studies[END_REF]. Further support for a role of the temporal lobe in major depression is findings from a functional MRI study showing that the temporal lobes are involved in regulation of emotions [START_REF] Beauregard | The functional neuroanatomy of major depression: an fMRI study using an emotional activation paradigm[END_REF]. Hippocampal atrophy in depression [START_REF] Pittenger | Stress, depression, and neuroplasticity: a convergence of mechanisms[END_REF] and during normal aging [START_REF] Lupien | Cortisol levels during human aging predict hippocampal atrophy and memory deficits[END_REF] has been associated with increased cortisol levels, potentially reflective of physiological and environmental stress. One animal study indicated that psychosocial stress could be related to cell death in the temporal cortex [START_REF] Lucassen | Antidepressant treatment with tianeptine reduces apoptosis in the hippocampal dentate gyrus and temporal cortex[END_REF].

WMLs predicted major depression in addition to the effect of temporal lobe atrophy. Crosssectional associations between WMLs and depression have been shown repeatedly, especially for MRI and mainly from clinical studies [START_REF] Kramer-Ginsberg | Neuroanatomic localization of magnetic resonance imaging signal hyperintensities in geriatric depression[END_REF][START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF][START_REF] Kumar | Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression[END_REF][START_REF] Kumar | Autonomous neurobiological pathways to late-life major depressive disorder: clinical and pathophysiological implications[END_REF], although not all studies support this association [START_REF] Rainer | Data from the VITA Study do not support the concept of vascular depression[END_REF][START_REF] Skoog | The prevalence of white-matter lesions on computed tomography of the brain in demented and nondemented 85-year-olds[END_REF]. Our finding that WMLs preceded major depression is in agreement with three previous longitudinal studies using MRI [START_REF] Godin | White matter lesions as a predictor of depression in the elderly: the 3C-Dijon study[END_REF][START_REF] Steffens | Cerebrovascular disease and evolution of depressive symptoms in the cardiovascular health study[END_REF][START_REF] Teodorczuk | White matter changes and late-life depressive symptoms: longitudinal study[END_REF]. However, two longitudinal population-based studies did not support this association [START_REF] Ikram | Vascular brain disease and depression in the elderly[END_REF][START_REF] Versluis | Progression of cerebral white matter lesions is not associated with development of depressive symptoms in elderly subjects at risk of cardiovascular disease: The PROSPER Study[END_REF]. WMLs most likely reflect ischemic demyelination [START_REF] Pantoni | Pathogenesis of leukoaraiosis: a review[END_REF]. The association between depression and changes in the white matter has given rise to the "vascular depression" hypothesis [START_REF] Alexopoulos | Vascular depression' hypothesis[END_REF] which postulates that depression in the elderly may have a vascular origin. Our results support this view, especially regarding major depression.

Brain atrophy and WMLs did not predict occurrence of minor depression during follow-up, suggesting that this less severe form of depression may have a different etiology than major Olesen, PJ 15 depression [START_REF] Beekman | Major and minor depression in later life: a study of prevalence and risk factors[END_REF]. Our findings suggest that structural neuropathological changes in the temporal lobes and WMLs are related to more severe depression rather than to the milder forms. This is supported by cross-sectional studies suggesting that temporal lobe atrophy [START_REF] Kumar | Late-onset minor and major depression: early evidence for common neuroanatomical substrates detected by using MRI[END_REF][START_REF] Shah | Cortical grey matter reductions associated with treatment-resistant chronic unipolar depression. Controlled magnetic resonance imaging study[END_REF]) may be related to severity of depression rather than to depression per se. However, minor depression was related to frontal lobe atrophy in the study by [START_REF] Kumar | Late-onset minor and major depression: early evidence for common neuroanatomical substrates detected by using MRI[END_REF]. Differences may be explained by differences between population-based and clinical studies, cross-sectional and longitudinal studies and the use of somewhat different diagnostic criteria. We diagnosed minor depression based on DSM-IV criteria (n=58) or ICD codes (n=5), while [START_REF] Kumar | Late-onset minor and major depression: early evidence for common neuroanatomical substrates detected by using MRI[END_REF] only diagnosed according to DSM-IV with the additional requirement that the symptoms should be present for at least one month. Thus, they may have looked at a more severe form of the disease compared to our study. Further, they included only those who had their fist onset of depression after age 60.

