Structure and conformation of linear peptides VII.

The tripeptide, L-valyl-glycyl-glycine (C₉H₁₇N₃O₄, molecular weight = 231), crystallizes in the monoclinic space group C2, with a = 24.058(3)Å, b = 4.801(1), c = 10.623(2), β = 110.02(1)° and Z = 4. The structure was determined by direct methods and refined to a final R-index of 0.043 for 830 reflections (sinθ/Λ ≤ 0.53 A^-1) with I> 1.0s?. The molecule exists as a zwitterion. The peptide units are trans and one of them shows significant deviations from planarity (Δω₂ = 9.3°). The peptide chain repeat distance, 1C^α-3Cα, is 7.23Å and the molecule displays a highly extended conformation with backbone torsion angles of ψ₁ = 123.1°, ω₁ = - 179.4°, ø₂ = - 155.1°, ψ;₂ = 154.7°, ω₂ = 170.7°, ø₃ = - 146.6° and ψ₃ = 180.0°. For the valyl side chain, χ₁₁ = - 52.5°, χ₁₂ = 174.2°. The packing involves hydrogen-bonded interactions between successive molecules related by the β-translation of the lattice, giving rise to the familiar parallel β-sheet structure which appears to be the most extended one observed to date.     

Structure and conformation of linear peptides

The crystal structure of t-Boc-glycyl-L-phenylalanine (C₁₄H₂₂N₂O₅, molecular weight = 298) has been determined. Crystals are monoclinic, space group P2₁, with a = 7.599(1)Å, b = 9.576(2), c = 12.841(2), β = 97.21(1)°, Z = 2, D_m = 1.149, D° = 1.168 g · cm^-3. Trial structure was obtained by direct methods and refined to a final R-index of 0.064 for 1465 reflections with I> 1s?. The peptide unit is trans planar and is nearly perpendicular to the plane containing the urethane moiety. The plane of the carboxyl group makes a dihedral angle of 16.0° with the peptide unit. The backbone torison angles are ω₀ = - 176.9°, ø₁ = - 88.0°, ψ₁ = - 14.5°, ω1 = 176.4°, ø₂ = - 164.7° and ψ2 = 170.3°. The phenylalanine side chain conformation is represented by the torsion angles χ₁ = 52.0°, χ₂ = 85.8°.     

Structure and conformation of linear peptides. X. Structure of glycyl-glycyl-L-phenylalanine hydrochloride

The crystal structure of a tripeptide, glycyl-glycyl-L-phenylalanine HCl (C₁₃H₁₈N₃O₄ ± HCl, molecular weight = 316.5) has been determined. The crystals are orthorhombic, space group P2₁2₁2₁, with a = 4.877 (2) Å, b = 9.956(3), c = 32.690(5) and Z = 4. The final R-index is 0.043 for 1325 reflections (sinØ/Λ ± 0.55 Å^-1) with I > 2.0 s? (I). The N-terminal of the molecule is protonated and the C-terminal exists in an un-ionised state. The peptide units are trans and one of them shows significant deviations from planarity (¶Δω₁¶ = 11.3°). The peptide backbone is folded with torsion angles of: ø₁ = 165.5°, ω₁ = — 168.7°, ø₂ = 63.6°, ø₂ = — 153.6°, ω₂ = 176.5°, ø₃ = — 72.2° and Φ₃ = 166.5°. For the side chain of phenylalanine, X₁ = — 79.5° and X₂ = 86.8°. An intramolecular water bridge links the two ends of the molecule.     

Crystal structure of tert.-butyloxycarbonyl-L-prolyl-D-alanyl-D-alanyl-N-methylamide Dimeric β-sheet formation

