Fig 1.
Electronic configuration of the peptide amide bonds and conformational and H-bonding propensity of the polypeptide backbone.
(A) The dependence of interactions of the adjacent peptide amide bonds on location in the ψ/φ space of the polypeptide backbone (the diagram is adapted from the ref. [45]). The variation in φi changes mutual orientation of the peptide bonds: the bond planes are approximately perpendicular to each other in the helical region 1 (φi = −90°±30°) and approximately coplanar in the extended strand region 2 (φi = −150°±30°). The variation in ψi changes the extent of backbone H-bonding in the helical sub regions 1a–1c. (B) Two-electron stabilizing interactions of the peptide amide bonds, depicted using the canonical amide MO’s: (a) the generalized anomeric effect π2(Ni‒C’i-1 = O)→σ*(Cαi‒C’i) which is maximized when the Cαi‒C’i bond, the best hyperconjugative σ acceptor at Cαi, overlaps the Ni lp that is in the entire helical region 1 (φi = −90°±30°), and homohyperconjugation n(C’i-1 = O)→π3*(Ni+1‒C’i = O) maximized in the α-helix region 1a (ψi = ‒30°±30°); (b) homohyperconjugation π2(Ni‒C’i-1 = O)→π3*(Ni+1‒C’i = O), maximized in the 27-ribbon (C7eq and C7ax) region 1b (ψi = 90°±30°); (c) homohyperconjugation n(C’i-1 = O)→π3*(Ni+1‒C’i = O) and n(C’i = O)→π3*(Ni‒C’i-1 = O), maximized in the PPII-helix region 1c (ψi = 150°±30°); (d) the extended (double) hyperconjugation π2(Ni‒C’i-1 = O)→π(CαiRR’)→π3*(Ni+1‒C’i = O) maximized in the C5 region 2 (φi = ‒150°±30°). (C) Modern resonance model of the amide bonding and the dependence of conformational and H-bonding propensity of the polypeptide backbone on electronic configuration of the peptide amide bonds, see the text section a.(i).
Fig 2.
Conformational diversity in the binary complexes of extended oligopeptide strands.
The geometries and energies obtained by quantum-mechanical modeling of the two-stranded β-sheets 6–8 (Computational Methods). The individual strands in these complexes optimize either to the C5 or the C7eq (27-ribbon) geometries, and their conformations are same in the antiparallel complexes (C5↑C5↓ or C7eq↑C7eq↓) and mixed in the parallel complexes (C7eq↑C5↑); the antiparallel complexes with mixed strand conformations (C7eq↑C5↓) are unstable in unconstrained optimizations. (A) The antiparallel complexes of the tetrapeptides (AcNH-Ala3-NH2)2 displaying the edge-to-edge topoisomerism: the assembly creates either two or one large H-bonded (HB) ring. 1a: the C5↑C5↓ complex with two large HB rings; 1b: the C7eq↑C7eq↓ complex with one large HB ring; 1c: the C5↓C5↑ complex with one large HB ring; 1d: the C7eq↓C7eq↑ complex with two large HB rings. (B) The parallel complexes of the hexapeptides (AcNH-Ala5-NH2)2 displaying the edge-to-edge topoisomerism: here all the H-bonded rings are equivalent but complex formation involves the edges with either two or three intrachain H-bonds. 2a: the C7eq↓C5↓ complex involving the edges with two intrachain H-bonds; 2b: the C5↓C7eq↓ complex involving the edges with three intrachain H-bonds. The large difference in the energy of the edge-to-edge topoisomers is not observed in the case of the binary complexes of the oligopeptides with the odd number of the peptide bonds. (C) The relative energies of the 3a: C5↓C5↑, 3b(≡2a): C7eq↓C5↓, and 3c: C7eq↑C7eq↓ complexes of the hexapeptides (AcNH-Ala5-NH2)2. (D) The segments comprising two consecutive strands form stable β-hairpins (antiparallel assembly) when the two strands are either (a) both highly polarized (C5↑C5↓) or (b) both moderately polarized (C7eq↑C7eq↓) (color-coding as in Fig 1). In contrast, when one strand is highly polarized and the other is moderately polarized, these segments are expected to form (c) β-solenoid coils (parallel assembly, C7eq↑C5↑) or (d) unstable β-hairpins (antiparallel assembly C7eq↑C5↓) which are prone to convert into β-arches; similarly (e) when one strand is highly polarized and the other is least-polarized (the configuration described by a large contribution of the structure I, Fig 1C), the segment may form a hairpin (C5↑C5*↓) which is also prone to convert into β-arch.
Table 1.
Folding constants σXaa of the canonical amino acids:a,b.
Fig 3.
Folding constants σXaa and the energy of backbone-backbone H-bonding.
The calculated average backbone-backbone H-bond distance in the 310-helices AcNHG(Xaa)GGGNH2 (shown in the right hand panel, calculated at the B3LYP/D95** level of the theory, cf. Computational Methods) vs. the folding constants σXaa for all except the ionized Xaa residues listed in Table 1.
Fig 4.
FPi plots for small all-α and all-β soluble proteins.
The folding potential at the residue i (FPi, calculated from Eq. (1)), is plotted (Y-axis) against the residue number i (X-axis). The multiple alignments are taken from the SMART database (smart.embl-heidelberg.de) and the reference below. Note the characteristic FPi profiles of the secondary structure elements and the variation in average FPi values of those elements, (α) or
(β): (A) VHP (villin headpiece) domain, accession # SM00153; (B) WW domain, accession # SM00456: (a)
(β1) > 0; (b)
(β1) < 0; (C) HOX (homeobox) domain: (a)
(α1) > 0; (b)
(α1) < 0 [70]; (D) Tudor domain, accession # SM00333: (a)
(β1) > 0; (b)
(β1) < 0. The helical and extended segments of the protein chain are shaded red, and yellow or light yellow, respectively.
Fig 5.
FPi as a probe of the three-dimensional structure of proteins.
(A) The patterns in the plots of ΔFPi-1→i+1 (Eq. 2) vs. the residue number, characteristic of the archetypal ‘helix’, ‘strand’ and ‘turn’. (B) Characteristic clusters of the data sets in the plots of FPi vs. the ‘slope’ of FPi, ΔFPi-1→i+1, which correspond to the three archetypal elements of the secondary structure: e.g. the presence of the archetypal ‘helix’ will be marked by a compact cluster of data sets in the center of the plot. The ordinate of this cluster will vary since the optimal FPi value for ‘helix’ depends on the medium’s capacity to polarize the protein, vide infra. Note that ‘strand’ and ‘turn’ have each two avatars: (i) ‘C5 strand’ and ‘C7eq strand’, and (ii) ‘ FPi>>0 turn’ (defined here as the three- or five-residue segment that incorporates Gly in the centre) and ‘ FPi<<0 turn’. (C) The presence of the archetypal antiparallel ‘sheet’ would be marked by a circular distribution of data sets that combines the ‘C5 strand’/‘turn’ or ‘C7eq strand’/‘turn’ clusters while the presence of the parallel ‘sheet’ would be marked by a combination of the ‘C5 strand’ and ‘C7eq strand’ clusters, cf. Fig 2. This is illustrated by examples of de novo designed three-stranded antiparallel β-sheets (three-stranded β meanders), two- and three-stranded parallel β-sheets, and two-stranded parallel β-sheets embedded in left-handed coils from the C-terminal domains of the penicillin binding protein PBP2x from Streptococcus pneumoniae, PDB ID 1k25: (a) KGEWTFVNGKYTVSINGKKITVSI, ~50% in β structure, H2O, pH 3, 25°C (C5↑C5↓C5↑-meander) [71]; (b) TWIQNGSTKWYQNGSTKIYT, 20–30% in β structure, H2O, pH 3.25, 10°C (C5↑C5↓C5↑-meander) [72]; (c) RGWSLQNGKYTLNGKTMEGR, ~35% in β structure, 10%D2O/H2O or D2O, pH 5, 0–10°C (C7eq↑C7eq↓C7eq↑-meander) [73]; (d) C5↑C7eq↑-parallel sheet, cf. the FPi plot. The C-termini of two strands are connected by the D-prolyl-1,1-dimethyl-1,2-diaminoethane unit (diamine linker D-Pro-DADME), ~64% ‘folding-core’ residues (F5-V8 and R11-L14) in β structure at 10°C, 10%D2O/H2O, 100 mM sodium acetate buffer, pH 3.8 [74]; (e) C7eq↑C5↑C7eq↑-parallel sheet, cf. the FPi plot. The C-termini of strands 1 and 2 are connected by the diamine D-Pro-DADME while the N-termini of strands 2 and 3 are connected by the diacid formed from (1R,2S)-cyclohexanedicarboxylic acid (CHDA) and Gly, 4°C, 10%D2O/H2O, 2.5 mM sodium [D3]acetate buffer, pH 3.8 [75]; (f) the C7eq strands from two C5↑C7eq↑-parallel sheets in the left-handed coils of PBP2x from Streptococcus pneumoniae, PDB ID 1k25; (g) the C5 strands from two C5↑C7eq↑-parallel sheets in the left-handed coils of PBP2x, PDB ID 1k25.
