Computational Methods for Structural and Functional Studies of Alzheimer's Amyloid Ion Channels

Abstract

Aggregation can be studied by a range of methods, experimental and computational. Aggregates form in solution, across solid surfaces, and on and in the membrane, where they may assemble into unregulated leaking ion channels. Experimental probes of ion channel conformations and dynamics are challenging. Atomistic molecular dynamics (MD) simulations are capable of providing insight into structural details of amyloid ion channels in the membrane at a resolution not achievable experimentally. Since data suggest that late stage Alzheimer’s disease involves formation of toxic ion channels, MD simulations have been used aiming to gain insight into the channel shapes, morphologies, pore dimensions, conformational heterogeneity, and activity. These can be exploited for drug discovery. Here we describe computational methods to model amyloid ion channels containing the β-sheet motif at atomic scale and to calculate toxic pore activity in the membrane.

1. Introduction

Alzheimer’s disease (AD) is characterized by the presence of extracellular plaques, intracellular neurofibrillary tangles, and the loss of synapses and neurons in the brain of AD patients [1]. As a subclass of fatal protein deposition diseases [2–8], termed amyloidosis, AD is caused by misfolded, water insoluble aggregates of amyloid-β (Aβ) peptides [5]. During their self-assembly into mature fibrils, Aβ peptides explore various organizations including small oligomers (globular and fibril-like) and protofibrils (straight, bent, and annular) [9, 10]. Although early studies pointed to fibrillar deposits of Aβ peptides in the extracellular plaques as directly associated with the cause of the disease [11], the current amyloid cascade hypothesis in AD points to small Aβ oligomers as the main toxic species [12–16]. However, the mechanism of the amyloid toxicity is still not entirely understood.

The interaction of Aβ with the cell membrane is a fundamental chemical feature in the mechanism of AD pathogenesis [17–19]. Upon binding to the cell membrane, Aβ undergoes conformational changes to insoluble β-sheet-rich aggregates ranging from small oligomers to fibrils [20–22]. The oligomeric Aβ aggregates are responsible for disrupting cellular function, inducing cytotoxicity [23] through ion channel formation [24]. The evidence for the presence of amyloid ion channel was first reported two decades ago, by exploiting planar lipid bilayer (PLB) measurements [25–28]. The experiments discovered that Aβ induced unregulated ionic flux across model membranes through the formation of non-gated ion channels. Subsequently, atomic force microscopy (AFM) provided the images of amyloid channels formed by Aβ peptides [12, 29] and by other disease-related amyloid species [12], suggesting that channel formation is a general feature for amyloids. The AFM images revealed that the amyloid channels exhibited various shapes from rectangular with four subunits to octahedral with eight. The heterogeneity in the Aβ channel conformations was further confirmed by recent extensive molecular dynamics (MD) simulations [30–42]. These showed that Aβ channels consisted of β-sheet-rich subunits with morphologies and dimensions in good agreement with the imaged AFM channels [12, 29]. The simulations of other amyloids and β-hairpin peptides showed that the subunit-assembly morphology is a common feature for the membrane embedded β-sheet channels [43–45].

To form an ion channel, small oligomers of Aβ insert into the membrane and assemble into common β-sheet-rich structural motifs. Recent studies indicated that small fibril-like Aβ oligomers [46] with a solvent exposed hydrophobic face [47] and parallel β-sheet structures [48] could induce neurotoxicity, providing an Aβ oligomer morphology with potential relevance to AD. These membrane-inserted small oligomers can easily align to form the toxic amyloid ion channels. While experimental tools are limited in defining the channel structure in the membrane environment, computational studies can provide their three-dimensional, atomic-level conformation. Here, we detail the computational methods of how to model β-sheet channels and to calculate pore activity in the membrane.

