Here a local distortion means a twist away from an ideal helix ribbon diagram generated by a genuine helical curve S4f , S4j and S5 Figs in the SI for additional examples of DNA ribbon diagrams.
The protein atoms in b are colored as follows: H in gray, C in green, N in blue and S in yellow. Our model consists of a series of helical curves each one best fits the coordinates of a quadruple of backbone atoms.
The individual curves could differ largely from each other depending on the extent of their deviations from a genuine helical curve. The deviation represents the structural difference among different biomolecular helices. Specifically we have defined a helix score for a protein helix residue Eq 2 that includes both the deviation from the standard protein helix and the minimum RMSD achieved by the curve fitting algorithm.
Either the score or the local deviations from a genuine helical curve could be visualized for individual protein residues or DNA nucleotides. A systematic survey over all the protein and DNA structures in the PDB is currently under way for the structural and functional significance of the helix score. As shown in Table 1 a preliminary study on a set of 3, x-ray structures with a resolution between 1.
The data are obtained on all the dssp [ 22 ] assigned helices on a set of 3, x-ray structures with a resolution between 1. There are , helix residues in total. The residues with high helix scores indicated by different colors are concentrated in the ligand binding sites where the ligand could be either a DNA molecule Fig 3 or a compound Fig 4 or other protein subunits S1 Fig.
One key advantage of a consistent helix score is that the scores for different homologs in the same protein family could be used to determine their structural similarity conservation and variation Fig 4. In addition, with our model a polyline could be constructed for each biomolecular helix by connecting together the centers of the individual helical curves along either a protein helix Fig 4b and S1 Fig or a DNA strand S4g and S5 Figs.
For ease of reference, we call such a polyline helix center polyline. As illustrated in Fig 4b the abrupt changes turns in such a polyline occur often at a protein-ligand interface. Compared with the protein helices it is more tricky to quantify the deviations from a genuine helical curve for DNA helices because of their large structural variations.
However our model is still able to provide a qualitative description for local deviations such as the twist away Fig 3b from an ideal helix ribbon diagram generated by a genuine helical curve S4f , S4j and S5 Figs. In b each bend in a polyline indicates a deviation from the helix center polyline for a genuine helical curve, the latter is a straight line. Such bends are concentrated at the ligand binding sites. It is a well-known problem in the modeling of a biomolecular helix as a series of low-degree splines that if the curves pass exactly through every backbone atom then the ribbon diagram generated by the model is choppy.
On the other hand, if additional steps are applied or more than four backbone atoms are used for spline computation in order to smooth out the choppiness, then the side chains could become detached from the ribbon. The choppiness or detachment is inherent with a helix model that uses a series of splines where either the degrees of the splines are not high enough or the number of splines is not large enough for an accurate representation of a general helical curve that best fits the backbone atoms.
Specifically the choppiness is due to nonsmooth changes in curvature along a biomolecular backbone while the detachment results from the spatial differences between the backbone atoms and the spline model. Though efforts have been made in the past [ 16 , 18 ] to smooth out either the choppiness or detachment, either of them remains for the visualization of biomolecular helices in general and DNA helices in particular [ 17 , 18 ] please see S4 Fig.
In our model the choppiness and detachment are simultaneously reduced to a great extent because the model itself is composed of a series of helical curves each one best fits a quadruple of backbone atoms. Similarly the averaging process keeps the distance between a backbone atom and its closest point on the model close to the minimum achieved by the curve fitting algorithm and thus the detachment problem is greatly alleviated. Fig 6 illustrates the differences between the ribbon diagram generated by our model and the diagrams by two previous programs.
Please see the supporting information for the comparisons with four other molecular visualization programs see S2 Fig. Our helix ribbon diagrams are most similar to the iconic ribbon diagram hand-drawn by Jane Richardson [ 7 ] see S3 Fig.
It is also rather similar to the ribbon diagram by UCSF Chimera [ 16 ] that uses a series of splines each one fits to five backbone atoms Fig 6d. In contrast to the ribbon diagram by UCSF Chimera, our model minimizes the distance between a backbone atom and the ribbon diagram.
The two figures illustrate the differences between the helix ribbon diagrams generated by the model and the helix ribbon diagrams generated using a series of cubic Hermite splines that pass through every backbone atom. The latter is colored in purple and drawn in sausage-shape and overlayed upon the former. As is clear by the comparison, the diagrams generated by Hermite splines are choppy while those by our model are much more smooth.
The protein structure is 1TIM pdbid for which Prof. Jane Richardson had hand-drawn an iconic ribbon diagram [ 7 ]. The helices are oriented as close as possible to their orientations in her diagram see S4 Fig. Shown in a is the diagram generated by our model, in b the diagram by the program PyMOL [ 18 ]. Additional steps have been applied to smooth out the choppiness in c. The side-chains in d could become detached. When four successive backbone P atoms are used to generate a ribbon diagram for a DNA helix, there often exist large variations among the diagrams for different DNAs and obvious deviations from a diagram that is generated using a single genuine helical curve please see S5a Fig of the SI for an ideal helix ribbon diagram generated by our model using a single genuine helical curve.
The variation and deviation are partly due to the small helix turn angle in a typical DNA helix. If instead of using all the successive P atoms, when only the first atoms of every triple of consecutive P atoms are used to compute the model, the resulting helix ribbon diagram becomes much similar to both a protein helix diagram S4h and S4j Fig and an ideal helix ribbon diagram S5a Fig.
In this case the turn angle per atom is very close to that in a typical protein helix. The program is written in Qt5. As illustrated in S1 Fig the accuracy of our model is not affected by the resolutions and R-factors of protein x-ray structures.
The side chain detachment from the ribbon diagram for a low resolution protein structure. The protein is a homo-octomer composed of eight identical subunits pdbid 3ZC1, 3. No detachments are discernible in this helix ribbon diagram. The helix center polylines are shown in orange. The diagrams are colored as in Fig 2 of the main paper. In addition to the comparisons with the two previous molecular visualization programs PyMOL and UCSF Chimera described in the main paper, we have also compared the helix ribbon diagram generated for 1TIM pdbid by our model with those by four other molecular visualization programs S2 Fig and with the iconic diagram hand-drawn by Jane Richardson S3 Fig The protein structure is 1TIM pdbid.
The arrows point to the locations where the diagrams are choppy. Compared with protein helices DNA helices have larger variations among themselves and larger deviations from a genuine helical curve. This figure shows the DNA ribbon diagrams by five previous molecular visualization programs and their comparisons with the ribbon diagrams generated by our model.
The structure is a leucine zipper protein pdbid 1A02 with a bound dsDNA. The two polylines in g are the helix center polylines. The two figures, h and i , are respectively the helix ribbon diagram generated by our model using a series of quadruples of atoms with each atom is the first of a triple of consecutive P atoms along a DNA strand, and its overlay with the ribbon diagram generated using successive four P atoms. The two figures i, j are the same except that the heavy atoms are displayed in the latter.
The helix center polyline is a straight line for the first stand of the theoretical B-DNA model but base-pairing requirement forces its second strand to deviate from a genuine helical curve. Headless Linux chimera Compiled on Debian 4 etch. Instructions Documentation Runs on Windows 7 or later. See production version for installation instructions Runs on Windows 7 or later. Release notes. See production version for installation instructions Compiled on CentOS 5.
See production version for installation instructions For web servers. Instructions Documentation Runs on Tru64 5.
My Notes. Categories Prerequisites. No Prerequisites. No Corequisites. Course Level. First year. Topics Covered. Bonding models: Discrete molecules. Bioinorganic Chemistry.
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