Fig 6.
Effect of a polar dielectric on peptide bond polarization in a model of TC5b mini-protein.
The structure of the simplified model of TC5b, 9: AcAAAAAAAAGGPAAGAPPPA-NH2, obtained by full unconstrained optimization (HF/3-21G, gas phase) of the peptide chain placed in the conformation defined by the φ and ψ angles reported for the NMR ensemble of TC5b; the final structure was re-optimized in water taken as a continuous dielectric (the Onsager model as implemented in the Gaussian suite, cf. Computational Methods), until the default convergence criteria were fully met again. The backbone torsion angles of the TC5b NMR structure PDB ID 1l2y [50] and the ab initio structures 9a (in gas phase) and 9b (in a polar dielectric) are compared in the table on the right-hand side of the panel. (B) Dependence of charge polarization of the secondary peptide bonds Δe (the difference (au) in H and O Mulliken populations of the m peptide bond [33]) on m—that is on bond location along the polypeptide chain in the models 9a and 9b of the mini-protein TC5b. The immersion of the TC5b model in a polar solvent results in the increase in Δe along the entire chain i.e. in a considerable increase in charge polarization of the polypeptide backbone.
Fig 7.
Folding potential, medium properties and secondary structure preferences of the polypeptide backbone.
(a) The FPi values that ensure stability of the periodic secondary structure in a non-polar environment such as the lipid matrix of the bilayer membrane or vacuum: the optimal FPi range for the α-helix’ is ‒0.6-‒0.3 (color-coding as in Fig 1) and the optimal FPi ranges for β structure is <‒0.6 (C5 strand) and ‒0.3–0 (C7eq strand). The less polarized segments are malleable in a non-polar aprotic medium and may adopt helical (31-helix, PPII-helix, α*-helix) folds while the least polarized segments of the polypeptide backbone, e.g. a sequence of consecutive ‘ FPi>>0 turns’ (Fig 5), may adopt the extended (C5* strand) folds depending on molecular embedding. (b) The FPi values that ensure stability of the periodic secondary structure in a moderately polarizing environment such as the bilayer membrane interface, the interior of a soluble protein globule or the interior of the DNA duplex: the optimal FPi range for the α-helix’ is ‒0.3–0 and the optimal FPi ranges for β structure is <‒0.3 (C5 strand) and 0–0.3 (C7eq strand). (c) The FPi values that ensure stability of the periodic secondary structure in a polar medium such as the physiological 1:1 electrolyte solution: the range of the optimal FPi values for the α-helix is now 0–0.3 while the somewhat less and more polarized segments are likely to form β-sheets. The most polarized segments are now likely to form ‘ FPi<<0 turns’ or PPII-helix. The sequence of consecutive ‘ FPi>>0 turns’ forms a random coil in an aqueous buffer unless it is stabilized by molecular embedding in helical (31-helix, PPII-helix, α*-helix) or extended (C5* strand) folds. (d) The FPi values that ensure stability of the periodic secondary structure in the hypothetical highly polarizing environment such as the pre-organized ionic grid e.g. on the surface of a DNA or RNA strand (the sequence of consecutive ‘ FPi>>0 turns’ is likely to form here an α*-helix), or the microenvironment of the extended β structure of β solenoid or amyloid filament, vide infra.
Fig 8.
Folding potential, folding template and three-dimensional structure of soluble globular proteins.
The insert shows the plot of the folding potential FPi for the segment of the polypeptide backbone which has high helical propensity in the aqueous environment: the 14-residue site which triggers coiled-coil formation in cortexillin I [85]. In the physiological 1:1 electrolyte solution, this segment is stabilized by the mutual polarization of the α-helix and the transient ionic matrix with the lattice constant of 7 Å (the Ghosh-Debye-Hückel matrix, see the text and S1 Appendix). The effect of polarization is maximized when the helix termini replace the corresponding salt ions in the vertices of the lattice which are separated by the distances [(7Δxij)2+(7Δyij)2+(7Δzij)2]1/2 (Å) where Δxij, Δyij, Δzij are whole numbers and the sum |Δxij|+|Δyij|+|Δzij| is odd. Thus the ‘allowed’ α-helix is a vector whose length is defined by the |Δxij|,|Δyij|,|Δzij| combinations equal to: {1,0,0}/7 Å, {1,1,1}/12 Å, {2,1,0}/15.6 Å etc. The length of the α-helix in the diagram is 21 Å which fulfils the above condition when the helix fits into the matrix along the grid line (|Δxij|,|Δyij|,|Δzij| = {3,0,0}, |τmin| = 0°), as shown here in both projections, or along the diagonal of the 2×2 segment of 4 unit cells (|Δxij|,|Δyij|,|Δzij| = {2,2,1}, |τmin| = 48°) (where |τmin| is the smallest vector/grid-line angle).
Fig 9.
Electronic configuration of the polypeptide backbone and rate of folding of helix-bundle proteins.
The folding rate constants ln kf (sec-1) vs. Nh/Nt (‘helix’- FPi fraction) where Nh is the number of residues with the ‘helix’ FPi: 0±0.05–0.3±0.05, cf. Fig 7(c), and Nt is the total number of residues in the helix-bundle domains, counted from the N-terminal residue of the first α-helix to the C-terminal residue of the last α-helix as defined by the DSSP protocol implemented in the RCSB PDB database. The present set includes the data for 16 small proteins with the natural, wild-type sequences and for 5 domains modified or engineered for fast folding [87–100] Nt ≤ ~80 aa, PDB ID’s: 1ayi, 1ba5, 1fex, 1imp, 1mbk, 1prb, 1ss1, 1st7, 1uzc, 1yrf, 2a3d, 2abd, 2jws, 2jwt, 2no8, 2wqg, 3kz3: ♦ wild-type domains; ◊ the domains modified/engineered for fast folding.
Fig 10.
Electronic configuration of the polypeptide backbone and secondary structure propensity.
(A) Experimental α-helix propensities: (a) The averaged relative α-helix propensity data obtained in the site-directed mutagenesis studies of both peptides and proteins, adjusted so that Δ(ΔGf) = 0 for Ala and Δ(ΔGf) = 1 for Gly [101–108], vs. the NMR shielding tensors σ(Cα)Xaa (310-helix AcG(Xaa)GGGNH2; GIAO//B3LYP/D95**, cf. Computational Methods and S1 Table): ♦ glycine and amino acids whose Cβ and Cγ are the methyl, methylene or methine groups, r2 = 0.83; ▲proline; ◊ any other amino acids including three highly fluorinated amino acids, r2 = 0.52 [107]; trendlines obtained by fitting 2nd order polynomial functions; (b) The Lifson-Roig propagation free energies for the amino acids whose Cβ and Cγ are the methyl, methylene or methine groups, in 88% methanol-water [109]; (c) The Lifson-Roig propagation free energies for the same set of amino acids in 40% (cyan) and 90% (navy) trifluoroethanol-water [109]. The propensities are determined at the sites in the helices interior. (B) Experimental β-sheet propensities from site-directed mutagenesis (kcal mol-1, Δ(ΔGf) = 0 for Gly in (D) and Δ(ΔGf) = 0 for Ala in (E), (F) and (G)) vs. calculated NMR shielding tensors σ(Cα)Xaa (AcGGGGGXaaNHMe in β-hairpin (Ib turn); GIAO//B3LYP/D95**, cf. Computational Methods and S1 Table): (a) zinc-finger β-hairpin, site 3, r2 = 0.89 (edge strand, the guest site is not H-bonded) [110]; (b) Ig binding B1 domain of streptococcal protein G, r2 = 0.83 (variant E42A/D46A/T53A, site 44, edge strand, the guest site is H-bonded) [111]; (c) Ig binding B1 domain of streptococcal protein G, r2 = 0.84 (variant I6A/T44A/T51S/T55/S, site 53, central strand) [112]; (d) Ig binding B1 domain of streptococcal protein G, r2 = 0.76 (I6A/T44A, site 53, central strand) [113,114]. Δ(ΔGf) for Pro in (b), (c) and (d) set at the minimum value of 3 kcal mol-1 [112]; trendlines obtained by fitting 4th order polynomial functions.
