Visualisation of Cyclic and Multi-Branched Molecules with VMD

1. Introduction

Molecular visualisation aims to highlight the connectivity and important structural features of a molecule and hence facilitate the conceptual understanding necessary for solving structure-function relationships. Abstract representations, such as ribbon[1, 2, 3] or cartoon diagrams[1], have long been preferred over explicit representation of the atomic positions for proteins. However, there are currently few abstract visualisations widely available for other classes of molecules. In particular, aside from DNA, the visualisation of cyclic molecules and multi-branched molecules is largely neglected by current molecular visualisation packages.

Polysaccharides, in particular, are comprised of chains of cyclic sugar residues, often multi-branched. These molecules have an enormous variety of roles to play in biological organisms, from structural molecules to the molecular recognition and cell signalling roles played by many glycoproteins. For example, the elucidation of the mechanisms that govern how oligosaccharides are accommodated in the binding sites of lectins, antibodies and enzymes is currently of major interest. However, the high incidence of incorrect carbohydrate stereochemistry and glycosidic linkages for glycoprotein entries in the PDB database[4, 5, 6] illustrates the difficulty with identifying incorrect structures by researchers less familiar with the intricacies of carbohydrate structure, stereochemistry and favoured ring conformations. For this reason, tools have been developed for general glycan structure verification. The Carbohydrate Structure Suite (CSS)[7] contains the pdb-care program, a verification service for the nomenclature of a saccharide unit that is able to identify and assign carbohydrate structures using only atom types and their 3D atom coordinates[4], The glycoconjugate Data Bank (GDB) can be used to verify N-glycan primary structures.[8] However, even where the stereochemistry and ring structures are correct, the glycan components of glycoproteins can exhibit incorrect ring pucker conformations as a result of the crystal structure refinement process. None of these tools incorporates analysis of the carbohydrate ring pucker parameters, which currently involves separate calculation using available codes.[9] Highlighting altered carbohydrate ring pucker is also useful for analysis of carbohydrate-protein interactions, which often involve a change of ring conformation from low-energy chair conformations, to the higher-energy but relatively stable boat and twist-boat conformations.

In previous work, we developed a standalone application, CarboHydra, to test two novel visualisation algorithms for carbohydrate structures, which we named PaperChain and Twister.[10] These visualisations provide control over the level of detail shown for carbohydrate structures. The PaperChain visualisation highlights the conformation of a ring with a polygon that is coloured according to the ring pucker coordinates. The Twister visualisation is intended to serve the same purpose for carbohydrates as ribbon diagrams do for proteins, tracing the backbone conformation of polysaccharide chains. Here, a curved ribbon highlights the backbone linkages, with the twist of the strand revealing the relative orientation of each successive ring, an important conformational detail in polysaccharides. In addition, Twister is useful in revealing the backbone network of complex multibranched polysaccharides, which are difficult to trace when viewed in typical ball-and-stick representations.

The CarboHydra prototype established the efficacy of the algorithms and initial response from the community of carbohydrate researchers demonstrated a need for these visualisations. However, CarboHydra had limited utility: it did not include any additional molecular visualisations, such as secondary structure or “cartoon” representations for proteins, and was developed solely for Windows platforms. This is an instance of a commonly recognised problem - there is a pressing need to incorporate innovations in visualisation into existing molecular visualisation packages to make them available to a wider community.[11]

We chose the Visual Molecular Dynamics (VMD) package[12] in the first instance for implementation of our algorithms. VMD is widely available and VMD source code is freely accessible available on the web and by remote CVS access. This approach has the added advantage of combining these novel visualisations with those already extant in VMD, thus enabling novel views of glycoproteins and carbohydrate-binding proteins. A further advantage of the incorporation process is that it led to the generalization and improvement of the PaperChain and Twister algorithms. The algorithms were validated on a variety of structures, options for limiting the size of rings were added and the ring-detection procedure was altered so that all cycles are detected, not just those in saccharide residues. In addition, a uniform colour mapping scheme for all rings was implemented: a one-dimensional colour scale based solely on the puckering amplitude as defined by Cremer and Pople.[13] This colour scheme clearly differentiates between planar rings and various degrees of pucker.