The crystal structure of the tripeptide t-Boc-L-Pro-D-Ala-D-Ala-NHCH₃, monohydrate, (C₁₇H₃₀N₄O₅·H₂O, molecular weight = 404.44) has been determined by single crystal X-ray diffraction. The crystals are mono-clinic, space group P2₁, a = 9.2585(4), b = 9.3541(5). c = 12.4529(4) Å, β= 96.449(3)°, Z = 2. The peptide units are in the trans and the tBoc-Pro bond in the cis orientation. The first and third peptide units show significant deviations from planarity (Δω=5.2° and Δω=3.7°, respectively). The backbone torsion angles are: φ¹, = -60°, ψ_1/= 143.3°, ω₁= -174.8°, φ₂= 148.4°, ψ₂= -143.1°, ω₂= -179.7°, φ₃= 151.4°, ψ₃= -151.9°, ω₃= -176.3°. The pyrrolidine ring of the proline residue adopts the C₂— C^γ conformation. The molecular packing gives rise to an antiparallel β-sheet structure formed of dimeric repeating units of the peptide. The surface of the dimeric β-sheet is hydrophobic. Water molecules are found systematically at the edges of the sheets interacting with the urethane oxygen and terminal amino groups. Surface catalysis of an L-Ala to D-Ala epimerization process by water molecules adsorbed on to an incipient β-sheet is suggested as a mechanism whereby crystals of the title peptide were obtained from a solution of tBoc-Pro-D-Ala-Ala-NHCH₃.     

Cystine peptides Antiparallel β-sheet conformation of the cyclic biscystine pep tide [Boc-Cys-Ala-Cys-NHCH3]2

The crystal structure analysis of the cyclic biscystine peptide [Boc-Cys¹-Ala²-Cys³-NHCH₃]₂ with two disulfide bridges confirms the antiparallel β-sheet conformation for the molecule as proposed for the conformation in solution. The molecule has exact twofold rotation symmetry. The 22-membered ring contains two transannular NH ? OC hydrogen bonds and two additional NH ? OC bonds are formed at both ends of the molecule between the terminal (CH₃)₃COCO and NHCH₃ groups. The antiparallel peptide strands are distorted from a regularly pleated sheet, caused mainly by the L-Ala residue in which φ=– 155° and ψ= 162°. In the disulfide bridge C^α (1)-C^β (1)-S(1)-(3′)-C^β(3′)-C^α(3′), S—S = 2.030 Å, angles C^β SS = 107° and 105°, and the torsional angles are –49, –104, +99, –81, –61°, respectively. The biscystine peptide crystallizes in space group C2 with a = 14.555(2) Å, b = 10.854(2) Å, c = 16.512(2)Å, and β= 101.34(1) with one-half formula unit of C₃₀H₅₂N₈O₁₀S₄· 2(CH₃)₂SO per asymmetric unit. Least-squares refinement of 1375 reflections observed with |F| > 3σ(F) yielded an R factor of 7.2%.     

Structure and conformation of linear peptides XII. Structure of tryptophanyl-glycyl-glycine dihydrate

The crystal structure of a tripeptide, tryptophanyl-glycyl-glycine dihydrate (C₁₅H₁₈N₄O₄·2H₂O, molecular weight = 354) has been determined. The crystals are orthorhombic, space group P2₁2₁2₁ with a= 7.875 (1) A,b= 9.009(1), c= 24.307(1) and Z = 4. The final R-index is 0.058 for 1488 reflections ((sin θ/λ≤ 0.6 A^?1) with I < 2σ(I). The molecule exists as a zwitterion, with terminal NH⁺₃ and COO^? groups. The peptide units are trans and nearly perpendicular to the plane of the carboxyl group. The backbone torsion angles are: ψ₁= 132.7°, ω₁= 174.2°, φ₂ 88.2°, ψ= 8.6°, ω₂ - 179.8°, φ= - 85.2°, ψ₃₁, = - 178.1°, ψ₃₂ 5.0°. For the sidechain of tryptophan, χ₁= - 171.6°, χ₂ 101.0°.     

Structure and conformation of linear peptides. IX. Structure of l-tyrosyl-l-phenylalanine

The dipeptide, l -tyrosyl-l -phenylalanine (C₁₈H₂₀N₂O₄, molecular weight = 346) crystallizes as a monohydrate in the orthorhombic system, space group P2₁2₁2₁ with a = 5.744(2), b = 8.284(2), c = 35.518(6)Å, Z = 4. The structure was solved by direct methods and refined to a final R-index of 0.060. The peptide unit is trans and planar, and makes a dihedral angle of 93° with the plane of the carboxyl group. The backbone torsion angles are given by: ø₁ = 164.7°, ω₁ = 177.0°, φ₂ = – 70.1°, ø₂ = 146.6°. The values of the side-chain torsion angles (χ₁, χ₂) are (47.3°, 79.9°) for tyrosine and (– 75.1°, 75.9°) for phenylalanine. The planes of the two (side-chain) aromatic rings make a dihedral angle of 142.6° and their centres are separated by 9.3 Å.     