The strengths of the study include the population-based sample, the longitudinal design and the comprehensive examinations performed by experienced psychiatric nurses. Furthermore, to minimize the risk that brain changes reflected preclinical dementia rather than depression, we excluded participants with a MMSE score less than 26 both at baseline and at follow-up.

We will discuss some limitations and methodological issues. First, participants in the CT scans had a lower mortality rate, less often stroke, dementia and other mental disorders according to the Swedish Hospital Discharge Register compared to non-participants [START_REF] Simoni | Prevalence of CT-detected cerebral abnormalities in an elderly Swedish population sample[END_REF] and may thus be healthier than the general population. However, there were no differences in hospitalization with major or minor depression between participants and nonparticipants. Second, we cannot exclude the possibility that those who developed depression would have developed dementia if we had included a longer follow-up. Third, some of the subgroups were rather small and results should be interpreted cautiously. Future studies on Olesen, PJ 16 larger samples are necessary to confirm our findings. Fourth, attrition is an issue that must be considered in follow-up studies. However, our attrition rate at follow-up was only 15.3%. To further reduce the influence of attrition, we used the Swedish Hospital Discharge Register to obtain diagnoses of depression in those lost to follow-up. However, this probably still underestimates the true incidence, as most cases of depression are not hospitalized. Fifth, visual rating of cortical atrophy and WMLs on CT is a rather crude method. The inter-rater Kappa values for agreement between the rater and a neuroradiologist was "fair" (kappa = 0.30) for WMLs, "moderate" for temporal lobe atrophy (kappa = 0.43) and "fair" for the other cortical regions (kappa = 0.29-0.36). If anything, the lack of perfect agreement most likely attenuates the observed relationship. CT is less sensitive than MRI in detecting WMLs and is more severely affected by bone hardening artifacts, which is particularly severe in the region of the medial temporal lobe [START_REF] Frisoni | Structural imaging in the clinical diagnosis of Alzheimer's disease: problems and tools[END_REF]. Nonetheless, visual rating of the temporal lobe has been found to be highly predictive for the discrimination of Alzheimer's disease versus control patients [START_REF] Wahlund | Visual rating and volumetry of the medial temporal lobe on magnetic resonance imaging in dementia: a comparative study[END_REF]. Further, CT is better in delineating clinically relevant WMLs [START_REF] Lopez | Computed tomography--but not magnetic resonance imaging--identified periventricular white-matter lesions predict symptomatic cerebrovascular disease in probable Alzheimer's disease[END_REF] and comparable to MRI in detecting brain atrophy [START_REF] Frisoni | Structural imaging in the clinical diagnosis of Alzheimer's disease: problems and tools[END_REF] and may be more suitable than MRI for the elderly, as it is less sensitive to motion artefacts.

CT is also the most used brain imaging tool world-wide. Sixth, all scans were rated by a single person which may increase the risk for systematic error.

The results from this longitudinal population-based study suggest that temporal lobe atrophy and WMLs represent independent pathways to major depression in the elderly, even if they may have shared risk factors. The finding that neurodegeneration and cerebrovascular disease are related to major depression may have implications for treatment and prevention, as these changes have been related to preventable factors, such as hypertension and obesity.

  was defined as Korotkoff phase 5. Hypertension was defined as SBP≥140 mm Hg and/or DBP≥90 mm Hg and/or taking antihypertensive medication. Blood samples were taken after overnight fasting. Plasma glucose and serum cholesterol concentrations were measured. The diagnosis of stroke was based on information from self-reports, close informants and the Swedish Hospital Discharge Register. Diagnoses of myocardial infarction, angina pectoris and claudicatio intermittens were based on self-report and key informant interviews. Diabetes mellitus was defined based on a physician's diagnosis, being on antidiabetic therapy or having two fasting venous or capillary whole blood glucose values ≥7.0 mmol/L.

Olesen, PJ 17 DISCLOSURE

 17 DG has received honoraria from the Albuquerque Area Indian Health Board and Shire Pharmaceutical, Ltd.; and receives research support from the NIH [NIA 5R03AG026098 (PI)] and the Swedish Research Council. LP serves on the editorial boards of Acta Neurologica Scandinavica and International Journal of Alzheimer Disease. IS has served on scientific advisory boards for Pfizer Inc. and AstraZeneca; has served on an editorial advisory board for International Psychogeriatrics; receives royalties from publishing Alzheimers sjukdom och andra kognitiva sjukdomar (English title: Alzheimer's Disease and Other Cognitive Disorders (Liber 2003)); serves on speakers' bureaus for Shire plc, Janssen-Cilag, Pfizer Inc., Novartis, and Esai Inc.; and has received research support from the Swedish Research Council, the Alzheimer's Association, and the Bank of Sweden Tercentenary Foundation. The authors PJO, MS, SÖ and XG report no biomedical financial interests or potential conflicts of interest.