Fig 11.
as a measure of conformational and H-bonding propensity of the polypeptide backbone.
(A) as a probe of backbone mobility: (a) The mean temperature factors Bi of the backbone N atoms in α-helices vs. mean FPi of those helices,
(α), in the xylanase from Thermoascus auranticus, PDB ID 1i1wA [115]. Helical residues are assigned according to the Swiss-PDBViewer: helix A 6–12, B 24–27, C 32–38, D 51-54, E 64–76, F 93–96, G 101–117, H 143–147, I 151–163, J 182–197, K 215–227, L 245–257, M 292-301; (b) The mean temperature factors Bi of the backbone N atoms in β strands vs. mean FPiof those strands,
(β). The strand residues are assigned according to the Swiss-PDBViewer and DSSP protocol implemented in the RCSB PDB database: N 17–22, O 41–46, P 79–81, Q 124–127, R 132–134, S 138–140, T 168–173, U 202–206, V 208–210, W 232–236, X 239–242, Y 264–266, Z 279–281. The trendlines are obtained by fitting 2nd and 4th order polynomial functions. (B)
and the energy of backbone-backbone H-bonding. Δ(ΔGf) vs. FPi for the single-site amide-to-ester X(i)ξ substitutions (Δ(ΔGf) = ΔGf,WT‒ΔGf,X(i)ξ) in Pin1 WW domain. The data shown for the mutants in which the perturbed amide donates, but does not accept, a hydrogen bond (thermal, GdnHCl, pH 7.0; PDB ID 2kcf) [116,117]. The trendline is obtained by fitting 4th order polynomial function. (C)
and the amyloid fibril-forming capacity of oligopeptides. The data for the total of 942 unique hexapeptide structures are taken from the WALTZ-DB database of amyloid forming peptides [118]; excluding the Pro-containing peptides, the sample comprises 240 amyloidogenic and 702 non-amyloidogenic hexapeptides. The mean FPi of each hexapeptide,
(peptide), is defined as the mean of FPi of the two central residues. The amyloid fibril-forming capacity of the hexapeptides with
within a specific 0.05 range (‒0.750±0.025 etc.) is defined as the frequency of the amyloidogenic peptides within this
range in the entire amyloidogenic sample (240 entries), normalized by the frequency of both amyloidogenic and non-amyloidogenic peptides within the same
range in the total hexapeptide sample (942 entries).
Fig 12.
Electronic configuration of the polypeptide backbone and canonical peptide recognition by the PDZ domains.
Binding affinities ΔGb of the PDZ domains vs. mean FPi of the peptide ligands (ΔGb in kcal mol-1, the width of the FPi averaging window is given in the brackets). The data from S2 and S3 Tables in ref. [120] unless indicated otherwise, for 18 out of 33 PDZ domains identified in the literature to bind at least a dozen or so peptides with Kd<100 μmol (no discernible dependence of ΔGb on
in 3 cases, r2<0.25 in 11 cases, and in 1 case the fit depends on an outlier) [120–123]: (A) MAGI2 PDZ2, r2 = 0.52 (5); (B) PTP-BL, r2 = 0.52 (5); (C) MAGI1 PDZ6, r2 = 0.32 (8); (D) Lin7C, r2 = 0.38 (8); (E) AF6, r2 = 0.42 (5) [121]; (F) SAP97 PDZ1, r2 = 0.55 (8); (G) OMP25, r2 = 0.27 (8); (H) Scrb1 PDZ3, r2 = 0.31 (5); (I) PSD95 PDZ1, r2 = 0.77 (8); (J) Chapsyn110 PDZ2, r2 = 0.60 (8); (K) MAGI3 PDZ1, r2 = 0.53 (8); (L) SAP102 PDZ2, r2 = 0.42 (8); (M) PSD95 PDZ2, r2 = 0.59 (8); (N) SAP97 PDZ2, r2 = 0.53 (8); (O) Erbin, r2 = 0.40 (5) [121]; (P) TIAM1+TIAM2, r2 = 0.34 (5) [122]; (Q) γ-Syntrophin1, r2 = 0.42 (8); (R) RGS3, r2 = 0.48 (5). The
regions associated with peptides’ propensities for the α-helix, C5 and C7eq folds are shaded red, yellow and light yellow, respectively, cf. Fig 1; the regions shaded grey mark the putative ΔGb minima.
Fig 13.
Electronic configuration of the polypeptide backbone and stability of large-to-small hydrophobic variants.
The figure presents the Δ(ΔGf) vs. plots for the single-site Xaa(i)Ala mutations in helices and sheets (Δ(ΔGf) = ΔGf,WT‒ΔGf,Xaa(i)Ala,
= ⅓ (FPi-1+ FPi + FPi+1); Xaa = F, I, L, M, T, V, W, Y). The ‘helix’ and ‘strand’ residues are assigned based on the DSSP protocol implemented in the RCSB PDB database; the trendlines are obtained by fitting polynomial functions [125–131]: (A) The Δ(ΔGf) data for the α-helices in: (a) staphylococcal nuclease (GdnHCl, pH 7.0 [125], PDB ID 1nuc), villin headpiece subdomain (thermal, pH 7.0 [126], PDB ID 1yri, the data set of the highest
(shown) is not included in the calculation of the trendline), and acyl coenzyme A binding protein (GdnHCl, pH 5.3 [87], PDB ID 2abd); (b) bacteriophage T4 lysozyme (thermal, pH 3.0 [127,128], PDB ID 2lzm, the complete scattergram, including the four data sets of the highest
, is shown in the insert). (B) The Δ(ΔGf) data for the β-sheet strands in: (a) fibronectin type III domains of human tenascin TNfn3 (3rd module, PDB ID 1ten) and fibronectin FNfn10 (10th module, PDB ID 1fnf) (thermal, urea, GdnHSCN, pH 5.0) [129,130]; (b) immunophilin FKBP12 (urea, pH 7.5 [131], PDB ID 2ppn, the data set of the highest
(shown) is not included in the calculation of the trendline); (c) staphylococcal nuclease (GdnHCl, pH 7.0 [125], PDB ID 1nuc, the data set of the highest
(not shown) is not included in the calculation of the trendline).
Fig 14.
Electronic configuration of the polypeptide backbone and canonical peptide recognition by the PDZ domains.
(A) Folding template FT and the 3D structure of the PDZ domains: the putative ‘key’ surface charges of the PDZ fold are the termini of the α1 helix-[CO2− loop] and the α2 helix arrays (→), and the cross-β arrays (»») capped by a reverse turn (G248 (C’ = O)) and a bulge (T234 (C’ = O)/E235 (C’ = O)). The structure in the diagram is the second PDZ domain of syntenin, PDB ID 1r6j. (B) The projected fit of the putative key surface charges δ+ and δ‒ into the Ghosh-Debye-Hückel matrix. (C) The predicted by the folding-template model and the observed interatomic distances (Å) between the key surface charges δ+ and δ− (the average distances to the T234 O/E235 O atoms in the bulge are used). (D) Two cross-β {β1-β6-β4-β3-β2} arrays of peptide bonds that anchor the oligopeptide ligand via backbone-backbone H-bonds to N-H of the residue i = ‒2 and to C’ = O of the residue i = ‒4. (E) The oligopeptide values at the ΔGb maximum (determined from Fig 12 for the 14 entries with β sheet register confirmed by the X-ray or NMR structure determination) plotted against
(PDZ/sheet) i.e. the average FPi values of the 15 residues involved in the two cross-β arrays which are shown in the panel D. For a detailed account of the model of peptide recognition by the PDZ domains see S3 Appendix.
