Coassembly of Peptides Derived from β-Sheet Regions of β-Amyloid

Abstract

In this paper, we investigate the coassembly of peptides derived from the central and C-terminal regions of the β-amyloid peptide (Aβ). In the preceding paper, J. Am. Chem. Soc.2016, DOI: 10.1021/jacs.6b06000, we established that peptides containing residues 17–23 (LVFFAED) from the central region of Aβ and residues 30–36 (AIIGLMV) from the C-terminal region of Aβ assemble to form homotetramers consisting of two hydrogen-bonded dimers. Here, we mix these tetramer-forming peptides and determine how they coassemble. Incorporation of a single ¹⁵N isotopic label into each peptide provides a spectroscopic probe with which to elucidate the coassembly of the peptides by ¹H,¹⁵N HSQC. Job’s method of continuous variation and nonlinear least-squares fitting reveal that the peptides form a mixture of heterotetramers in 3:1, 2:2, and 1:3 stoichiometries, in addition to the homotetramers. These studies also establish the relative stability of each tetramer and show that the 2:2 heterotetramer predominates. ¹⁵N-Edited NOESY shows the 2:2 heterotetramer comprises two different homodimers, rather than two heterodimers. The peptides within the heterotetramer segregate in forming the homodimer subunits, but the two homodimers coassemble in forming the heterotetramer. These studies show that the central and C-terminal regions of Aβ can preferentially segregate within β-sheets and that the resulting segregated β-sheets can further coassemble.

Introduction

Interactions among β-sheets are critical in the aggregation of the β-amyloid peptide (Aβ) to form oligomers and fibrils in Alzheimer’s disease.¹ Two regions of the 40- or 42-residue peptide adopt β-sheet structure and promote aggregation: the central region and the C-terminal region.² The central region comprises the hydrophobic pentapeptide LVFFA (Aβ_17–23), and the C-terminal region comprises the hydrophobic undecapeptide AIIGLMVGGVV (Aβ_30–40) or the hydrophobic tridecapeptide AIIGLMVGGVVIA (Aβ_30–42).

Elucidating the roles of the central and C-terminal regions of Aβ is critical to understanding Aβ aggregation. These two regions assemble differently in the fibrils and in the toxic oligomers that cause synaptic dysfunction and cell death. In Aβ_1–40 fibrils, the peptide forms parallel β-sheets, with the central and C-terminal regions laminated together.^3,4 In the oligomers, the peptide is thought to form β-hairpins comprising antiparallel β-sheets.⁵

In the preceding paper,⁶ we incorporated residues from the central and C-terminal regions into macrocyclic β-sheet peptides 1, and we determined how the peptides assembled in aqueous solution.⁶ Peptides 1 consist of a heptapeptide strand, a template strand containing the unnatural amino acid Hao, and two δ-linked ornithine turn units.⁷⁻⁹ We incorporated residues LVFFAED (Aβ_17–23) and residues AIIGLMV (Aβ_30–36) into the heptapeptide strands of peptides 1a and 1b, respectively. We incorporated isoleucine residues (I₈ and I₁₁) into the template strand to promote assembly and lysine residues (K₉ and K₁₀) to maintain solubility. ¹H NMR studies of peptides 1a and 1b show that the peptides assemble to form sandwich-like homotetramers, consisting of two hydrogen-bonded dimers.

Incorporation of a single isotopic label into peptides 1 facilitated the identification and quantification of the tetramers. The peptides [¹⁵N]1a and [¹⁵N]1b each contain a single ¹⁵N-labeled amino acid in the center of the heptapeptide strand. Peptide [¹⁵N]1a contains an ¹⁵N label in the F₂₀ residue; peptide [¹⁵N]1b contains an ¹⁵N label in the G₃₃ residue. ¹H,¹⁵N HSQC studies show only the resonances associated with the ¹⁵N label, reducing each spectrum to two crosspeaks: The ¹H,¹⁵N HSQC spectrum of peptide [¹⁵N]1a shows one crosspeak associated with the monomer and another associated with the homotetramer. The ¹H,¹⁵N HSQC spectrum of peptide [¹⁵N]1b also shows one crosspeak associated with the monomer and another associated with the homotetramer.

