Peptide Plane Research Articles

Crystal structure of deoxygenated limulus polyphemus subunit II hemocyanin at 2.18 Å resolution: Clues for a mechanism for allosteric regulation

The crystal structure of Limulus polyphemus subunit type II hemocyanin in the deoxygenated state has been determined to a resolution of 2.18 A. Phase information for this first structure of a cheliceratan hemocyanin was obtained by molecular replacement using the crustacean hemocyanin structure of Panulirus interruptus. The most striking observation in the Limulus structure is the unexpectedly large distance of 4.6 A between both copper ions in the oxygen-binding site. Each copper has approximate trigonal planar coordination by three histidine N epsilon atoms. No bridging ligand between the copper ions could be detected. Other important new discoveries are (1) the presence of a cis-peptide bond between Glu 309 and Ser 310, with the carbonyl oxygen of the peptide plane hydrogen bonded to the N delta atom of the copper B ligand His 324; (2) localization of a chloride-binding site in the interface between the first and second domain; (3) localization of a putative calcium-binding site in the third domain. Furthermore, comparison of Limulus versus Panulirus hemocyanin revealed considerable tertiary and quaternary rigid body movements, although the overall folds are similar. Within the subunit, the first domain is rotated by about 7.5 degrees with respect to the other two domains, whereas within the hexamer the major movement is a 3.1 degrees rotation of the trimers with respect to each other. The rigid body rotation of the first domain suggests a structural mechanism for the allosteric regulation by chloride ions and probably causes the cooperative transition of the hexamer between low and high oxygen affinity states. In this postulated mechanism, the fully conserved Phe49 is the key residue that couples conformational changes of the dinuclear copper site into movements of the first domain.

NMR order parameter analysis of a peptide plane aligned in a lyotropic liquid crystal

A full order parameter analysis has been carried out on a peptide plane of gramicidin A in aligned phospholipid bilayers. The most ordered molecular axis was determined to be the helical long axis of the molecule, possessing an order parameter of 0·93 ± 0·03 parallel to the bilayer normal, and an axial symmetry of -0·06 ± 0·04.

The crystal structure of 1-(Na-trifluoracetylalanyl)-indoline

Abstract The crystal structure of the title compound, C13H13N2F3O2, (NTFAAI hereafter) has been determined from three-dimensional X-ray diffraction data. The structure is monoclinic, C2, with a = 19.023(5), b = 7.574(2), c = 10.405(2), Å, β = 114.17(2)°, V = 1368(1) Å3 and Z = 4. The structure was solved by direct methods and refined by full-matrix least-squares calculations to a final residual of 0.051 for 1030 observed reflections [I≥3σ(I)]. The molecule comprises an indole ring bound to a trifluoracetyl group via an alanine. Both the six- and five-membered rings are coplanar to a very good approximation, since they form a dihedral angle of 1.6(2) degrees. The trifluorocarbon group is tetrahedrally coordinated with the two carbonyl oxygens located on their peptide plane. All bond distances and angles demonstrate no significant deviations from standard values.

Analysis of Polypeptide Backbone T1 Relaxation Data Using an Experimentally Derived Model

The time scale of internal motion of the Ala 3-Leu 4 peptide linkage plane of gramicidin A in its channel conformation is analyzed by interpreting solid-state 15N T 1 measurements taken at 4.7 and 9.4 T. The T 1 relaxation measurements have been interpreted using a structural model of local motion which has previously been experimentally determined. According to this model, the individual peptide plane motion is a rotational diffusion subject to a harmonic restoring potential about an axis through successive α carbons. The results which best fit the model to the data reported here and to previously determined information about the motions of the gramicidin channel suggest that the correlation time for librations of the Ala 3-Leu 4 peptide linkage is 36 ns. This suggests that the peptide backbone motions of the gramicidin channel may be on the same time scale as the translational motion of a cation in the channel.