Fig 15.
Electronic configuration of the polypeptide backbone versus complexity of tertiary structure and order of oligomerization in soluble and integral membrane proteins.
The FPi vs. ΔFPi-1→i+1 plots, cf. Fig 5, may characterize the relationship between distribution of backbone density and organization of globular structure. For α-helices, narrow distribution of the folding potential values and the slope values, ΔFPi-1→i+1 ~0, generates compact clusters of the data points. As the complexity of α structure increases and the exposure to the medium decreases, this clusters shift from FPi >0 to FPi <0 region in the case of soluble proteins, see the panels in (A), and in the opposite direction, from FPi <0 to FPi >0 region in the case of integral membrane proteins, see the panels in (B). The same trends are discernible in the FPi vs. ΔFPi-1→i+1 plots for the antiparallel β sheets that assemble ‘C5 strands’ or ‘C7eq strands’ and ‘FPi>>0 turns’, panels (C) and (D), even though large differences in the folding potential values and wide distribution of the slope values, from ΔFPi-1→i+1 ~ ‒1 to ΔFPi-1→i+1 ~ 1, generate in this case circular distribution of data points. (A) (a) The peripheral stalk helix of F0F1 ATP synthase from E. coli (b2 subunit in the top diagram in the right-hand panel), UniProt # P0ABA0: residues A32-K122 (the hinge region, the dimerization region, and the C-terminal δ-domain-binding region); (b) One of the two 160Å-long helices of colicin Ia (residues R351-K470) that span the periplasmic space, linking the receptor-binding domain to the other domains, PDB ID 1cii; (c) The parallel α-helical coiled coil cortexillin I, PDB ID 1d7m; (d) The Leu-zipper segment of the GCN4 bZIP protein PDB ID 2dgc: the ‘helix’ cluster is shifted to the FPi ~0 region; (e) The pattern of the multi-helix bundle which functions as an enzyme within a heterooligomeric complex: the ‘helix’ cluster is partly shifted into the FPi<0 region. The structure shown is the catalytic domain of the guanine nucleotide exchange factor (Ddl homology (DH) domain) of human PAK-interacting exchange protein, PDB ID 1by1. (B) (a) Transmembrane segment of the peripheral stalk of F0F1 ATP synthase from E. coli (b2 subunit in the diagram in the centre, color-coded orange), UniProt # P0ABA0: residues A11-A31; (b) Transmembrane α-helices of human glycophorins A, B, C and E: UniProt #’s P02724, P06028, P15421, and P04921. The glycophorin helices apparently are brought together in the membrane by the dimerization of the extra-membrane domains; (c) The transmembrane α subunit of the membrane associated acetylcholine receptor from Torpedo marmorata, PDB ID 2bg9; the five transmembrane subunits of this receptor do not form a tight oligomer structure and are held in place by the extra-membrane subunits; (d) Bacteriorhodopsin, a membrane protein (light-driven proton pump) from Halobacterium salinarum; the biological assembly is the homotrimer, PDB ID 1fbb; (e) Glycerol facilitator (GlpF), a membrane channel protein of the aquaporin family; the biological assembly is a homotetramer, PDB ID 1fx8; (f) Subunit c of F0F1 ATP synthase from E. coli (color-coded blue in the diagram in the centre): the biological assembly is a homodecamer, PDB ID 1ijp. (C) (a) The single-sheet protein, the central β-sheet (residues A81-D205) of the Borrelia burgdorferi spirochete antigen, outer surface protein A (OspA), PDB ID 2g8c; (b) The β sandwich C-terminal domain of the α-amylase from Geobacillus stearothermophilus, PDB ID 1qho; (c) The strands βF(H88-A97) and βH(S115-T123) of the homotetramer of transthyretin, buried in the tetramer interior, PDB ID 5l4j. (D) (a) 16-stranded β barrel, the monomeric integral outer-membrane porin OmpF from E. coli, PDB ID 1opr; (b) 16-stranded β barrel, the trimeric integral outer-membrane porin OmpG from E. coli, PDB ID 2f1c.
Fig 16.
Electronic configuration of the polypeptide backbone versus complexity of tertiary structure and order of oligomerization.
(A) The histograms compare the distribution of the α-helix and β-sheet in the chemokine and CHROMO domains [140,141]. The βββα folds of these two domains are very similar but the roles of the N-terminal and C-terminal segments are reversed: the chemokines use the C-terminal helix to bind the substrates while the CHROMO domains use the N-terminal β-hairpin. The expected difference in the
distribution is indeed found (β1 cyan, β2 light cyan, β3 yellow, α1 red): (a) In chemokines, the binding function involves the C-terminal β3 and α1, and indeed the N-terminal β1 and β2 are the archetypal ‘C5 strands’ (
largely <0) and anchor the structure while the C-terminal α1 will only be stable when it is partially buried (
tends to be <0, PDB IDs: 1b3a, 1cm9, 1dok, 1eih, 1el0, 1eot, 1esr, 1f2l, 1f9p, 1g2t, 1g91, 1ha6, 1il8, 1j9o, 1m8a, 1mgs, 1ncv, 1nr4, 1o80, 1qg7, 1qnk, 1rhp, 2hcc, 2kol, 2kum, 2l4n, 2q8r, 2ra4, 3n52, 3ona, 3tn2, 4hcs, 4hsv); (b) In the CHROMO domains (binding involves the N-terminal β1 and β2), the C-terminal α1 is the archetypal ‘helix’ (0<
<0.2) and anchors the structure while the N-terminal β1 and β2 strands (also 0<
<0.2) will be stabilized when they are either partially buried and therefore less polarized (turning C7eq), or attached to a cross-β structure and therefore more polarized (turning C5) (PDB IDs: 1ap0, 1g6z, 1kna, 1pdq, 2b2v, 2d9u, 2dnt, 2dnv, 2dy8, 2ee1, 2epb, 2fgg, 2k1b, 2rsn, 2rso, 3fdt, 3gv6, 3i91, 3mts, 3r93, 3tzd). (B) The FPi plots for bZIP proteins (PDB IDs: 1ci6, 1dgc, 1dh3, 1gd2, 1jnm, 1nwq, 1t2k, 1s9k, 2c9l, 2e43). The multiple alignment suggests that
and function of each distinct segment of bZIP helix are related. Based on the assignments in Fig 7(c), the basic N-terminal segment has the ‘C7eq strand’
, the mid-region segment has the ‘C5 strand’
, and the C-terminal segment has the ‘helix’
. Thus, the folding potential FPi of each segment appears optimized to ensure stability of the helical fold in three different environments created in the complex of bZIP dimer and DNA duplex.
Fig 17.
Folding template and tertiary structure of soluble globular proteins.
(A) The interaction of sperm whale apomyoglobin, PDB ID 1a6m, with the transient cubic lattice of the ionic atmosphere in the physiological 1:1 electrolyte solution: mutual polarization of the polypeptide backbone and the Ghosh-Debye-Hückel matrix stabilizes the protein/electrolyte system when the ends of the helices A-H of the globin fold replace the corresponding salt ions in the vertices of the matrix with the 7 Å lattice constant. The ‘template box’ has dimensions 42×42×21 (Å). (B) In the case of Alcaligenes euthropus flavohemoglobin, PDB ID 1cqxB, the ‘template box’ has dimensions are 49×35×21 (Å) and it is polar along each Cartesian axis and so it is chiral. (C) Manual search for the best fit of the termini of the A-H helices of both globins into the Ghosh-Debye-Hückel matrix yields the coordinates shown in this panel (partial charges δ+ and δ− of the helix termini are represented by the N and O atoms of the residues assigned as the terminal helix residues by the Swiss-PDBViewer with one exception of the N terminus of the helix B in 1a6m where PDBViewer assignment is erroneous; the Cartesian coordinate system is left-handed). (D) The calculated and the observed matrices of the interatomic distances (Å) between the helix termini in: ○ sperm whale apomyoglobin, PDB ID 1a6m, and ◊ Alcaligenes euthropus flavohemoglobin, PDB ID 1cqxB (based on the coordinates listed in the panel C). (E) The calculated and the observed matrices of the interatomic distances (Å) between the Nξ atoms of the ‘reporter’ lysines in the congeners of Borrelia spirochete antigen OspA (PDB IDs 2af5, 2fkg, 2fkjA, 2fkjB, 2fkjC, 2g8c, 2hkd, 2i5v, 2i5z, 2ol6, 2ol7A, 2ol7B, 2ol8, 2oy1, 2oy5, 2oy7, 2oy8, 2oyb, 2pi3, 3ckaA, 3ckaB, 3ckf, 3ckg, 3ec5, 3eexA, 3eexB). See S4 Appendix for the definition of the plotted data.
