Bioinformatics Advance Access originally published online on May 3, 2006
Bioinformatics 2006 22(14):1790-1791; doi:10.1093/bioinformatics/btl164
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
TopoICE-R: 3D visualization modeling the topology of DNA recombination
1 Department of Mathematics, University of Iowa Iowa City, IA 52242, USA
2 Hypnagogic Software Vancouver, BC, Canada
*To whom correspondence should be addressed.
 |
ABSTRACT |
|---|
 TOP ABSTRACT REFERENCES |
|---|
TopoICE-R is a three-dimensional visualization and manipulation software for solving 2-string tangle equations and can be used to model the topology of DNA bound by proteins such as recombinases and topoisomerases.
Availability: This software, manual and example files are available at www.knotplot.com/download for Linux, Windows and Mac.
Contact: idarcy{at}math.uiowa.edu
Knot theory has many applications in molecular biology. Proteins such as recombinases and topoisomerases can knot and link circular DNA molecules. For example, Figure 1 shows a model that has been proposed for the protein Cre recombinase (Guo et al., 1997). This protein binds to a circular DNA molecule, cuts the DNA at two specific sites, exchanges the cleaved ends and rejoins the ends, producing a knot (Figure 1A) or a link (Figure 1B).
|
A 2-string tangle consists of two strings embedded in a three-dimensional (3D) ball where the endpoints of the strings are fixed on the boundary of the ball. Some examples of 2-string tangles are shown in Figure 2. A protein-complex binding two segments of DNA can be modeled using 2-string tangles (Ernst and Sumners, 1990). The protein-complex is modeled by the ball and the two segments of DNA bound by protein are represented by the two strings inside this ball.
|
TopoICE-R (Topological Interactive Construction Engine-R) solves 2-string tangle equations modeling protein action on circular DNA. This is a very simple model of protein-DNA binding, but from this simple model, much information can be gained. Tangles have a number of applications in studies of protein–DNA binding: (1) as a language for modeling protein–DNA binding; (2) as a tool to uniquely determine the topology of protein-bound DNA; (3) to predict experimental outcomes and to direct experiments.
The main idea is that when modeling protein-DNA reactions, one would like to know how to draw the DNA. For example, are there any crossings trapped by the protein complex? How do the DNA strands exit the complex? Is there significant bending? Tangle analysis cannot determine the exact geometry of the protein-bound DNA, but it can determine the overall entanglement of this DNA, after which other techniques may be used to more precisely determine the geometry.
TopoICE-R is a part of KnotPlot, a program for visualizing and manipulating knots in 3D (freely available at KnotPlot.com). TopoICE-R solves most biologically relevant 2-string tangle equations involving the rational class of knots/links (also called 4-plat or 2-bridge). This class includes most small crossing knots including the majority of knots observed in biological experiments. The mathematics of rational tangles is used to solve these equations and relies on results in knot theory (Darcy, 2005; Culler et al., 1987; Ernst, 1996). Not all tangles are rational, but the notation of rational tangles is used to draw the figures in KnotPlot (however, knowledge of rational tangles is not required to use this software). This notation leads to diagrams which could be significantly improved for biological modeling. To obtain more biologically likely configurations, one can energy minimize and otherwise manipulate these images in 3D using standard KnotPlot commands (Scharein, 1998). 3D models can also be more informative (Vazquez et al., 2005).
For example, the mechanism shown in Figure 3A has been proposed for Xer recombination (Colloms et al., 1997). In Figure 3A we show only the tangle modeling the DNA bound by the Xer protein complex. Xer is shown binding three crossings (top). Xer then cuts the DNA, interchanges the ends, reseals the DNA resulting in the introduction of a fourth crossing (bottom). Xer is known to produce a seven crossing knot when acting on the six crossing link shown in Figure 3B (top) (Bath et al.). We obtain a model of this reaction (Figure 3C) by inputting this proposed mechanism into TopoICE-R as well as the substrate and product topologies of the circular DNA acted upon by Xer (which can be determined experimentally). Figure 3B shows a more 3D version of this model. The sphere represents Xer. The 3D models were obtained using KnotPlot to energy minimize the diagrams in Figure 3C.
|
The model in Figure 4 has also been proposed for Xer recombination (Colloms et al., 1997). One can use TopoICE-R to show that this mechanism cannot change the six crossing link of Figure 3B into a seven crossing rational knot. In this case, if one inputs the mechanism in Figure 4, this six crossing link, and any seven crossing rational knot, then TopoICE-R will output that there are no solutions. Hence the mechanism in Figure 4 cannot change this six crossing link into a seven crossing rational knot. However, there are two non-rational (and non-prime) seven crossing knots. TopoICE-R cannot currently handle non-rational knots. However, other mathematical methods exist which show that these non-rational seven crossing knots cannot result from this six crossing link via the mechanism in Figure 4, thus determining that this is not a possible protein mechanism for Xer recombination (Darcy, 2001).
|
One can also use TopoICE-R to solve for possible protein mechanisms. Solving 2-string tangle equations can also be an intermediate step in finding models for proteins that bind more than two segments of DNA (I. Darcy, J. Luecke and M. Vazquez personal communication).
