Limits...
An Accurate Model for Biomolecular Helices and Its Application to Helix Visualization.

Wang L, Qiao H, Cao C, Xu S, Zou S - PLoS ONE (2015)

Bottom Line: Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves.An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve.Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance.

View Article: PubMed Central - PubMed

Affiliation: The College of Computer Science and Technology, Jilin University, Changchun, Jilin, China.

ABSTRACT
Helices are the most abundant secondary structural elements in proteins and the structural forms assumed by double stranded DNAs (dsDNA). Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves. In this paper we model a helix as a series of different but all bona fide helical curves; each one best fits the coordinates of four consecutive backbone Cα atoms for a protein or P atoms for a DNA molecule. An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve. Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance. When applied to helix visualization, the ribbon diagrams generated by the model are less choppy or have smaller side chain detachment than those by the previous visualization programs that typically model a helix as a series of low-degree splines.

No MeSH data available.


Related in: MedlinePlus

The model accuracy.The spatial differences between the backbone atoms and their closest points on the helix ribbon diagram generated by the model are barely visible (indicated by the arrows) for either (a) an ultra-high resolution protein structure (pdbid 1EJG) or (b) a medium-resolution structure (pdbid 2RH1). The backbones of the helices are shown in stick-and-ball with the diameter of the ball to be the same as the thickness of the ribbon. The Cα atoms are colored in cyan. A detachment occurs when a Cα atom is not positioned inside the ribbon diagram. The larger the difference is between a Cα atom and its closest point on the model, the larger its detachment from the diagram. The protein helix diagrams in both the main paper and Supporting Information (SI) are colored as follows according to residue’s helix score (Eq 2): 0.0–20.0 in green, 20.0–50.0 in celeste, 50.0–100.0 in yellow, 100.0–200.0 in magenta, > 200.0 in red. Except for Fig 1, all the figures in both the main paper and SI are prepared using our own molecular visualization program written in C++/openGL/Qt.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4488352&req=5

pone.0129653.g002: The model accuracy.The spatial differences between the backbone atoms and their closest points on the helix ribbon diagram generated by the model are barely visible (indicated by the arrows) for either (a) an ultra-high resolution protein structure (pdbid 1EJG) or (b) a medium-resolution structure (pdbid 2RH1). The backbones of the helices are shown in stick-and-ball with the diameter of the ball to be the same as the thickness of the ribbon. The Cα atoms are colored in cyan. A detachment occurs when a Cα atom is not positioned inside the ribbon diagram. The larger the difference is between a Cα atom and its closest point on the model, the larger its detachment from the diagram. The protein helix diagrams in both the main paper and Supporting Information (SI) are colored as follows according to residue’s helix score (Eq 2): 0.0–20.0 in green, 20.0–50.0 in celeste, 50.0–100.0 in yellow, 100.0–200.0 in magenta, > 200.0 in red. Except for Fig 1, all the figures in both the main paper and SI are prepared using our own molecular visualization program written in C++/openGL/Qt.

Mentions: The application of the model to a set of 27,105 X-ray protein structures in the PDB with a resolution from 0.46Å to 3.5Å and less than 70% sequence identity confirms the model’s accuracy. Though the RMSDs (Δis in Eq 2) between the backbone Cα atoms and their closest points on the model range from 0.0 − 0.3Å for all the 262,266 DSSP-assigned protein helices, more than 95% of the helix residues have their Δis less than 0.08Å. As illustrated in Fig 2, the deviations between the experimental Cα positions and the model are barely discernible for the protein structures ranging from ultra-high resolution (pdbid 1EJG, 0.46Å), to medium resolution (pdbid 2RH1, 2.6Å), and to low resolution structures (pdbid 3ZC1, 3.3Å, S1 Fig in the Supporting Information (SI)). In general, the model accuracy is not affected by the residue’s helix score. For DNAs, the spatial difference between a backbone P atom and its closest point on the model could be large with a typical value from 0.0Å to 0.5Å(Fig 3a). Even with the relatively large difference between the model and the P atoms in DNAs, our model is superior to all the previous helix models for DNAs because the generated curves conform to a genuine helical curve much better than a series of splines generated by the previous models do (Please see S4f, S4j and S5 Figs in the SI for examples).