Structure and conformation of linear peptides

The crystal structure of a dipeptide tert-butyloxycarbonyl-l -alanylglycine monohydrate (C₁₀H₁₈N₂O₅·H₂O), molecular weight 264, has been determined. The crystals are monoclinic, space group P2₁, with a= 10.767(1), b= 6.317(1), c= 10.981(2) Å, β= 109.15(2)°, and Z= 2, D_c= 1.24 g cm^?3. The structure was solved by direct methods and refined to 3 final R-index of 0.045 for 856 reflections (sin θ/λ < 0.55 Å^?1) with I > 2 σ. The N-terminus of the molecule blocked with the t-Boc group is uncharged and the C-terminus exists in an unionized state. The peptide unit is trans and shows slight deviations from planarity. (Δω= 3.1°). The peptide backbone is folded, with torsion angles of φ₁= -76.0(5), ψ₁= 164.3(4), ω₁= 176.9(5), φ₂= 116.1(5), ψ₂₁= - 2.8(7) and ψ₂₂= 177.8(4)°. The conformation about the urethane bond (C5–N1) is trans. The urethane group is essentially planar. The conformation of the boc group is trans–trans.     

Design of peptides: synthesis,crystal structure and molecular conformation of N-Boc-L-Val-δPhe-L-Ile-OCH3

The dehydro-peptide Boc-L-Val-δPhe-L-Ile-OCH₃ was synthesized by the azlactone method in the solution phase. The peptide crystallized from a methanol/dimethyl sulfoxide (95:5) mixture in space group P6₁, with a=b= 15.312(1), c= 22.164(5) Å. The structure was determined by direct methods and refined to an R value of 0.098 for 1589 observed reflections [I≥ 1.5 σ(I)]. The peptide adopts an S-shaped conformation with torsion angles: ø₁=-127(1), ψ₁= -44(1), ø₂, = 67(1), ψ₂, = 37(1), ø₃,=-82(1)°. The side-chain torsion angles in δPhe of X¹₂= 1(2), X^2.1₂= 7(2) and X_2.22 = 177(1)° indicate that the δPhe residue is essentially planar. In valyl residue the two side-chain torsion angles are X¹₁= -65(1) and X²₁= 177(1), whereas the torsion angles in Ile are X^1,1₃= 72(2), X^1,2₃= -159(2), X²₃= 150(2)°. This is the first peptide which does not adopt a folded conformation for a sequence with a δPhe at the (i+ 2) position. The molecular packing in the crystals is stabilized by several hydrogen bonds: N₁-H₁?O₁’= 2.77(1) Å, N₂-H₂?O₁’= 2.95(1) Å, N₃-H₃?O₂=2.85(1) Å and a possible weak interaction N₂-H₂?O₁’3.29(1) Å- within the columns of molecules along the c-axis and van der Waals forces between the columns. © Munksgaard 1996.     

Conformation and hydrogen bonding of N-formylpeptides: crystal and molecular structure of N-formyl-l-alanyl-l-aspartic acid†

Crystals of N-formyl-l -alanyl-l -aspartic acid (C₈H₁₁N₂O₆) grown from aqueous methanol solution are orthorhombic, space group, P2₁2₁2₁ with cell parameters at 294 K of a = 13.619(2), b = 8.567(2), c = 9.583(3)Å, V = 1118.1ų, M.W. = 232.2, Z = 4, D_m= 1.38g/cm³ and D_x= 1.378g/cm³. The crystal structure was solved by the application of direct methods and refined to an R value of 0.075 for 1244 reflections with I ≥ 3σ collected on a CAD-4 diffractometer. The structure contains two short inter-molecular hydrogen bonds: (i) between the C-terminal carboxyl OH and the N-acyl oxygen (2.624(3)Å), a characteristic feature found in many N-acyl peptides and (ii) between the aspartic carboxyl OH and the peptide oxygen OP1 (2.623(3)Å). The peptide is nonplanar (ω= 165.5(6)°). The molecule takes up a folded conformation in contrast to N-formyl peptides which form extended β-sheets; the values of ø₁, Ψ₁, ø₂, Ψ¹₂, and Ψ²₂ are, respectively –65.7(6), 152.0(5), –107.2(5), 30.9(5), and –150.3(6). The aspartic acid side chain conformation is g^? with χ¹= 73.1(5). The formyl group, as expected, is transplanar [OF-CF-N1-CA1 = -4.0(8)°]. The presence of the short O–H … O hydrogen bond emerges as a structural feature common to this peptide and several other N-formyl peptides. There are no C-H … O hydrogen bonds in this structure.     