Chemical shift and electric field gradient tensors for the amide and carboxyl hydrogens in the model peptide N-acetyl-D,L-valine. Single-crystal deuterium NMR study

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper the authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for amore » proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide plane, is essential. The main purpose of this work is to investigate this relationship for the amide hydrogen CS tensor. The amide hydrogen CS tensor will also provide orientational information for peptide bonds in proteins complementary to that from the nitrogen CS and EFG tensors and the nitrogen-hydrogen heteronuclear dipole-dipole coupling which have been used previously to determine protein structures by solid-state NMR spectroscopy. This information will be particularly valuable because the amide hydrogen CS tensor is not axially symmetric. In addition, the use of the amide hydrogen CS interaction in high-field solid-state NMR experiments will increase the available resolution among peptide sites.« less

Peptide group chemical shift computation

AbstractIt has been found that protein NH protons on top of a peptide group plane experience large upfield conformation shifts. The joint analysis of this effect and other known effects of the peptide group on proton chemical shifts has led to a two‐term empirical expression for peptide group proton chemical shift computation as a function of protein backbone conformation. Both terms are expressed by McConnell's point‐dipole shielding expressions, one referred to an axis perpendicular to the peptide plane and origin in the coordinate centre of the OCN atoms and the other referred to an axis along the carbonyl bond and origin close to the oxygen atom. Values for the two constants have been determined by least‐squares fitting of the C‐α, H and amide NH chemical shifts of the protein ubiquitin. As a cross‐check on the validity of the expression, the C‐α, H and NH shifts of ribonuclease and BPTI (basic pancreatic trypsin inhibitor) have been computed. The general agreement between the observed and computed shifts and the correlation coefficients found (0.72 on average) indicate that the expression accounts for the main physical effects of the protein peptide group on the proton chemical shifts. It is shown that, together with ring current shifts, the expression explains the main characteristics of the C‐α, H and amide NH chemical shifts in proteins.

Solvent effects on the energetics of prolyl peptide bond isomerization

Racemic Ac-Gly-[β,δ-(13)C]Pro-OMe was synthesized, and the kinetics and thermodynamics of the isomerization of its prolyl peptide bond were determined in nine solvents by using NMR and IR spectroscopy. The free energy of activation is 1.3 kcal/mol larger in water than in aprotic solvents, and correlates with the ability of a solvent to donate a hydrogen bond but not with solvent polarity. These results are consistent with conventional pictures of amide resonance, which require transfer of charge between oxygen and nitrogen during isomerization. Similar medium effects may modulate the stability of planar peptide bonds in the active site of peptidyl-prolyl cis-trans isomerases (PPIases) and during the folding, function, or lysis of proteins.

Helix-forming tendencies of amino acids depend on the restrictions of side-chain rotamer conformations: crystal structure of the tripeptide GAI in two crystalline forms.

In our attempts to design crystalline alpha-helical peptides, we synthesized and crystallized GAI (C11H21N3O4) in two crystal forms, GAI1 and GAI2. Form 1 (GAI1) Gly-L-Ala-L-Ile (C11H21N3O4.3H2O) crystals are monoclinic, space group P2(1) with a = 8.171(2), b = 6.072(4), c = 16.443(4) A, beta = 101.24(2) degrees, V = 800 A3, Dc = 1.300 g cm-3 and Z = 2, R = 0.081 for 482 reflections. Form 2 (GAI2) Gly-L-Ala-L-Ile (C11H21N3O4.1/2H2O) is triclinic, space group P1 with a = 5.830(1), b = 8.832(2), c = 15.008(2) A, alpha = 102.88(1), beta = 101.16(2), gamma = 70.72(2) degrees, V = 705 A3, Z = 2, Dc = 1.264 g cm-3, R = 0.04 for 2582 reflections. GAI1 is isomorphous with GAV and forms a helix, whereas GAI2 does not. In GAI1, the tripeptide molecule is held in a near helical conformation by a water molecule that bridges the NH3+ and COO- groups, and acts as the fourth residue needed to complete the turn by forming two hydrogen bonds. Two other water molecules form intermolecular hydrogen bonds in stabilizing the helical structure so that the end result is a column of molecules that looks like an incipient alpha-helix. GAI2 imitates a cyclic peptide and traps a water molecule. The conformation angles chi 11 and chi 12 for the side chain are (-63.7 degrees, 171.1 degrees) for the helical GAI1, and (-65.1 degrees, 58.6 degrees) and (-65.0 degrees, 58.9 degrees) for the two independent nonhelical molecules in GAI2; in GAI1, both the C gamma atoms point away from the helix, whereas in GAI2 the C gamma atom with the g+ conformation points inward to the helix and causes sterical interaction with atoms in the adjacent peptide plane. From these results, it is clear that the helix-forming tendencies of amino acids correlate with the restrictions of side-chain rotamer conformations. Both the peptide units in GAI1 are trans and show significant deviation from planarity [omega 1 = -168(1) degrees; omega 2 = -171(1) degrees] whereas both the peptide units in both the molecules A and B in GAI2 do not show significant deviation from planarity [omega 1 = 179.3(3) degrees; omega 2 = -179.3(3) degrees for molecule A and omega 1 = 179.5(3) degrees; omega 2 = -179.4(3) degrees for molecule B], indicating that the peptide planes in these incipient alpha-helical peptides are considerably bent.

