TwiDDL

Introduction

Welcome to TwiDDL, a very powerful database/search engine that enables a user to search for and study the twist of DNA and RNA in known high-resolution double-helical structures. The database includes a new conformational parameter called the twist of supercoiling, Tw^SC, and multiple factors which can influence that twist, including, but not limited to the six rigid-body base-pair-step parameters (Shift, Slide, Rise, Tilt, Roll, Twist or Tw^SP) that describe the spatial disposition of neighboring base pairs.

The user can find the values of Tw^SC associated with the DNA and RNA base-pair steps in almost all nucleic-acid containing structures stored in the Protein Data Bank (Berman et al. 2000) and the Nucleic Acid Database (Berman et al. 1992). New values of Tw^SC can be added to TwiDDL by contacting the database administrator. To get started using TwiDDL, simply select the Search option under TwiDDL in the green menu bar.

Copyright © Lauren A. Britton & The Olson Group

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Difference in Twist:

For each base-pair step in a molecule the user can specify the difference between the twist of supercoiling, Tw^SC, and that of either relaxed, ideal B-DNA (with 10.5 base pairs per full 360° helical turn), i.e., ΔTw^B = Tw^SC – Tw^B-DNA, or the step-parameter twist, Tw^SP, i.e., ΔTw^SP = Tw^SC – Tw^SP.

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Tw^SC:

A local conformational parameter, newly described for real DNA structures (Britton et al. 2009) and only available through TwiDDL, which is consistent with the definitions introduced over forty years ago by mathematicians to characterize the intertwining of two closed space curves (Călugăreanu 1961; White 1969; Fuller 1971). That is, the sum of the Tw^SC over all base-pair steps of a closed double helical structure plus the writhing number, a mathematical description of the global folding of the helical axis, gives a topologically invariant integer called the linking number. We have found that Tw^SC can give insight into the molecule as a whole or segments of interest, including the sensitivity of this parameter to molecular distortions associated with bound proteins and melted states. The user can select a range of values or a range of magnitudes in the difference in Tw^SC . Typical values of Tw^SC span the range 1° - 100°.

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Tw^SP:

Step-parameter twist for individual base-pair steps in a double-helical molecule. One of the six rigid-body parameters commonly used to describe the spatial arrangements of neighboring base pairs in high-resolution DNA and RNA structures (Dickerson et al. 1989). The sum of the Tw^SP over all base-pair steps of a closed double helix plus the writhing number, a mathematical description of the global folding of the double-helical axis, does not necessarily give an integer. Step parameters included in TwiDDL are computed with the 3DNA software package (Lu & Olson 2003).

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Buckle:

One of the six rigid-body parameters commonly used to describe the spatial arrangements of hydrogen-bonded Watson-Crick base pairs in high-resolution DNA and RNA structures (Dickerson et al. 1989). The values of Buckle stored in the database correspond to the angle between the normals of the bases when viewed in projection along a plane perpendicular to the short, pseudo-dyad axis of the base pair (Lu & Olson 2003). The user can select a range of values or a range of magnitudes of Buckle. Typical values span the range -90° to 90°.

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Kinking:

Kinking is a measure of the net bending of a DNA or RNA base-pair step, extracted from the Tilt and Roll angles as (Tilt² + Roll²)^½. Non-zero values of kinking are correlated with Tw^SC if the shearing is also non-zero. The user can select a range of values of kinking. Typical values span the range 0.° to 175°.

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Shearing:

Shearing is a measure of the net lateral displacement of a DNA or RNA base-pair step, extracted from the Shift and Slide angles as (Shift² + Slide²)^½. Non-zero values of shearing are correlated with TwSC if the kinking is also non-zero. The user can select a range of values of shearing. Observed values span the range 0.Å to 9Å

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PDBID(s):

Data from TwiDDL are based on structures taken from the Protein Data Bank (PDB) (Berman et al. 2000). The user can enter any currently available PDBID (PDB structural identifier), such as 1kx5, and see if information about the twisting of double-helical DNA or RNA in the structure is also stored in TwiDDL. Not all structures in the PDB pass the standards needed in order to be used in TwiDDL.

