Dicyanovinylnaphthalenes for neuroimaging of amyloids and relationships of electronic structures and geometries to binding affinities

Abstract

The positron-emission tomography (PET) probe 2-(1-[6-[(2-fluoroethyl)(methyl)amino]-2-naphthyl]ethylidene) (FDDNP) is used for the noninvasive brain imaging of amyloid-β (Aβ) and other amyloid aggregates present in Alzheimer’s disease and other neurodegenerative diseases. A series of FDDNP analogs has been synthesized and characterized using spectroscopic and computational methods. The binding affinities of these molecules have been measured experimentally and explained through the use of a computational model. The analogs were created by systematically modifying the donor and the acceptor sides of FDDNP to learn the structural requirements for optimal binding to Aβ aggregates. FDDNP and its analogs are neutral, environmentally sensitive, fluorescent molecules with high dipole moments, as evidenced by their spectroscopic properties and dipole moment calculations. The preferred solution-state conformation of these compounds is directly related to the binding affinities. The extreme cases were a nonplanar analog t-butyl-FDDNP, which shows low binding affinity for Aβ aggregates (520 nM K_i) in vitro and a nearly planar tricyclic analog cDDNP, which displayed the highest binding affinity (10 pM K_i). Using a previously published X-ray crystallographic model of 1,1-dicyano-2-[6-(dimethylamino)naphthalen-2-yl]propene (DDNP) bound to an amyloidogenic Aβ peptide model, we show that the binding affinity is inversely related to the distortion energy necessary to avoid steric clashes along the internal surface of the binding channel.

Extracellular amyloid-β (Aβ) senile plaques (SPs) and neurofibrillary tangles (NFTs) of intraneuronal hyperphosphorylated tau peptide aggregates are a characteristic pathology found in the brains of patients with Alzheimer’s disease (AD) and other neurodegenerative diseases (1). Accurate detection of these aggregates in the brains of living AD patients allows early diagnosis and potential treatments to reverse or retard disease progression. The fluorescent thioflavin T and Congo red dyes are traditionally used to label protein aggregates in brain slices for postmortem diagnosis of AD. Unlike these charged molecules, the uncharged fluorescent naphthalene derivative 1,1-dicyano-2-[6-(dimethylamino)naphthalen-2-yl]propene (DDNP) (Fig. 1), also an excellent staining dye in vitro, is capable of crossing the blood–brain barrier. The fluorinated DDNP analog, 2-(1-[6-[(2-fluoroethyl)(methyl)amino]-2-naphthyl]ethylidene) (FDDNP), can be synthesized with the ¹⁸F positron emitter and was used as the first molecular imaging probe for the regional assessment of Aβ and tau deposition in the brains of living AD patients (2–5).

Fig. 1.

Structures of synthesized FDDNP analogs.

Previous studies have shown that it is the neutral and hydrophobic properties of DDNP and its analogs that enable it to recognize the β-sheet domains in amyloid-like aggregates, making it an effective in vitro and in vivo imaging probe (6, 7). Recently, DDNP and other amyloid-imaging probes have been cocrystallized with short amyloid-forming segments of the Aβ and tau polypeptides that form fibrils similar to those formed with the full protein (8). These truncated systems contain stacks of self-complementary β-sheets tightly bound to each other in a motif called a steric zipper. The fibrils formed by the steric zippers are similar to those formed by the full-length parent sequence in morphology, diameter, helical pitch, cross-β diffraction pattern, fibril seeding capacity, stability, and dye binding (8–10). Numerous investigations have shown that although the steric zippers do not contain all of the elements of complexity contained in the parent systems, they serve as excellent models for full-length fibrils (8, 11). Recently, the VQIVYK steric zipper model from tau has been used to develop a small polypeptide inhibitor of not only truncated peptide aggregation but also aggregation of two tau constructs as well (12). The X-ray structures solved with DDNP bound to the VQIVYK steric zipper suggested transient binding of DDNP along a hydrophobic channel that runs the length of the longitudinal fibril axis (or fibril spine). The presence of a “smear” of electron density along the binding channel indicated that there may be multiple sites that DDNP binds, unlike the more discrete binding sites associated with charged molecular probes that preferred highly localized sites near complementary charged residues. Molecular docking was used in the crystallographic study to identify the preferred binding modes and sites of DDNP along the fibril channel, while also managing to recapitulate the experimentally observed transient docking phenomenon.