In this paper, we ask whether these peptides prefer to coassemble or to segregate.¹⁰ To address this question, we mix peptides 1a and 1b and characterize the oligomers that form. ¹H NMR studies show that peptides 1a and 1b form a mixture of homotetramers and heterotetramers, but the ¹H NMR spectrum of the mixture is largely indecipherable. To characterize the complex mixture of homotetramers and heterotetramers, we use the ¹⁵N-labeled peptides [¹⁵N]1a and [¹⁵N]1b and ¹H,¹⁵N NMR spectroscopy. ¹H,¹⁵N HSQC, in conjunction with Job’s method of continuous variation, reveals that the peptides form three heterotetramers in 3:1, 2:2, and 1:3 stoichiometries, in addition to the two homotetramers. The following describes the characterization of these five tetramers and the equilibria among them.

Results and Discussion

Peptides 1a and 1b Coassemble upon Mixing

The ¹H NMR spectrum of pure peptide 1a at 8.0 mM predominately shows the homotetramer; the ¹H NMR spectrum of pure peptide 1b at 8.0 mM shows the monomer and the homotetramer. In a 1:1 mixture of peptides 1a and 1b at 8.0 mM total concentration, the ¹H NMR spectrum shows many new resonances: The resonances from the homotetramer of peptide 1a diminish greatly and the resonances from the homotetramer of peptide 1b nearly disappear. New resonances appear in the spectrum in the aromatic region between 6 and 9 ppm and also in the methyl region below 1 ppm. Several new Hao methoxy (Hao_OMe) resonances appear between 4 and 4.5 ppm. The Hao_OMe resonance from the homotetramer of peptide 1a diminishes greatly and the Hao_OMe resonance from the homotetramer of peptide 1b almost completely disappears. The multitude of new resonances in the spectrum of the 1:1 mixture suggests that several new oligomers form, rather than just one. Figure 1 shows the ¹H NMR spectra of pure 1a, pure 1b, and the 1:1 mixture.

Figure 1.

¹H NMR spectra of (a) peptide 1a at 8.0 mM, (b) peptide 1b at 8.0 mM, and (c) the 1:1 mixture of peptides 1a and 1b at 8.0 mM total concentration in D₂O at 600 MHz and 298 K. Dotted lines illustrate how the resonances from the 1:1 mixture compare with the resonances of pure 1a and pure 1b.

Peptides 1a and 1b Form Heterotetramers

We have previously shown that related macrocyclic β-sheets can assemble to form tetramers.¹¹ In the preceding paper,⁶ we established that both peptide 1a and peptide 1b form tetramers by measuring the diffusion coefficients (D) with DOSY NMR.⁶ Here, we use DOSY NMR to determine whether the species that form upon mixing peptides 1a and 1b are also tetramers. The homotetramers of peptides 1a and 1b have diffusion coefficients of about 12 × 10^–11 m²/s in D₂O at 298 K. The diffusion coefficients of the species that predominate in the 1:1 mixture are comparable, 11.4 × 10^–11 m²/s (Table 1), indicating that these species are also tetramers.

Table 1. Diffusion Coefficients (D) of Peptides 1a and 1b in D₂O at 298 K.

	MWtetramera (Da)	conc (mM)	D (×10–11m2/s)	oligomer state
1a	7068	8.0	11.8 ± 1.0	A4 homotetramer
1b	6572	16.0	11.9 ± 1.1	B4 homotetramer
1a + 1b		8.0b	11.4 ± 1.1	heterotetramers

^aMolecular weight calculated for the neutral (uncharged) peptide.

^bTotal concentration of the 1:1 mixture of peptides 1a and 1b.

In this paper, we describe the homotetramers and heterotetramers formed by peptides 1a and 1b using the letters A and B. The homotetramers are designated A₄ and B₄, and the 3:1, 2:2, and 1:3 heterotetramers are designated A₃B₁, A₂B₂, and A₁B₃. Two topological isomers of the A₂B₂ heterotetramer could form: one consisting of two homodimers (A·A and B·B); the other consisting of two heterodimers (A·B and A·B). Figure 2 illustrates the homotetramers and heterotetramers, where a single β-strand represents either peptide 1a or 1b.

Figure 2.

Cartoons illustrating homotetramers and heterotetramers, in which peptide 1a is represented by a blue arrow and peptide 1b is represented by a red arrow.

