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. 2021 Feb 22;61(2):743-755.
doi: 10.1021/acs.jcim.0c01144. Epub 2021 Feb 5.

Understanding Ring Puckering in Small Molecules and Cyclic Peptides

Lucian Chan  1 , Geoffrey R Hutchison  2   3 , Garrett M Morris  1
Affiliations

Understanding Ring Puckering in Small Molecules and Cyclic Peptides

Lucian Chan et al. J Chem Inf Model. .

Abstract

The geometry of a molecule plays a significant role in determining its physical and chemical properties. Despite its importance, there are relatively few studies on ring puckering and conformations, often focused on small cycloalkanes, 5- and 6-membered carbohydrate rings, and specific macrocycle families. We lack a general understanding of the puckering preferences of medium-sized rings and macrocycles. To address this, we provide an extensive conformational analysis of a diverse set of rings. We used Cremer-Pople puckering coordinates to study the trends of the ring conformation across a set of 140 000 diverse small molecules, including small rings, macrocycles, and cyclic peptides. By standardizing using key atoms, we show that the ring conformations can be classified into relatively few conformational clusters, based on their canonical forms. The number of such canonical clusters increases slowly with ring size. Ring puckering motions, especially pseudo-rotations, are generally restricted and differ between clusters. More importantly, we propose models to map puckering preferences to torsion space, which allows us to understand the inter-related changes in torsion angles during pseudo-rotation and other puckering motions. Beyond ring puckers, our models also explain the change in substituent orientation upon puckering. We also present a novel knowledge-based sampling method using the puckering preferences and coupled substituent motion to generate ring conformations efficiently. In summary, this work provides an improved understanding of general ring puckering preferences, which will in turn accelerate the identification of low-energy ring conformations for applications from polymeric materials to drug binding.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Two distinct pseudo-rotated conformations (white, lilac) of (a) azepane and (b) methylcyclohexane. The best RMSD between conformations are 0.60 Å and 0.67 Å respectively. The RDKit implementation of the RMSD calculation was used. Pseudo-rotation and the concomitant change in substituent orientation, e.g., axial and equatorial methyl groups in panel (b), can lead to diverse geometries.
Figure 2
Figure 2
Definition of the substituent orientation angles α and β. Methylcyclohexane is used as an example, with a mean plane (gray) cutting through the 6-membered ring. The methyl substituent is axial to the mean plane (α = 0.24 rad). O denotes the origin, which is also the geometrical center of the ring. The points S and P are projections of the methyl carbon and the ring atom that is attached to the methyl carbon onto the mean plane. The point Q lies in the mean plane such that points O, P, and Q are collinear. The angle β is defined by the angle between S, P, and Q, and β = −2.25 rad in this example.
Figure 3
Figure 3
6-membered ring conformations: (a) chair, (b) half-chair, (c) boat, and (d) twist boat.
Figure 4
Figure 4
Analysis of 7-membered rings with no endocyclic double bonds. (a) Joint distribution and marginal distribution of the ring puckering amplitudes (q2, q3). This shows that twist-chair and chair conformations (indicated by a red box) are frequently observed in the lowest-energy conformation, followed by boat and twist boat conformations (indicated by a black box). The half-chair (indicated by a dark green box) is the transition structure from chair to boat, and it is occasionally observed. The shape of monocyclic rings is conserved, while there is some variation in bicyclic and polycyclic rings. Note that the color boxes only show the coarse boundary of the conformational clusters. (b) Example of the chair conformation found in cycloheptane (hydrogen atoms not shown). (c) Histogram showing the count of molecules with varying numbers of heteroatoms in rings found in the chair or twist-chair conformation. (d) Coupled phase angles of the chair and twist-chair conformations, as indicated by the red box in (a). This plot reveals the minimum energy pseudo-rotation pathway of the chair and twist-chair conformations. This relationship holds for general 7-membered rings with or without heteroatoms.
Figure 5
Figure 5
