Alice Qinhua Zhou

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (ϕ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed ϕ/ψ combinations. The “bridge region” (ϕ ≤ 0° and −20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of ϕ/ψ angles in 850 non‐homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B‐factor less than 30 Å2. We show that the distribution of ϕ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.

Predicting the side‐chain dihedral angle distributions of nonpolar, aromatic, and polar amino acids using hard sphere models

The side‐chain dihedral angle distributions of all amino acids have been measured from myriad high‐resolution protein crystal structures. However, we do not yet know the dominant interactions that determine these distributions. Here, we explore to what extent the defining features of the side‐chain dihedral angle distributions of different amino acids can be captured by a simple physical model. We find that a hard‐sphere model for a dipeptide mimetic that includes only steric interactions plus stereochemical constraints is able to recapitulate the key features of the back‐bone dependent observed amino acid side‐chain dihedral angle distributions of Ser, Cys, Thr, Val, Ile, Leu, Phe, Tyr, and Trp. We find that for certain amino acids, performing the calculations with the amino acid of interest in the central position of a short α‐helical segment improves the match between the predicted and observed distributions. We also identify the atomic interactions that give rise to the differences between the predicted distributions for the hard‐sphere model of the dipeptide and that of the α‐helical segment. Finally, we point out a case where the hard‐sphere plus stereochemical constraint model is insufficient to recapitulate the observed side‐chain dihedral angle distribution, namely the distribution P(χ3) for Met. Proteins 2014; 82:2574–2584.

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.

Intrinsic α-helical and β-sheet conformational preferences: A computational case study of alanine

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α‐helix, β‐sheet, or other backbone dihedral angle ( ϕ ‐ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α‐helical structures, while experiments on small peptides observe that β‐sheet‐like conformations predominate. We perform molecular dynamics (MD) simulations of a hard‐sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard‐sphere MD simulations, we show that (1) β‐sheet structures are roughly three and half times more probable than α‐helical structures, (2) transitions between α‐helix and β‐sheet structures only occur when the backbone bond angle τ (NCαC) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the “bridge” region of ϕ ‐ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high‐resolution protein crystal structures. Our results emphasize the importance of hard‐sphere interactions and local stereochemical constraints that yield strong correlations between ϕ ‐ψ conformations and τ.

Reply to: Comment on “Revisiting the Ramachandran plot from a new angle”

Dear Brian, With this letter, we reply to Porter and Rose, who in a recent paper1 and in their Comment on “Revisiting the Ramachandran plot from a new angle” assert that sidechain hydrogen bonding is the primary determinant of the observed population of φ/ψ backbone dihedral angles in the “bridge region” (φ ≤ 0° and −20° ≤ ψ ≤ 40°). Our manuscript “revisiting the Ramachandran plot from a new angle”2 shows that steric considerations alone predict the observed backbone dihedral angle distributions. In this response, we reinterate three main points. The calcuated Ramachandran plot depends critically on the value of the bond angle τ (between C′, Cα, and N). Specifically, as τ increases within the range 100° ≤ τ ≤ 120°, configurations in the “bridge region” with φ ≤ 0° and −20° ≤ ψ ≤ 40° change from being disallowed at τ = 100° to be allowed at τ = 115° and above. In fact, this result dates back to 1965,3 but most often Ramachandran plots are drawn for a single value of τ, typically τ = 110°. The τ dependence is generally not considered. We analyzed a database4 of high-resolution protein structures and plotted the backbone dihedral angles of all amino acids on Ramachandran plots as a function of their bond angle τ. (See Fig. 2 in Ref.2) In agreement with the predictions of Ramachandran and colleagues,3 the bridge region is populated by amino acids with large values of τ, while φ and ψ combinations in the bridge region are not frequently observed for amino acids with smaller values of τ. Thus, an increased population of structures in the bridge region at large τ is consistent with the predictions from steric interactions alone for every amino acid type. The analysis and conclusions of Porter and Rose suggest that hard–sphere interactions alone cannot explain the observed distribution of backbone dihedral angles. For example, they state in the abstract that the “forbidden [bridge] region is well-populated in folded proteins, which can provide longer-range intramolecular hydrogen-bond partners.” However, using only a hard sphere model, Ramachandran and colleagues predicted the φ and ψ combinations as a function of τ that are observed in proteins of known structure. In particular, they showed that φ and ψ combinations in the bridge region are not forbidden at large τ. It is certainly possible that hydrogen-bonding may influence the adopted value of τ (which in turn may then influence the allowed values of φ and ψ), but the existence of φ and ψ combinations within the bridge region is not on its own prime facia evidence of the role of hydrogen bonding.

Intrinsic α-helical and β-sheet conformational preferences: A computational case study of alanine: Intrinsic α-Helical and β-Sheet Conformational Preferences

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α‐helix, β‐sheet, or other backbone dihedral angle ( ϕ ‐ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α‐helical structures, while experiments on small peptides observe that β‐sheet‐like conformations predominate. We perform molecular dynamics (MD) simulations of a hard‐sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard‐sphere MD simulations, we show that (1) β‐sheet structures are roughly three and half times more probable than α‐helical structures, (2) transitions between α‐helix and β‐sheet structures only occur when the backbone bond angle τ (NCαC) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the “bridge” region of ϕ ‐ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high‐resolution protein crystal structures. Our results emphasize the importance of hard‐sphere interactions and local stereochemical constraints that yield strong correlations between ϕ ‐ψ conformations and τ.

Intrinsic alpha-helical and beta-sheet preferences: A computational case study of Alanine

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α‐helix, β‐sheet, or other backbone dihedral angle ( ϕ ‐ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α‐helical structures, while experiments on small peptides observe that β‐sheet‐like conformations predominate. We perform molecular dynamics (MD) simulations of a hard‐sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard‐sphere MD simulations, we show that (1) β‐sheet structures are roughly three and half times more probable than α‐helical structures, (2) transitions between α‐helix and β‐sheet structures only occur when the backbone bond angle τ (NCαC) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the “bridge” region of ϕ ‐ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high‐resolution protein crystal structures. Our results emphasize the importance of hard‐sphere interactions and local stereochemical constraints that yield strong correlations between ϕ ‐ψ conformations and τ.