The complex mixture of monomers, homotetramers, and heterotetramers can give as many as 16 resonances in the ¹H NMR spectrum: two from the A monomer and A₄ homotetramer; two from the B monomer and B₄ homotetramer, four from the A₃B₁ heterotetramer, four from the A₁B₃ heterotetramer, and either two or four from the A₂B₂ heterotetramer. The A₂B₂ heterotetramer would give four resonances if both the A·A/B·B and A·B/A·B topological isomers formed, but only two resonances if just one of the two isomers formed.

Elucidation of the A₂B₂ Topological Isomer

We used peptides [¹⁵N]1a and [¹⁵N]1b to elucidate the dimers within the A₂B₂ heterotetramer. In the preceding paper,⁶ we used these peptides and ¹⁵N-edited NOESY to help establish the pairing of the dimers within the A₄ and B₄ homotetramers.⁶ Here, we compare the ¹⁵N-edited NOESY spectra of pure [¹⁵N]1a and pure [¹⁵N]1b to that of the 1:1 mixture to determine which A₂B₂ topological isomer forms (Figure 3). The spectra show that the A₂B₂ heterotetramer consists of an A·A and a B·B homodimer, and not of two A·B heterodimers (Figure 4).

Figure 3.

¹⁵N-Edited NOESY spectra of (a) peptide [¹⁵N]1a at 8.0 mM, (b) peptide [¹⁵N]1b at 8.0 mM, and (c) the 1:1 mixture of peptides [¹⁵N]1a and [¹⁵N]1b at 8.0 mM total concentration in 9:1 H₂O/D₂O at 600 MHz and 293 K. The G₃₃Hα corresponds to the pro-R α-proton and the G₃₃Hα′ corresponds to the pro-S α-proton. Crosspeaks associated with chemical exchange of peptide 1b between the monomer and the B₄ and A₂B₂ tetramers are labeled EX. Dotted lines illustrate how the crosspeaks from the 1:1 mixture compare with the crosspeaks of pure [¹⁵N]1a and pure [¹⁵N]1b.

Figure 4.

NOEs involving the ¹⁵NH protons within the A₂B₂ heterotetramer. (a) The A·A homodimer with blue arrows illustrating the NOEs observed within the dimers. (b) The B·B homodimer with red arrows illustrating the NOEs observed within the dimers. (c) The A·B heterodimer (not formed).

The ¹⁵N-edited NOESY spectrum of the 1:1 mixture of peptides [¹⁵N]1a and [¹⁵N]1b shows four distinct sets of resonances: two sets associated with the A₂B₂ heterotetramer; one set associated with the A₄ homotetramer; and one set associated with the B monomer (Figure 3c). In addition to the NOEs, the spectrum also shows crosspeaks associated with chemical exchange between the monomer of peptide [¹⁵N]1b and the A₂B₂ heterotetramer.

The A₂B₂ heterotetramer gives two sets of resonances: one set from the F₂₀NH proton of peptide [¹⁵N]1a and the other set from the G₃₃NH proton of peptide [¹⁵N]1b. The F₂₀NH proton of peptide [¹⁵N]1a gives a strong interresidue NOE to the F₁₉Hα proton and a weaker intraresidue NOE to the F₂₀Hα proton. Figure 4a summarizes these NOEs. An intermolecular NOE between the F₂₀NH and the A₂₁Hα protons is not observed as a separate crosspeak because the F₂₀Hα and the A₂₁Hα resonances overlap.¹² The F₂₀NH proton gives an additional NOE to the A₂₁Hβ protons, which corroborates the proximity of these residues (Figure S2). An intermolecular NOE is not observed between the F₂₀NH proton of peptide [¹⁵N]1a and the L₃₄Hα proton of peptide [¹⁵N]1b (Figure 3c); an intermolecular NOE is also not observed between the F₂₀NH proton of peptide [¹⁵N]1a and the G₃₃NH proton of peptide [¹⁵N]1b (Figure S3). The absence of these two NOEs indicates that peptide [¹⁵N]1a is not part of an A·B heterodimer (Figure 4c).

