Which ring sizes are puckered

Additionally, the Cremer—Pople representation is atom-order-dependent, and we standardize the atom ordering in the ring before calculation. Bond orders, connectivity, and element types are used to determine this standardized order see Appendix 1.

Other canonical atom numberings may also be used. We also take the volume of the amino acid into account when ordering the backbone ring atoms in cyclic peptides. The priority increases with volume, so tryptophan, tyrosine, and phenylalanine have higher ranks, while glycine has the lowest. The rank order of amino acids can be found in Appendix 1, Table S1. Note that this ordering is only applied to the cyclic peptides.

It is well known that the preferred orientation of ring substituents changes under ring inversion, and neighboring substituents can also influence their preferred orientation. We followed the framework proposed by Cremer 32 to describe the position of substituents unambiguously. Methylcyclohexane is used as an example, with a mean plane gray cutting through the 6-membered ring. 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. With this complete representation for the ring puckering motion and substituent orientation, we can investigate their coupled motion extensively and develop ring puckering potentials for conformer sampling, similar to their acyclic counterparts.

Ring inversion is the interconversion of cyclic conformers that have equivalent ring shapes. Such interconversion can be characterized by Cremer—Pople representation. The substituent orientation also changes during inversion. In particular, we are interested in the coupled ring bond rotations and the associated change in substituent orientation during pseudo-rotation. Inspired by the functional forms studied in previous work, 33 three models are proposed see Appendix 1, eqs S18—S Equation S19 maps the puckering parameters to endocyclic torsion angles, while eq S20 helps explain the rotational dependence between the substituent exocyclic torsion angle and endocyclic torsion angle.

Note that eq S19 is a mapping for the general N -membered ring, and the functional form proposed by de Leeuw et al. Cremer—Pople puckering parameters not only provide quantitative descriptions of puckered N -membered rings but also allow efficient conversion from puckering parameters to Cartesian coordinates, as shown by Cremer.

The default values of bond lengths and bond angles are specified in Tables S2 and S3 in Appendix 1. The calculation of the x -, y -, and z -coordinates from puckering parameters, specified bond lengths, and bond angles is discussed in Appendix 1. To sample low-energy ring conformations efficiently, we used kernel density estimation KDE to learn the ring puckering preferences and generate puckering values from the model.

A Gaussian kernel was used for the density estimation. The samples were then converted to different z -coordinates to give distinct ring conformations. Using the relationship between endocyclic torsion angles and exocyclic torsion angles see Appendix 1, eq S20 with appropriate parameters see Appendix 2, Table S8 , we can update the ring substituent position accordingly.

Note that the exocyclic bond angles are kept fixed in the sampling. This approach is in contrast to traditional knowledge-based sampling methods, 29 , 35 , 36 where ring templates and heuristic rules are used to sample ring conformations, and substituent positions are then assigned by minimizing a clash function or force field energy. Our approach does not require force field minimization, although as discussed below, minimization can also improve cases where the actual bond lengths or angles differ slightly from our model.

Molecules from COD and ZINC contain hydrogen, boron, carbon, nitrogen, oxygen, fluorine, silicon, phosphorus, sulfur, chlorine, bromine, and iodine. Molecules with carbon, nitrogen, oxygen, and sulfur in a ring with up to 20 atoms were considered. Molecules with inconsistent geometries, such as hydrogen atoms or consecutive double bonds contained in a ring, were excluded from the analysis. The peptide data sets contain head-to-tail cyclic tetrapeptides and cyclic pentapeptides, i.

Their sequences are composed of 14 of the 20 naturally occurring l -amino acids see Appendix 3, Table S9. For all molecules from ZINC and the cyclic peptides, experimental-torsion distance geometry with basic knowledge 41 was used to generate initial geometry, followed by geometry optimization using the GFN2 method 42 and conformer sampling using the iterative metadynamics sampling and genetic crossover iMTD-GC method implemented in the CREST program.

Such fragmented molecules were excluded from our analysis. To demonstrate the effectiveness of using puckering preferences in sampling ring conformation, we selected 20 simple molecules, including monocyclic rings with and without endocyclic double bonds and substituents see Appendix 3, Table S A value of 0 indicates a circle and 1 indicates an ellipse.

To assess the performance of our proposed sampling method, we computed the heavy atom root-mean-square deviation RMSD and torsion fingerprint deviation TFD 47 between the generated conformations and the lowest-energy reference conformation sampled from CREST. Furthermore, three metrics, namely, squared circular correlation coefficient R circ 2 , mean angular error MAE , and standard deviation of the angular error, were used to assess the predictive performance of our proposed models.