We have synthesized a number of FDDNP analogs (Fig. 1) that differ in size both at the electron-donating amine and electron-withdrawing dicyanovinyl moieties. Herein, we report the effects of chemical modifications on the molecular geometries, spectroscopic properties, and binding to Aβ fibrils. We then use molecular docking to study the binding modes of these molecules to the established tau steric zipper model. The binding information is used to rationalize the effects of chemical substitutions and changes in molecular geometry on the binding affinity.

Experimental Results and Discussion

Naphthalene Derivatives.

Fluorescent compounds 4–11 (Fig. 1) were prepared based on an established synthetic methodology (for details see Materials and Methods and SI Appendix) (3, 13, 14). FDDNP and its analogs are environmentally sensitive fluorophores that undergo a significant change in absorption/emission wavelength upon binding to SPs or NFTs (3, 7, 15). Fluorescence microscopy revealed an intense fluorescence of SPs and NFTs with minimal background fluorescence in postmortem AD brain specimens stained with FDDNP analogs. The binding affinity of each FDDNP analog was measured using radioactive competitive-binding assays with [¹⁸F]FDDNP. Addition of nonradioactive 4b, 6b, 7b, 8b, 9c, 10b, or 11b displaces [¹⁸F]FDDNP from the Aβ fibril-binding site. This indicates that the analogs share the same [¹⁸F]FDDNP-binding site on the Aβ aggregates (Fig. 2, Upper). All compounds, except 9c, exhibit rather similar nanomolar binding affinity to Aβ fibrils (K_i; Table 1). Compound 9c has only weak binding to Aβ fibrils, also reflected in its poor ability to label Aβ aggregates in human brain specimens (Fig. 2, Lower).

Fig. 2.

(Upper) Confocal fluorescence micrograph of a NFT and SP labeled with 10 μM FDDNP vs. constrained DDNP (10b) and t-butyl DDNP (9c). Digitally captured image produced by laser-scanning Leica TCS SP MP inverted confocal microscope with an argon laser (excitation wavelength, 488 nm). (Scale bar: 50 μm.) Note the poor labeling ability of the t-butyl analog 9c, as opposed to the more planar FDDNP and 10b. (Lower) Radioactive competitive binding curves of [¹⁸F]FDDNP vs. nonradioactive FDDNP (red circles), 10b (blue triangles), and 9c (green squares) in the presence of Aβ(1–40) fibrils. Each symbol represents the mean value of three determinations per each concentration of competitor. Error bars indicate ±SD.

Table 1.

Selected structural, spectroscopic, and binding data for synthesized DDNP analogs