The G₃₃NH proton of peptide [¹⁵N]1b gives an interresidue NOE to the I₃₂Hα proton and intraresidue NOEs to the G₃₃Hα and G₃₃Hα′ protons (Figure 3c). The G₃₃NH proton also gives an intermolecular NOE to the L₃₄Hα proton.¹² This NOE confirms that the B·B homodimer forms within the A₂B₂ heterotetramer and rules out the A·B heterodimer. Figure 4b summarizes these NOEs.¹³ Collectively, the ¹⁵N-edited NOESY studies establish that the A·A/B·B topological isomer that forms exclusively is the A₂B₂ heterotetramer.

¹H,¹⁵N HSQC Reveals That Peptides [¹⁵N]1a and [¹⁵N]1b Form Three Heterotetramers: A₃B₁, A₂B₂, and A₁B₃

We compared the ¹H,¹⁵N HSQC spectra of pure [¹⁵N]1a and pure [¹⁵N]1b to that of the 1:1 mixture to show which crosspeaks are associated with heterotetramers.⁶ The ¹H,¹⁵N HSQC spectrum of the 1:1 mixture of peptides [¹⁵N]1a and [¹⁵N]1b at 8.0 mM total concentration shows 10 new crosspeaks (14 crosspeaks in total). The crosspeaks are sharp and distinct, indicating that the tetramers exchange slowly on the NMR time scale. The two crosspeaks designated 1 and 2 come from the monomer and homotetramer of peptide [¹⁵N]1a; the two crosspeaks designated 3 and 4 come from the monomer and homotetramer of peptide [¹⁵N]1b. The 10 remaining crosspeaks designated 5–14 come from the heterotetramers. Figure 5a shows the ¹H,¹⁵N HSQC spectrum of the 1:1 mixture of peptides [¹⁵N]1a and [¹⁵N]1b. Table 2 summarizes the chemical shifts of crosspeaks 1–14.

Figure 5.

¹H,¹⁵N HSQC spectra of 8.0 mM mixtures in 9:1 H₂O/D₂O at 600 MHz and 293 K of peptides: (a) [¹⁵N]1a and [¹⁵N]1b; (b) [¹⁵N]1a and 1b; (c) 1a and [¹⁵N]1b. The asterisk (*) indicates a crosspeak from a minor unidentified species associated with peptide [¹⁵N]1b.

Table 2. Chemical Shifts of Peptides [¹⁵N]1a and [¹⁵N]1b.

	δ F20		δ G33
crosspeak	1H	15N	1H	15N	species
1	8.32	122.3			A monomer
2	8.56	121.3			A4 homotetramer
3			8.39	112.5	B monomer
4			9.33	115.8	B4 homotetramer
5	8.81	124.9			A2B2 heterotetramer
6			9.03	116.2	A2B2 heterotetramer
7	8.69	125.7			A3B1 heterotetramer
8	8.66	121.1			A3B1 heterotetramer
9	8.60	119.3			A3B1 heterotetramer
10			7.94	112.8	A3B1 heterotetramer
11	8.92	120.9			A1B3 heterotetramer
12			8.74	116.1	A1B3 heterotetramer
13			9.25	115.8	A1B3 heterotetramer
14			9.17	115.1	A1B3 heterotetramer

^a1H,¹⁵N HSQC spectrum was recorded for the 1:1 mixture at 8.0 mM in 9:1 H₂O/D₂O at 293 K.

The remaining crosspeaks 5–14 come from the A₃B₁, A₂B₂, and A₁B₃ heterotetramers. Crosspeaks 5 and 6 are prominent and strikingly similar in intensity to each other. These two crosspeaks come from the A₂B₂ heterotetramer. Crosspeaks 7–14 are weaker and are also similar in intensity to each other. These eight crosspeaks are associated with the A₃B₁ and A₁B₃ heterotetramers.

We mixed peptides [¹⁵N]1a and 1b and also mixed peptides 1a and [¹⁵N]1b to assign crosspeaks 7–14 to the respective peptides. Figure 5b,c shows the ¹H,¹⁵N HSQC spectra of these mixtures of labeled and unlabeled peptides. The ¹H,¹⁵N HSQC spectrum of peptides [¹⁵N]1a and 1b shows that crosspeaks 1, 2, 5, 7, 8, 9, and 11 come from peptide [¹⁵N]1a; the ¹H,¹⁵N HSQC spectrum of peptides 1a and [¹⁵N]1b shows that crosspeaks 3, 4, 6, 10, 12, 13, and 14 come from peptide [¹⁵N]1b. These spectra confirm that half of the crosspeaks come from peptide 1a and that half of the crosspeaks come from peptide 1b.

