15.12.02 · orgchem / biomolecules-aa-protein

Peptide bond geometry: planarity, resonance, and the Ramachandran plot

stub3 tiersLean: nonepending prereqs

Anchor (Master): Creighton — Proteins: Structures and Molecular Properties, 2e (1993)

Intuition Beginner

The peptide bond linking one amino acid to the next is not a freely rotating single bond. The nitrogen of the amide group has a lone pair that can overlap with the adjacent carbon-oxygen double bond. This creates resonance: the nitrogen lone pair delocalises onto the oxygen, giving the carbon-nitrogen bond partial double-bond character. The result is that the six atoms of the peptide group lie in a single flat plane.

Because the C-N bond has partial double-bond character, rotation around it is blocked. This planarity is one of the strongest constraints on how a protein chain can fold. The backbone can only rotate around the two single bonds on either side of the rigid planar peptide unit: the N-to-C $_{α}$ bond and the C $_{α}$ -to-carbonyl bond.

The two rotatable backbone bonds are described by the torsion angles $ϕ$ (phi, the N-C $_{α}$ bond) and $ψ$ (psi, the C $_{α}$ -C bond). Not all combinations of $ϕ$ and $ψ$ are physically possible — many angles bring atoms so close together that their electron clouds collide. The Ramachandran plot maps every possible ( $ϕ$ , $ψ$ ) pair and marks which regions are allowed (no atomic collisions) and which are forbidden (steric clash). Alpha helices and beta sheets each occupy a characteristic region of the plot, which is why these secondary structures are so common in folded proteins.

Visual Beginner

The peptide bond is a flat ribbon connecting two alpha carbons. The six coplanar atoms are C $_{α}$ (i)-C(=O)-N(H)-C $_{α}$ (i+1). The oxygen and the hydrogen on nitrogen are trans to each other in the default (energetically preferred) arrangement. The two rotating bonds flanking the planar unit carry the torsion angles $ϕ$ and $ψ$ .

Worked example Beginner

Identify which torsion angles define backbone conformation, and explain why the peptide bond itself does not rotate.

Consider a tripeptide fragment Ala-Gly-Ser. Between each pair of residues lies a peptide bond (C=O)(NH). This amide linkage is planar because the nitrogen lone pair delocalises into the carbonyl, giving the C-N bond roughly 40% double-bond character. The torsion angle around this C-N bond (called $ω$ , omega) is therefore clamped near 180 degrees (the trans configuration).

The two bonds that do rotate are the N-C $_{α}$ bond ( $ϕ$ ) and the C $_{α}$ -C bond ( $ψ$ ). For each residue, the pair ( $ϕ$ , $ψ$ ) specifies the local backbone shape. When $ϕ \approx - 5 7^{\circ}$ and $ψ \approx - 4 7^{\circ}$ , the backbone adopts the right-handed alpha-helical conformation. When $ϕ \approx - 12 0^{\circ}$ and $ψ \approx + 12 0^{\circ}$ , the backbone is in the extended beta-strand conformation. Other angle combinations are forbidden because the side-chain atoms would crash into backbone atoms on neighbouring residues.

Check your understanding Beginner

Exercise (easy, multiple choice).

Why is the peptide bond planar?

A. The carbon atom is sp $^{2}$ hybridised and enforces a trigonal geometry B. Nitrogen lone-pair delocalisation into the carbonyl gives the C-N bond partial double-bond character C. Hydrogen bonding between backbone groups forces the atoms into one plane D. The amino acid side chains are too large to allow rotation

Hint

Draw the two resonance structures of the amide bond. What does the charge-separated structure imply about the C-N bond order?

Answer

B. The amide nitrogen lone pair delocalises into the carbonyl $π^{*}$ orbital, producing a resonance contributor with a C=N double bond. This partial double-bond character locks the six atoms of the peptide unit into a plane. Hydrogen bonding (C) stabilises secondary structures but does not cause planarity of the individual peptide bond.

Exercise (medium, short-answer).

Explain why glycine has many more allowed conformations on the Ramachandran plot than alanine.

Hint

The forbidden regions on the Ramachandran plot arise from steric clashes between atoms. Glycine has the smallest possible side chain. What does this mean for the severity of those clashes?