Previously, we analysed the value of the Twister and PaperChain visualisations for a selection of carbohydrate structures. The efficacy of the two visualisations is trivial to show in the much more rapid recognition of ring location, ring type and ring pucker for the PaperChain visualisation and relative residue orientation for the Twister visualisation that results. However, the effectiveness of these visualisation techniques is more difficult to quantify where non-quantitative judgements, such as key insights, are involved. Here we focus on visualisations of glycoproteins and lectins, which are made possible by the combination of Twister and PaperChain with the other visualisations implemented into VMD.

In our first example, the ease of locating incorrect structures with our current visualisations is demonstrated on a glycoprotein structure. The second example concerns a chitolectin. Here we visualize this carbohydrate-binding protein to assess whether ring puckering plays a role in carbohydrate binding and to determine whether the use of the PaperChain and Twister visualisations facilitates the development of key insights into the carbohydrate binding mechanism in this class of molecules.

2. Methodology

The VMD package is written in the C++ programming language with the OpenGL graphics library and comprises a large set of classes. Additions were made to the BaseMolecule and DrawMolItem classes to incorporate the PaperChain and Twister visualisations into VMD. In all cases, the visualisations are subject to the powerful VMD selection functions, whereby the visualisation is applied to only the selected atoms in the current molecular structure.

2.4. Rendering PaperChain

The PaperChain visualisation depicts the conformation of individual rings by fitting a polyhedron through the participating atoms and the ring centroid. The rings found (both oriented and unoriented rings) are rendered as bipyramids with a user-adjustable height, H. The normal to the ring is calculated using Newell’s method[16] and the tops of the pyramids are located a height H above the centroid in the direction of the ring normal. The base of each pyramid is the (possibly non-planar) closed polygon formed by the ring. Only rings which have all atoms selected are rendered.

2.4.1. Ring colour mapping

In our original CarboHydra implementation, the colour of a hexose ring was defined according to a red, green, blue (RGB) colour scheme, as:

$$R=\mid \mathit{sin}\left(\theta \right)\mid \ast Q$$

(3)

$$G=\mid \mathit{cos}\left(\theta \right)\mid \ast Q$$

(4)

$$B=\mid \mathit{sin}\left(3\varphi \right)\mathit{sin}\left(\theta \right)\mid \ast Q$$

(5)

where R is the red component, G is the green component and B is the blue component and θ, ϕ and Q the Cremer-Pople puckering parameters.[13] While this scheme has the advantage of clearly differentiating between the canonical conformations of hexose rings (see Table 1), it is not general for all rings. In addition, the colour of planar rings is arbitrarily defined. Therefore, we implement here a general one dimensional colour scale for all rings with 3 or more atoms. To achieve this, we investigated a variety of colouring schemes, including using the new Hill-Reilly puckering parameters.[9] However, all approaches using puckering angles are problematic, as the puckering angles calculated vary according to the stipulated start point of the ring. For a particular ring type, such as proline rings or glucose rings, common convention has decided the atom order. Unfortunately, implementing this would complicate the ring-finding algorithm with a large number of heuristics. Therefore, we require a universal parameter that is invariant with respect to the starting point of the ring. The Cremer-Pople puckering amplitude has this property.

Table 1.

Comparison of the colouring schemes for 6-membered rings used in the original CarboHydra implementation[10] and this work. The values for the Cremer-Pople puckering parameters for each canonical structure are as listed in Hill at al.[9]. (ϕ and θ in °, Q in Å.) Planar rings, though not listed, appear as black in the old scheme, red in our new scheme.