NMR			Spectroscopic		Binding			X-ray			Calculated
Compound	δ (H-5)	δ (H-7)	λmax (abs*)	λmax (em)	ϕ†	Δν (cm−1)	Ki (nM)¶	NCar‡ (Å)	Σωi§ (°)	ωtorsion (°)	NCar (Å)	ωtorsion (°)	rms (Å)||
DDNP	6.85	7.18	438	560	0.030	4,970	10	1.362	359.9	31.0	1.375	37.1	0.10
								1.375	360.0	143.7	1.374	143.8	0.11
FDDNP	6.95	7.20	431	553	0.016	5,065	0.20	n/d	n/d	n/d	1.388	37.7	—
											1.388	143.2	—
4b	6.82	7.12	455	564	0.021	4,250	0.46	n/d	n/d	n/d	1.372	36.2	—
											1.372	145.1	—
6b	6.58	6.81	434	567	0.018	5,400	0.43	1.369	359.8	33.3	1.375	37.3	0.25
								1.374	348.4	152.6	1.374	143.8	0.10
7b	6.71	7.03	455	566	0.020	4,310	0.19	n/o	n/o	n/o	1.364	36.3	—
								1.369	359.9	148.8	1.364	145.1	0.09
8b	7.07	7.33	428	569	0.014	5,790	0.30	n/o	n/o	n/o	1.401	37.9	—
								1.411	347.8	146.0	1.402	143.1	0.25
9c	6.91	7.04	374	595	0.013	9,930	520	n/d	n/d	n/d	1.390	75.4	—
											1.390	110.6	—
10b**	6.84	7.18	443	541	0.006	4,090	0.01	1.377	360.0	35.6	1.377	31.9	0.15
††								1.366	359.2	−10.3	1.373	−29.0	0.28
11b	6.83	7.16	470	566	0.137	3,610	0.12	1.360	360.0	2.9	1.369	0.0	0.06
								n/o	n/o	n/o	1.369	180.0	—

n/d, not determined; n/o, not observed; —, uncalculated value.

*Absorption (abs) and emission (em) measured in CH₂Cl₂ (nm), a solvent that mimics the microenvironment of the Aβ fibril-binding site.

^†Quantum yields determined relative to DDNP.

^‡Distance between amine nitrogen and aromatic naphthalene carbon.

^§Sum of bond angles about amino nitrogen.

^¶High binding affinity to Aβ fibrils. Binding affinities were determined in PBS (pH 7.4) containing up to 1% ethanol.

^||Heavy atom rmsd with respect to the X-ray structure.

**Orange crystal.

^††Red crystal.

The ketone intermediates did have good affinities for amyloid fibrils in vitro (16). We tested the [¹⁸F]fluoroethyl (1-{6-[(2-fluoroethyl)(methyl)amino]naphthalen-2-yl}ethanone) (ADMAN) derivative in vivo in humans, which showed significant nonspecific (nonamyloid) binding, consistent with the membrane-intercalating properties of the 2-(dialkylamino)-6-acylnaphthalenes (17). This reduces ketone effectiveness for in vivo use in humans, and this report concentrates on the binding affinities and properties of the amyloid-specific dicyanovinyl compounds.

NMR Spectra.

¹H NMR spectra reflect the structural changes upon formal substitution of the acetyl group for the dicyanovinyl acceptor group, most notably through a decrease in chemical shift of proton H-1 from ∼8.3 to 8.0 ppm attributable to modified magnetic anisotropy of the side chain (see SI Appendix). The ¹H NMR spectra also provide insights into the ground-state molecular geometry in solution, particularly around the nitrogen atom. Planar geometries support efficient delocalization of the nitrogen electron pair into the aromatic ring and result in increased shielding and smaller chemical shifts for protons H-5 and H-7 (δ; Table 1). In compounds with nonplanar arrangement of the substituents around the donor nitrogen (5, 8a, 8b), chemical shifts of the corresponding protons are substantially larger. The distinct coupling pattern in solution ¹H NMR spectra of compound 8b and related piperidine and piperazine derivatives shows that at room temperature, the six-membered ring is fixed in a chair conformation (18). This is in agreement with the ground-state calculations for 8b, in which the heavy atom angles in the six-membered rings are shown to be between 108° and 112° (see Structure and Modeling). Similar NMR spectral results were obtained for compounds with analogous electron-donating groups, which were concluded to contain nonplanar amines (13, 14). For compound 6b, which exists both in planar and nonplanar forms in the solid state, ¹H chemical shifts for protons H-5 and H-7 were found to be relatively small in solution. This indicates a greater propensity toward the planar arrangement about the nitrogen, allowing for efficient conjugation with the naphthalene ring system.

Absorption and Emission Spectra.