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NDBID(s):

Data from TwiDDL are based on structures taken from the Nucleic Acid Database (NDB) (Berman et al. 1992). The user can enter any currently available NDBID (NDB structural identifier), such as pd0287, and see if information about the twisting of double-helical DNA or RNA in the structure is also stored in TwiDDL. Not all structures in the NDB pass the standards needed in order to be used in TwiDDL.

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Exclude PDBID(s):

The user can exclude one or more PDBIDs (Protein Data Bank structural identifiers) from a search. For example, entering 1kx eliminates three nucleosome crystal structures and two NMR-derived structures with 1kx in the PDBID.

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Exclude NDBID(s):

The user can exclude one or more NDBIDs (Nucleic Acid Database structural identifiers) from a search. For example, entering zd eliminates 44 Z-DNA structures.

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Experimental Method:

The type of measurement used to determine the structures characterized in TwiDDL: X-Ray crystallography or NMR.

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Enter Sequence:

The user can search for structures that contain all or part of a given base sequence. This option will return any structure with the specified entry and highlight the sequence of interest in green on the Results Page, making it clear where the sequence appears in the selected structures. The search is limited to the five common bases (A, C, G, T, U).

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Select Step:

In addition to searching for long sequences, the user can search for a particular base-pair step. This step will be highlighted in purple on the Results Page. The search is limited to the 16 common DNA and RNA base-pair steps, i.e., all sequential combinations of successive A·T (or A·U) and G·C base pairs.

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Resolution:

X-ray crystal structures are determined at different levels of resolution, i.e., accuracy, based on the interplanar spacing of reflected X-rays. The lower the resolution, the more accurate (or better resolved) the data.

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Space Group:

The notation describing the symmetry of the crystal and specifying the combination of symmetry operations that generate the crystal lattice from the unit cell.

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Structure Titles:

This search option allows the user to search for any word included in title of a Protein Data Bank file. The syntax used for this search is much like others that are widely available. For example, desired phrases should be placed between quotation marks, a minus sign will exclude a word/phrase, and different search items need to be separated by spaces. For example, -"Z-DNA" spermine "PHOSPHATE ONLY", will result in one item returned.

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Structure Primary Citation:

This search option allows the user to search for any word included in the literature citation associated with a Protein Data Bank file. The syntax used for this search is much like others that are widely available. For example, desired phrases should be placed between quotation marks, a minus sign will exclude a word/phrase, and different search items need to be separated by spaces. For example, -"j.mol.biol." 1995 -"Z-DNA", will result in 39 items returned.

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Structure Classification:

The entries in the Protein Data Bank (Berman et al. 2000) and Nucleic Acid Database (Berman et al. 1992) include a structure classification, selected by the scientists who determined the individual structures, that specifies the nature of the biomolecule(s) in the structure. The user can choose one or more of the currently available classifications to delimit the dataset. More than one classification can be chosen by simultaneously pressing the control key and clicking on the line of interest.

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Search Criteria:

The upper left portion of the results page will display a list of all criteria entered into the simple or advanced search page that resulted in the list of TwIDs your are viewing. Below it you will see a link to this search which you may copy and paste into email to share with others, or bookmark in your browser in order to get back to these results. Below that you will find the total number of entries in TwiDDL that matched your search criteria (like "476 matching results.")

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Update Search:

Clicking on the small boxes on the left of each row allows the user to select certain TwIDs for further manipulations of the following types:

1. Remove the selected TwIDs from the current search, using the Remove button on the menu bar. (The selection can be added back to the set of structures by clicking on the Not TwID(s)= links towards the top of the page)
2. Obtain simple statistical information — including the average, minimum, and maximum values of Tw^SC and other local conformational parameters — for the base-pair steps in the selected structures. The user can select the type of data and the sequence context, i.e., dimeric or tetrameric, in which the data are tabulated. Choosing Selected TwIDs and then clicking on Calculate in the top bar opens a new window, which presents the desired results.
3. Obtain the corresponding statistical information for the base-pair steps in all structures that meet the search criteria. Choosing All TwIDs and then clicking on Calculate in the top bar opens a new window, which presents the desired results.