Conformer	Cremer-Pople Coordinates			Original Carbohydra Colours			Colour	Revised Carbohydra Colours			Colour
	ϕ	θ	Q	R	G	B		R	G	B
1C4	0-360	180	0.57	0.0	0.57	0.0		0.0	1.0	0.13
4C1	0-360	0	0.57	0.0	0.57	0.0		0.0	1.0	0.13
1,4B	240	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
B1,4	60	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
2,5B	120	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
B2,5	300	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
3,6B	0	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
B3,6	180	90	0.76	0.76	0.0	0.0		0.0	0.0	1.0
1H2	270	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
2H1	90	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
2H3	150	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
3H2	330	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
3H4	30	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
4H3	210	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
4H5	270	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
5H4	90	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
5H6	150	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
6H5	330	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
6H1	30	51	0.42	0.33	0.26	0.33		0.88	1.0	0.0
1H6	210	129	0.42	0.33	0.26	0.33		0.88	1.0	0.0
1S3	210	88	0.62	0.62	0.02	0.62		0.0	1.0	0.75
3S1	30	92	0.62	0.62	0.02	0.62		0.0	1.0	0.75
5S1	90	92	0.62	0.62	0.02	0.62		0.0	1.0	0.75
1S5	270	88	0.62	0.62	0.02	0.62		0.0	1.0	0.75
6S2	330	88	0.62	0.62	0.02	0.62		0.0	1.0	0.75
2S6	150	92	0.62	0.62	0.02	0.62		0.0	1.0	0.75
1E	240	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E1	60	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
2E	120	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E2	300	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0
3E	360	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E3	180	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
4E	240	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E4	60	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0
5E	120	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E5	300	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
6E	360	55	0.45	0.37	0.26	0.0		0.69	1.0	0.0
E6	180	125	0.45	0.37	0.26	0.0		0.69	1.0	0.0

Open in a new tab

Here we colour all rings according to the Cremer-Pople puckering amplitude, which is defined for all rings with size >= 3. The puckering amplitude is mapped to a one-dimensional colour scale, allowing for any three-colour range in one dimension for puckering amplitudes ranging from 0.0 Å to 2.0 Å (any value higher than this is truncated to 2.0). Our default colour range is a “hot-to-cold” scale, ranging from red for planar rings, through yellow, green, cyan and blue. Rings with puckering amplitudes approaching 2.0 Å are mapped to magenta. However, we have set the colouring stationary points to be non-uniform, to suit particularly the most common pentose and hexose rings. The stationary points are set at: 0.0 (red), 0.4 (yellow), 0.56 (green), 0.64 (cyan), 0.76 (blue) and 2.0 (magenta) Å.

A comparison between the original and our new colour mapping schemes for canonical conformations of pyranose rings is shown in Table 1. While puckering amplitude is not unambiguously associated with a particular conformation, this table makes it clear that there is a strong correlation between them. The puckering amplitudes tend to increase from planar rings (red), through half-chairs (yellow), envelopes (yellow-green) , chairs (green), twist-boats (cyan) and boats (blue). Larger rings are associated with higher puckering amplitudes, effectively separating the non-aromatic 5-membered rings such as proline and furanose (which typically map to yellow) from the 6-membered rings. As a further utility for users, we have incorporated the calculated ring puckering amplitude into the VMD atom selection language, giving users the useful ability to apply particular visualisations based on puckering amplitude.

3. Results and Discussion

The default hot-to-cold colour scale for PaperChain as applied to representative cycloalkane structures is illustrated in Fig. 1. Here planar (Fig. 1(a)) cyclopropane and (b) cyclobutane are both coloured red, while the characteristic envelope conformation of cyclopentane, (c), is yellow. In cyclohexane, (d), the lowest energy chair structure is green, the twist-boat conformation cyan and the boat conformation blue. The puckered conformations of cycloheptane and cyclooctane (crown conformation) both appear as deep blue. Larger, more dramatically puckered rings are coloured magenta, as for the α-cyclodextrin structure shown in Fig. 6(e).

The envelope glycoproteins of HIV and SIV are the molecular agents of cell attachment and membrane fusion and are thus of considerable interest. Fig. 2 shows our visualisation of the crystal structure of an unliganded and fully-glycosylated Simian Immunodeficiency Virus GP120 envelope glycoprotein at 4 Å resolution, as reported in Chen et al.[19] In Fig. 2(a), the SIV the PaperChain visualisation is applied to the glycan components only, using the default colour scale for the ring pucker. In (b), only rings of puckering amplitudes not associated with the low-energy chair conformations of the pyranose rings are highlighted. This was achieved with the new selection statements we added to VMD (i.e “select pucker 0.0 to 0.9 or pucker 0.6 to 1.0” - refer to Table 1 for typical amplitude values). From the yellow and blue colours displayed for the glycan components, it is clear that a number of the saccharide rings exhibit unusual puckering amplitudes and conformations for pyranose rings: biologically unlikely envelope conformations are coloured yellow and yellow-green, while twist-boats are cyan and boats blue. These atypical ring puckering amplitudes are likely a result of the harmonic restraints applied to the glycans during crystal structure refinement inadvertently forcing incorrect ring conformations. Similar errors in ring pucker, including highly puckered proline residues (Q > 0.5, mapping to green rather than yellow in our colour scheme) and non-planar aromatic rings, can be seen for a number of other structures in the PDB database. The PaperChain visualisation thus has broad applicability as a simple check for ring conformations and, therefore, also has utility for molecular model building, where steric clashes during energy minimization procedures can also lead to errors in ring conformation.