Building protein backbones from C alpha coordinates.

An automatic procedure for building polyalanine backbones from guiding alpha-carbon positions is presented. Polyalanine backbones are built based on the geometric restraints of angle N-C alpha-C and the knowledge of main-chain dihedral angle distributions. A building module constructs a list of polyalanine backbones that follow exactly the C alpha trace. Then a selection module selects one backbone with the largest portion of phi-psi pairs in favoured regions. Several test cases on C alpha coordinates from X-ray refined structures give acceptable results. Less than 10% of the peptide planes are incorrectly built, and the result is not sensitive to random shift up to 0.5 A of C alpha coordinates.

Dynamics of the hydrate and amide groups of crystalline ribonuclease and lysozyme

We have used 2H magnetic resonance to study orientational ordering and dynamics of the hydrate and exchangeable hydrogens of crystalline RNase and lysozyme. In these proteins, a predominant fraction of the hydrate deuterons have negligible quadrupole coupling indicating that the solvate is orientationally disordered at room temperature. This observation is reconciled with the crystallographic observation of a substantial fraction of the water being “ordered” by proposing that water molecules readily move among most of the solvent locations including those sites identified in the X-ray structures. Support for this proposition is based on the observation that spin relaxation of the solvate is characterized by a single relaxation time indicating that the solvate deuterons are exchange averaged in the NMR experiment. With regard to the amide deuterons, the residual quadrupole coupling shows that the peptide planes librate with arms amplitude of 12−15° (287 K). Compared to a crystalline peptide ( T 1 ⪢ 100 s) or solid anhydrous poly-γ-benzyl-L-glutamate ( T 1 ≈ 1 s), spin relaxation of the amide deuterons in these hydrated proteins ( T 1 ≈ 0.2 s) is very efficient. Relaxation results are interpreted with a damped Langevin oscillator model and indicate that reorientation of the protein backbone has a distinctly stochastic nature as opposed to that of undamped solid-like oscillatory modes. Furthermore, while the hydrate is important in damping or plasticizing the backbone dynamics, it is apparently not entirely responsible for this effect.

Deuterium quadrupole coupling in N-acetylglycine and librational dynamics in solid poly (.gamma.-benzyl-L-glutamate)

To study the dynamics of peptide groups in solid proteins, we have accurately determined the principal components and molecular orientation of the electric field gradient tensor for the exchangeable deuterons in monoclinic N-acetylglycine by single-crystal deuterium nuclear magnetic resonance. These results are compared with the principal components of the amide deuterons in solid poly(gamma-benzyl-L-glutamate) measured in powder samples over a wide temperature range (140-400 K). The comparison indicates that in the solid polypeptide the N-D bonds undergo a small-amplitude torsional reorientation (libration) perpendicular to the peptide plane. To estimate dynamic rates, longitudinal relaxation times (T1 values) are reported for N-acetylglycine and poly(gamma-benzyl-L-glutamate). T1 values for the carboxyl and amide deuterons in N-acetylglycine are approximately 100 s, whereas for the amide deuterons in the polypeptide T1 approximately 1 s, also indicating that the N-D bonds are not stationary in the polypeptide. We determine from the reduced quadrupole coupling tensor the mean-square amplitude for the libration and show that it increases linearly with temperature. A simple qualitative theory for the relaxation times is presented on the basis of the assumption that the N-D reorientation is described either as a diffusion process in a square well or as a damped Langevin oscillator with a harmonic restoring force. The conclusion is that the short relaxation times of the polypeptide amide deuterons result from substantial frictional effects on reorientation that increase with temperature.