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TwID:

TwiDDL's unique structural identifier. Each TwID corresponds to a single structure, making it possible to differentiate each of the structures that make up the ensemble of models derived from NMR studies and sometimes constitute a single crystal structure. That is, even though all the models included in an NMR-based structural entry have the same PDBID, each NMR model has its own TwID. Data can be sorted in ascending or descending order of TwID. Clicking on an individual TwID leads the user to a new page with details of the twist of supercoiling and other related parameters characterizing the specific structure.

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Number of Base Pairs:

The number of base pairs found in the structure. Data can be sorted in ascending or descending order.

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Sequence:

The nucleotides that make up the leading strand of the DNA or RNA structures that meet the search criteria. Data can be sorted alphabetically.

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Title:

The title given in the PDB file associated with the selected structures. Data can be sorted alphabetically.

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PDBID:

The Protein Data Bank (PDB) unique structural identifier. Clicking on the PDBID opens a new window that brings the user directly to the PDB site corresponding to the TwiDDL TwID. Data can be sorted alphabetically.

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NDBID:

The Nucleic Acid Database (NDB) unique structural identifier. Clicking on the NDBID opens a new window that brings the user directly to the NDBID site corresponding to the TwiDDL TwID. Data can be sorted alphabetically.

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Experimental Method:

The type of measurement used to determine the selected structures: X-Ray crystallography or NMR. Data can be sorted alphabetically.

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Step Details:

The details of each step are presented in a show/hide menu in order to save space. This table includes the six rigid-body base-pair step parameters (Shift, Slide, Rise, Tilt, Roll, Twist or Tw^SP), Tw^SC, the net kinking per base-pair step, and the net shearing per base-pair step. See the Advanced Search Page for additional information about these parameters.

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TwID:

TwiDDL's unique structural identifier. Each TwID corresponds to a single structure, making it possible to differentiate each of the structures that make up the ensemble of models derived from NMR studies and sometimes constitute a single crystal structure. That is, even though all the models included in an NMR-based structural entry have the same PDBID, each NMR model has its own TwID.

TwiDDL Context Help

PDBID:

The Protein Data Bank (PDB) unique structural identifier. Clicking on any PDBID in the list of selected structures opens a new window that brings the user directly to the PDB site corresponding to the TwiDDL TwID.

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NDBID:

The Nucleic Acid Database (NDB) unique structural identifier. Clicking on any NDBID in the list of selected structures opens a new window that brings the user directly to the NDBID site corresponding to the TwiDDL TwID.

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Visualization of ΔTw:

A visualization tool that shows how the difference, ΔTw, in the twist of supercoiling (Tw^SC) with respect to that of B DNA (Tw^B-DNA) or relative to the step-parameter twist (Tw^SP), changes along the selected structure. Color-coded images with the values of ΔTw^B-DNA = Tw^SC – Tw^B-DNA or ΔTw^SP = Tw^SC – Tw^SP mapped on the base-pair steps are obtained by choosing the desired option with the radio button below the color-coding bar. This tool, created using MATLAB (version 7.7.0.471 (R2008b), available from The Mathworks, Inc., Natick, MA), allows the user to rotate the model and zoom in/out by using the tools at the top of the model box. (Note that Tw^SC are Tw^SP are the same for relaxed B DNA.)

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Title:

The title given in the PDB file associated with the selected structure.

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Primary Citation:

The complete literature citation associated with a Protein Data Bank file.

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Sequence:

The nucleotides that constitute the leading strand of the DNA or RNA in the specified structure.