Our second example concerns the lectin family of proteins, which bind sugars with very high specificity. Protein Family 18 chitolectins are homologous to the catalytically active chitinases, but the inactive chitolectins simply bind and do not hydrolyse oligosaccharides, due to a mutation in an active site residue. A series of recent investigations into the X-ray structures and carbohydrate binding properties of SPX-40 family of chitolectins revealed that these proteins bind chitin-like oligosaccharides in a similar mode to the chitinases,[21, 22] within a groove with 9 subsites.[23, 24, 25, 26, 20] A key component of the sugar hydrolysis mechanism for Family 18 chitinases is known to be distortion of the N-acetylglucosamine ring at the binding site from a chair to a boat conformation.[27, 28, 21, 24, 29] However, although a similar distortion of a sugar ring to boat conformation has been seen to occur in the binding of chito-oligosaccharides to human cartilage glycoprotein[23], no commentary on possible ring distortions was made in three recent studies of related chitolectins.[25, 26, 20]

Fig. 3 shows PaperChain visualisations of four N-acetylglucosamine oligosaccharides (GlcNAc_n , n=3−6) bound in complex with the SPG-40 goat secretory glycoprotein.[20] This novel combination of visualisations renders the location and conformation of the rings much clearer than the depictions in the original work.[20] The SPG-40 protein is glycosylated: the main image in Fig. 3 shows a pendant oligosaccharide with six residues (6-acetylglucosamine, GlcNAC₆). The second residue in this chain, though coloured green, is actually distorted into a boat conformation. This is an example of the puckering amplitude not being unambiguously associated with ring conformation: the ring is coloured green, as for most chairs. Both the bound GlcNAC₆ oligosaccharide in the main image and the GlcNAC₅ oligosaccharide (inset (a)) show increased puckering amplitudes for the first and third residues, as evinced by green-blue colour. It is also clearly apparent in the PaperChain visualisations that binding alters the pucker of the penultimate (deep blue) residue in the GlcNAC₆ chain, deep within the binding pocket at location −2, which is in the boat conformation. This fact was not mentioned in the original work,[20] although a related lectin, human cartilage glycoprotein (HCGP39), has been observed to force a skewed boat conformation for the sugar residue at the −1 binding site. [23, 24] The last residue of GlcNAC₅ is in the same location in the binding site and is distorted to a envelope conformation, as is made evident by the yellow colour. The shorter oligosaccharides, GlcNac₄ (inset (b)) and GlcNac₃ (inset (c)), show puckering amplitudes around 0.56 (green), which are associated with undistorted chair conformations for the rings.

The SPG-40 protein binds longer oligosaccharides with high affinity, and we suggest that alteration in ring pucker of the saccharide ligand may be necessary for tight binding. The shorter oligosaccharides, GlcNac₃ and GlcNac₄, which do not show ring distortions, bind with low affinities and do not form stable complexes in solution.[20] We found that a similar situation exists for the binding of N-acetylglucosamine oligosaccharides to the related sheep secretory glycoprotein, SPS-40 (not shown).[26] Again, the shorter oligosaccharides (n=3 and n=4) do not reach location −1 on the binding site and show undistorted ring conformations, while longer oligosaccharides show distorted conformations at position −1. Here ring distortion is also associated with stronger binding: the GlcNac₃ and GlcNac₄, ligands bind weakly to SPG-40, while GlcNAc₅ and GlcNAc₆ bind with considerable strength.[20] Thus, we propose that ring distortions are likely to be a key component of the strong binding of oligosaccharides to the chitolectins, a role similar to that played by chair-to-boat ring flips in the sugar hydrolysis mechanism of the related chitinases.[27, 28, 21, 24, 22]