Answer

Glycine's side chain is a single hydrogen atom. The forbidden regions on the Ramachandran plot are produced by van der Waals collisions between the side chain and neighbouring backbone atoms (particularly the carbonyl oxygen and amide hydrogen). With only a hydrogen as its side chain, glycine experiences almost no steric clash at any ( $ϕ$ , $ψ$ ) combination, so it can adopt torsion angles that are forbidden for all other amino acids. This is why glycine is common in tight turns and loops.

Formal definition Intermediate+

Amide resonance and the peptide bond. The peptide bond is an amide linkage ( $- CO - NH -$ ) whose electronic structure is described by two resonance contributors:

C (= O) - NH ⟷ C (- O^{-}) = N^{+} H

The charge-separated contributor contributes roughly 40% to the resonance hybrid, giving the C-N bond partial double-bond character. The resonance stabilisation energy of the amide bond is approximately 20 kcal/mol (84 kJ/mol), making it significantly more stable than a simple single bond. This resonance energy is the thermodynamic driving force for planarity: rotation around the C-N bond would destroy the orbital overlap that enables delocalisation.

Trans preference. In the trans configuration, the two C $_{α}$ atoms are on opposite sides of the peptide bond. In the cis configuration, they are on the same side, creating steric clash between the two alpha carbons and their substituents. The trans ratio is approximately 1000:1 for non-proline residues. The energy penalty for the cis configuration is roughly 2--3 kcal/mol (8--13 kJ/mol).

Backbone torsion angles. For residue $i$ , the two backbone torsion angles are:

$ϕ_{i}$ : rotation about the N $_{i}$ -C $_{α, i}$ bond. Defined by the four atoms C $_{i - 1}$ -N $_{i}$ -C $_{α, i}$ -C $_{i}$ .
$ψ_{i}$ : rotation about the C $_{α, i}$ -C $_{i}$ bond. Defined by the four atoms N $_{i}$ -C $_{α, i}$ -C $_{i}$ -N $_{i + 1}$ .
$ω_{i}$ : rotation about the C $_{i}$ -N $_{i + 1}$ peptide bond. Clamped near 180 $^{\circ}$ (trans) or 0 $^{\circ}$ (cis).

The peptide bond $ω$ is the only backbone torsion angle that is essentially fixed by electronic structure (resonance). The remaining two degrees of freedom per residue ( $ϕ$ and $ψ$ ) determine the backbone conformation.

Ramachandran plot. The Ramachandran plot is a two-dimensional map with $ϕ$ on the x-axis (range $- 18 0^{\circ}$ to $+ 18 0^{\circ}$ ) and $ψ$ on the y-axis (same range). For each ( $ϕ$ , $ψ$ ) pair, a hard-sphere model evaluates whether any pair of non-bonded atoms on neighbouring residues approach closer than the sum of their van der Waals radii. The original calculations by Ramachandran, Ramakrishnan, and Sasisekharan (1963) used a simplified model considering only the C $_{α}$ -H, C=O, and N-H groups plus the side-chain C $_{β}$ atom.

The plot divides into three zones:

Allowed regions: no steric clashes. These correspond to the core secondary structures (right-handed alpha helix, beta sheet, left-handed polyproline helix).
Generously allowed regions: minor clashes that can be tolerated, especially for residues with small side chains. Found at the edges of the allowed regions.
Disallowed regions: severe steric overlaps. Very few residues are found here in experimental structures; their presence often indicates modelling errors.

Secondary structure on the Ramachandran plot. The characteristic ( $ϕ$ , $ψ$ ) values for common secondary structures are:

Secondary structure	$ϕ$	$ψ$
Right-handed alpha helix ( $α_{R}$ )	$- 5 7^{\circ}$	$- 4 7^{\circ}$
Beta sheet (antiparallel)	$- 12 0^{\circ}$	$+ 12 0^{\circ}$
Beta sheet (parallel)	$- 11 9^{\circ}$	$+ 11 3^{\circ}$
Left-handed alpha helix ( $α_{L}$ )	$+ 5 7^{\circ}$	$+ 4 7^{\circ}$
Polyproline II (PPII) helix	$- 7 8^{\circ}$	$+ 14 9^{\circ}$
3 $_{10}$ helix	$- 4 9^{\circ}$	$- 2 6^{\circ}$