Structure of cyclic peptides: the crystal and solution conformation of cyclo(Phe-Phe-Aib-Leu-Pro)

A solid-state and solution conformation analyses of the cyclopentapeptide cyclo(Phe-Phe-Aib-Leu-Pro) has been carried out by X-ray diffraction and nuclear magnetic resonance techniques. The structure of the hexagonal crystals, grown from a methanol solution [a=b= 16.530(4) Å, c= 21.356(9) Å, space group P6₅, Z = 6], shows the presence of one intramolecular N-H?O=C hydrogen bond with the formation of a γ-turn (C₇). The Aib³ residue, at the center of the γ-turn, presents unexpected values of the torsion angles [φ= 70.5° and ψ= -73.8°], which have been observed only once before for this helicogenic residue. A cis peptide bond occurs between Leu⁴ and Pro⁵; all other peptide bonds are trans. The overall conformation for the cyclopentapeptide with one cis-peptide bond on one side and an intramolecular γ-turn on the opposite side results in an equatorial topology of the side-chains of the Phe¹, Phe² and Leu⁴ residues. Indeed, the C^α-C^βand C^β-C^γ bonds of these residues lie approximately in the mean plane of the cyclic ring system. The structure is compared with data in the literature on cyclic pentapeptides. In addition the Pro-Phe-Phe moiety shows a conformation similar to that observed in other larger cyclic bioactive peptides, which indicates a reduced number of conformations for this sequence. The solution study was carried out in three different solvent systems: chloroform, acetonitrile and methanol in the temperature interval 220–300 K. In all three solvents the room temperature spectra show that the peptide is conformationally nonhomogeneous. In acetonitrile at low temperatures it is possible to reduce the conformational equilibrium to two predominant conformers which differ for the cis-trans isomerism of the Leu⁴-Pro⁵ peptide bond.     

Crystal and molecular structure of l-valyl-l-lysine hydrochloride

l -Valyl-l -lysine hydrochloride, C₁₁N₃O₃H₂₃ HCl, crystallizes in the monoclinic space group P2, with a = 5.438(5), b = 14.188(5), c = 9.521(5) Å, β= 95.38(2)° and Z = 2. The crystal structure, solved by direct methods, refined to R = 0.036, using full matrix least-squares method. The peptide exists in a zwitterionic form, with the N atom of the lysine side-chain protonated. The two γ-carbons of the valine side-chain have positional disorder, giving rise to two conformations, χ¹¹₁= -67.3 and 65.9°, one of which (65.9°) is sterically less favourable and has been found to be less popular amongst residues branching at β-C. The lysine side-chain has the geometry of g^? tgt, not seen in crystal structures of the dipeptides reported so far. Interestingly, χ³₂ (63.6°) of lysine side-chain has a gauche⁺ conformation unlike in most of the other structures, where it is trans. The neighbouring peptide molecules are hydrogen bonded in a head-to-tail fashion, a rather uncommon interaction in lysine peptide structures. The structure shows considerable similarity with that of l -Lys-l -Val HO in conformational angles and H-bond interactions [4].     

Structure of N-Boc-L-Pro-dehydro-Leu-NHCH3

The peptide N-Boc-L-Pro-dehydro-Leu-NHCH₃ was synthesized to examine the nature of β-bend as a result of dehydro-Leu in the sequence. The peptide crystallizes from methanol-water mixture at 4° in orthorhombic space group P22₁2₁ with a = 5.726(1)Å, b = 14.989(4) Å, c = 24.131(9) Å, V = 2071(1) ų, Z = 4, dm = 1.064(5)gcm^-3 and dc = 1.0886(5)gcm^-3. The structure was solved by direct methods using SHELXS 86 and it was refined by full-matrix least-squares procedure to an R value of 0.059 for 957 observed reflections. The peptide is found to adopt a β-bend type II conformation with φ₁=– 51(1)°, ψ₁= 133(1)°, φ₂= 74(2)° and ψ₂= 8(2)°. The β-bend is stabilized by an intra-chain hydrogen bond between the carbonyl oxygen of ith residue and the NH of (i + 3)th residue. The five-membered pyrrolidine ring of Pro-residue adopts an ideal C^γ-exo conformation with torsion angles of χ₁¹=– 25(1)°, χ₁²= 38(1)°, χ₂=– 34(1)°, χ₁⁴= 20(1)° and χ₁⁰= 2(1)°. The side chain conformation angles of dehydro-Leu residue are χ₂= 12(2)°, χ₂^2.1=– 112(2)° and χ₂^2.2= 136(2)°. The crystal structure is stabilized by a network of hydrogen bonds and van der Waals interactions.     