2. Materials: Recruiting Monomer Conformations

2.1. U-Shaped Peptides with the β-Strand-Turn-β-Strand Motif

Amyloids tend to aggregate to form a highly ordered fibrillar structure. In this organization, peptides fold into the U-shaped β-strand-turn-β-strand motif, which associates into stacked β-sheets with intermolecular hydrogen bonds (H-bonds). Recent computational and NMR studies defined several amyloid peptides with such U-shaped motif [49–53]. Using their reported atomic coordinates, these peptides were recruited in computational studies for the atomistic modeling of amyloid channels in aqueous and lipid environments [30–43, 46, 54–57].

1. Aβ_16–35 peptide:The U-shaped Aβ peptide was first introduced by a computational model using molecular dynamics (MD) simulations [49]. The Aβ_16–35 peptidecontainsan intramolecular salt bridge between residues Asp23 and Lys28 near a turn at Val24-Asn27 (Fig. 1a).

2. Aβ_17–42 peptide: A combination of hydrogen/deuterium-exchange nuclear magnetic resonance (NMR) data, side-chain packing constraints from pairwise mutagenesis, solid-state NMR (ssNMR), and electron microscopy (EM) defined Aβ_1–42 fibril (pdb code: 2BEG) [50]. The Aβ_1–42 peptide provided the coordinates for residues 17–42, while the N-terminal coordinates (residues 1–16) were missing due to disorder. The Aβ_17–42 peptide has a turn at Ser26-Ile31 and the salt bridge of Asp23/Lys28 (Fig. 1b).

3. Aβ_9–40 peptide: Studies using ssNMR defined small Aβ_1–40 protofibrils (pdb codes: 2LMN and 2LMO) [51]. The N-terminal coordinates (residues 1–8) were missing due to disorder. The Aβ_9–40 peptide has a turn at Asp23-Gly29 and the same salt bridge of Asp23/Lys28 (Fig. 1c).

4. Aβ_11–40 peptide: Comprehensive ssNMR techniques defined Aβ_1–40 fibrils [52]. The N-terminal coordinates (residues 1–10) were missing due to disorder. The Aβ_11–40 peptide has a turn at Val24-Ala30, but has a shifted inter β-strand contacts within the U-shaped motif. Unlike the previous NMR models (item 3 above), the peptide did not contain the salt bridge of Asp23/ Lys28 (Fig. 1d).

5. The U-shaped motif is a general feature of amyloid organization. Other amyloids, such as β₂-microglobulin fragment (K3 peptide, pdb code: 2E8D) [53] (Fig. 1e) and the second WW domain of CA150 (pdb code: 2NNT) [58], also exhibit the U-shaped motif with the β-strand-turn-β-strand motif.

Fig. 1.

Monomer conformations recruited for the molecular dynamics (MD) simulations of β-sheet channels in the lipid bilayers. The U-shaped amyloid peptides with the β-strand-turn-β-strand motif for (a) the computational Aβ_16–35, (b) the NMR-derived Aβ_17–42, (c) the ssNMR Aβ_9–40, (d) the ssNMR Aβ_11–40, and (e) the ssNMR K3_20–41 peptides. The β-hairpin motif for the synthetic (f) protegrin-1 (PG-1) and (g) MAX1 peptides. In the peptide ribbon, hydrophobic, polar/Gly, positively charged, and negatively charged residues are colored white, green, blue, and red, respectively. Yellow sticks in PG-1 denote the disulfide bonds

2.2. β-Hairpin Peptides

Monomeric or dimeric amyloids tend to form a β-hairpin, an aggregate intermediate that facilitates membrane insertion [46]. Conversion to the U-shaped structure in the oligomerization process with β-hairpin monomers or small oligomers followed by membrane insertion takes place in the membrane. The membrane insertion mechanism of amyloid β-hairpins is similar to that of the cytolytic cationic β-hairpins, such as protegrin-1 (PG-1) and MAX peptides. These β-hairpins are also capable of forming ion channels. [44, 45, 59].

1. PG-1 peptide: A small cationic β-hairpin peptide consisting of 18 amino acids is capable of forming β-sheet channels [44, 45]. PG-1 is an antimicrobial peptide (AMP) with a great antibiotic potency [60]. NMR determined the PG-1 β-hairpin structure in solution with the data confirming to the presence of two antiparallel β-strands linked by a β-turn and stabilized by two disulfide bonds [61–64] (Fig. 1f).