Counterexamples to common slips

"The peptide bond never rotates." The barrier to rotation around the peptide bond is approximately 20 kcal/mol, which is substantial but not infinite. Cis-trans isomerisation does occur, especially for proline residues, and can be the rate-limiting step in protein folding.
"The Ramachandran plot applies to all atoms in a protein." The plot describes only backbone torsion angles. Side-chain conformations are described by separate chi ( $χ$ ) angles, each with their own steric constraints (rotamer libraries).
"Forbidden regions are always unoccupied." Glycine routinely populates the "forbidden" left-handed helical region. Some strained conformations are functionally important — for example, residues in enzyme active sites often adopt unusual backbone angles to position catalytic groups precisely.

Key result Intermediate+

The Ramachandran steric map. For a dipeptide unit with a generic side chain (modelled as a C $_{β}$ atom), the allowed ( $ϕ$ , $ψ$ ) combinations are determined by evaluating van der Waals overlap between four key atom pairs:

C $_{β}$ of residue $i$ with the carbonyl oxygen of residue $i - 1$ .
C $_{β}$ of residue $i$ with the amide hydrogen of residue $i + 1$ .
The carbonyl oxygen of residue $i - 1$ with the amide hydrogen of residue $i + 1$ .
The carbonyl oxygen of residue $i$ with the amide hydrogen of residue $i$ (intra-residue).

Each pair defines a forbidden range of torsion angles where the interatomic distance falls below the sum of van der Waals radii. The intersection of all four forbidden sets yields the disallowed regions of the Ramachandran plot.

For glycine (no C $_{β}$ ), pairs 1 and 2 are absent, and the allowed region expands dramatically — glycine can access roughly 60% of the full ( $ϕ$ , $ψ$ ) space, compared to roughly 20% for alanine and less for larger side chains.

Resonance energy and the rotational barrier. The rotational barrier around the peptide C-N bond is directly related to the amide resonance energy. Rotation destroys the planar overlap between the nitrogen lone pair and the carbonyl $π^{*}$ orbital, costing the full resonance stabilisation:

Δ G_{rotation}^{‡} \approx E_{resonance} \approx 20 kcal/mol

This makes peptide bond isomerisation a slow process at room temperature (half-life on the order of minutes to hours for non-enzymatic cis-trans interconversion), which is why prolyl isomerases exist to accelerate this step during protein folding.

Exercises Intermediate+

Exercise 2 (medium, short-answer).

The trans ratio for non-proline peptide bonds is approximately 1000:1. Estimate the free energy difference between the two configurations at 298 K. For proline, the trans ratio drops to roughly 4:1. Explain why.

Hint

Use $Δ G^{\circ} = - R T ln K$ with $R T = 0.592$ kcal/mol at 298 K. For proline, consider what is different about its side chain.

Answer

For non-proline: $Δ G^{\circ} = - 0.592 \times ln (1000) \approx - 0.592 \times 6.9 \approx - 4.1$ kcal/mol. The trans configuration is favoured by about 4.1 kcal/mol.

For proline, the side chain bonds back to the backbone nitrogen, forming a pyrrolidine ring. This means the C $_{α}$ of the preceding residue does not clash with a free N-H in the cis configuration (there is no N-H on proline — it is a secondary amine). The steric difference between trans and cis is therefore much smaller, reducing the energetic penalty for the cis form.

Exercise 3 (medium, short-answer).

A protein crystal structure is reported with a non-glycine residue at ( $ϕ = + 6 0^{\circ}$ , $ψ = + 4 0^{\circ}$ ), in the left-handed helical region of the Ramachandran plot. Is this necessarily an error? Under what circumstances might this be genuine?

Hint

The left-handed helical region is "forbidden" for most residues but not for glycine. Some non-glycine residues do appear there in high-quality structures.