For all compounds except 9c, replacement of the acetyl acceptor group by the dicyanovinyl side chain resulted in considerable bathochromic shifts of the absorption maxima from 350–380 to 400–470 nm (λ_max; Table 1). This observation is consistent with previous studies that demonstrated a propensity for the dicyanovinyl to be planar and conjugated with the donor group (19). The lack of red shift in 9c is the result of the acceptor being forced out of the plane of conjugation because of the bulky t-butyl substituent. The absorption maxima are also dependent on the extent of conjugation of the donor group, although the effect is less pronounced.

The emission maxima of these compounds are independent of the geometry about the amine but occur at a higher wavelength for analog 9c, in which the acceptor group is highly nonplanar. Emission maxima are also red-shifted with increasing solvent polarity (SI Appendix, Table S4). Large red shifts indicate an increased dipole moment in the excited state compared with that of the ground state, consistent with the formation of an intramolecular charge-transfer excited state (ICT) (see SI Appendix) (20, 21). It should be noted that for strongly solvatochromatic compounds, an anomalous blue shift in water is observed because of interactions with the solvent cage. This blue-shifting phenomenon has been long established in the literature (3).

Fluorescence-emission intensities depend on the rate of ICT excited-state depopulation. In viscous microenvironments or upon binding to amyloid aggregates, double-bond isomerization or rotational relaxation is restricted and becomes much slower, leading to ∼10-times enhanced fluorescence yields over in bulk solution (ϕ; Table 1) (16).

Structure and Modeling.

Single crystal X-ray diffraction provided solid-state structures of DDNP, 5, 6b, 7b, 8b, 10b, and 11b. [The structures for DDNP have been deposited in the CSD, www.ccdc.cam.ac.uk/products/csd (reference code NAFZUP). All available X-ray data, including coordinates, are available for all structures in SI Appendix.] In the case of 6b, two conformers were present in the crystal. The distinct conformations are attributable to the orientation of the dicyanovinyl, which can be rotated syn or anti with respect to the C6-C7 aromatic bond (Fig. 3). We have defined the torsion angle responsible for the orientation of the dicyanovinyl as ω_torsion. Analog 10b crystallized into two distinct crystal polymorphs, colored red and orange, which arises because of cyclohexenyl-ring conformations that orient the dicyanovinyl either above or below the plane of the naphthalene ring.

Fig. 3.

Syn and anti orientations of the dicyanovinyl group with respect to the C7-C6 aromatic bond. The syn conformation is defined as 0° ≤ |ω_torsion| < 90° and the anti conformation as 90° ≤ |ω_torsion| ≤ 180°.

The X-ray structures exhibit an sp²-like planar arrangement of the substituents around the naphthalene ring, providing maximal conjugation of the nitrogen lone pair with the aromatic system. The X-ray structures revealed the syn conformation of 6b to be planar and the anti to be slightly puckered. Azetidine rings, such as the one in 6b, are nonplanar, with a slight 1.3 kcal/mol nitrogen inversion barrier (22). However, planar azetidine rings have been reported previously in other crystal structures in which the azetidine nitrogen is conjugated with a π system (23). The pyrrolidine ring in 7b adopts an envelope conformation. The other cyclic analogs do not allow planarization about the amine nitrogen without a higher energetic penalty. For these analogs, distortion from planarity at the amine results in a slight loss of conjugation, which causes a lengthening of the bond distance between the amine nitrogen and aromatic carbon of the naphthalene ring (N-C_ar; Table 1). The mean N-C_ar X-ray distances for the planar amines listed in Table 1 are 1.368 Å, and 1.393 Å for the nonplanar amines. This difference in bond distances for the planar and nonplanar compounds has been observed in a related set of DDNP analogs with structures determined by neutron diffraction (13). These molecules demonstrated N-C_ar distances of 1.371 Å for the planar amines and 1.426 Å for the nonplanar amines.