2. MAX peptides: Synthetic amphiphilic cationic peptides, MAX1 and MAX35, can form β-barrels inducing membrane leakage [59]. The MAX peptides consisting of 20 amino acids and contain alternative hydrophobic (Val or Ile) and hydrophilic (Lys) residues connected by a reciprocal turn, -V^DPPT-, where ^DP denotes the D-amino acid proline (Fig. 1g).

2.3. Lipids

To simulate amyloid channels in a membrane environment, a unit cell containing two layers of lipids is constructed. In the middle of the unit cell, simple van der Waals (vdW) spheres representing lipid headgroups are placed in two parallel planes (or membrane surfaces) separated by expected bilayer thickness [65, 66]. Dynamics are performed on the spheres with constraints on their respective planes and with the embedded channel held rigid, resulting in vdW spheres that are randomly distributed onto the planes and well packed around the channel. The lipid molecules are randomly selected from the library of pre-equilibrated states and replaced with pseudo-vdW spheres at the positions of the lipid headgroup constituting the lipid bilayer topology. Simulations employ both zwitterionic and anionic lipid bilayers with various lipids in the liquid phase. Each lipid used in the simulations exhibits different phase transitions yielding different physical properties for the cross-sectional area per lipid, A_cross, and headgroup distance, D_HH. Thus, with a proper choice for the number of lipid molecules, the optimal value of the lateral cell dimensions can be determined. The following list shows the lipid molecules used in the amyloid channel simulations.

1. DOPC: 1,2-dioleoyl-sn-glycero-3-phosphocholine, zwitterionic, A_cross = 72.4 Ų and D_HH = 36.7 Å at 30 °C [67].

2. DOPS: 1,2-dioleoyl-sn-glycero-3-phosphoserine, anionic, A_cross = 65.3 Ų and D_HH = 38.4 Å at 30 °C [68].

3. POPC: 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylcholine, zwitterionic, A_cross = 68.3 Ų and D_HH = 37.0 Å at 30 °C [67].

4. POPE: 1-palmitoyl-2-oleoyl-sn-glycero-3- phosphoethanolamine, zwitterionic, A_cross = 56.0 Ų and D_HH = 41.3 Å at 30 °C [69].

5. POPS: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine, anionic, A_cross = 55.0 Ų at 27 °C [70].

6. POPG: 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylglycerol, anionic, A_cross = 62.8 Ų and D_HH = 36.0 Å at 37 °C [71].

The zwitterionic lipid bilayer is constituted with DOPC lipids. Various mixed lipid bilayers with combination of each zwitterionic and anionic lipid molecule, DOPS:POPE (1:2 mole ratio), POPC: POPS (3:1 mole ratio), and POPC:POPG (4:1 mole ratio) are used for representing the anionic bilayer system. For the mixed lipid bilayers, averaged values of A_cross and D_HH are taken based on a mole ratio.

3. Methods

Atomistic MD simulations with explicit atom representations for protein, lipid, water, and ion are performed using the CHARMM [72] program with the NAMD [73] parallelcomputing code on a Biowulf cluster at the National Institute of Health, Bethesda, MD (http://biowulf.nih.gov). Updated CHARMM [72] all-atom additive force field for lipids (C36) [74] and the modified TIP3P water model [75] are used to construct the set of starting points and to relax the systems to a production-ready stage. The bilayer system containing an Aβ channel/barrel, lipids, salts, and water normally has 200,000 atoms depending on the size of Aβ channel/ barrel. In the pre-equilibrium stages, a series of minimizations is performed for the initial configurations to remove overlaps of the alkane chains in the lipids and to gradually relax the solvents around the harmonically restrained peptides. The initial configurations are gradually relaxed through dynamic cycles with electrostatic cutoffs (12 Å). The harmonic restraints are gradually diminished with the full Ewald electrostatics calculation and constant temperature (Nosé—Hoover) thermostat/barostat at 303 K. For t< 30 ns, our simulation employ the NPAT (constant number of atoms, pressure, surface area, and temperature) ensemble with a constant normal pressure applied in the direction perpendicular to the membrane. After t = 30 ns, the simulations employ the NPT ensemble. Production runs are generally performed up to 100 ns, and averages are taken after 30 ns, discarding initial transients.