Answer

It is not necessarily an error, though it is unusual. Approximately 2--5% of non-glycine residues in high-resolution crystal structures appear in the left-handed helical region. These are most commonly asparagine, aspartate, and serine residues, often found in tight turns or at the N-terminus of alpha helices (the "N-cap" position). If the overall structure is high resolution (better than 2.0 A) and the electron density at this residue is clear, the conformation may be genuine. However, a cluster of non-glycine residues in disallowed regions would indicate a modelling problem.

Exercise 4 (hard, short-answer).

Prolyl isomerisation is often the rate-limiting step in protein folding. Explain the molecular basis for this kinetic bottleneck and describe how the enzyme cyclophilin (a peptidyl-prolyl isomerase) accelerates the process.

Hint

The rotational barrier around the peptide bond is about 20 kcal/mol. What is the half-life at room temperature for a first-order process with this barrier? How might an enzyme lower the barrier?

Answer

The 20 kcal/mol rotational barrier around the peptide bond corresponds to a half-life of roughly 10--100 seconds at 25 $^{\circ}$ C for non-enzymatic cis-trans interconversion. For proline residues, where the cis population is non-negligible (~5--30% depending on sequence context), a significant fraction of newly synthesised polypeptide chains contain cis peptide bonds that must isomerise to trans before the native fold can form. This isomerisation is slow compared to other folding events (hydrogen bond formation, hydrophobic collapse), making it the kinetic bottleneck.

Cyclophilin accelerates prolyl isomerisation by a mechanism that involves twisting the substrate peptide bond out of planarity in the enzyme active site. The enzyme binds the proline-containing peptide and distorts the amide geometry, partially breaking the resonance stabilisation and thereby lowering the rotational barrier. The active site contains a network of hydrogen bonds and hydrophobic contacts that stabilise the twisted, partially rotated transition state. Catalytic rate enhancements of $1 0^{4}$ -- $1 0^{6}$ fold are typical, reducing the isomerisation half-life from seconds to microseconds.

Exercise 5 (hard, short-answer).

A Ramachandran plot generated from a 1.8 A resolution crystal structure shows 95% of non-glycine residues in the most-favoured regions, 4% in additionally allowed regions, and 1% in disallowed regions. Assess the quality of this structure and suggest what the outlier residues might represent.

Hint

Compare the statistics to typical benchmarks for high-resolution structures. What percentage of residues is expected in each region for a well-refined structure at this resolution?

Answer

For a structure at 1.8 A resolution, typical benchmarks are: $\geq$ 90% in the most-favoured regions, $\leq$ 10% in additionally allowed, and $<$ 0.5% in disallowed regions. The reported statistics (95% most-favoured, 4% additionally allowed, 1% disallowed) are acceptable overall, with the 95% figure indicating good backbone geometry.

The 1% in disallowed regions warrants inspection. Possible explanations include: (a) genuine strained conformations in functionally important regions such as active sites or binding interfaces; (b) residues in tight turns (particularly type I and type II beta turns, where the $i + 1$ or $i + 2$ residue may adopt unusual angles); (c) modelling errors such as register shifts or incorrect side-chain rotamer assignments that propagate to distort the backbone; or (d) crystal packing artefacts. Each outlier should be examined individually in the electron density map to confirm the conformation is supported by the data.

Peptide bond isomerism and advanced Ramachandran analysis Master

The peptide bond exists in two geometric isomers: trans ( $ω \approx 18 0^{\circ}$ ) and cis ( $ω \approx 0^{\circ}$ ). For non-proline residues, the trans isomer dominates by roughly 1000:1 because the two C $_{α}$ atoms in the cis arrangement suffer severe steric repulsion. The situation changes dramatically for proline, where the trans ratio is approximately 4:1. This difference has profound consequences for protein folding kinetics and structural diversity.

Proline cis-peptide bonds. Proline's pyrrolidine ring bonds to the backbone nitrogen, eliminating the N-H group and replacing it with the ring carbons. In the cis isomer, the steric clash between the preceding C $_{α}$ and proline's C $_{δ}$ is comparable in magnitude to the clash between the preceding C $_{α}$ and proline's C $_{α}$ in the trans isomer. The two configurations are therefore much closer in energy. X-ray crystallographic surveys reveal that approximately 5--7% of X-Pro peptide bonds in proteins adopt the cis configuration, compared to approximately 0.03% for non-proline bonds.

