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.
Keywords: Amyloid channel, β-Sheet channel, Lipid bilayer, Molecular dynamics simulations, CHARMM, NAMD
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].
Aβ16–35 peptide:The U-shaped Aβ peptide was first introduced by a computational model using molecular dynamics (MD) simulations [49]. The Aβ16–35 peptidecontainsan intramolecular salt bridge between residues Asp23 and Lys28 near a turn at Val24-Asn27 (Fig. 1a).
Aβ17–42 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 Aβ1–42 fibril (pdb code: 2BEG) [50]. The Aβ1–42 peptide provided the coordinates for residues 17–42, while the N-terminal coordinates (residues 1–16) were missing due to disorder. The Aβ17–42 peptide has a turn at Ser26-Ile31 and the salt bridge of Asp23/Lys28 (Fig. 1b).
Aβ9–40 peptide: Studies using ssNMR defined small Aβ1–40 protofibrils (pdb codes: 2LMN and 2LMO) [51]. The N-terminal coordinates (residues 1–8) were missing due to disorder. The Aβ9–40 peptide has a turn at Asp23-Gly29 and the same salt bridge of Asp23/Lys28 (Fig. 1c).
Aβ11–40 peptide: Comprehensive ssNMR techniques defined Aβ1–40 fibrils [52]. The N-terminal coordinates (residues 1–10) were missing due to disorder. The Aβ11–40 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).
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.
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].
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).
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, -VDPPT-, 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, Across, and headgroup distance, DHH. 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.
DOPC: 1,2-dioleoyl-sn-glycero-3-phosphocholine, zwitterionic, Across = 72.4 Å2 and DHH = 36.7 Å at 30 °C [67].
DOPS: 1,2-dioleoyl-sn-glycero-3-phosphoserine, anionic, Across = 65.3 Å2 and DHH = 38.4 Å at 30 °C [68].
POPC: 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylcholine, zwitterionic, Across = 68.3 Å2 and DHH = 37.0 Å at 30 °C [67].
POPE: 1-palmitoyl-2-oleoyl-sn-glycero-3- phosphoethanolamine, zwitterionic, Across = 56.0 Å2 and DHH = 41.3 Å at 30 °C [69].
POPS: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine, anionic, Across = 55.0 Å2 at 27 °C [70].
POPG: 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylglycerol, anionic, Across = 62.8 Å2 and DHH = 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 Across and DHH 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).
3.2. Generating Full-Length Aβ1–42 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 Aβ1–16 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 Aβ17–42 and Aβ9–40, two Aβ1–42 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 Aβ1–42. Both Aβ1–42 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).
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).
3.4. D-Enantiomer Aβ1–42 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.
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 Aβ17–42 and full-length Aβ1–42 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].
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 Aβ1–42 barrels.
3.6. Pyroglutamate (pE) Modified Aβ Peptides
Pyroglutamate-modified Aβ (AβpE3–42) 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 Aβ1–42, 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 Aβ1–42 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.
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.
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].
In order to see the ions’ behavior in the pore, the potential of mean force (PMF), ΔGPMF, representing the relative free energy profile for each ion across the bilayer can be calculated [32–35, 44] (see Note 5).
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].
To correlate the charge fluctuations with experimental ion conductance, the maximum conductance, gmax, representing the ion transport can be calculated from the equilibrium simulations [36, 42] (see Note 6).
Acknowledgements
This project has been funded in whole or in part with Federal funds from the Frederick National Laboratory for Cancer Research, National Institutes of Health, under contract HHSN261200800001E. This research was supported [in part] by the Intramural Research Program of NIH, Frederick National Lab, Center for Cancer Research. The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products or organizations imply endorsement by the US Government.
Footnotes
In the simulations, pore structures can be examined by HOLE program [86]. The program allows us to visualize and analyze the pore or cavity in biomolecules such as ion channels.
Aβ channels/barrels were modeled with 12–36 Aβ peptides. Different numbers of Aβ monomers produced channels/barrels with different outer and pore dimensions. Preferred sizes of Aβ channels/barrels were found to be in the range of 16–24 Aβ peptides, i.e., 16–24 β-strands lining the pores. The smaller one (12-mer) collapsed and the larger one (36-mer) was not supported by the bilayer [32, 35]. This range was also found to hold for other toxic β-sheet channels; K3 channels with 24 β-strands [43], 18- and 24-mer human islet amyloid polypeptide (hIAPP) channels [87], PG-1 channels with 16–20 β-strands [44, 45], and MAX channels with 20 β-strands [59].
The β-sheet secondary structure was determined by the STRIDE program [88]. “Straightness” of the strand was calculated by β-strand order parameter, where θα is the angle between the positional vectors connecting two Cα atoms, and Nv is the total number of vector pairs. The averaged β-strand B-factor (or Temperature factor) was calculated from the root-mean-squared (RMS) fluctuations [89] relative to the starting point during the simulations with a simple correlation of where denotes averaging over simulation time. Percent of β-sheet content based on the intermolecular backbone H-bonds between β-strands was calculated.
The PMF is calculated by using the equation of . Here, kB is the Boltzmann constant, T is the simulation temperature, is the equilibrium number density of ions, and ρbulk is the averaged ion density in the bulk region. Accurate equilibrium PMF relevant to ion permeation should be obtained from free energy calculations with the umbrella sampling method [90]. Nevertheless, given the simulation trajectory without additional multiple equilibrium runs for sampling, ion-density-based PMF calculations are useful to obtain an estimate of the relative free energy changes for ions, providing an outline for pore ion permeation [91, 92].
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