Quantum mechanical (QM) geometry optimizations were performed at the M06–2X/6–311+G(d,p) level in the gas phase (details in Materials and Methods). The compounds were all modeled in both the syn and anti orientations of the dicyanovinyl group. The optimized structures agreed well with the geometries of the available X-ray structures (Table 1 and SI Appendix, Fig. S1), yielding an average heavy atom rmsd of 0.15 Å. The QM geometry optimizations showed that the syn and anti orientations are nearly isoenergetic, with an average difference of 0.4 kcal/mol (SI Appendix, Table S1). It has been proposed previously that the dipole moment of DDNP is related to binding affinity (2, 24). We analyzed the charge distribution of these molecules by mapping the electrostatic potential (ESP) to the molecular surface of each analog (SI Appendix, Fig. S2). The ESP surfaces of all of the analogs are very similar, with the primary difference between them being their shapes. This is most prominently highlighted by comparing the two most planar analogs with the highest binding affinities, 10b and 11b, to the least planar analog with the lowest binding affinity, 9c.

Amyloid Binding Model

A steric zipper pseudofibril of the VQIVYK tau sequence was built as a model in which to rationalize the relative binding affinities of the analogs in Fig. 1 (see Materials and Methods). Two unique channels run along the fibril spine, which we have denoted as the tyrosine and lysine channels, named for the prominent amino acids characterizing the respective channels (SI Appendix, Fig. S3 and S4). Eisenberg and coworkers (8) observed that the negatively charged fluorescence probe Orange-G preferentially bound the electrostatically positive lysine channel, whereas the neutral probes, DDNP and curcumin, preferred the tyrosine channel. The binding preferences were revealed by a registration shift in β-sheet mating in the steric zipper, enlarging either the tyrosine channel, as in the case of DDNP and curcumin, or the lysine channel, as in the case of Orange-G, to facilitate binding. We have only considered binding to the tyrosine channel. The program AutoDock Vina (25) was used to flexibly dock all of the molecules in Fig. 1 to the rigid VQIVYK pseudofibril model. Side chains were kept rigid during the docking in the same fashion as for Eisenberg and coworkers, because several computational tests showed that the tightly packed environment of the fibril channel does not provide room for side-chain reorganization upon ligand binding. This greatly diminishes the effect that an induced fit would have on ligand binding.

The docking results for each analog recapitulated the multiple binding modes along the fibril spine observed in the X-ray crystallographic density (Fig. 4A). It is likely that DDNP and its analogs bind to localized sites along the fibril spine, which is suggested by the ability of the nonsteroidal anti-inflammatories (NSAIDs) naproxen and ibuprofen to displace FDDNP from fibrils at low concentrations (5.7 nM and 11 μM, respectively) (26). However, because of the absence of well-resolved crystallographic density in the fibril channel and the lack of easily identifiable anchors on FDDNP and its analogs [such as the negative charges of Orange-G that clearly place it proximal to the lysine residues (8)], it is difficult to exactly delineate the preferred binding mode. Analysis of the binding modes of each analog immediately justifies the little effect that drastic changes at the amine position have on binding affinity. The amine points directly along the spine of the binding channel, so changes in size along this axis can easily be accommodated without introducing steric clashes with the sides of the binding channel (Fig. 4B). This is most prominently demonstrated by the similarity in binding affinity between 11b, containing a dimethyl-substituted amine, and 8b, containing a methylpiperidine ring. It was noted above that the large dipole moments of DDNP and its analogs (computed range of 8–12 Debye) could be important in binding. The polar contacts present between the bound probe, tyrosine oxygen atoms (Fig. 4 D and F), and valine N termini and stabilization of the negative (dicyanovinyl) and positive (amine) ends of the molecule could be significant factors in binding.

Fig. 4.

(A) Docking of each dicyanovinyl analog from Fig. 1 yielded a “smear” of poses down the binding channel. (B) The channel accommodates planar molecules of different sizes at the amine position, as shown by the substitution of a methylpiperidine in 8b for the dimethylamino group in 11b, which have similar affinities. Differences in binding affinity can be rationalized by the ability of the smaller and more planar analogs, such as 11b (C and D), to fit within the channel with minimal distortion. Larger and less planar molecules, such as 9c (E and F), require greater distortion to fit within the pocket. In C and F, solid spheres show the atomic radii of the ligand and the transparent surface represents the molecular surface of the protein. Dashed lines represent polar contacts within 3.0 Å between the ligand and pseudofibril.