Assigning the ¹H,¹⁵N HSQC Crosspeaks of the A₃B₁ and A₁B₃ Heterotetramers

To assign which of the crosspeaks 7–14 come from the A₃B₁ heterotetramer and which come from the A₁B₃ heterotetramer, we compared ¹H,¹⁵N HSQC spectra of 3:1 and 1:3 mixtures of peptides [¹⁵N]1a and [¹⁵N]1b to that of the 1:1 mixture. In the spectra of the 3:1, 1:1, and 1:3 mixtures, the relative intensities of crosspeaks 1–14 vary, but the chemical shifts do not. The f₁ projections of the ¹H,¹⁵N HSQC spectra conveniently illustrate the relative intensities of the crosspeaks as one-dimensional ¹⁵N spectra. Figure 6 shows the f₁ projections of pure [¹⁵N]1a, the 3:1, 1:1, and 1:3 mixtures, and pure [¹⁵N]1b.

Figure 6.

¹⁵N spectra from the f₁ projections of the ¹H,¹⁵N HSQC spectra of mixtures of peptides [¹⁵N]1a and [¹⁵N]1b. Spectra were recorded at 8.0 mM total concentration and varying mole fractions of peptide in 9:1 H₂O/D₂O at 600 MHz and 293 K. The mole fraction of peptide [¹⁵N]1b is designated χ_B.

The systematic variation of the crosspeaks as a function of the mole fraction χ_B clearly establishes which crosspeaks are associated with the A₃B₁ heterotetramer and which are associated with the A₁B₃ heterotetramer. Crosspeaks 7–10 have maximum relative intensities at χ_B = 0.25 and come from the A₃B₁ heterotetramer. Crosspeaks 11–14 have maximum relative intensities at χ_B = 0.75 and come from the A₁B₃ heterotetramer. Figure 7 illustrates relative integrations of the crosspeaks versus the mole fraction of peptide [¹⁵N]1b, χ_B.

Figure 7.

Plot of the relative integrations of crosspeaks 1–14 versus the mole fraction of peptide [¹⁵N]1b, χ_B. The intensities were measured by integrating the crosspeaks in the ¹H,¹⁵N HSQC spectra of the mixtures of peptides [¹⁵N]1a and [¹⁵N]1b.

Job’s Method of Continuous Variation

We used Job’s method to determine the relative stabilities of the homotetramers and the heterotetramers of peptides [¹⁵N]1a and [¹⁵N]1b. Although this method was first introduced to study inorganic complexes, it is useful in all areas of chemistry for studying molecular association.^14,15 Job’s method is performed by mixing two compounds “A” and “B” in varying ratios while keeping the total concentration constant. The amount of a complex that forms is then plotted versus the mole fraction to give a plot known as a “Job plot”. The appearance of the Job plot reflects the stoichiometry and relative stability of each complex. The mole fraction at which the maximum amount of the complex forms corresponds with its stoichiometry. For example, an A₁B₂ heterotrimer would give a maximum in a 1:2 mixture (χ_B = 0.67).

We applied Job’s method to peptides [¹⁵N]1a and [¹⁵N]1b, recording ¹H,¹⁵N HSQC spectra for nine samples at 8.0 mM total concentration.¹⁶ We plotted the sum of the relative integrals of the ¹H,¹⁵N HSQC crosspeaks for each species versus the mole fraction of peptide [¹⁵N]1b, χ_B. For example, we plotted the curve for the A₃B₁ heterotetramer species using the sum of the relative integrals of crosspeaks 7–10. Figure 8 illustrates the resulting Job plot.

Figure 8.

Job plot for peptides [¹⁵N]1a and [¹⁵N]1b showing the relative integrations of the monomers, homotetramers, and heterotetramers versus the mole fraction of peptide [¹⁵N]1b, χ_B. The curves reflect a monomer–tetramer equilibrium model fitted to the data. The error bars reflect the standard deviations among the individual measurements used to determine the relative integrations of A₃B₁, A₂B₂, and A₁B₃. The relative stabilities determined for each species are ϕ_4,4 = 1.00, ϕ_4,3 = 0.22, ϕ_4,2 = 0.67, ϕ_4,1 = 0.12, ϕ_4,0 = 0.12, ϕ_1,1 = 0.36, and ϕ_1,0 = 2.20.