The circular correlation coefficient and the angular error circular distance between the predicted and actual angles are defined by eqs S22 and S23 in Appendix 1, respectively. RDKit 23 was used to read molecules, generate conformations, and write conformers. A relatively small number of conformational clusters were observed for 5- to 8-membered rings, reflecting their canonical conformations. As expected, the chair conformation is more frequently observed than the boat conformation.

In contrast, the presence of endocyclic double bonds or shared aromatic bonds restricts both puckering and pseudo-rotation.

These relationships hold for both simple monocyclic rings and complex bi- and polycyclic rings. Phase—phase couplings are evident in some conformational clusters. This coupled motion suggests the minimum energy pathway of the chair—twist-chair pseudo-rotation. As suggested by Bocian et al. In bicyclic and polycyclic rings, the adjacent rings and bulky substituents sometimes induce significant steric clashes and result in concomitant changes in conformational preferences.

The increase in amplitude q 2 and decrease in amplitude q 3 indicate a conformational change from chair to half-chair 0. The pseudo-rotations are free in these clusters, i. Analysis of 7-membered rings with no endocyclic double bonds.

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.

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.

To assess the effect of the endocyclic double bonds on conformational preferences, we selected 7-membered rings with one and two endocyclic double bonds. We further separated the observations by the location of endocyclic double bonds. Figure S6 in Appendix 3 shows three conformational clusters in 7-membered rings with single endocyclic double bonds, and they correspond to the chair, half-chair, and boat conformations, which are the same as the case without double bonds.

However, the population of the chair conformation decreases, while the population of half-chair and boat conformations increases. The pseudo-rotations in all three clusters are restricted. The half-chair conformation exhibits strong coupling between phase angles. As the number of endocyclic double bonds increases, the number of degrees of freedom of the ring system decreases.

The correlations in amplitudes are shown in Appendix 3, Figure S7. 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. Earlier, we saw how anti-periplanar alignment of a donor bond orbital with an acceptor antibond orbital could explain conformational preferences in heteroalkanes.

Exactly the same principle applies to a transition state of a reaction, except that the effect is actually much larger than for equilibrium geometries. The fixed anti-periplanar relationships shown below can be exploited:. There is a vast body of chemistry dealing with both other substituents, and multiply substituted cyclohexane rings most of which is beyond the scope of the present lectures.

Only two examples are noted here:. The lesson we learn here is that when two large groups are on adjacent atoms in the cyclohexane ring, the di-equatorial conformation can result in increased steric repulsions between the two groups. Under these circumstances, the ring may flip to a di-axial conformation, where the two large groups are now as far apart as they can be for an example see here , but where each of these groups now encounters more 1,3-diaxial compressions themselves.

This can all be summarised as follows:. Another way of locking a cyclohexane ring is to fuse it with a second such ring, to form a ring system known as decalin. This locked conformation can again be exploited in reactions. In the diagram below, starting from assigning the two ring junction substituents as axial, the rest of the two rings can be inferred.

Thus all the substituent bonds shown in red are axial and are anti-periplanar with respect to each other. This allows e. By discovering s of examples in the very large area of steroid chemistry rings A and B above are the first of four rings in steroids , and classifying them according to the rules above, Barton created the area of conformational analysis, and in the process won the Nobel prize.

The conformational property of five-membered-ring pentoses in the structure of DNA was noted above. The enzymic hydrolysis of the glycosidic bond is catalyzed by diverse enzymes generically termed glycoside hydrolases hereafter GHs or glycosidases. The many sequence-based families of glycosidases have served as a rich hunting ground for enzymologists for years. Not only are these enzymes of fundamental interest, providing paradigms for enzymic catalysis that extend beyond the bounds of carbohydrate chem.

The wide utility of glycosidases, from their industrial harnessing in the hydrolysis of plant biomass to their roles in human physiol. A fascinating thread of this research, and one with major impact on the design of enzyme inhibitors, is the conformational anal. These GH families provide a large pallet of enzymes with which chemists have attempted to depict the conformational landscape of glycosidase action.

In this Account, we review three-dimensional insight into the conformational changes directed by glycosidases, primarily from structural observations of the stable enzyme-ligand species adjacent to the transition state or states and of enzyme-inhibitor complexes. We further show how recent computational advances dovetail with structural insight to provide a quantum mech.