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Total Tw^SC:

The sum of the Tw^SC values for all base-pair steps in the selected structure.

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Total Turns^SC:

The number of helical turns in the selected structure, given by the quotient (Total Tw^SC) ÷ 360°.

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Total Tw^SP:

The sum of the Tw^SP values for all base-pair steps in the selected structure.

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Number of base pairs:

The number of base pairs found in the structure.

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Experimental Method:

The type of measurement used to determine the structure: X-Ray crystallography or NMR.

The two experimental methods accepted by TwiDDL are X-Ray Crystallography and NMR.

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Space Group:

The notation describing the symmetry of the crystal and specifying the combination of symmetry operations that generate the crystal lattice from the unit cell.

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Resolution:

X-ray crystal structures are determined at different levels of resolution, i.e., accuracy, based on the interplanar spacing of reflected X-rays. The lower the resolution, the more accurate (or better resolved) the data.

TwiDDL Context Help

Structure Classification:

The entries in the Protein Data Bank (Berman et al. 2000) and Nucleic Acid Database (Berman et al. 1992) include a structure classification, selected by the scientists who determined the individual structures, that specifies the nature of the biomolecule(s) in the structure.

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Twist Comparisons:

A show/hide list that displays Tw^SC, Tw^SP, ΔTw^SP, and ΔTw^B-DNA, and the base-pair-step number at which these values occur in the selected structure. The list can be ordered by the entries in any column by clicking on the column header. Click once for ascending order and twice for descending order. The values of ΔTw^SP and ΔTw^B-DNA are color coded in blue and red to draw attention to negative or positive values, respectively.

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Step Parameters:

A show/hide list that displays the six rigid-body base-pair-step parameters (here labeled Shift^SP, Slide^SP, Rise^SP, Tilt^SP, Roll^SP, Tw^SP), two quantities based on those step parameters (Kinking^SP, Shearing^SP), and the base-pair-step number at which these values occur. The list can be ordered by the entries in any column by clicking on the column header. Click once for ascending order and twice for descending order.

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Base Pair Details:

A show/hide list that displays the chemical identities and residue numbers (Base ID I, Base ID II) of the paired bases in the selected structure, the identities of the complementary strands (Chain ID I, Chain ID II), the names of the bases (Residue ID I, Residue ID II), the numbers of the bases (Residue Num I, Residue Num II), and the six rigid-body base pair parameters (Shear, Stretch, Stagger, Buckle, Propeller, Opening) that describe the spatial arrangement of the pair bases. The list can be ordered by the entries in any column by clicking on the column header. Click once for ascending order and twice for descending order. (Note that a header that ends with a I holds information about the base on Strand I and a header that ends with a II holds information about the base on Strand II.)

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Dimeric Step Statistics:

Clicking on the Open link brings the user to a new page with statistical information — the average, minimum, and maximum values of Tw^SC, ΔTw^SP, ΔTw^B-DNA, and the six rigid-body base-pair-step parameters (Tw^SP, Shift^SP, Slide^SP, Rise^SP, Tilt^SP, Roll^SP) — describing the base-pair steps within the selected structure. Values are presented in a dimeric context for the 16 possible combinations of consecutive Watson-Crick base pairs. That is, all steps with a given dimeric sequence are grouped together regardless of the identities of the base pairs that flank them. The number of steps that contribute to the averages is listed under Number of Matching Steps.

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Tetrameric Step Statistics:

Clicking on the Open link brings the user to a new page with statistical information — the average, minimum, and maximum values of Tw^SC, ΔTw^SP, ΔTw^B-DNA, and the six rigid-body base-pair-step parameters (Tw^SP, Shift^SP, Slide^SP, Rise^SP, Tilt^SP, Roll^SP) — describing the base-pair steps within the selected structure. Values are presented in a tetrameric context for the 256 possible combinations of consecutive base pairs. That is, all steps with a common dimeric sequence are further grouped in terms of the identities of the base pairs that flank the step. The number of steps that contribute to the averages is listed under Number of Matching Steps. (Note that the first and last steps of the structure will not have a flanking 5´or 3´ base pair. These terminal base-pair steps are easily identified from the blank spaces located on either side of the "trimer".