3.1. Constructing Amvloid Channels

The initial channel models are constructed by using the U-shaped β-strand-turn-β-strand motifs and β-hairpins. The U-shaped peptide or the β-hairpin is subject to a multifold rotational symmetry operation with respect to the pore axis, creating the annular channel conformation. Depending on the direction of the rotation, the U-shaped peptide generates two different channel topologies: CNpNC (where C and N represent C- and N-terminal β-strands respectively, and p denotes a central pore) and NCpCN channels (Fig. 2a). In Aβ channels, the CNpNC channel preserves a central pore, while the NCpCN channel collapses the pore due to the hydrophobic mismatch of the charged N-terminal strands with the lipid bilayer hydrophobic core [30, 31] (see Note 1). However, in contrast to Aβ channels, K3 channels preserve the pore with NCpCN topology, while CNpNC K3 channel collapses the solvated pore due to the hydrophobic mismatch [43] (Fig. 2b). The U-shaped peptides yield a double-layered annular β-sheet [32, 35]. The designed channels have a perfectly annular shape with the pore-lining inner strands forming a β-sheet through intermolecular backbone hydrogen bonds (H-bonds), but the outer strands do not form a β-sheet due to the larger curvature at the channel periphery. In contrast, β-hairpins generate a single layered annular β-sheet [44, 45, 59] (Fig. 2c, d). Backbone H-bond formation is monitored during the simulations (see Note 2).

Fig. 2.

Computational models of β-sheet channel with the U-shaped and β-hairpin motifs. (a) Building annular channel structures in the membrane using (a) the NMR-based Aβ_17–42 and(b) the ssNMR K3_20–41 peptides. In the double-layered β-sheet channels, two different directions of peptide addition along the curvature yield the CNpNC (left) and NCpCN (right) channels (here, C: C-terminal, N: N-terminal, p: pore). Unlike the U-shaped peptides, β-hairpins generate a single layered annular β-sheet for (c) protegrin-1 (PG-1) and (d) MAX 35 channels. The PG-1 channels contain the antiparallel (turn-next-to-tail, left) and parallel (turn-next-to-turn, right) β-sheet arrangements in an NCCN packing mode. In the MAX channels, the β-hairpin arrangements give rise to two potential β-sheet motifs; turn-next-to-tail β-hairpins in NCCN packing mode (left) and turn-next-to-turn β-hairpins in NCNC packing mode (right). In both cases, the MAX β-hairpins form antiparallel β-sheets, positioning the positively charged Lys side chains into the central pore

3.2. Generating Full-Length Aβ_1–42 Peptides

The NMR-derived U-shaped Aβ peptides only provide N-terminally truncated coordinates due to conformational disorder [50, 51]. To create full-length Aβ peptides, the Aβ_1–16 coordinates in the absence of Zn²⁺ (pdb code: 1ZE7) [76] are used for the missing N-terminal portions of the peptides. For each combination of the N-terminal structure with the NMR U-shaped motifs of Aβ_17–42 and Aβ_9–40, two Aβ_1–42 conformers were generated (Fig. 3). Conformer 1 has a turn at Ser26-Ile31, and conformer 2 at Asp23-Gly29. In the latter conformer, two C-terminal residues, Ile41 and Ala42, were added to create Aβ_1–42. Both Aβ_1–42 conformers retained the U-shaped β-strand-turn-β-strand motif and can be divided into four domains: the extramembranous N-terminal fragment (residues 1–16 and 1–8 for conformer 1 and 2, respectively), solvated pore-lining β-strand (residues 17–25 and 9–22 for conformer 1 and 2, respectively), turn (residues 26–31 and 23–29 for conformer 1 and 2, respectively), and lipid-interacting C-terminal β-strand (residues 32–42 and 30–42 for conformer 1 and 2, respectively).