Solid-state nuclear magnetic resonance derived model for dynamics in the polypeptide backbone of the gramicidin a channel

The dynamics of the backbone of the gramicidin A transmembrane cation channel in dimyristoylphosphatidylcholine bilayers have been investigated using solid state 15N nuclear magnetic resonance (n.m.r.) spectroscopy. With the temperature-dependent fluidity of the bilayer, the rates of motions in the helical gramicidin channel can be modulated. It is shown that in the gel phase, all substantial motions of the channel are slow on the timescale of the n.m.r. experiment (3.5 kHz). The use of oriented samples in which the axis of global channel rotation is aligned parallel to the magnetic field enables separation of global and local dynamics. Spectra obtained from oriented bilayer samples containing single-site 15N-labeled gramicidin at 8 °C are analyzed to yield a spatial model for local backbone motion. This model includes the axis of motion, the mean orientation, and the maximum amplitude of displacement for individual peptide planes. Specific sites in the first turn of the amino terminus were investigated, with emphasis on the Ala3 and Leu4 linkages, for which the orientation of the 15N chemical shift tensor with respect to the molecular frame has been determined. The effect of two well-characterized bilayer defect structures, parabolic focal conics and oily streaks, is included in the spectral simulations. It is found that only relatively small amplitude motions are possible at the two sites, with amplitudes of not more than ±8 ° and ±15 ° for the Ala3 and Leu4 sites, respectively. Detailed characterization of the bilayer surface geometry in the oriented samples is presently the major limiting factor in the use of this technique for probing the spatial extent of local motions in integral membrane proteins.

A molecular dynamics investigation of the elastomeric restoring force in elastin

A repetitive polypentapeptide organized as a connected chain of beta-bends is believed to be an important structural element of elastin, the major elastomer in biological systems. Molecular dynamics simulations were carried out on hydrated polymers of (Val-Pro-Gly-Val- Gly)18 at various extensions. Analysis of the fluctuations of backbone angles in relaxed elastin showed that particularly large-amplitude torsional motions occur in phi and psi angles of residues connecting sequentially adjacent hairpin bends. Many such motions reflect peptide plane librations that result from anticorrelated crankshaft rotations of psi i and phi i+1. These effects were much reduced in stretched polymer models. The conformational entropy of relaxed and stretched elastin models was estimated using a treatment due to Meirovitch, and gave a calculated decrease in entropy of about 1 cal/mol deg when the polymer was stretched to 1.75 times its original length. There are large changes in solvent-accessible surface area during the initial stages of elastin stretching. Collectively these results suggest that hydrophobic interactions make contributions to elastin entropy at low extensions, but that librational mechanisms make larger contributions to the elastic restoring force at longer extensions.

Crystal structures of recombinant human dihydrofolate reductase complexed with folate and 5-deazafolate

The 2.3-A crystal structure of recombinant human dihydrofolate reductase (EC 1.5.1.3, DHFR) has been solved as a binary complex with folate (a poor substrate at neutral pH) and also as a binary complex with an inhibitor, 5-deazafolate. The inhibitor appears to be protonated at N8 on binding, whereas folate is not. Rotation of the peptide plane joining I7 and V8 from its position in the folate complex permits hydrogen bonding of 5-deazafolate's protonated N8 to the backbone carbonyl of I7, thus contributing to the enzyme's greater affinity for 5-deazafolate than for folate. In this respect it is likely that bound 5-deazafolate furnishes a model for 7,8-dihydrofolate binding and, in addition, resembles the transition state for folate reduction. A hypothetical transition-state model for folate reduction, generated by superposition of the DHFR binary complexes human.5-deazafolate and chicken liver.NADPH, reveals a 1-A overlap of the binding sites for folate's pteridine ring and the dihydronicotinamide ring of NADPH. It is proposed that this binding-site overlap accelerates the reduction of both folate and 7,8-dihydrofolate by simultaneously binding substrate and cofactor with a sub van der Waals separation that is optimal for hydride transfer.