The Job plot shows that the A₂B₂ heterotetramer predominates over a wide range of mole fractions. At low mole fractions, χ_B ≤ 0.25, the A₄ homotetramer predominates. At high mole fractions, χ_B ≥ 0.75, the B monomer and B₄ heterotetramer predominate. The A₂B₂ heterotetramer reaches a maximum concentration at a mole fraction χ_B slightly greater than 0.50. The A₃B₁ heterotetramer and the A₁B₃ heterotetramer form to a lesser extent, reaching a maximum concentration at low and high mole fractions χ_B, respectively.

Simulated Job Plots of Homotetramers and Heterotetramers

We generated simulated Job plots reflecting different homotetramer and heterotetramer stabilities to help interpret the data in Figure 8. We used an implementation developed by Collum and co-workers that readily accommodates homotetramer and heterotetramer equilibria.¹⁷⁻¹⁹ We simulated a Job plot for a statistical distribution of homotetramers and heterotetramers and Job plots in which one of the heterotetramers is favored. These plots demonstrate how the relative stabilities of the tetramers affect the shapes of the curves. Figure 9 illustrates the resulting Job plots; the relative integrations of the species are plotted versus the mole fraction χ_B.

Figure 9.

Simulated Job plots that show the relative integrations of the monomers, homotetramers, and heterotetramers versus the mole fraction of B, χ_B. (a) A statistical distribution of homotetramers and heterotetramers; ϕ_4,4 = ϕ_4,3 = ϕ_4,2 = ϕ_4,1 = ϕ_4,0 = 1. (b) A₂B₂ heterotetramer is favored; ϕ_4,2 = 2 and ϕ_4,4 = ϕ_4,3 = ϕ_4,1 = ϕ_4,0 = 1. (c) A₃B₁ heterotetramer is favored; ϕ_4,3 = 2 and ϕ_4,4 = ϕ_4,2 = ϕ_4,1 = ϕ_4,0 = 1. (d) A₁B₃ heterotetramer is favored; ϕ_4,1 = 2 and ϕ_4,4 = ϕ_4,3 = ϕ_4,2 = ϕ_4,0 = 1. (e) A statistical distribution of homotetramers and heterotetramers that also includes monomers; ϕ_4,4 = ϕ_4,3 = ϕ_4,2 = ϕ_4,1 = ϕ_4,0 = 1 and ϕ_1,1 = ϕ_1,0 = 1. (f) A statistical distribution of homotetramers and heterotetramers that also includes monomers, where the B monomer is favored ϕ_4,4 = ϕ_4,3 = ϕ_4,2 = ϕ_4,1 = ϕ_4,0 = 1, ϕ_1,1 = 1, and ϕ_1,0 = 2.

In the implementation by Collum and co-workers, the relative concentrations of the homotetramers and heterotetramers are calculated from equations based on a homotetramer-heterotetramer equilibrium model. The parameters ϕ_N,n are ascribed to each of the homotetramers and heterotetramers in the equations, where the N and n are integers in which the value of N describes the oligomer size and the value of n describes the number of “A” subunits. The value of each ϕ_N,n reflects the relative stability of each homotetramer or heterotetramer. The parameters ϕ_4,4, ϕ_4,3, ϕ_4,2, ϕ_4,1, and ϕ_4,0 describe the relative stabilities of A₄, A₃B₁, A₂B₂, A₁B₃, and B₄, respectively. When each tetramer is equally stable, all parameters are equal (e.g., ϕ_4,4 = ϕ_4,3 = ϕ_4,2 = ϕ_4,1 = ϕ_4,0 = 1) and a statistical distribution of homotetramers and heterotetramers forms.

The Job plot of a statistical distribution of homotetramers and heterotetramers is symmetrical, where the maximum of each curve reflects the tetramer stoichiometry. In the 1:1 mixture, the A₂B₂ heterotetramer predominates, with smaller fractions of the A₃B₁ and A₁B₃ heterotetramers in equal amounts, and with traces of the A₄ and B₄ homotetramers in equal amounts. In the 3:1 mixture, the A₃B₁ heterotetramer predominates, with smaller fractions of the A₄ homotetramer and A₂B₂ heterotetramer, and with traces of the A₁B₃ heterotetramer. Similarly, in the 1:3 mixture, the A₁B₃ heterotetramer predominates, with smaller fractions of the B₄ homotetramer and A₂B₂ heterotetramer, and with traces of the A₃B₁ heterotetramer. Figure 9a illustrates the Job plot for a statistical distribution of homotetramers and heterotetramers.