Solid state and solution conformation of Boc-L-Met-Aib-L-Phe-OMe

The conformation of the peptide Boc-L-Met-Aib-L-Phe-OMe has been studied in the solid state and solution by X-ray diffraction and ¹H n.m.r., respectively. The peptide differs only in the N-terminal protecting group from the biologically active chemotactic peptide analog formyl-L-Met-Aib-L-Phe-OMe. The molecules adopt a type-II ß-turn in the solid state with Met and Aib as the corner residues (øMet =- 51.8^o, øMet = 139.5^o, øAib = 58.1^o, øAib = 37.0^o). A single, weak 4 -> 1 intramolecular hydrogen bond is observed between the Boc CO and Phe NH groups (N—O 3.25 Å, N-H—O 128.4^o). ¹Hn.m.r. studies, using solvent and temperature dependencies of NH chemical shifts and paramagneti radical induced line broadening of NH resonances, suggest that the Phe NH is solvent shielded in CDCI₃ and (CD₃)₂SO. Nuclear Overhauser effects observed between Met Cα H and Aib NH protons provide evidence of the occurrence of Met-Aib type-II ß-turns in these solvents.     

The crystal structure of Boc-Pro-Val-Gly-NH2, with a remark on the conformation of the valyl residues in peptides

The crystal structure of Boc-Pro-Val-Gly-NH₂ has been determined: monoclinic; P2₁; a = 9.331 (3) Å, b = 9.532 (4), c = 23.080 (9), β= 91.33 (3)R, Z = 4; R = 0.053 for 3400 reflections with ˙Fo˙,>α(Fo). There are two independent but very similar molecules in the crystal. The peptide main chains are in an extended form, and packed in two kinds of antiparallel β sheets, the (φ, Φ) angles of the central Val residues are (-156°, 146°) and (-139°, 155°), and the mean length of the N- H . 0 hydrogen bonds in the sheets is 2.965 Å. A detailed study of the conformations of the Val residues in oligopeptide crystals shows that the preferred conformation of Val in peptides is: the (φ, Φ) angles close to those of the antiparallel β sheet, and C^γ1 and C^γ2, against N with respect to the C^α– C^β bond, at either (trans, gauche) or (-gauche, gauche). The mean π(NC^αC') angle of such Val residues is 107.9(9)°. A twisting in the β sheets is also discussed.     

Structure and conformation of linear peptides

L-tyrosyl-L-tyrosine crystallizes as a dihydrate in the orthorhombic system, space group C222₁, with a = 12.105(2), b = 12.789(2), c = 24.492(3) Å, Z = 8. The structure was solved by direct methods and refined to a final R-value of 0.059 for 1740 observed reflections. The molecule exists as a zwitterion, the peptide unit is trans planar, and the backbone torsion angles correspond to an extended conformation, with e₁ = 149.4°, e₂ = - 161.2°, e₂ = 158.3°. The values of the side-chain torsion angles (χ₁, χ₂) are (- 58.8°, - 63.1°) for the first tyrosine and (- 171.7°, - 116.5°) for the second. The planes of the aromatic rings are nearly parallel (dihedral angle of 6.1°), and their centers are separated by 10.9 Å. The carboxyl plane forms a dihedral angle of 23.8° with the plane of the peptide bond.     