7-membered rings with two endocyclic double bonds and their associated phase angle coupling. (a) 1,3-Cycloheptadiene, and (b) the highly coupled phase angles of the low-energy conformations observed in 7-membered rings with double bonds at the 1 and 3 positions. (c) 1,4-Cycloheptadiene and (d) again, the highly coupled phase angles of the low-energy conformations observed in 7-membered rings with double bonds at the 1 and 4 positions. Monocyclic, bicyclic, and polycyclic rings are all included in our analysis, and it should be noted that the double bond can also be a shared aromatic bond. The relative location of the endocyclic double bonds imposes different constraints on the system and results in visibly different phase–phase couplings.
Figure 6
Figure 6
(a) Marginal distribution of the ring puckering amplitude (q2, q3, q4, q5, q6) preferences for two conformational clusters of all-cis conformation in cyclic tetrapeptides (colored red and blue). The two clusters are defined by the α orientation angle of the amide carbonyl oxygen, where U indicates α < π/2, and D indicates α > π/2. The CCCC–DDDD conformations are colored blue, while CCCC–UDDD are colored red. In panel (a), two modes are observed in puckering amplitudes for both clusters, indicating the presence of multiple subclusters. (b) Pairwise joint distribution of the ring puckering amplitude (q2, q3, q4, q5, q6) preferences for two conformational clusters of all-cis conformation in cyclic tetrapeptides. The puckering preferences of CCCC–DDDD conformations are more concentrated than those in CCCC–UDDD conformations.
Figure 7
Figure 7
Example conformation from (a) subcluster 1 and (b) subcluster 2. Hydrogen atoms and side chains are not shown in panels (a) and (b). (c) Ring eccentricity values for two subclusters of CCCC–DDDD conformations are colored purple (subcluster 1) and green (subcluster 2). The main chain–side-chain and side-chain–side-chain intramolecular interactions give rise to diverse geometries.
Figure 8
Figure 8
Substituent orientation angle preferences for (a) carbonyl functional groups and (b) methyl functional groups, attached to small rings with and without endocyclic double bonds. Panel (a) shows that the carbonyl groups tend to be equatorial to the mean plane (α ≈ π/2) in small rings, while panel (b) shows that the orientation of a methyl group tends to be restricted when it is attached to a ring atom that is linked to a neighboring ring atom with a shared endocyclic double bond.
Figure 9
Figure 9
Substituent orientation angle preferences of amide carbonyl groups in cyclic tetrapeptides with CCCC–DDDD conformations, where C denotes cis-amides and D indicates α > π/2, where α is the orientation angle of the ring “substituent” amide carbonyl oxygen: (a) preferred α angles and (b) preferred β angles. Both sets of plots show strong coupling motion between each of the four backbone carbonyl oxygen atoms to avoid steric clashes and/or align main chain–side-chain and side-chain–side-chain intramolecular interactions. An example with the main chain–side-chain interaction and side-chain–side-chain interactions (yellow dotted line) in (c) subcluster 1 and (d) subcluster 2.
Figure 10
Figure 10
Predictions of the (a) α and (b) β orientation angles of a carbonyl group at position 1 in a 6-membered ring chair conformation. The mean angular errors (MAEs), standard deviation of angular errors (shown in parentheses), and the squared circular correlation coefficients are reported. The low squared circular correlation in panel (b) is ascribed to the rigidity of β orientation angles in small rings. (c) Predictions of the first endocyclic torsion angles in a 6-membered ring chair conformation. The predictive performance of other endocyclic torsion angles can be found in Appendix 2, Table S7. (d) Predictions of exocyclic torsion angles of a carbonyl group in all positions for ring sizes up to 16. All proposed models show excellent agreement with the actual substituent orientation angles and torsion angles, with low mean angular errors and high squared circular correlation coefficients.
Figure 11
Figure 11
Alignment of conformations generated by our method (in lilac) and the lowest-energy conformation sampled by CREST (in white) for (a) cycloheptane and (b) 4,4-dimethylcyclohexanone. The sampled conformations are very similar to the lowest-energy conformation, with RMSD values of 0.12 Å and 0.16 Å and TFD values of 0.06 and 0.05, respectively. The torsion deviations are small in both cases, and the deviation in bond lengths and bond angles leads to larger RMSD values. RDKit was used to compute the RMSD and TFD values. Figures were generated using PyMOL.
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