The appearance of the Job plot changes if any of the tetramers are favored or disfavored. If the A₂B₂ tetramer is favored, the A₂B₂ curve shows a pronounced increase and the A₃B₁ and A₁B₃ curves diminish slightly (Figure 9b). If the A₃B₁ tetramer is favored, the A₃B₁ curve shows a pronounced increase and the A₂B₂ curve diminishes slightly (Figure 9c). If the A₁B₃ tetramer is favored, the A₁B₃ curve shows a pronounced increase and the A₂B₂ curve diminishes slightly (Figure 9d).

Analysis of the Job Plot

We modified the implementation by Collum and co-workers to accommodate the equilibrium of the monomers with the homotetramers and heterotetramers. In our implementation, the relative concentrations of the monomers, homotetramers, and heterotetramers are calculated from equations based on a monomer–homotetramer–heterotetramer equilibrium model. The parameters ϕ_1,1 and ϕ_1,0 reflect the relative stabilities of the monomers A and B. The Job plot of a statistical distribution of homotetramers and heterotetramers that also includes the monomers is similar to the Job plot without monomers, except that the fraction of each tetramer is slightly diminished (Figure 9e). If the equilibrium favors one of the two monomers, a greater fraction of that monomer forms (Figure 9f).

We analyzed the data from our Job’s method experiment by nonlinear least-squares fitting of the model to the data. During the fit, the parameters ϕ_4,3, ϕ_4,2, ϕ_4,1, ϕ_4,0, ϕ_1,1, and ϕ_1,0 were allowed to vary, while the parameter ϕ_4,4 remained fixed at 1. Figure 8 illustrates the Job plot with the fitted curves (ϕ_4,4 = 1.00, ϕ_4,3 = 0.22, ϕ_4,2 = 0.67, ϕ_4,1 = 0.12, ϕ_4,0 = 0.12, ϕ_1,1 = 0.36, ϕ_1,0 = 2.20).

The model fits the data well. The quality of the fit corroborates that peptides [¹⁵N]1a and [¹⁵N]1b form a mixture of homotetramers and heterotetramers. The appearance of the resulting plot does not resemble the statistical distribution shown in Figure 9e. The Job plot shows little or no preference for the A₂B₂ heterotetramer, but it does show suppression of the A₃B₁ and A₁B₃ heterotetramers.

The Job’s method of continuous variation study and nonlinear least-squares fitting of the data establish that peptides 1a and 1b prefer to segregate within the heterotetramers. The suppression of the A₃B₁ and A₁B₃ heterotetramers shows that the A·B heterodimer subunit is disfavored and that heterotetramers containing an A·B heterodimer subunit are less stable. This finding explains why the A₂B₂ heterotetramer contains two homodimers rather than two heterodimers. Peptide 1a, which contains Aβ_17–23, prefers to pair with itself to form a hydrogen-bonded homodimer; peptide 1b, which contains Aβ_30–36, prefers to pair with itself to form a hydrogen-bonded homodimer.

Molecular Models of A₂B₂ Heterotetramers

We constructed energy-minimized models of A₂B₂ heterotetramers to help understand the preferential pairing of peptides 1a and 1b to form homodimers. By combining the monomer subunits of the models of the A₄ and B₄ homotetramers developed in the preceding paper,⁶ and re-minimizing, we generated two models of the A₂B₂ heterotetramers: the A·A/B·B topological isomer that was observed, and the A·B/A·B topological isomer that was not. Figure 10 illustrates the resulting models of these two topological isomers.

Figure 10.

Molecular models of the topological isomers of the A₂B₂ heterotetramer of peptides 1a and 1b. (a) The A·A/B·B topological isomer. (b) The A·B/A·B topological isomer. Each model is a minimum-energy structure (local minimum) generated with MacroModel using the MMFFs force field with GB/SA water solvation.