Table 2 ,

 2 Model I) and adjusted (Table 2, Model II and III) models. Individuals with any temporal lobe atrophy at baseline more often developed major depression (6.4% versus 2.2%, OR=2.81, 95% CI 1.04-7.55) during follow-up than those with no atrophy (Table 2, Model II) adjusted for confounders (age, gender, baseline

	Olesen, PJ 11

Table 2 ,

 2 Model II) compared to those with no or mild WMLs at baseline.

Table 1

 1 Baseline Characteristics of the Study Population and Those Who Developed Major or Minor Depression Over 5 years Follow-up

		Baseline sample	Major depression	Minor depression
			during follow-up	during follow-up
		(n=525 a )	(n=20 a )	(n=63 a )
	Characteristic	n (%) or mean (SD)	n (%) or mean (SD)	n (%) or mean (SD)
	Women	360 (68.6%)	17 (85%)	49 (77.8%)
	Age (years)	72.7 (4.6)	73.2 (4.6)	72.7 (4.4)
	Age distribution (years)
	70	381 (72.6%)	13 (65%)	45 (71.4%)
	78	86 (16.4%)	5 (25%)	13 (20.6%)
	82	47 (9.0%)	2 (10%)	4 (6.3%)
	86	11 (2.1%)	0	1 (1.6%)
	Education
	0-7 years	156 (30.8%)	6 (33.3%)	21 (34.4%)
	8-10 years	182 (35.9%)	9 (50%)	16 (26.2%)
	≥ 11 years	169 (33.3%)	3 (16.7%)	24 (39.3%)
	MMSE	28.4 (1.1)	28.1 (1.2)	28.1 (1.1)
	Blood pressure,	156.7(22.4)/82.7(11.5) 156.2(15.5)/81.2(11.1) 151.2(24.1)/80.1(11.9)
	SBP/DBP (mmHg)
	Serum cholesterol	5.90 (1.10)	5.52 (1.00)	6.06 (1.32)
	(mmol/l)
	Antidepressant treatment	37 (7.0%)	11 (55.0%)	3 (4.8%)
	Cardiovacular drugs b	148 (28.2%)	8 (40.0%)	17 (27.0%)
	Moderate-severe WMLs	52 (9.9%)	5 (25%)	5 (7.9%)
	Cortical atrophy	296 (56.4%)	14 (70%)	40 (63.5%)
	DBP, diastolic blood pressure; MMSE, Mini-Mental State Examination; SBP, systolic blood
	pressure; WMLs, white matter lesions.

a Due to missing values, the group sizes of the following measures were reduced: baseline sample

ACKNOWLEDGEMENTS

We would like to thank Tomas Marlow and Kristoffer Bäckman for statistical assistance, both at the Neuropsychiatric Epidemiology Unit, University of Gothenburg, Sweden.

This study was funded by grants from the Swedish Research Council (No. 11267, 2005(No. 11267, -8460, 825-2007-7462)-7462), the Swedish Council for Working Life and Social Research (No. 2001-2835, 2001-2646, 2003-0234, 2004-0150, 2006-0020, 2006-1506, 2004-0145, 2006-0596, 2008-1111, 2008-1229), The Bank of Sweden Tercentenary Foundation, the Alzheimer's Olesen, PJ 18 Association Zenith Award (ZEN-01-3151), the Alzheimer's Association Stephanie B. Overstreet Scholars (IIRG-00-2159), the Swedish Brain Power, Sylwans stiftelse, Söderström Königska, Fredrik och Ingrid Thurings stiftelse, Selma Anderssons stiftelse and the EU FP7 project LipiDiDiet, Grant Agreement No. 211696. The funders had no role in the planning of the study or interpretation of the results.

-education (n=507), blood pressure (n=520), serum cholesterol (n=522); major depressioneducation (n=18); minor depression -education (n=61), serum cholesterol (n=62).

b Antihypertensives, anticoagulants, cholesterol-and triglyceride lowering, and antidiabetics

Olesen, PJ