Analysis of the top-ranking poses of each molecule showed that the smaller and more planar molecules (e.g., 11c; Fig. 4 C and D) better fit the binding channel than the larger molecules (e.g., 9c, Fig. 4 E and F). Molecules with larger substitutions at the dicyanovinyl position prefer greater degrees of nonplanarity in the free global minimum conformation and, therefore, required more distortion of the ω_torsion dihedral to prevent steric clashes of the C6 side chain with the binding channel upon binding. We further examined the magnitude of the ω_torsion distortion by performing QM/molecular mechanical (QM/MM) optimizations of the docked poses at the M06–2X/6–311+G(d,p):Universal Force Field (UFF) level of theory. The QM region was defined as the ligand, whereas the MM system was defined as the rest of the system and held rigid during the calculation. During the QM/MM optimizations, noticeable differences in the potential energy surfaces between the docking force field and QM/MM were observed. For example, the lowest-energy docked pose of 11b in the tyrosine channel had a ω_torsion value of −37.3° and an out-of-plane twisting of the amine group on the naphthalene, whereas after QM/MM optimization, ω_torsion decreased to 1.5° and was also accompanied by a planarization of the amine group. The planarization of ω_torsion after the QM/MM optimization corresponds to a lower distortion energy on the M06–2X/6–311+G(d,p) potential energy surface (SI Appendix, Fig. S5).

Upon examination of all of the QM/MM optimized complexes, a qualitative trend was found between the energy required to distort ω_torsion and the binding affinity of the molecule (Fig. 5). The constrained DDNP analog 10b is locked into a near-planar conformation and has the highest binding affinity. Analog 11b, which has a hydrogen substitution at the dicyanovinyl position, prefers a planar conformation and, correspondingly, also has a high binding affinity. The molecules with a methyl substitution at the dicyanovinyl position, 4b, 6b, 8b, FDDNP, and DDNP, fall within a similar region of the graph. DDNP has 50-fold lower affinity than FDDNP and the other methyl-substituted analogs (10 vs. ∼0.2 nM). The program QikProp (version 3.0.001w; Schrodinger) was used to compare the molecular properties of these compounds (SI Appendix, Table S2). DDNP has notably less hydrophobic surface area and thus a lower predicted water/octanol partition coefficient. Similar analysis can also be applied to distinguish the difference in binding affinity between 10b and 11b. Both of these molecules require little distortion to fit the binding pocket, yet 11b has both a lower predicted log(P) value and less hydrophobic contact surface area (SI Appendix, Table S3). Analog 9c had the lowest binding affinity but also required significantly more distortion energy to fit the fibril channel than any of the other analogs.

Fig. 5.

Plot of the K_i vs. the energy to distort ω_torsion from the global minimum gas-phase conformation to the value in the QM/MM optimized structure.

Conclusions

A series of FDDNP analogs have been synthesized (Fig. 1) and characterized using NMR, spectroscopic, and computational methods. Two of these molecules, 10b and 11b, showed improved affinity to amyloid fibrils over the parent molecule FDDNP. Improved binding affinities are essential for imaging probes to visualize and appropriately quantify amyloid aggregation within the tissue target. Through the use of the steric zipper–binding model for DDNP bound to the VQIVYK segment of tau (8), the differences in relative binding affinities of these imaging probes has been attributed to the distortion required for the molecules to fit within the binding channels that run along the fibril spine. Molecules with larger substitutions at the dicyanovinyl position, such as 9c, preferred highly nonplanar conformations in solution and required the largest magnitude of distortion to fit within the binding channel. Efforts to (i) modify (lower or increase) the binding affinities to some amyloids (e.g., Aβ) and (ii) provide a differential binding modification between amyloids (e.g., Aβ and tau aggregates) could produce imaging probes with selective sensitivity and specificity for different imaging agents. This approach offers a framework for fine-tuning the binding properties of neurofibrillary tau-specific (or Aβ-specific) imaging probes in parallel with X-ray microcrystallography at atomic resolution in cocrystallization experiments.