The glycosidase-mediated hydrolysis of the acetal or ketal bond in a glycoside may occur with either inversion or retention of the configuration of the anomeric carbon. Inversion involves a single step and transition state, whereas retention, often referred to as the double displacement, is a two-step process with two transition states. The single transition state for the inverting enzymes and the two transition states those flanking the covalent intermediate in the double displacement have been shown to have substantial oxocarbenium ion character.

The dissociative nature of these transition states results in significant relative pos. The delocalization of lone-pair electrons from the ring oxygen that stabilizes the cationic transition state implies that at, or close to, the transition states the pyranose will be distorted away from its lowest energy conformation to one that favors orbital overlap.

Over the preceding decade, research has highlighted the harnessing of noncovalent interactions to aid this distortion of the sugar substrates from their lowest energy chair conformation to a variety of different boat, skew boat, and half-chair forms, each of which favors catalysis with a given enzyme and substrate.

The blossom of computational approaches, such as ab initio metadynamics, has underscored the quantum mech. Conformational analyses highlight not only the itineraries used by enzymes, enabling their inhibition, but are also reflected in the nonenzymic synthesis of glycosides, wherein chemists mimic strategies found in nature. Ligand design for selective complexation of metal ions in aqueous solution.

A review on the role of steric strain in ligand design for size-match selectivity of macrocycles toward metal ions. About res.

Host-guest complexes of calix[4]tubes - prediction of ion selectivity by quantum chemical calculations VI. Highly selective complexation of metal ions by the self-tuning tetraazacalixpyridine macrocycles. Tetrahedron , 65 , 87 — 92 , DOI: Elsevier Ltd. While no interaction was obsd. Macrocycles occupy a unique segment of chem. In the past decade, their chem. As a consequence, this structural type has now been successfully tested on most biol. The goal of this article is to put into perspective the current applications, opportunities, and challenges assocd.

Accordingly, the first part of this article is dedicated to the drug discovery aspects of macrocycles and highlights salient features of their medicinal chem. This section is organized by target class, a choice aimed at providing the reader an appreciation of the structural diversity generated for each class. To give the reader an appreciation of the tools available to construct macrocyclic scaffolds, the site and method of the pivotal macrocyclization step are indicated in the figures.

Readers are referred to the source articles for further details. In the second part, the technologies and synthetic approaches that already have demonstrated utility or possess a high potential for macrocycle-based drug discovery are discussed. Finally, a perspective on the future of synthetic macrocycles in medicinal chem. Macrocycles are ideal in efforts to tackle difficult targets, but our understanding of what makes them cell permeable and orally bioavailable is limited.

A significant no. Moreover, insight from a group of de novo designed oral macrocycles in clin. However, the no. How Proteins Bind Macrocycles.

Villar, Elizabeth A. Nature Publishing Group. The potential utility of synthetic macrocycles MCs as drugs, particularly against low-druggability targets such as protein-protein interactions, has been widely discussed. There is little information, however, to guide the design of MCs for good target protein-binding activity or bioavailability. To address this knowledge gap, we analyze the binding modes of a representative set of MC-protein complexes. The results, combined with consideration of the physicochem.

We addnl. The exploration of macrocycles for drug discovery-an underexploited structural class. Drug Discovery , 7 , — , DOI: Natural products comprised of a macrocycle ring structure have proven their therapeutic applications as antibiotics, immunosuppressants as well as anticancer agents. Despite this, macrocyclic compds. Terrett and colleagues review the properties and features of current macrocycle drugs, emphasizing the vast potential of synthetic macrocycles in drug discovery.

Macrocyclic natural products have evolved to fulfil numerous biochem. A macrocycle provides diverse functionality and stereochem.

This can result in high affinity and selectivity for protein targets, while preserving sufficient bioavailability to reach intracellular locations.

Despite these valuable characteristics, and the proven success of more than marketed macrocycle drugs derived from natural products, this structural class has been poorly explored within drug discovery. This is in part due to concerns about synthetic intractability and non-drug-like properties. This Review describes the growing body of data in favor of macrocyclic therapeutics, and demonstrates that this class of compds. Conformational analysis of the sugar ring in nucleosides and nucleotides.

New description using the concept of pseudorotation. A statistical classification of the no. A , , — , DOI: Ionescu, Andrei R. The conformation of the six-membered ring of pyranosyl sugars has pronounced effects on the phys. We present a method to det. Finally, we make the first detn. For both anomers, a transition state with five coplanar atoms was found. The method is based on constrained Car-Parrinello ab initio mol. The constraints are derived from the normal modes of six-membered rings and are described in terms of the canonical conformations 1C4 chair, 1,4B boat, and OS2 skew-boat.