Fig 18.
Electronic configuration of the polypeptide backbone and metamorphic equilibria.
(A) Chameleon sequence SASF2 attached to N-terminal segments of λ Cro and p22 Cro repressors. When attached to the 35-residue N-terminal segments of p22 Cro (PDB ID 1rzs) or λ Cro (PDB ID 5cro) repressors, the sequence SASF2 mimics the conformations of the native C-terminal segments of these repressors, folding into an α-helix in the first case and into a β-hairpin in the second case [143]: (a) The FPi plot for the p22 Cro/SASF2 conjugate. The chameleon sequence SASF2 is preceded by a flexible ‘hinge’ formed by the short C5 strand (W30-E32, = ‒0.1080) and the PPII helix (V33-P35,
= ‒0.4542), which extends back towards the helices α1, α2 and α3 (PDB ID 1rzs) so that the main chain makes U-turn placing SASF2 in the helix bundle; (b) The FPi plot for the λ Cro/ SASF2 conjugate. The segment preceding SASF2 is the long helix α3 (S28-H35,
= 0.1787) (PDB ID 5cro) and the backbone cannot make U-turn. (B) Human lymphotactin. Under physiological conditions, human lymphotactin exists in the equilibrium between the canonical chemokine monomer PDB ID 1j8i and the homodimer of the Greek-key β-sheet PDB ID 2jp1 [144,145]: (a) The FPi plot for the monomeric chemokine-like conformer. The misalignment of the antiparallel C5 and C7eq strands (β3 and β4) creates a flexible ‘hinge’ at the end of β4 so that the low-
helix α1 can bury itself on the concave surface formed by the β structure and the unstructured, ‘S-S attached’ N-terminal segment; (b) The FPi plot for the dimeric Greek-key conformer of lymphotactin. The stabilization of α1 is not possible when the extension of the three-stranded β2↓β3↑β4↓ sheet into the four-stranded one β2↓β5↑β4↓β1↑ obliterates the ‘hinge’ (β4 is lengthened due to additional alignment of β1) and flattens the lymphotactin surface (the N-terminal segment folds into β1). (C) E. coli transcription factor RfaH. The N-terminal (NTD) and C-terminal (CTD) domains of RfaH are connected by a flexible linker which allows either for tight interaction or complete separation of the two domains. The arrangement determines the fold of CTD: (a) The FPi plot for the CTD partially buried in the NTD, PDB ID 2oug; (b) The FPi plot for the autonomous CTD isolated in the aqueous environment, PDB ID 2lcl. (D) GB98/GA98 variants of the streptococcal albumin- and immunoglobulin-binding proteins. The FPi plots for the 56-residue GB1 congeners and the alternation of folds produced in each case by the replacement of a single residue (mutation sites are marked by the green vertical bars) [146,147]: (a) The FPi plot for the variant PDB ID 2lhe (GB98-T25I/L20A); (b) The FPi plot for the variant PDB ID 2lhg (GB98-T25I); (c) The FPi plot for the variant PDB ID 2lhd (GB98); (d) The FPi plot for the variant PDB ID 2lhc (GA98≡GB98-Y45L). (E) Human mitotic spindle protein Mad2 [148]: (a) The FPi plot for the five-stranded β sheet of Mad2 with the C-terminal hairpin in the C5↓C5↑ configuration, PDB ID 1duj; (b) The FPi plot for the five-stranded β sheet of Mad2 with the C-terminal hairpin in the C7eq↓C7eq↑ configuration, PDB ID 1s2h.
Fig 19.
Electronic configuration of the polypeptide backbone and molecular recognition in formation of α structure: Folding of α-MoRFs [149–152].
(A) The complex between the TAZ1 domain of the transcriptional coactivator CREB-binding protein (CBP, the 4-helix-bundle IDP receptor) with the activation domain of CITED2 (IDP), PDB ID 1r8u [150]: (a) The FPi vs. ΔFPi-1→i+1 plot for the activation domain of CITED2. The domain is unstructured in the free form in aqueous solution as expected given its FPi/ΔFPi-1→i+1 pattern: FPi<0; (b) The N-terminal segment of the activation domain of CITED2 is helical in the complex with TAZ1 where it is deeply buried (cf. the helix within the green outline) while the C-terminal segment, exposed to solvent, remains unstructured; (c) The FPi vs. ΔFPi-1→i+1 plot for the CBP TAZ1 domain shows pronounced archetypal ‘helix’ propensity, cf. Fig 5. Note that the α-helices of this domain do not incorporate ‘C5 strand’ segments which would be expected to stabilize the bundle structure—in fact, the assembly is stabilized by the chelation of three Zn2+ ions; (d) The projected fit of the putative key surface charges δ+ and δ− (the termini of the five helices shown in the Swiss-PDBViewer projection) into the Ghosh-Debye-Hückel matrix, and the correlation between the predicted by the folding-template model and the observed interatomic distances (Å) between the charges δ+ and δ−. (B) The complex between the α-MoRF of the measles virus N protein and nucleocapsid-binding domain of the measles virus P protein, PDB ID 1t6o [151,152]: (a) The FPi vs. ΔFPi-1→i+1 plot for the α-MoRF. The FPi profile is helical (approximately constant FPi) but ~0.3 is too high for the aqueous environment and the domain is disordered in solution; (b) Given its FPi/ΔFPi-1→i+1 pattern, the measles virus α-MoRF is expected to fold into a helix not when it is buried but when it remains in the solvent shell of the binding protein, benefiting from the synergistic stabilization of the ionic matrix, and this is indeed found in the complex, cf. the helix in the blue outline; (c) The FPi vs. ΔFPi-1→i+1 plot for the nucleocapsid-binding domain shows pronounced ‘helix’ propensity characteristic of helix bundles, cf. Fig 15A; (d) The projected fit of the putative key surface charges δ+ and δ− (the termini of the four helices shown in the Swiss-PDBViewer projection) into the Ghosh-Debye-Hückel matrix, and the correlation between the predicted by the folding-template model and the observed interatomic distances (Å) between the charges δ+ and δ−.
Fig 20.
Electronic configuration of the polypeptide backbone and molecular recognition in formation of β structure: Folding of inteins [153,156].
The FPi assignment of secondary-structure propensity vs. distribution of side chain charges in the two-stranded antiparallel β-sheet βN↑βC↓ of 15 inteins and intein-like domains of the known 3D structure. (A) The architecture of the horseshoe-like fold of inteins: (a) the antiparallel assembly of the 30–35 residue-long strands βN and βC into the βN↑βC↓ sheet constitutes the major feature of the HINT fold. Each strand comprises four segments, βNa’-βNa-βNb-βNb’ and βCa’-βCa-βCb-βCb’ (cf. the labels color-coded blue and red, respectively), which are marked by the changes in the direction of the main chain (produced by the inherent right-handed twist of the polypeptide backbone and the insertion of turns); (b) the putative assembly of the full-length βN and βC strands into the βN↑βC↓ sheet. The interactions of the terminal-segment pairs, βNa’-βCb’ and βNb’-βCa’, may contribute to the stabilization of the correct register in the initial stages of folding; (c) in the native state, the βN↑βC↓ sheet comprises the middle-segment pairs βNa-βCb and βNb-βCa since the C-terminal segments of both strands, βNb’ and βCb’, are folded towards the protein interior. (B) The FPi assignment of secondary-structure propensity vs. distribution of the side chain charges in the case of the full ‘symmetry’ of backbone polarization of the middle-segment pairs βNa-βCb and βNb-βCa, shown within the green rectangles in the schematic representation of the βN↑βC↓ sheet. The PDB ID-labeled diagrams show FPi plots, DSSP assignments, and the sequences of the 30–35 residue-long βN and βC strands with D, E marked by red squares and K, R marked by blue squares. The four segments of each βN and βC strand are defined based on the DSSP/Swiss-Prot assignments and the inspection of the 3D structures, and are shaded yellow or light-yellow in the FPi plots depending on the secondary-structure preferences; the latter are assigned based on Figs 5 and 7. (C) The FPi assignment of secondary-structure propensity vs. distribution of side chain charges in the case of the partial ‘symmetry’ of backbone polarization of the middle-segment pairs βNa-βCb and βNb-βCa. The ‘matching’ βNa-βCb pairs are shown within the green rectangles and the ‘mismatched’ βNb-βCa pair within the red rectangles in the schematic representation of the βN↑βC↓ sheet. (D) The FPi assignment of secondary-structure propensity vs. distribution of side chain charges in the absence of the ‘symmetry’ of backbone polarization of the middle-segment pairs βNa-βCb and βNb-βCa, shown within the red rectangles in the schematic representation of the βN↑βC↓ sheet. For a detailed report on the discussed data see S5 Appendix.