The models show that the A₂B₂ heterotetramers can form sandwich-like structures that are similar to the homotetramers. Both topological isomers consist of two, four-stranded β-sheets that laminate together through hydrophobic packing. The side chains of L₁₇, F₁₉, and A₂₁ from peptide 1a and of A₃₀, I₃₂, L₃₄, and V₃₆ from peptide 1b form hydrophobic surfaces that pack in the hydrophobic core of each heterotetramer. The interface between the A·A and B·B homodimers in the A·A/B·B topological isomer is uniformly packed. In contrast, the interface between the two A·B heterodimers in the A·B/A·B topological isomer is densely packed at one end and lightly packed at the other (Figure 10b).

The A·A homodimer of peptide 1a exhibits a large hydrophobic surface, with intimate contacts between the side chains of L₁₇, F₁₉, and A₂₁. The large F₁₉ and small A₂₁ residues fit together well to help provide a uniformly packed surface (Figure 11a). The B·B homodimer of peptide 1b also exhibits a large hydrophobic surface, with intimate contacts between the side chains of A₃₀, I₃₂, L₃₄, and V₃₆. These residues also provide a uniformly packed surface (Figure 11b). The A·B heterodimer exhibits a hydrophobic surface with intimate contacts between the side chains of L₁₇, F₁₉, and A₂₁ from peptide 1a and the side chains of I₃₂, L₃₄, and V₃₆ from peptide 1b. The side chains do not pack uniformly, but rather the side chains pack densely at one end of the dimer and pack lightly at the other (Figure 11c).

Figure 11.

Molecular models of the homodimer and heterodimer subunits of the A₂B₂ heterotetramers of peptides 1a and 1b.

These molecular models suggest that differences between the homodimers and heterodimers formed by peptides 1a and 1b dictate the observed differences in the A₂B₂ heterotetramer stability. The uniform packing of the A·A and B·B homodimers appears to drive the formation of the observed A₂B₂ heterotetramer. The non-uniform packing of the A·B heterodimer appears to suppress the formation of the A₃B₁ and A₁B₃ heterotetramers, and also the alternative topological isomer of the A₂B₂ heterotetramer.

Conclusion

In framing the question behind these studies, we set out to determine whether peptides derived from the central and C-terminal regions of Aβ prefer to coassemble or to segregate. We found that the answer is more nuanced, at least in the context of the model system provided by peptides 1. Peptides 1a and 1b can coassemble, but the resulting heterotetramers reflect a preference to segregate within the dimer subunits. The heterotetramers comprising heterodimers are disfavored, while the heterotetramers comprising homodimers are not. These findings recapitulate the segregation within Aβ_1–40 fibrils, in which the central region assembles to form a hydrogen-bonded β-sheet and the C-terminal region assembles to form a hydrogen-bonded β-sheet.³ The two β-sheets coassemble through hydrophobic contacts.

¹⁵N-Isotopic labeling, ¹H,¹⁵N NMR spectroscopy, and Job’s method of continuous variation proved essential in these studies. Incorporation of a single ¹⁵N-isotopic label provided a sensitive and non-perturbing spectroscopic probe. ¹⁵N-Labeled peptides are readily prepared from commercially available ¹⁵N-labeled amino acids using solid-phase peptide synthesis. ¹H,¹⁵N HSQC facilitated identification of the monomers, homotetramers, and heterotetramers. Job’s method of continuous variation assigned the resonances of each monomer and tetramer and established the relative stability of the tetramers. ¹⁵N-Edited NOESY established the identity of the topological isomer of the A₂B₂ heterotetramer.

These techniques, which proved useful for elucidating the assembly and coassembly of β-sheet peptides, should also be valuable in broader contexts. Peptide and protein assemblies occur widely in coiled coils, helix bundles, and collagen helices, as well as in amyloid oligomers and other β-sheet supramolecular assemblies. We envision that ¹⁵N-isotopic labeling in conjunction with ¹H,¹⁵N NMR spectroscopy and Job’s method will also be valuable for studying these assemblies.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.6b06001.

• Figures S1–S5, showing NMR spectroscopic data; materials and methods; mathematical derivation for the monomer–homotetramer–heterotetramer equilibrium model; and procedures for nonlinear least-squares fitting of the Job plot data (PDF)

The authors declare no competing financial interest.