The PAW derived trajectories are in agreement with previous suggestions in the literature that pseudo-rotation is an important feature of such conformational interconversion. The dynamics nature as well as the internal coordinate-based constraints provide a method which can reliably accommodate pseudo-rotation. To det. In all cases where exptl. The conformational flexibility of the glycosaminoglycans GAGs are known to be key in their binding and biol.

In this work, we employ enhanced sampling mol. We first perform unbiased MD simulations of glucose anomers and the epimers glucoronate and iduronate. These calcns. However, by applying our recently developed msesMD simulation method multidimensional swarm enhanced sampling mol. For the force field employed, we find that in general the calcd. This accords with recent exptl. Glycoside hydrolases GHs distort carbohydrate ring geometry along particular "catalytic itineraries" during the cleavage of glycosidic bonds, illustrating the relationship between substrate conformation and reactivity.

Previous theor. However, kinetic accessibility of carbohydrate puckering conformations and the role of exocyclic groups have not yet been thoroughly addressed. Here we present the first complete library of low-energy local min. These were obtained by a thorough theor. Furthermore, these data enable evaluation of previous hypotheses of why enzymes perturb ring geometries from the low-energy equatorial chair 4C1 conformation. They show that the relative thermodn. For some sugars, particular puckers offer both catalytically favorable electronic structure properties, such as anomeric carbon partial charge, and low kinetic barriers to achieve a given puckering conformation.

Overall, this study reveals a more comprehensive understanding of why particular puckering geometries are favored in carbohydrate catalysis concomitant with the complexity of glycobiol. Conformations of cycloheptane. A relatively complete calcn. The various paths for pseudorotation and the various transition states are rigorously characterized. The pseudorotation paths of cycloheptane can be visualized as occurring on a helical track wound around a torus.

The results give the best agreement with the available rotational constants. Conformations of cyclooctane and some related oxocanes. A , 85 , — , DOI: A potential-energy function is detd. A model is developed that provides a representation for the interconversion of the conformations of 8-membered rings. The boat-chair form is the min.

In the case of the oxocanes, the O atoms have definite preferred positions. Conformation of cyclohexadecane. NMR data indicated that the [] conformation of cyclohexadecane is 1.

The mol. Conformational Study of the Structure of Free Crown In addn. Comparison between the structure of the S6 conformation of 18c6 and the S4 lowest energy conformation of crown-4, as well as other important conformations of both mols.

It is concluded that the correlation energy is necessary to have an accurate energy order of the predicted conformations. A rationalization of the conformational energy order in terms of the hydrogen bonding and conformational dihedral angles is given. It is also suggested that to have a better energy order of the predicted conformations at the MM3 level, better empirical force fields corresponding to the hydrogen bond interactions are needed.

A conformational search was performed for the crown-4 12c4 -alkali metal cation complexes using two different methods, one of them is the CONFLEX method, whereby eight conformations were predicted. The calcd. Larger relative energy differences are attributed to larger differences between the B3LYP and MP2 optimized geometries.

Binding enthalpies BEs were calcd. The agreement between the calcd. BEs is discussed. The conformational properties of calix[4]arenes, calix[6]arenes, calix[8]arenes, and oxacalixarenes. The [1n]metacyclophanes known as calixarenes, obtainable in ring sizes contg. The conformational characteristics of these mols. The 1H NMR data are commensurate with a cone conformation for the cyclic tetramers and cyclic pentamers, a winged or hinged conformation for the cyclic hexamers, and a pleated-loop conformation for the cyclic octamers.

The conformational implications of the temp. General definition of ring puckering coordinates. A unique mean plane is defined for a general monocyclic puckered ring. The geometry of the puckering relative to this plane is described by amplitude and phase coordinates which are generalizations of those introduced for cyclopentane by Kilpatrick, Pitzer, and Spitzer No math.

A short treatment of the four-, five-, and six-membered ring demonstrates the usefulness of this concept. An example is given of the anal. B , , — , DOI: The intrinsic conformational preferences of proline analogs having double bonds between carbon atoms in their rings have been investigated using quantum mech.

For this purpose, the potential energy surface of the N-acetyl-N'-methylamide derivs. We found that the double bonds affect the ring puckering and the geometric internal parameters, even though the backbone conformation was influenced the most.

Results indicate that the formation of double bonds between carbon atoms in the pyrrolidine ring should be considered as an effective procedure to restrict the conformational flexibility of prolines.