Fig 21.
Effect of pH on conformational and H-bonding propensity of the polypeptide backbone.
(A) Conformational equilibria of islet amyloid polypeptide (amylin) [157]: (a) The FPi plot of amylin at high pH and the putative β-sheet conformation of the peptide. Assuming σHis≡σH° in Table 1, the segment L16-T30 has β-hairpin potential in the aqueous buffer: L16-N21 = ‒0.0690 (C5 strand), N22-I26
= 0.6667 (turn), and L27-T30
= ‒0.0964 (C5 strand); (b) The FPi plot for amylin at low pH and the putative helical conformation of the peptide. Assuming σHis≡σH+ in Table 1, the segment T9-N22 has unambiguous α-helical potential in the aqueous buffer,
= 0.1746. (B) Acid-induced loop-to-helix transition in influenza hemagglutinin [158]. The trimeric glycoprotein hemagglutinin from influenza virus acts as a fusogen at low pH of endocytic vesicles. The activity is contingent on a large-scale structural rearrangement crucial for delivering the viral contents into host cells. The rearrangement involves inter alia conversion of B-loop of hemagglutinin (residues 55–76) into a long α-helix: (a) The FPi vs. ΔFPi-1→i+1 plot for B-loop at high pH. The segment has a helical FPi profile but very low
and it is accordingly unstructured; (b) The FPi vs. ΔFPi-1→i+1 plot for B-loop at low pH. The helical data cluster is now shifted into the stable ‘helix’ region,
> 0. (C) Partial unfolding of the translocation-domain helices of the α-pore forming diphteria toxin at low pH [159]. The toxin invades a cell by crossing the endosome membrane via the process mediated by the C-terminal segment of the all-α domain T (translocation domain) and triggered by the reduced pH in the endosomal lumen: (a) At the standard physiological pH, the toxin is well-structured and the C-terminal segment of the domain T is buried under the helices TH1-TH4, PDB ID 1f0l; (b) At low pH, the TH2, TH3 and TH4 helices become completely disordered, PDB ID 4ow6 [159]. As a result, the C-terminal helices are exposed and can interact with the membrane; (c) The FPi vs. ΔFPi-1→i+1 plot for the domain T at the neutral pH. The plot shows the characteristic pattern of a soluble multi-helix bundle, cf. Fig 15A(e), where α-helices incorporate ‘C5 strand’ segments necessary to stabilize the compact tertiary structure; (d) The FPi vs. ΔFPi-1→i+1 plot for the domain T at low pH: the folding potential FPi becomes more positive for the entire domain (the ‘C5 strand’ segments are ‘titrated out’ which destabilizes the tertiary structure); (e)-(h) The FPi vs. ΔFPi-1→i+1 plots for the α-helices TH3 and TH4 at the neutral pH, panels (e) and (g), and at the low pH, panels (f) and (h). In both cases the folding potential shifts from FPi≤0 in panels (e) and (g) (the α-helices which are stable in the interior of a compact structure) to FPi ≥0.3 in panels (f) and (h) (the α-helices which are unstable except in a highly polarizing environment cf. Fig 7). (D) Acid-induced unfolding and aggregation of transthyretin [38,162–172]: (a) The superposed FPi plots for transthyretin at pH >7 and pH 4, and the DSSP assignments for the native monomer (homotetramer subunit, β sandwich fold). The red and purple outlines mark the strand and turn segments most affected by the reduction of pH: FPi of the V30-F33 segment (βB strand) shifts from ‘C5 strand’ to ‘helix’ propensity, and the two ‘turn’ segments (D-E≡D* and E-F≡E*) are destabilized. In addition, FPi of βC and βE segments shifts from ‘C5 strand’ to ‘C7eq strand’ propensity. These changes destabilize the outer β sheet of transthyretin βC↓βB↑βE↓βF↑; (b) Putative amyloidogenic monomers of transthyretin generated by step-by-step dismantling and rearrangement of transthyretin β sandwich consistent with the destabilizing FPi shifts and the solid state NMR [162–164], spin-labelling [165,166], immunoreactivity [167] and H/D exchange (HXMS) [168,169] studies; (c) The pathway of acid-induced unfolding and aggregation of transthyretin [38], and the topology of annular octamers [170–172] and protofibrils [169].
Fig 22.
Electronic configuration of the polypeptide backbone and conformational behavior of Aβ proteins.
(A) Folding potential, medium effect and secondary structure of monomeric Aβ. The FPi plots for Aβ peptides are juxtaposed with the color-coded bars representing medium effects cf. Fig 7 (note that at pH 7, σHis is average of the H0 and H+ constants since pKa values of Aβ histidines are in the 6.8-7.0 range [174,175]): (a) Nonpolar environment: e.g. bilayer membrane/lipid matrix (FPi plot for Aβ1–43). Elements of the E11-E22 and C-terminal segments are expected to adopt the C7eq fold while the array of consecutive ‘turns’ D23-M35 may be stabilized as the ‘C5* strand’; in contrast, the E3-D7 segment may adopt a helical conformation. The G25-V39 segment of Aβ1–40 bound to DMPC bilayer (multilamella vesicles composed of 1,2-dimyristoyl-sn-glycero-3-phosphocholine, high P/L ratio) is indeed reported to fold into a parallel β structure [176,177]. On the other hand, the E3-D7 residues buried in the CDR loops of the complexes with monoclonal antibodies are found to be helical: PPII- (PDB ID’s 2ipu, 3bae) or 310- (PDB ID 4hix) [178]. (b) Moderately polarizing environment: e.g. H2O/TFE (HFIP) solutions or micelle interfaces (FPi plot for Aβ1-42). The E11-E22 and D23-M35 segments are expected to display α-helix and α*-helix propensities, respectively; the E3-D7 segment is expected to remain disordered since it lacks a well-defined conformational propensity. Several reports confirm that Aβ peptides adopt an all-α fold in the environments of micellar interfaces or aqueous solutions of fluorinated alcohols (see e.g. PDB ID 1iyt) [179–184]. (c) Polar environment: e.g. aqueous buffers (red FPi plot for Aβ1–40 at pH 7; cyan FPi plot for Aβ1–43 at pH 8–9). In view of the FPi patterns, the E11-E22 and D23-M35 segments are expected to remain disordered in a neutral aqueous buffer. However, the E11-E22 segment may sample helical conformations while the CHC (L17-A21), E11-Q15, and C-terminal residues may sample either the C5 (pH 8, longer isoforms) or the C7eq conformations. In agreement with these expectations, experimental evidence suggests that Aβ monomers form in aqueous solution collapsed coils [185–188], devoid of secondary structure [189,190], but the evidence of stabilization of residual secondary structure of Aβ in some conditions is also reported (e.g. PDB ID 2lfm and 2otk) [191–194]. (d) Highly polarizing environment: e.g. the environment within an amyloid fibril (FPi plot for Aβ1-46). The E11-E22 and D23-M35 segments are now expected to adopt C5 and C7eq conformations respectively. The distribution of amyloid-fiber forming capacities, cf. Fig 11C, is consistent with this expectation. (B) Electronic Configuration of the Polypeptide Backbone and Aggregation of Aβ. (a) The Aβ1-42 dimer obtained by modelling studies based on the SAXS data for the stoichiometric Aβ1-42 complexes with 8-hydroxyquinolines [200]; (b) The FPi plot shows the anticipated ‘strand’ configurations in the Aβ homodimer at pH 5-6 i.e. under the conditions that accelerate fibrillization (light blue curve H+/E−, blue curve H+/E0) [203,204]; (c) The antiparallel coiled coil as a model of Aβ dimer structure: the favoured antiparallel dimerization of Aβ in aqueous solutions matches the CHC and C-terminal segments that both adopt either the C7eq or C5 conformations. The antiparallel assembly could in addition be stabilized by H-bonding between the segments of consecutive ‘turns’ V24-G37 which may adopt the C5* fold in the dimer. The intermolecular residue contacts implied by this model are observed in some Aβ aggregates as shown in the insert [201]. By analogy to the two-stranded antiparallel β-sheet of inteins, cf. Fig 20, the antiparallel Aβ dimer is expected to fold into a left-handed coiled-coil, shown in the diagram with a left-handed superhelical twist; (d) The parallel coiled coil as a model of Aβ dimer structure: the favoured parallel dimerization of Aβ in aqueous solutions would match the CHC and ‘turns’ segments, the C7eq and C5* folds respectively, in both combinations. This mode of assembly yields out-of-register parallel β-sheets expected to fold with ease into parallel β-barrels. The intermolecular residue contacts implied by this model, e.g. F19 vs. I31 or L34, are in fact observed in some Aβ oligomers and aggregates [202]. However, neither parallel dimer nor parallel barrel are likely to form and persist in absence of a stabilizing molecular ‘template’.