An Accurate Model for Biomolecular Helices and Its Application to Helix Visualization.

Wang L, Qiao H, Cao C, Xu S, Zou S - PLoS ONE (2015)

The model accuracy.The spatial differences between the backbone atoms and their closest points on the helix ribbon diagram generated by the model are barely visible (indicated by the arrows) for either (a) an ultra-high resolution protein structure (pdbid 1EJG) or (b) a medium-resolution structure (pdbid 2RH1). The backbones of the helices are shown in stick-and-ball with the diameter of the ball to be the same as the thickness of the ribbon. The Cα atoms are colored in cyan. A detachment occurs when a Cα atom is not positioned inside the ribbon diagram. The larger the difference is between a Cα atom and its closest point on the model, the larger its detachment from the diagram. The protein helix diagrams in both the main paper and Supporting Information (SI) are colored as follows according to residue’s helix score (Eq 2): 0.0–20.0 in green, 20.0–50.0 in celeste, 50.0–100.0 in yellow, 100.0–200.0 in magenta, > 200.0 in red. Except for Fig 1, all the figures in both the main paper and SI are prepared using our own molecular visualization program written in C++/openGL/Qt.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4488352&req=5

pone.0129653.g002: The model accuracy.The spatial differences between the backbone atoms and their closest points on the helix ribbon diagram generated by the model are barely visible (indicated by the arrows) for either (a) an ultra-high resolution protein structure (pdbid 1EJG) or (b) a medium-resolution structure (pdbid 2RH1). The backbones of the helices are shown in stick-and-ball with the diameter of the ball to be the same as the thickness of the ribbon. The Cα atoms are colored in cyan. A detachment occurs when a Cα atom is not positioned inside the ribbon diagram. The larger the difference is between a Cα atom and its closest point on the model, the larger its detachment from the diagram. The protein helix diagrams in both the main paper and Supporting Information (SI) are colored as follows according to residue’s helix score (Eq 2): 0.0–20.0 in green, 20.0–50.0 in celeste, 50.0–100.0 in yellow, 100.0–200.0 in magenta, > 200.0 in red. Except for Fig 1, all the figures in both the main paper and SI are prepared using our own molecular visualization program written in C++/openGL/Qt.
Mentions: The application of the model to a set of 27,105 X-ray protein structures in the PDB with a resolution from 0.46Å to 3.5Å and less than 70% sequence identity confirms the model’s accuracy. Though the RMSDs (Δis in Eq 2) between the backbone Cα atoms and their closest points on the model range from 0.0 − 0.3Å for all the 262,266 DSSP-assigned protein helices, more than 95% of the helix residues have their Δis less than 0.08Å. As illustrated in Fig 2, the deviations between the experimental Cα positions and the model are barely discernible for the protein structures ranging from ultra-high resolution (pdbid 1EJG, 0.46Å), to medium resolution (pdbid 2RH1, 2.6Å), and to low resolution structures (pdbid 3ZC1, 3.3Å, S1 Fig in the Supporting Information (SI)). In general, the model accuracy is not affected by the residue’s helix score. For DNAs, the spatial difference between a backbone P atom and its closest point on the model could be large with a typical value from 0.0Å to 0.5Å(Fig 3a). Even with the relatively large difference between the model and the P atoms in DNAs, our model is superior to all the previous helix models for DNAs because the generated curves conform to a genuine helical curve much better than a series of splines generated by the previous models do (Please see S4f, S4j and S5 Figs in the SI for examples).

Bottom Line: Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves.An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve.Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance.

View Article: PubMed Central - PubMed

Affiliation: The College of Computer Science and Technology, Jilin University, Changchun, Jilin, China.

ABSTRACT
Helices are the most abundant secondary structural elements in proteins and the structural forms assumed by double stranded DNAs (dsDNA). Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves. In this paper we model a helix as a series of different but all bona fide helical curves; each one best fits the coordinates of four consecutive backbone Cα atoms for a protein or P atoms for a DNA molecule. An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve. Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance. When applied to helix visualization, the ribbon diagrams generated by the model are less choppy or have smaller side chain detachment than those by the previous visualization programs that typically model a helix as a series of low-degree splines.

No MeSH data available.


Related in: MedlinePlus