Systematics in the interaction of metal ions with the main-chain carbonyl group in protein structures

An analysis of the geometry of metal binding by peptide carbonyl groups in proteins is presented. Such metal ions are predominantly calcium in known protein structures. Cations tend to be located in the peptide plane, near the C = O bond direction. This distribution differs from that observed for water molecules bound to carbonyl oxygens. Most metal ions are bound to carbonyl oxygens of peptides in turns or in regions with no regular secondary structure. More infrequent binding interactions occur at the C-terminal end of alpha-helices or at the edges and sides of beta-sheets, where the geometrical preferences of the metal-carbonyl interaction may be satisfied. In many proteins carbonyl groups that are one, two, or three residues apart along the polypeptide chain bind to the same cation; these structures show a limited number of main-chain conformations around the metal center.

Crystal structure, conformation, and potential energy calculations of the chemotactic peptide N-formyl-L-Met-L-Leu-L-Phe-OMe.

The tripeptide N-formyl-L-Met-L-Leu-L-Phe-OMe (FMLP-OMe) crystallizes in the orthorhombic system, space group P 2(1)2(1)2(1), with the following unit-cell parameters: a = 21.727, b = 21.836, c = 5.133 A, Z = 4. The structure has been solved and refined to a final R of 0.068 for 1838 independent reflexions with I greater than 2 omega (I). The peptide backbone is folded at the Leu residue (phi L = -67.7, psi L = -49.1 degrees) without intramolecular hydrogen bonds. Considering each peptide plane, the Leu side-chain is oriented on the same side of that of the Phe residue and on the opposite side of that of the Met residue, respectively. The crystal conformation differs from all the other conformations proposed for FMLP-OMe and the anionic form of N-formyl-L-Met-L-Leu-L-Phe-OH (FMLP) in solution accounts for the amphiphilic character of the peptide, giving rise, through intermolecular hydrogen bonds, to a stacking of molecules which could be maintained in the aggregation states experimentally observed in solvents of low polarity. Intramolecular potential energy calculations have been carried out in order to compare the energies of the various backbone conformers.

DNA packing in filamentous bacteriophages.

in that the is assumed to have the smoothest possible distribution of electron density. Contributions from side chains of varying size and disposition are subsumed in the smoothness assumption. Model­ ing by this procedure with data to 3 A resolution axially and 4 A resolution radially produced a model that is a gently bent, continuous IX-helix of 1 3 turns. The axis of approximately the first five turns is approximately parallel to the main virion axis (Figure 10 of Reference 81) . The overall shapes of the three models are similar, as indicated by the lattice diagram of Figure 4. Ff Subunit Structure Determination Opella and his coworkers ( 108) have undertaken to determine the structure of the Ff subunits by measuring the nuclear magnetic spin interaction tensors for all 49 peptide backbone planes in the molecule. The spin interaction data, including dipole-dipole spin coupling, chemical shift anisotropy, and quadrupole interactions, yield a limited set of orientation angles for each peptide plane relative to its neighbors and to the main structure axis. The data also provide information on radial positioning due to the dependence of dipole-dipole interactions on distance. The set Table 4 Structural parameters for the protein coats Parameter Ff Xf Pfl PO References Symmetry of helix Rise per subunit (A) 16.0-16.2b 2.85 2.78-3.05 2.78-2.96 37,80,8�88, 101, 112 Rotation per subunitC _30.00b _66.7° -65.9--66.r -66.7° 77,85,88, 101, 112, 157 Pitch of helix' (A) 16.0-16.2b 15.4 15.0-16.6 15.0-15.8 37,80,85,88,101, 112 Symmetry designationd CSS2.0 CISS.4 CISS.4-- CISS.46 CISS.4 75 Symmetry designation (2/10; 3/15) (2/11; 3/17) (2/11; 3.17) (2/11; 3/17) 91 Subunit IX-helix content and orientation CD amplitudesf 18,33, 138 [111208 (cm2 deg dmol-') -27,000 -18,000 -35,000 -31,000 [111m (em2 deg dmol-') -41,000 -15,000 -32,000 -38,000 % IX-Helix 80-100 40--6 5 80-100 80-100 Raman 1650 cm -I amide I band 136, 137, 139 Deconvolved components 1648 (0.92) 1646 (0.71) 1652 (1.0) 1645 (0.82) 1667 (0.08) 1658 (0.29) 1666 (0.08) % IX-Helix 92 71 100 82 Infrared 1650 em-I amide I band 43,44 % IX-Helix 95-100 90-100 Average a-helix inclination to axis Birefringence 20-30° 145 Infrared dichroism 37±W 30± 10° 43, 44 NMR _10° -0, 20° 29, 108 • Helical parameters observed by fiber diffraction for various experimental conditions of temperature, humidity, and chemical modification. b Ff possesses fivefold rotational symmetry (76, 77, 104); the translation and rotation per pentamer of subunits are listed. cThe rotation per is limited to a narrow range afvalues, even far large changes in experimental conditions (91). d Symmetry notation of Klug et al (63a) (see text and Reference 75). An alternative notation gives the number af subunits and the number of helical turns in the apparent structural repeat, such as 27u/5t = 5.4 ult or 7Iu/13t = 5.46 u/t far Pfl (8\). 'N otation developed in a theoretical treatment of the symmetries of the filamentous phages (see text and Reference 91). f See Figure 6. Ul IV 0 > - Crl ..., > t' DNA PACKING IN FILAMENTOUS PHAGE 525