Materials and Methods

Syntheses of Naphthalene Derivatives.

In preparing fluorescent compounds 4–11 (Fig. 1), the 6-acyl-2-naphthols 1–3 were subjected to the Bucherer reaction with open-chain and cyclic amines that are not sensitive to slightly acidic aqueous environment. Aziridine and azetidine rings are too reactive under the Bucherer reaction conditions, and, therefore, the ketones 5 and 6a were prepared by direct nucleophilic substitution of the methoxy group in (6-methoxy-2-naphthyl)methyl ketone with the respective aziridine and azetidine lithium salts. In the last step of the synthesis, the ketones were subjected to the Knoevenagel reaction with malononitrile to yield the dicyanovinyl naphthalene analogs. Because of the high reactivity of the aziridine ring, ketone 5 could not be transformed into the expected product, and decomposition occurred. Naphthaldehyde 11a, prepared by a modification of a known procedure (27), gave its Knoevenagel product in good yield. Full experimental details for the synthesis and characterization of each molecule are described in SI Appendix.

QM Structure Calculations.

FDDNP analogs from Fig. 1 with X-ray structures in either the syn or anti conformation were directly optimized to the nearest ground-state minimum using M06–2X/6–311+G(d,p) in Gaussian09 (28) with tight convergence. For analogs with a crystal structure of only the syn or anti conformation, the relationship ω_syn ∼ 180 − ω_anti was used to estimate the starting structure. This relationship held quite well for the optimized structures (R² = 0.99; SI Appendix, Fig. S2). For analogs without X-ray structural data, the global minimum conformation was located using a 5,000-step Monte Carlo Multiple Minimum (MCMM) gas-phase conformational search with OPLS2005 performed in MacroModel (version 9.9.111; Schrodinger) was used as the starting point. Geometries of the QM-calculated and X-ray structures were superimposed using Maestro (version 9.2; Schrodinger) giving an average heavy atom RMSD of 0.15 Å (SI Appendix, Fig. S1).

Amyloid Binding Model Construction.

The biological unit of the VQIVYK steric zipper was obtained from ref. 8 without DDNP explicitly modeled. The biological unit was duplicated into a 4 × 3 × 8 steric zipper with PyMOL (version 1.3; Schrodinger) using the crystallographic symmetry information included with the model. This was done in an identical manner as that of Eisenberg and coworkers (8), and a superposition of our model to theirs shows they are nearly identical, with corresponding atom–atom deviations of ≤ 0.5 Å (SI Appendix, Fig. S2). We constructed a larger model to more comprehensively include long-range electrostatics in both the docking and QM/MM simulations.

Molecular Docking and QM/MM Calculations.

AutoDock Vina was used to perform the docking simulations (25) with the QM-optimized analogs serving as the input ligands. The receptor was prepared for docking using the PyMOL AutoDock plugin (29). Tyrosine and lysine channels located toward the center of the model were chosen for docking, each with a 12 × 39 × 21 Å rectangular docking region, more than large enough to encompass each entire channel separately. The pseudofibril was held rigid during both docking and QM/MM optimization, because the close packing of the amino acid residues within the channel prevents the side chains from reorganizing upon ligand binding. Individual docking simulations were performed for each channel. Default docking parameters were used for AutoDock Vina, and the top-ranked/lowest-energy docked conformation was used as the best pose. We confirmed that the best pose for each analog was located toward the center of each channel. This pose served as the input to the QM/MM calculations performed in Gaussian09 (28) at the M06–2X/6–311+G(d,p):UFF level of theory.