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Graphs:

Three simple graphs depict the variation along the chain and the differences between Tw^SC and Tw^SP.

1. Line: Twist vs. Base-pair Step. The color-coded line graph shows how the two twists, Tw^SC in purple and Tw^SP in green, vary along the length of the molecule.
2. Point: Twist vs. Base-pair Step. The color-coded points show the how two twists, Tw^SC in purple and Tw^SP in green, vary along the length of the molecule.
3. Scatter: Tw^SC versus Tw^SP. The scatter plot clarifies the differences in the two twist values at selected steps in the structure. If the twists are identical, the points will lie along the diagonal of the plot. The deviations from this line pinpoint the steps where Tw^SC and Tw^SP differ. If the molecule adopts a relaxed B-DNA structure, all the points will be located at a single point where Tw^SC = Tw^SP = 34.3°.

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TwiDDL Files:

The drop down list allows the user to collect a file with all the data in TwiDDL characterizing the selected structure. This file, which contains the values of Tw^SC and several closely related conformational variables, can be opened with most spreadsheet programs. The file includes values of Tw^SC for both the Open linear structure stored in the Protein Data Bank (Berman et al. 2000) and a hypothetical Closed structure, which includes an added step that connects the first and last base pairs. The latter model is included so that the user can see what the linking and writhing numbers (Lk and Wr) would be if the structure were closed. The characterizations of the two structural forms include data for each base-pair step as well as the sums of the various twists and the number of helical turns at the top of the twist columns. The data labeled TwistOAve are the Tw^SC values listed on the website. The data labeled TwistCAve are the corresponding values for the hypothetical Closed structure. Complete mathematical details are provided in our recent paper (Britton et al. 2009)

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Structure Input File:

This is the input PDB file used to calculate Tw^SC and the related conformational parameters stored in TwiDDL. Click on the file name to download the contents.

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3DNA Output Files:

These are the complete set of output files generated upon 3DNA (Lu & Olson 2003) analysis of the selected structure. Mouse over the file name in the list or visit http://3dna.rutgers.edu/ for further descriptions of each file.

1. Berman, H.M., Olson, W.K., Beveridge, D.L., Westbrook, J., Gelbin, A., Demeny, T., Hsieh, S.H., Srinivasan, A.R., Schneider, B. (1992) The Nucleic Acid Database. A comprehensive relational database of three-dimensional structures of nucleic acids. Biophys. J. 63, 751-759.
2. Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E. (2000) The Protein Data Bank. Nucleic Acids Res. 28, 235-242.
3. Britton, L.A., Olson, W.K., Tobias, I. (2009) Two Perspectives on the twist of DNA. arXiv:0903.1657v1 [q-bio.BM].
4. Călugăreanu G. (1961) Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants. Czech. Math. J. 11, 588-625.
5. Dickerson R. E., Bansal, M., Calladine, C. R., Diekmann, S., Hunter, W. N., Kennard, O., von Kitzing, E., Lavery, R., Nelson, H. C. M., Olson, W. K., Saenger, W., Shakked, Z., Sklenar, H., Soumpasis, D. M., Tung, C.-S., Wang, A. H.-J. & Zhurkin, V. B. (1989) Definitions and nomenclature of nucleic acid structure parameters. J. Mol. Biol. 208, 787-791.
6. Fuller F. B. (1971) The writhing number of a space curve. Proc. Natl. Acad. Sci., USA 68, 815-819.
7. Lu, X.J., Olson, W.K. (2003) 3DNA: a software package for the analysis, rebuilding and visualization of three-dimensional nucleic acid structures. Nucleic Acids Res. 31, 5108-5121.
8. White J. H. (1969) Self-linking and the Gauss integral in higher dimensions. Amer. J. Math. 91, 693-728.