Structural versatility of peptides from Cα,α‐dialkylated glycines. I. A conformational energy computation and x‐ray diffraction study of homo‐peptides from Cα,α‐diethylglycine

AbstractConformational energy computations on a derivative and a homo‐dipeptide of Cα,α‐diethylglycine were performed. In both cases the N‐ and C‐terminal groups are blocked as acetamido and methylamido moieties, respectively. It was found that the Cα,α‐diethylglycine residues are conformationally restricted and that the minimum energy conformation corresponds to the fully extended C5 structure when the NCαC′ bond angle is smaller than 108° (as experimentally observed). The results of the theoretical analysis are in agreement with the crystal‐state structural propensity of the complete series of N‐trifluoroacetylated homo‐peptides of this Cα,α‐dialkylated residue from monomer to pentamer, determined by x‐ray diffraction and also described in this work. Interestingly, for the first time, a crystallographically planar peptide backbone was observed (in the protected tripeptide). A comparison with peptides of Cα,α‐dimethylglycine, Cα‐methyl, Cα‐ethylglycine, and Cα,α‐di‐n‐propylglycine indicates that the fully extended conformation becomes more stable than the helical structures when both amino acid side‐chain Cβ atoms are substituted.

Mutual orientation of three magnetic tensors in a polycrystalline dipeptide by dipole-modulated 15N chemical shift spectroscopy

This study demonstrates the mutual orientation of three tensor interactions in a single NMR experiment. The orientation of the 15N chemical shift tensor relative to the molecular frame has thus been determined in polycrystalline L-[1-13C] alanyl-L-[15N] alanine. The 13C–15N and 15N–1H dipole interactions are determined using the 1H dipole-modulated, 13C dipole-coupled 15N spectrum obtained as a transform of the data in t2. From simulations of the experimental spectra, two sets of polar angles have been determined relating the 13C–15N and 15N–1H dipoles to the 15N chemical shift tensor. The values determined are βCN =106°, αCN =5° and βNH =−19°, αNH =12°. The experiment verifies, without reference to single crystal data, that σ33 lies in the peptide plane and σ22 is nearly perpendicular to the plane.

Ribbon models of macromolecules

A smooth 3D ribbon model of a protein is easily constructed by creating a set of nearly parallel B-spline curves fitted to the peptide plane. These models may be coded by residue to depict such information as secondary structure, residue type or temperature factors. The computation of the curves defining the ribbon model is explained in detail. Solid surface models of the protein backbone may be rendered, using the ribbon curve as a basis. Nucleic acid molecules may be represented as ribbon models in much the same fashion. The method is applicable to both vector and raster devices, and is illustrated with the Evans and Sutherland PS300 and the Silicon Graphics Iris workstation.