Fig 23.
A model for in vitro dimerization of Aβ peptides: Effects of concentration, small-molecule modulators, and surface/interface support.
Formation of the dimer described in Fig 22B is contingent on the ‘unfolding’ of the collapsed-coil ensemble of Aβ. This transition will be facilitated by transferring the protein from an aqueous solution to a less polar environment which drives the N-terminal half of Aβ into a helical conformation. Such a transfer can be achieved in several ways: (A) If Aβ concentration in an aqueous buffer is sufficiently high, c>c*, the protein initially forms micelle-like aggregates [229–231]. The protein is thus buried in a low-permittivity folding basin and its N-terminal half adopts a helical conformation which ‘unwinds’ the collapsed coil. (B) If Aβ concentration is too low to generate pseudomicellar aggregates, c<c*, dimerization may be catalysed by the detergents and detergent-like amphipathic co-solutes [236–238]. E.g. SDS at submicellar concentrations is shown to form Aβ co-aggregates [239] in which protein’s N-termini are assembled in the center of the aggregate while the C-terminal chain segments protrude into solution. On the other hand, however, small-molecule co-solutes may also stabilize the collapsed-coil ensemble or the helical conformer of Aβ and thereby prevent dimerization [240–246]. (C) Binding of Aβ in a water/micelle or water/lipid membrane interface transfers the protein from an aqueous buffer into a less polar environment. The expected conformational transition is well documented, cf. Fig 22A(a) and 22A(b) [176,177,181–184], and may well contribute to the catalysis of polymerization by membranes and lipid rafts [247–254]. (D) (a) The (S)-cysteine can bring together two Aβ molecules via three-point binding of Asp-1, in spite of a degree of steric strain in either chelation mode; (b) The (R)-cysteine can tightly bind one Aβ molecule in a complex free of strain, but bringing in the second Aβ molecule is impossible due to prohibitive steric hindrance; (c) Thus, the (S)-cysteine would promote formation and release of the Aβ↑Aβ↓ dimer and therefore accelerate polymerization (the blue curve in the insert), while the (R)-cysteine would immobilize isolated Aβ molecules on the graphene surface and therefore slow down polymerization (the red curve in the insert).
Fig 24.
A model for nucleated polymerization of Alzheimer’s Aβ proteins.
(A) Domain swapping: Paranuclei and fibrils comprising parallel β-sheets. (a) The mechanism of conversion of the Aβ collapsed coils into out-of-register antiparallel dimers via split intein-like mechanism of molecular recognition, (1) at the Aβ concentration greater than the critical micelle concentration c > c*, and (2) at the Aβ concentration c < c*, in the presence of submicellar concentrations of SDS; (b) The staggered antiparallel Aβ dimer as the left-handed coiled-coil that has in addition left-handed superhelical twist, and the Aβ tetramer obtained via antiparallel association of the ‘free’ N-terminal segments (domain swapping); (c) Further aggregation via domain swapping yields a disk-shaped hexamer—paranucleus [204,264–268]. The circular complex places two dimers on top of each other. The characteristic trapezoid appearance of paranuclei in high-resolution AFM images [266], see the insert, appears to be consistent with the wedge-like shape. The strands stacked on top of each other are parallel; (d) The circular hexamer complex may also be stabilized by the edge-to-edge H-bonding within a ‘jelly-roll’-like structure which may convert into a 6-stranded antiparallel β barrel; (e) The limiting modes of stacking of the paranuclei which yield either tubular (Aβ amyloid pore [271]) or annular aggregates (Aβ nanoglobules [272]). The high-resolution AFM image of the initial stages of aggregation of the paranuclei shows stacking of disk-shaped hexamers and formation of a ring structure (red arrow). Catalysis of fibrillization by the intercalating cations and anions e.g. methylene blue, calmidazolium chloride, orcein-related O4 [276–278] suggests that conformational conversion of the antiparallel sheets β↑β’↓ and β”↑β”‘↓ of the paranuclei into parallel cross-β structure occurs in such stacks; (f) Morphological diversity of polymerization on mica support [42] appears to reflect two modes of paranuclei aggregation, and so does the structure of protofibril ‘on-path’ intermediates of fibrillization in solution [279–282]; (g) The cryoEM-derived structures of Aβ fibrils shows the expected assembly of two protofilaments comprising parallel cross-β sheets and aligned in the antiparallel fashion [283,284]; (h) Mechanism of fibril-surface catalysis of secondary nucleation [43,285,286]: formation of the Aβ dimers is facilitated by the binding of Aβ monomers along the fibril edges via antiparallel interlocking of the N-terminal segments; (i) The trimeric fibril which may be formed by remodeling of the fibril shown in panel (g) [288]. (B) Edge-to-edge assembly: Off-pathway oligomers, self-replicating non-fibrillar aggregates and fibrils comprising antiparallel β-sheets. (a) The Aβ trimer obtained by the edge-to-edge assembly. In contrast to the dimer, the trimer cannot fold into a coiled coil [154]; (b) Morphology of polymerization of Aβ on graphite [41] is consistent with the model of edge-to-edge assembly and FP-directed molecular recognition, see the text. The edge-to-edge Aβ tetramer cannot fold into a coiled coil either [154] but its polymerization via domain swapping may produce high-order oligomers that retain the staggered antiparallel alignment of strands [261,289–291]. By a combination of twist, bend and rise, such oligomers can fold into ‘jelly-roll’-like cylindrical structures; (c) Reversal of domain swapping and fragmentation within the ‘jelly-roll’-like folds of higher-order oligomers can yield fibrils comprising antiparallel cross-β structure [292,293]; (d) The alternative conversion of the ‘jelly-roll’-like cylinder involves reversal of domain swapping and the edge-to-edge closing of a β barrel. The homotrimer of tetramers can form in this way the 12-stranded antiparallel barrel which we believe represents the structure of the neuropathological Aβ globulomer [258,294] also isolated as the brain Aβ*56 oligomer [262,295,296]; (e) The 12-stranded antiparallel barrel can ‘capture’ Aβ dimers and tetramers via antiparallel interlocking of the ‘free’ N-terminal segments. This is likely the mechanism of self-replication of the off-pathway Aβ oligomers as shown in the diagram [260,297–299]. Note that the low-permittivity environment of the interior of a larger aggregate may promote strand→helix conversion in reversal of the initial stages of dimerization of Aβ [301]; (f) The alternative edge-to-edge aggregation of Aβ, the staggered (out-of-register) parallel assembly; (g) The 12-stranded antiparallel barrel may also ‘capture’ Aβ monomers that form a staggered parallel assembly and fold into 6-stranded out-of-register parallel barrel. This type of aggregation would account for the formation of the off-pathway Aβ oligomers 150±30 kDa [201,202] and the NU4-reactive Aβ oligomer ~80 kDa [300] (30-mer and 18-mer, respectively), and for the solid state NMR evidence of both antiparallel and parallel intermolecular contacts in the 150±30 kDa oligomers [201,202].