A further advantage of the PaperChain visualisation, is that the cyclic aromatic (red) and proline (yellow to green) residues with proteins are easily located, as shown in an alternative view of the SPG-40 protein in Fig. 4. The inset in this figure shows the interaction of the GlcNac₆ substrate with the aromatic tryptophan and tyrosine protein residues located on the floor of the binding groove. The PaperChain representation highlights the stacking orientation of these rings to the carbohydrate residues, which is not clearly apparent in the ball-and-stick representations. This is a common feature of carbohydrate-protein interactions: conserved aromatic amino acid residues are frequently present in carbohydrate-binding sites of proteins, where they are involved in CH-π stacking interactions with the C-H groups of bound sugar rings.[22, 30, 25] Finally, a combination of Twister and PaperChain (Fig. 5(a)) or just Twister (Fig. 5(b)) can be used to show clearly the 180° flip of successive sugar rings for the chito-oligosaccharides. Here, the clear twist in the connecting ribbon between rings highlights the alternating “up” and “down” orientations of the glucose residues - a preferred conformation that is characteristic of both chitin and cellulose polysaccharides.

Thus far, we have considered two illustrative examples of glyoproteins, demonstrating the utility of our new visualisations. To conclude, we present a number of non-protein cyclic molecular structures depicted with the PaperChain and Twister visualisations. In a PaperChain visualisation of sucrose (Fig. 6(a)), the pyranose ring (green, chair conformation) is immediately distinguishable from the furanose ring (yellow, envelope conformation). Visualisation of a morphine molecule (Fig. 6(b)) highlights the very different puckers of the rings in this molecule. These range from planar (red), thorough slight envelope (orange) to chair (green) and twist-boat (cyan). A similar example is the haem group (Fig. 6(c)), where the outermost rings are planar (coloured red), while the rings in the metal coordination centre are in slight envelope conformations (yellow/orange). Macrocyclic rings, such as in α-cyclodextrin (e), can be shown with PaperChain. Nanostructures can also be shown in novel views with PaperChain, an example being Buckminsterfullerene (Fig. 6 (d)). A combination of PaperChain and Twister yields useful depictions of of poly- and oligosaccharides (Fig. 6(f) and (g)) and DNA (h), where both the backbone twist and ring conformation is highlighted. For DNA, the deoxyribose rings are in envelope conformations and hence yellow, while the planar bases are red.

4. Conclusions

The incorporation of the PaperChain and Twister visualisations into the Visual Molecular Dynamics (VMD) package allows for unprecedented flexibility in the visualisation of glycoproteins and carbohydrate-binding proteins. These simplified abstract oligosaccharide representations encapsulate information on the ring conformation and glycosidic linkage orientation in such a way that non-expert users may quickly identify when molecular structure refinement procedures have resulted in deformation of sugar rings. A means for rapid validation of saccharide structures is potentially very useful, considering the large percentage of PDB entries for glycoproteins that have errors in carbohydrate stereochemistry and glycosidic linkage. The PaperChain visualisation reveals that, even where the stereochemistry and ring structures are correct, the glycan components of glycoproteins often exhibit incorrect ring pucker coordinates. Further advantages of the visualisations are depiction of the aromatic rings in amino acid residues and the consequent highlighting of the CH-π ring stacking interactions that are often a feature of protein-carbohydrate binding interactions. Both the Twister and the PaperChain visualisations can, of course, be animated for viewing molecular dynamics trajectories. This fourth dimension of time can thus highlight dynamic changes in the ring pucker (PaperChain) and backbone orientation (Twister).

We have demonstrated the efficacy of the two visualisations in that they assisted in the understanding of the mechanism of binding of oligosaccharides to protein Family 18 chitolectins, where we suggest that strong binding of chito-oligosaccharides by these lectins requires a conformational change of the rings at the −1 and −2 binding sites. However, in some sense the real test of the software will come now that the algorithms are publicly available, as a practical measure of utility is whether the software is widely used in achieving significant biological results.[11] If they do prove useful, the algorithms as described here may be incorporated into other molecular visualisation packages.