Fig. 3.

Schematic diagram for the constructions of full-length Aβ_1–42 peptides. The U-shaped Aβ monomers, Aβ_17–42 and Aβ_9–42, recover the missing N-terminal portions through the covalent connection with the solution structure of Aβ_1–16 (pdb code: 1ZE7), generating two Aβ_1–42 conformers (conformer 1 and 2) with different turns (from Jang et al. [8], reprinted with permission)

3.3. β-Barrel Topology of Aβ Channels

Amyloid channels can have conventional annular β-sheet channel and β-barrel topologies. To construct the channel structure with the conventional β-strands arrangement, monomers (U-shaped peptides or β-hairpins) were inserted without inclination with respect to the membrane normal, generating the annular channel topology (Figs. 2 and 4a). To construct the β-barrel structure, the monomers were inclined ~37° with respect to the pore axis, creating the β-barrel topology [34] (Fig. 4b). The β-barrel morphology mimics naturally occurring β-barrels observed in transmembrane proteins that are found frequently in the outer membranes of bacteria, mitochondria, and chloroplasts. The β-barrel motif is a large β-sheet composed of an even number of β-strands. Some known structures of β-barrel membrane proteins have β-strands ranging in number from 8 to 22 [77, 78] (see Note 3). Examples are shown here for the U-shaped amyloid β-barrels and β-hairpin barrels (Fig. 4c). In the simulations, the initial annular conformation is gradually lost during the relaxation of the lipid bilayer. No peptide dissociation from the barrels is observed at these time scales. The relaxed barrel conformation with localized β-sheet optimization leads to subunit formations. Heterogeneity in barrel conformations can be evaluated by several criteria (see Note 4).

Fig. 4.

Constructing the conventional β-sheet channel and β-barrel in the membrane. (a) The conventional β-sheet channel has the β-strands that orient parallel to the membrane normal, (b) while the β-strands that orient obliquely to the membrane normal generate β-barrel structure (from Jang et al. [8], reprinted with permission). Both form a barrel-stave pore. (c) Examples are shown for the 18-mer conformer 1 and 2 Aβ_1–42 barrels, and 10-mer MAX35 barrels in NCCN and NCNC packing modes

3.4. D-Enantiomer Aβ_1–42 Peptides

The standard CHARMM force field [72] is primarily designed for L-amino acids (“left-handed” isomers). To simulate D-amino acids (“right-handed” isomers), a protein force field for asymmetric isomers is required. D-amino acid is a mirror image of L-amino acid, indicating that they are identical, except for their backbone chirality. In the simulations, the L- and D-amino acids share the same backbone bonds and angles, indicating that the standard L-amino acids parameters can be used for the D-amino acids. However, the parameters include the dihedral angle cross term map (CMAP) correction [79], which was created for only L-amino acids, and cannot be directly applied to D-amino acids. Thus, in the simulation, a mirror-image CMAP term for D-amino acids reflecting the phi-psi CMAP matrix should be used [80]. Current version of CHARMM36 force field supports D-amino acids simulations.

3.5. Aβ Mutants

Naturally occurring point mutations in the amyloid precursor protein (APP) clustered around the central region of the Aβ residues are related to familial forms of AD [81]. However, designed synthetic point substitutions significantly alter the channel activity, suppressing Aβ toxicity.

1. F19P and F20C point substitutions: Two phenylalanine residues, Phe19 and Phe20, were replaced with Pro19 and Cys20, respectively (Fig. 5a). The F19P substitution in both truncated Aβ_17–42 and full-length Aβ_1–42 channels/barrels prevents pore activity and hence cellular toxicity, while the F20C substitution preserves the solvated pore with channel activity comparable to the wild type [33, 37, 39].