Cis-proline residues serve specific structural roles. They introduce sharp turns in the polypeptide chain that cannot be achieved with trans peptide bonds, creating compact loops in beta-turns and omega-loops. The cis-proline is a conserved feature in many protein families: for example, ribonuclease A contains two cis-proline residues (Pro-93 and Pro-114) that are essential for correct active-site geometry.

Prolyl isomerases. The slow cis-trans isomerisation of proline peptide bonds (half-life $\sim$ 10--100 s at 25 $^{\circ}$ C) creates a kinetic barrier to protein folding. Newly synthesised polypeptide chains emerging from the ribosome contain a mixture of cis and trans X-Pro bonds. The non-native isomers must convert to the correct configuration before the native fold can form, and this conversion is rate-limiting for many small proteins and for the refolding of denatured proteins in vitro.

Three structurally unrelated families of peptidyl-prolyl isomerases (PPIases) have evolved to catalyse this reaction: cyclophilins (sensitive to cyclosporin A), FK506-binding proteins (FKBPs), and parvulins. All three operate by a common mechanistic principle: binding and distorting the substrate peptide bond to partially break the amide resonance, lowering the rotational barrier. The catalytic proficiency of PPIases ( $k_{cat} / k_{non-enzymatic} \approx 1 0^{5}$ -- $1 0^{6}$ ) makes them among the most efficient enzymes known for a non-chemical (conformational) transformation.

Left-handed helices and the alpha $_{L}$ region. The Ramachandran plot's upper-left quadrant ( $ϕ > 0$ , $ψ > 0$ ) corresponds to left-handed helical conformations. For L-amino acids with side chains larger than hydrogen, this region is largely forbidden due to steric clash between the C $_{β}$ atom and the carbonyl oxygen of the preceding residue. Glycine, with no C $_{β}$ , freely accesses this region, and indeed left-handed helices are predominantly glycine-rich in natural proteins.

However, a small but nontrivial population of non-glycine residues occupies the $α_{L}$ region in high-resolution crystal structures. Asparagine is the most common non-glycine residue found here, with the side-chain amide group forming stabilising hydrogen bonds that compensate for the backbone strain. The $α_{L}$ conformation also appears at type II beta turns, where residue $i + 2$ adopts positive $ϕ$ values. These exceptions illustrate a general principle: the Ramachandran plot describes steric accessibility, not thermodynamic stability — local interactions (hydrogen bonds, electrostatic contacts, crystal packing) can stabilise conformations in marginally allowed or even disallowed regions.

Polyproline helices. Proline's restricted phi angle (clamped near $- 7 5^{\circ}$ by the pyrrolidine ring) and lack of an amide N-H hydrogen give rise to two distinct helical conformations that do not rely on intramolecular hydrogen bonds:

Polyproline I (PPI): All cis peptide bonds, right-handed helix, approximately 3.3 residues per turn, pitch ~1.9 A. Rare in proteins.
Polyproline II (PPII): All trans peptide bonds, left-handed helix, approximately 3.0 residues per turn, pitch ~9.4 A. Common and structurally important.

The PPII helix is not limited to proline-rich sequences. Unfolded and denatured proteins populate PPII-like conformations extensively — estimates suggest 20--40% of residues in disordered polypeptide chains adopt PPII dihedral angles. The PPII conformation is stabilised not by hydrogen bonds but by a combination of favourable solvation (exposed backbone carbonyls and amides interact with water) and steric preference. PPII helices serve as recognition motifs in signalling proteins: for example, SH3 and WW domains bind PPII helices on their partner proteins, reading out the sequence displayed on one face of the extended helix.

The Ramachandran plot as a structure-quality metric. The most important modern application of the Ramachandran plot is as a validation tool for macromolecular crystal structures. The MolProbity server and the validation tools in the PDB use updated, empirical Ramachandran distributions derived from high-quality reference structures rather than the original hard-sphere calculations. The empirical distributions are residue-specific: glycine, proline, pre-proline, and general (non-Gly, non-Pro) residues each have distinct allowed regions reflecting their different steric constraints.