Another program which solves tangle equations is Saka and Vazquez's TangleSolve (Saka and Vazquez, 2002). TopoICE-R implements the mathematics in (Darcy, 2005) and hence can find more solutions. However, not all solutions are found (Darcy, 2001). TopoICE-R also allows for 3D manipulation. However, TangleSolve can solve multiple systems of equations, modeling processive and distributive recombination. This is not yet an option in TopoICE-R. For more details regarding TopoICE-R, please see TopoICE-Rmanual.pdf TopoICE-Rexamples.pdf and TanglePrimer.pdf available at www.knotplot.com/download
Future directions We will add additional subroutines to solve other types of tangle equations including systems of tangle equations corresponding to multiple products including processive and distributive recombination. The mathematics does not yet exist for solving all types of 2-string tangle equations. In particular TopoICE-R only solves 2-string tangle equations involving the class of rational knots/links and does not always find all solutions to these equations. But the mathematics does exist for solving most biologically relevant 2-string tangle equations (for example Ernst and Sumners, 1990; Darcy, 2001; Vazquez and Sumners, 2004; Buck and Marcotte, 2005). For these types of equations, TopoICE-R will in the future solve these equations and have an option to output a proof as to whether or not all solutions have been found.
|
Acknowledgments |
|---|
We would like to thank Steve Levene for interesting discussions. We also thank Mariel Vazquez for her comments on an earlier version of this paper. This work was supported by a grant from the Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology to I.D. and S.D. Levene (NIH GM 67242) and by an Interdisciplinary Research Grant from The University of Iowa's Obermann Center for Advanced Studies to I. D., R. S., and S.D. Levene.
Conflict of Interest: none declared.
|
FOOTNOTES |
|---|
Associate Editor: Martin Bishop
Received on October 13, 2005; revised on March 26, 2006; accepted on April 26, 2006
|
REFERENCES |
|---|
|
TOPABSTRACTREFERENCES |
|---|
Bath, J., et al. (1999) Topology of Xer recombination on catenanes produced by lambda integrase. J. Mol. Biol, . 289, 873–883[CrossRef][Web of Science][Medline].
Buck, D. and Marcotte, C.V. (2005) Tangle solutions for a family of DNA-rearranging proteins. Math. Proc. Camb. Phil. Soc, . 139, 59–80[CrossRef].
Colloms, S.D., et al. (1997) Topological selectivity in Xer site-specific recombination. Cell, 88, 855–864[CrossRef][Web of Science][Medline].
Culler, M., et al. (1987) Dehn surgery on knots. Ann. Math, 125, 237–300[CrossRef].
Darcy, I. (2001) Biological distances on DNA knots and links: applications to Xer recombination. J. Knot Theor. Ramifications, 10, 269–294[CrossRef].
Darcy, I. (2005) Solving unoriented tangle equations involving 4-plats. J. Knot Theor. Ramifications, 14, 993–1005[CrossRef].
Ernst, C. (1996) Tangle equations. J. Knot Theor. Ramifications, 5, 145–159.
Ernst, C. and Sumners, D.W. (1990) A calculus for rational tangles: applications to DNA recombination. Math. Proc. Camb. Phil. Soc, . 108, 489–515.
Guo, F., et al. (1997) Structure of Cre recombinase complexed with DNA in a site-specific recombination synapse. Nature, 389, 40–46[CrossRef][Medline].
Saka, Y. and Vazquez, M. (2002) Tanglesolve: topological analysis of site-specific recombination. Bioinformatics, 18, 1011–1012
Scharein, R.G. (1998) Interactive topological drawing. PhD thesis, The University of British Columbia.
Vazquez, M. and Sumners, D.W. (2004) Tangle analysis of Gin site-specific recombination. Math. Proc. Camb. Phil. Soc, . 136, 565–582[CrossRef].
Vazquez, M., et al. (2005) Tangle analysis of Xer recombination reveals only three solutions, all consistent with a single three-dimensional topological pathway. J. Mol. Biol, . 346, 493–504[CrossRef][Web of Science][Medline].
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  I. K. Darcy, R. G. Scharein, and A. Stasiak 3D visualization software to analyze topological outcomes of topoisomerase reactions Nucleic Acids Res., June 1, 2008; 36(11): 3515 - 3521. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||