2. Unlike point substitution, Osaka mutant (ΔE22) eliminates residue Glu22 from the pore-lining β-strand [40]. As a result, pore-lining residues 10–21 for both conformers flip their side chains, while the other domains remain intact (Fig. 5b). The ΔE22 barrels show the membrane embedded β-sheet channel topology, indistinguishable from the wild-type Aβ_1–42 barrels.

Fig. 5.

Aβ mutants conformations. (a) Monomer conformations of the Aβ_1–42 wild type (top panels) and F19P and F20C mutants (highlighted in rectangular insets) with two different conformers, conformer 1 (left) with turn at Ser26-Ile31 and conformer 2 (right) with turn at Asp23-Gly29. (b) Monomer conformations of the Osaka mutant (ΔE22) with two different conformers, conformer 1 (left) and conformer 2 (right). Several important residues in the pore-lining strand are marked. In the peptide ribbon, hydrophobic, polar/Gly, positively charged, and negatively charged residues are colored white, green, blue, and red, respectively

3.6. Pyroglutamate (pE) Modified Aβ Peptides

Pyroglutamate-modified Aβ (Aβ_pE3–42) peptide is particularly associated with cytotoxicity in AD [82, 83]. The peptide is posttranslationally generated by cleavage of the first two N-terminal amino acids (Asp1 and Ala2) of Aβ_1–42, leaving an exposed Glu3 residue. Intramolecular dehydration catalyzed by the glutaminyl cyclase (QC) enzyme generates a lactam ring in Glu3, converting to the pyroglutamate (pE) residue [82, 83]. To simulate pyroglutamate (pE), the first two residues, Asp1 and Ala2, from each conformer 1 and 2 of Aβ_1–42 peptide are removed. The Glu3 residue is then converted into pE3 by generating the lactam ring (Fig. 6). The pE molecular topology was generated by the Avogadro software [84], since the pE residue is not included in the standard CHARMM [72] force field protocol. The Gaussian09 program [85] can be used to calculate parameters including partial charges, bond lengths, angles, and torsional angles for the atoms in the pE residue. The calculated parameters can be directly adopted in the CHARMM [72] program.

Fig. 6.

Conformations of pyroglutamate-modified Aβ (Aβ_pE) peptide. Monomer conformations of Aβ_pE3–42 with two different conformers, (a) conformer 1 with turn at Ser26-Ile31 and (b) conformer 2 with turn at Asp23-Gly29. (c) Molecular topology of the pyroglutamate at residue 3 (pE3). From Gilman et al. [42], reprinted with permission

3.7. Calculating Aβ Pore Activity

Amyloid channels/barrels preserve a large pore, ~1–2 nm, wide enough for conducting ions and water. In addition to counter ions to the system for neutralization, the bilayer systems contain Mg²⁺, K⁺, Ca²⁺, and Zn²⁺ at the same concentration of 25 mM to satisfy a total cation concentration near 100 mM, as well as Cl⁻, which mimics the physiological salt concentration. Cations can be trapped by the negatively charged amino acids in the solvated pore. The motions of the cations in the pore, which reflect the electrostatic interaction, can delineate the electrophysiological currents across the membrane. Several quantities calculated from the simulations can provide detailed information of the mechanism for ion permeation across the bilayer.

1. Probability distribution functions, P, for ions representing ionic permeation as a function of the distance along the pore center axis can be calculated over the simulations. Peaks in the distribution curve represent the cationic binding sites [30, 34, 40, 45, 59].

2. In order to see the ions’ behavior in the pore, the potential of mean force (PMF), ΔG_PMF, representing the relative free energy profile for each ion across the bilayer can be calculated [32–35, 44] (see Note 5).

3. To observe ion fluctuation across the pore, the change in total charge, ΔQ (C/ns), in the pore as a function of the simulation time can be calculated. In the calculations, different pore lengths with different cutoffs along the pore axis are used [36, 37, 40, 42].

4. To correlate the charge fluctuations with experimental ion conductance, the maximum conductance, g_max, representing the ion transport can be calculated from the equilibrium simulations [36, 42] (see Note 6).