A well-refined crystal structure at 2.0 A resolution or better should have at least 98% of non-glycine, non-proline residues in the favoured regions, with no more than 0.5% in outlier regions. Structures failing these thresholds almost certainly contain modelling errors — typically register shifts (incorrect sequence assignment in the electron density), main-chain tracing errors, or insufficient refinement. The Ramachandran analysis is performed automatically during PDB deposition, and persistent outliers are flagged for manual inspection.

The statistical basis for the empirical Ramachandran plot comes from the nontrivial database of structures at 1.8 A resolution or better with $R_{free}$ below 0.25. Kernel density estimation on the ( $ϕ$ , $ψ$ ) distributions of these reference structures produces smooth contour maps with defined probability thresholds (98%, 99.5%, and 99.95% for the favoured, allowed, and generously allowed contours respectively).

Computational prediction of backbone angles. Modern protein structure prediction methods, including AlphaFold and RoseTTAFold, predict ( $ϕ$ , $ψ$ ) distributions as intermediate outputs. AlphaFold2 outputs predicted backbone torsion angles as probability distributions (represented as sine and cosine values to handle the circular topology of angular data), which are then used to construct the 3D backbone model. The accuracy of these predictions is assessed in part by how well the predicted Ramachandran distributions match the empirical distributions from high-resolution structures.

Molecular dynamics force fields (AMBER, CHARMM, OPLS) include torsional potential terms for the $ϕ$ and $ψ$ angles that are parameterised to reproduce the observed Ramachandran distributions. Improper torsion terms enforce the planarity of the peptide bond by penalising deviations of $ω$ from 180 $^{\circ}$ (or 0 $^{\circ}$ for cis bonds). The balance between the torsional terms and the non-bonded (van der Waals and electrostatic) interactions determines the populations of different secondary-structure basins in simulations, and the accuracy of these populations relative to experimental data is a key benchmark for force-field quality.

Connections Master

Amino acid chemistry 15.12.01. The zwitterion structure of amino acids and the condensation reaction that forms peptide bonds establish the molecular unit whose geometry this chapter analyses. The planarity of the peptide bond is a direct consequence of the amide electronic structure introduced in the preceding unit.
Conformational analysis 15.01.02. The Ramachandran plot is an application of conformational analysis to the polypeptide backbone. The torsion angle ( $ϕ$ , $ψ$ ) language and the steric-clash analysis are identical in principle to the Newman projection analysis of ethane and butane, extended to a biopolymer with many more interacting atom pairs.
Enzyme mechanism 15.14.01. Enzyme active sites often contain residues in strained backbone conformations that position catalytic groups precisely. The energetic cost of these strained conformations is paid by the overall binding energy of the enzyme-substrate complex. Prolyl isomerases illustrate how enzymes catalyse conformational (not chemical) transformations.
Nucleic acid backbone conformation. The analogous structural concept in nucleic acids is the backbone torsion angle sequence $α$ , $β$ , $γ$ , $δ$ , $ϵ$ , $ζ$ (six angles per nucleotide compared to two per amino acid). A-RNA, B-DNA, and Z-DNA are distinguished by their characteristic torsion angle patterns, just as alpha helices and beta sheets are distinguished by ( $ϕ$ , $ψ$ ).
Protein structure prediction and design. AlphaFold2 and related methods predict ( $ϕ$ , $ψ$ ) distributions directly from sequence. Protein design (Rosetta) searches backbone torsion angle space for sequences compatible with a target fold. Both applications depend on accurate Ramachandran distributions as constraints on the conformational search.

Historical notes Master

The Ramachandran plot was introduced by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan in 1963 ("Stereochemistry of polypeptide chain configurations", Journal of Molecular Biology 7, 95--99). Ramachandran used a hard-sphere model with empirically chosen van der Waals radii to calculate which ( $ϕ$ , $ψ$ ) combinations were sterically allowed. The original plot predicted two broad allowed regions (corresponding to the right-handed helix and the beta sheet) and a smaller allowed region in the left-handed quadrant. The agreement with the limited experimental protein structures then available was striking, and the plot became a central tool in structural biology.