Peptide crystal growth via vapor diffusion

The structure of a dihydrated form of glycyl-L-tyrosyl-L-alanine (GYA) has been determined as part of a series of peptide structural investigations and development of microscale vapor diffusion experiments for peptide crystal growth. Crystals were grown by the hanging-drop method against sodium acetate. The tripeptide is a zwitterion in the crystal, adopting an extended conformation through glycine, a nearly perpendicular bend attyrosine and a reverse turn for the C-terminal carboxylate. Principal backbone torsion angles are ψ₁ 175(1)°, ω₂ 173(1)°, φ₂ -119(1)°, ψ₂ 120(1)°, ω₃3 172(1)°, φ₃ -73(1)°,ψ₃₁ -9(1)°, ψ₃₂ 171(1)°. The tyrosyl side chain adopts an unusual orientation (χ^1/2= -86(1)°). The relationship of the GYA.2H₂O structure to GYA sequences in proteins is examined, particularly as regards its helix-forming potential. Crystal data: C₁₄H₁₉N₃O₄.2H₂O, Mr = 345.36, orthorhombic, P2₁2₁2₁, a = 4.810 (4), b= 11.400(7), c = 30.162(23)Å, V=1653.8(24)Å^?3, Z = 4, Dx= 1.387 Mgm^?3, λ(CuK_α^?)= 1.540 Åμ= 9.053 mm^?1, F(000) = 736, T = 199K, R = 0.041 for 1458 observations with I ≥ 3σ(I).     

Conformation and crystal structure of L-prolyl-L-glutamic acid dihydrate

The crystal structure of the dipeptide L-prolyl-L-glutamic acid dihydrate, L-Pro-L-Glu · 2H₂O, C₁₀H₂₀O₇N₂, has been determined from three-dimensional X-ray diffractometer data. The dipeptide crystallizes in the space group P2₁ of the monoclinic system with two formula units in a cell of dimensions a= 5.629(2), b= 11.832(5), c= 10.485(4)Å, and β= 103.06(3)°. The structure was solved by direct methods and refined by least squares techniques to a final value of the conventional R-factor (on F) of 0.039 based on 1798 independent intensities with I ≥ 3s?(I). The dipeptide occurs as a zwitterion in the crystal with the pyrrolidine nitrogen atom protonated and the main chain carboxyl group deprotonated. The conformation of the peptide linkage is trans, the ω torsional angle being 173.7°. The pyrrolidine ring adopts the C_s-C^β endo conformation and the conformation of the glutamyl side chain is fully extended. There is considerable intermolecular hydrogen bonding in the crystals.     

Conformation of arginine side chain in a mini peptide. Molecular structure of acetyl-l-arginine-ethylamide

The crystal structure of N-α-acetyl-l -arginine ethylamide perchlorate (molecular formula: C₁₀H₂₁N₅O₂ ± HClO₄) has been determined from X-ray diffraction data. This arginine derivative has the two charged ends substituted by peptide units and thus becomes representative of an arginyl residue in a protein. The crystals are orthorhombic, space group P2₁,2₁,2₁, a = 7.485 (2), b = 28.623 (5), c = 7.261 (3) Å, Z = 4. The structure was solved by direct methods and refined by full matrix least-squares using 559 reflections to an R = 0.052. The molecule shows two planar peptide units with φ and ø values in the β pleated sheet region. The side chain torsion angles are in trans conformation, except the χ₁, angle which is in the gauche(-) region. This observation further illustrates that this is one of the favoured side chain conformations of arginine, together with the all-trans conformation. Symmetric double hydrogen bonds are observed between the guanidinium group and perchlorate anions. The H(N) and oxygen atoms of the amide groups also form hydrogen bonds.     

Crystal structure and conformation of glycyl-glycyl-sarcosine

Crystals of the tripeptide, glycyl-glycyl-sarcosine (C₇H₁₃N₃O₄) from aqueous methanol are orthorhombic, space group Pbcn with cell parameters at 294 K of a = 8.279(1), b = 9.229(4), c = 24.447(5) Å, V = 1868.0 ų, M.W. = 203.2, and Z = 8. The crystal structure was solved and refined using CAD-4 data (1171 reflections ≥ 3σ) to a final R-value of 0.053. The first peptide linkage is trans and planar whereas the second peptide link between Gly and sarcosine is cis and appreciably non-planar (w = 7.4°). The peptide backbone has an extended conformation at the N-terminal part but adopts a polyglycine-II type of conformation at the C-terminal part. The backbone torsion angles are: Ψ₁, =? 173.9, w₁=? 177.8, (φ, Ψ₂) = (-178.8, -170.8), w₂= 7.4, (φ₃, Ψ₃) = (-81.6, 165.6°).