Fig 25.
Morphology of Aβ aggregation on the NIBC monolayers on gold: The combined effects of cysteine chirality and wedge-like shape of Aβ paranuclei.
(a) The putative complex of the Aβ paranucleus on the monolayer surface involves backbone H-bonding of the extended H14-K16 segment to the isobutyryl carbonyls of N-isobutyrylcysteines [41]. The positively charged side chains of His-14 and Lys-16 extend in the same direction. (b) The topology of the self-assembled cysteine monolayer on gold [302]: The monolayer comprises pairs of long files of N-isobutyrylcysteines. (c) A model of the surface of L-NIBC monolayer [302], H14 and K16 side chain interactions with the L-NIBC isobutyryl carbonyls, and the putative tight packing of two Aβ paranuclei. The binding of the H14 side chain to the isobutyryl C = O of the neighbouring row of cysteines is unimpeded; the K16 side chain encounters an impediment but its length and flexibility make the binding possible. Thus, the tight packing of paranuclei is achieved via parallel alignment of the H14-K16 segments which directs all the complexed paranuclei to ‘wedge out’ in one direction i.e. promotes annular stacking and formation of large ring structures. (d) A model of the surface of D-NIBC monolayer [302], H14 and K16 side chain interactions with the D-NIBC isobutyryl carbonyls, and the putative tight packing of two Aβ paranuclei. Here the H14 side chain cannot bind to the isobutyryl C = O of the neighbouring row of cysteines; it encounters an impediment and lacks flexibility and length needed to overcome the hindrance. Thus, the tight packing on this surface is achieved via antiparallel alignment of the H14-K16 segments which directs the neighbouring paranuclei to ‘wedge out’ in opposite directions and thereby promotes tubular stacking and formation of elongated bar structures.
Fig 26.
Electronic configuration of the polypeptide backbone and molecular recognition in formation of β structure: Mechanism of aggregation of tau, α-synuclein, human prion hPrP and HET-s PFD.
(A) Tau proteins: (a) The FPi plot and secondary structure of the 46-residue fragment of Tau(267–312) bound to microtubules PDB ID 2mz7 [307]; (b) The FPi profile of the repeat domain construct K19 (R1-R3R4) at pH 7 is similar to the FPi profile of Aβ at pH 5. The FPi-based assignment of secondary structure is consistent with the solid-state NMR data on the K19 amyloid fibrils [310]. Note that at pH 5 the V337-E342 segment (VEVKSE) has α-helix propensity rather than C5 propensity required to stabilize the coiled-coil dimer, and K19 actually does not aggregate at low pH [310]. Nucleated polymerization, assumed to be the main pathway of fibrillization of tau [311–314], may involve disk-shaped hexameric intermediate analogical to the paranucleus of Aβ; (c) The annular assembly of the disk-shaped paranuclei and the subsequent conformational conversion (antiparallel→parallel β-structure) would yield fibrils consisting of two protofilaments which comprise parallel cross-β sheets in the antiparallel alignment. The solid-state NMR structure of β-sheet core of tau paired helical filaments confirms the expected arrangement [315]. (B) α-Synuclein: (a) The FPi plot shows secondary structure assignment for a putative tetramer (colour shading reflects helix propensity based on solution NMR data) [318,319], but the existence of such a tetramer is questioned [320,321]; (b) The micelle-bound monomer is helical PDB ID 1xq8 [322,323]; (c) The FPi profile of the ~35–40 residue-long amyloidogenic region of human α-synuclein which incorporates the NAC sequence essential to fibrillization of this protein. The pattern of backbone polarization corresponds to the C7eq-C5-C5*-C5 sequence of the anticipated ‘strand’ configurations. Thus, like Aβ and tau, α-synuclein is expected to form the antiparallel, out-of-register, coiled-coil dimer shown in the diagram; (d) The tubular (amyloid pore) [271,324,325] and annular (cf. the insert, diameter ~ 120 nm) [324,326] aggregates of α-synuclein may be formed by the stacking of the wedge-like disk-shaped hexamers analogical to the paranuclei of Aβ. Persistent oligomers of MW ~80 kDa and circular appearance (cf. the insert, diameter ~10 nm) are indeed observed during the polymerization in the presence of heme [326]; (e) Conformational conversion (antiparallel→parallel β structure) within the annular stacks of the paranucleus-like hexamers would yield fibrils consisting of two protofilaments which comprise parallel cross-β sheets in the antiparallel alignment. A recently proposed model of α-synuclein protofibril is consistent with this expectation [332]. (C) Prion proteins (PrP), conversion to parallel cross-β structure: (a) The FPi plot for the recombinant polypeptide hPrP23-144 (a model for Y145Stop variant of human prion, the mutation eliminates the entire α-helical region of hPrP) which undergoes a spontaneous conversion from a monomeric disordered state to the in-register parallel cross-β fibrillar form [335–337]. Ignoring the palindromic segment, see the text, the anticipated β structure configuration of the amyloidogenic region is the sequence C7eq-C5-C5*-C5 (β0-β1-β2-β3) by analogy to Aβ, tau, and α-synuclein. Thus, this region may also form the antiparallel, out-of-register, coiled-coil dimers which assemble via domain swapping into superhelical oligomers and yield fibrils comprising sheets of parallel cross-β structure; (b) The FPi vs. ΔFPi-1→i+1 plots for the native helices of hPrP at high and low pH. The plots suggest that the helix α1 is destabilized by reduction of pH while the helices α2 and α3 are becoming stable as the compact structure unravels at low pH; (c) The putative pathway of assembly and structure of the octameric paranucleus obtained at low pH [338–348]. The insert shows hPrP aggregates [349] which could be formed by tubular stacking of such octamers or similar higher-order oligomers; (d) The single-sheet parallel in-register cross-β structure of PrP [350,351]. (D) Prion proteins (PrP), conversion to β-solenoid fibrils. (a) The structure of fibrils of GPI-anchorless PrP 27–30 [352,353]. The protofilaments are formed by stacking four-rung left-handed solenoids that include nearly entire length of the protein; (b) The FPi plot for hPrP (omitting most of the N-terminal domain) and the proposed four-rung solenoid structure. The assignment of the strands marked by the green outlines follows the two-rung model [354] proposed as a revision of the original model of the left-handed β helix [355]; the strands β7 through β12 are assigned based on the FPi minima indicating the ‘C5 strand’ propensity. The proposed structure places Cys179 and Cys214 in register (orange arrows) and all Pro residues (brown arrows) in turns and loops. This structure is also consistent with the anticipated β structure configuration of the amyloidogenic region which can be described as the sequence of two ‘asymmetrically’ complementary arrays of alternant incipient strands: C5-C7eq-C5* followed by C7eq-C5-C7eq (β1-β2-β3 followed by β4-β5-β6 i.e. including the palindromic segment); (c) The model of self-propagation of the infectious prion: the head-to-tail domain swapping between the native conformer and the β solenoid conformer that involves interlocking of the βΑ and βΩ strands (marked by red outlines in FPi plot) via assembly of the parallel β sheet C7eq↓C5↓. (E) HET-s prion forming domain. (a) The superposed FPi plots for HET-s prion forming domains from P. anserina and F. graminearum, and the two-rung left-handed β solenoid fold that the domain from P. anserina adopts in amyloid fibrils [356–358]. The anticipated β structure configuration of the P. anserina domain is the sequence of two ‘asymmetrically’ complementary arrays of alternant incipient strands: C7eq-C5-C7eq-C5 followed by C5-C7eq-C5-C7eq (β1-β1'-β2-β3 followed by β4-β4'-β5-β6); (b) The superposed FPi plots for the HET-s prion forming domain from P. anserina at low pH which induces formation of a generic amyloid fold [363–367], and the M8 variant of this domain that forms toxic amyloids comprising antiparallel β structure [368–370].