The first experimental verification came from the X-ray crystal structures of myoglobin (Kendrew, 1958) and haemoglobin (Perutz, 1960), which showed that the backbone torsion angles of the alpha helix fell squarely in the allowed region predicted by Ramachandran. As more protein structures were solved through the 1960s and 1970s, the accumulated ( $ϕ$ , $ψ$ ) data populated the Ramachandran plot empirically, confirming and refining the theoretical predictions.

The concept of amide resonance as the origin of peptide bond planarity has its roots in Pauling's work on the nature of the chemical bond (1930s--1940s). Linus Pauling and Robert Corey's 1951 paper ("The structure of proteins: two hydrogen-bonded helical configurations of the polypeptide chain", Proceedings of the National Academy of Sciences 37, 205--211) used the planarity of the peptide bond as a fundamental constraint to derive the alpha helix and the beta sheet geometries. Their prediction of the alpha helix (3.6 residues per turn, hydrogen bonds between CO $_{i}$ and NH $_{i + 4}$ ) preceded its experimental confirmation by several years.

The proline cis-trans isomerisation problem was identified by Brandts and coworkers in 1975 as the explanation for slow-folding phases in protein refolding experiments. The discovery of peptidyl-prolyl isomerase activity by Gunter Fischer and coworkers in 1984, and the subsequent identification of cyclophilin as the target of the immunosuppressant cyclosporin A by Handschumacher and coworkers in 1984, connected peptide bond isomerism to immunoregulation and established PPIases as a major enzyme class.

The empirical Ramachandran distributions used in modern structure validation were developed by Gerald Kleywegt and T. Alwyn Jones in the 1990s and refined by the Richardson laboratory (MolProbity, 2003 onward). The transition from hard-sphere theoretical calculations to data-driven empirical distributions improved the sensitivity of Ramachandran analysis as a quality metric, particularly for residues with nontrivial steric environments (proline, pre-proline, glycine).

Bibliography Master

Founding papers.

Ramachandran, G. N., Ramakrishnan, C. & Sasisekharan, V., "Stereochemistry of polypeptide chain configurations", J. Mol. Biol. 7 (1963), 95--99.
Pauling, L. & Corey, R. B., "The structure of proteins: two hydrogen-bonded helical configurations of the polypeptide chain", Proc. Natl. Acad. Sci. USA 37 (1951), 205--211.
Pauling, L., Corey, R. B. & Branson, H. R., "The structure of proteins: two hydrogen-bonded helical configurations of the polypeptide chain", Proc. Natl. Acad. Sci. USA 37 (1951), 205--211.

Proline isomerisation and PPIases.

Brandts, J. F., Halvorson, H. R. & Brennan, M., "Consideration of the possibility that the slow step in protein denaturation reactions is due to cis-trans isomerism of proline residues", Biochemistry 14 (1975), 4953--4963.
Fischer, G., Bang, H. & Mech, C., "Determination of enzymatic catalysis for the cis-trans-isomerization of peptide bonds in proline-containing peptides", Biomed. Biochim. Acta 43 (1984), 1101--1111.
Handschumacher, R. E., Harding, M. W., Rice, J., Drugge, R. J. & Speicher, D. W., "Cyclophilin: a specific cytosolic binding protein for cyclosporin A", Science 226 (1984), 544--547.

Ramachandran analysis and structure validation.

Lovell, S. C., Davis, I. W., Arendall, W. B., de Bakker, P. I. W., Word, J. M., Prisant, M. G., Richardson, J. S. & Richardson, D. C., "Structure validation by Calpha geometry: phi,psi and Cbeta deviation", Proteins 50 (2003), 437--450.
Kleywegt, G. J. & Jones, T. A., "Phi/psi-chology: Ramachandran revisited", Structure 4 (1996), 1395--1400.

Textbook references.

Creighton, T. E., Proteins: Structures and Molecular Properties, 2nd ed. (W. H. Freeman, 1993), Ch. 5.
Ramachandran, G. N. & Sasisekharan, V., "Conformation of polypeptides and proteins", Adv. Protein Chem. 23 (1968), 283--437.
Chothia, C., "Structural invariants in protein folding", Nature 254 (1975), 304--308.