Interestingly, we also found that the N-acetyl-N'-methylamide deriv. The Cremer-Pople ring puckering anal. H-bonding in 2'-deoxycytidine, 2'-deoxyadenosine, 2'-deoxythymidine, and 2'-deoxyguanosine. We mapped for each deoxyribonucleoside the complete conformational energy surface and the corresponding pseudorotation path. We found only incomplete pseudorotation cycles, caused by ring inversion, which we coined as pseudolibration paths. On each pseudolibration path a global and a local min.

The investigation of H-bond free deoxyribonucleoside analogs revealed that removal of the H-bond does not restore the full conformational flexibility of the sugar ring. Our work showed that ring puckering predominantly dets.

In contrast no direct correlation between conformational energy and H-bond strength was found. The longest and weakest H-bonds are located in the local min. H-bonding in the puric bases has a more covalent character whereas in the pyrimidic bases the H-bond character is more electrostatic. We investigated how the mutual orientation of the CH2OH group and the base influences H-bond formation via two geometrical parameters describing the rotation of the substituents perpendicular to the sugar ring and their tilting relative to the ring center.

According to our results, rotation is more important for H-bond formation. O , via the delocalization energy. We found larger delocalization energies corresponding to stronger H-bonds for the puric bases.

The global min. The application of our new anal. The conformational anal. There are many factors that contribute to this complexity. These include a large no. To a greater extent than within acyclic mols. However, this coupling of bond rotations and transannular interactions enables the transmission of three-dimensional information from one side of a macrocycle to the other.

Making relatively small structural modifications to a macrocycle can result in local conformational changes that propagate along the ring to affect distal structural features. The factors that control how such changes can propagate are poorly understood and it is difficult to predict which modifications will result in significant conformational reorganizations of remote regions of a macrocycle.

This review discusses examples where small structural modifications to macrocyclic scaffolds change the conformational preferences of structurally remote regions of the ring. We will highlight evidence provided for conformational changes triggered by remote substituents and explanations about how these changes might occur in an effort to further understand the factors that control such phenomena.

Google Scholar There is no corresponding record for this reference. The Thermodynamics and Molecular Structure of Cyclopentane 1.

Published data on electron diffraction, Raman and infrared spectra, entropy and sp. The puckering of the cyclopentane ring is not of a definite type, but the angle of max. Although the chair conformation is the most stable conformation that cyclohexane can adopt, there is enough thermal energy for it to also pass through less favorable conformations before returning to a different chair conformation.

When it does so, the axial and equatorial substituents change places. The passage of cyclohexane from one chair conformation to another, during which the axial substituents switch places with the equatorial substituents, is called a ring flip. Methylcyclohexane is cyclohexane in which one hydrogen atom is replaced with a methyl group substituent. Methylcyclohexane can adopt two basic chair conformations: one in which the methyl group is axial, and one in which it is equatorial.

Methylcyclohexane strongly prefers the equatorial conformation. In the axial conformation, the methyl group comes in close proximity to the axial hydrogens, an energetically unfavorable effect known as a 1,3-diaxial interaction Figure 3. Thus, the equatorial conformation is preferred for the methyl group. In most cases, if the cyclohexane ring contains a substituent, the substituent will prefer the equatorial conformation.

Jonathan Mooney McGill University. Ring Strain and the Structures of Cycloalkanes There are many forms of cycloalkanes, such as cyclopropane, cyclobutane, cyclopentane, cyclohexane, among others. Chair Conformation of Cyclohexane - Equitorial and Axial There are two ways to draw cyclohexane because it can be in a hexagon shape or in a different conformational form called the chair conformation and the boat conformation.

The chair conformation drawing is more favored than the boat because of the energy, the steric hindrance, and a new strain called the transannular strain. The boat conformation is not the favored conformation because it is less stable and has a steric repulsion between the two H's, shown with the pink curve. This is known as the transannular strain, which means that the strain results from steric crowding of two groups across a ring.

The boat is less stable than the chair by 6. The boat conformation, however, is flexible, and when we twist one of the C-C bonds, it reduces the transannular strain.

When we twist the C-C bond in a boat, it becomes a twisted boat. Image used with permission William Reusch, MSU Although there are multiple ways to draw cyclohexane, the most stable and major conformer is the chair because is has a lower activation barrier from the energy diagram.

These are hydrogens in the axial form. Ring Strain Cycloalkanes tend to give off a very high and non-favorable energy, and the spatial orientation of the atoms is called the ring strain.

There are different types of ring strain: Transannular strain isdefined as the crowding of the two groups in a ring. Eclipsing strain, also known as torsional strain, is intramolecular strain due to the bonding interaction between two eclipsed atoms or groups. Bond angle strain is present when there is a poor overlap between the atoms.