DNA Knotting

This dissertation applies knot theory, DNA topology, linear algebra, statistics, probability theory and statistical mechanics to address questions about knotted, double-stranded DNA. The three main investigations are the cellular effects of knotting, the biophysics of knotting/unknotting and the unknotting mechanism of human topoisomerase IIá. The cellular effects of knotting were done in collaboration with Rick Deibler. The statistical mechanics were done in collaboration with Zhirong Liu and Hue Sun Chan. Cellular DNA knotting is driven by DNA compaction, topoisomerization, replication, supercoiling-promoted strand collision, and DNA self-interactions resulting from transposition, site-specific recombination, and transcription (Spengler, Stasiak, and Cozzarelli 1985; Heichman, Moskowitz, and Johnson 1991; Wasserman and Cozzarelli 1991; Sogo, Stasiak, Martinez-Robles et al. 1999). Type II topoisomerases are ubiquitous, essential enzymes that interconvert DNA topoisomers to resolve knots. These enzymes pass one DNA helix through another by creating an enzyme-bridged transient break. Explicitly how type II topoisomerases recognize their substrate and decide where to unknot DNA is unknown. What are the biological consequences of unresolved cellular DNA knotting? We investigated the physiological consequences of the well-accepted propensity of cellular DNA to collide and react with itself by analyzing the effects of plasmid recombination and knotting in E. coli using a site-specific recombination system. Fluctuation assays were performed to determine mutation rates of the strains used in these experiments (Rosche and Foster 2000). Our results show that DNA knotting: (i) promotes replicon loss by blocking DNA replication, (ii) blocks gene transcription, (iii) increases antibiotic sensitivity and (iv) promotes genetic rearrangements at a rate which is four orders of magnitude greater than of an unknotted plasmid. If unresolved, DNA knots can be lethal and may help drive genetic evolution. The faster and more efficiently type II topoisomerase unknots, the less chance for these disastrous consequences. How do type II topoisomerases unknot, rather than knot? If type II topoisomerases act randomly on juxtapositions of two DNA helices, knots are produced with probability depending on the length of the circular DNA substrate. For example, random strand passage is equivalent to random cyclization of linear substrate, and random cyclization of 10.5 kb substrate produces about 3% DNA knots, mostly trefoils (Rybenkov, Cozzarelli, and Vologodskii 1993; Shaw and Wang 1993). However, experimental data show that type II topoisomerases unknot at a level up to 90-fold the level achieved by steady-state random DNA strand passage (Rybenkov, Ullsperger, and Vologodskii et al. 1997). Various models have been suggested to explain these results and all of them assume that the enzyme directs the process. In contrast, our laboratory proposed (Buck and Zechiedrich 2004) that type II topoisomerases recognize the curvature of the two DNA helices within a juxtaposition and the resulting angle between the helices. Furthermore, the values of curvature and angle lie within their respective bounds, which are characteristic of DNA knots. Thus, our model uniquely proposes unknotting is directed by the DNA and not the protein. We used statistical mechanics to test this hypothesis. Using a lattice polymer model, we generated conformations from pre-existing juxtaposition geometries and studied the resulting knot types. First we determined the statistical relationship between the local geometry of a juxtaposition of two chain segments and whether the loop is knotted globally. We calculated the HOMFLY (Freyd, Yetter, and Hoste et al. 1985) polynomial of each conformation to identify knot types. We found that hooked juxtapositions are far more likely to generate knots than free juxtapositions. Next we studied the transitions between initial and final knot/unknot states that resulted from a type II topoisomerase-like segment passage at the juxtaposition. Selective segment passages at free juxtapositions tended to increase knot probability. In contrast, segment passages at hooked juxtapositions caused more transitions from knotted to unknot states than vice versa, resulting in a steady-state knot probability much less than that at topological equilibrium. In agreement with experimental type II topoisomerase results, the tendency of a segment passage at a given juxtaposition to unknot is strongly correlated with the tendency of that segment passage to decatenate. These quantitative findings show that there exists discriminatory topological information in local juxtaposition geometries that could be utilized by the enzyme to unknot rather than knot. This contrasts with prior thought that the enzyme itself directs unknotting and strengthens the hypothesis proposed by our group that type II topoisomerases act on hooked rather than free juxtapositions. Will a type II topoisomerase resolve a DNA twist knot in one cycle of action? The group of knots known as twist knots is intriguing from both knot theoretical and biochemical perspectives. A twist knot consists of an interwound region with any number of crossings and a clasp with two crossings. By reversing one of the crossings in the clasp the twist knot is converted to the unknot. However, a crossing change in the interwound region produces a twist knot with two less nodes. Naturally occurring knots in cells are twist knots. The unknotting number, the minimal number of crossing reversals required to convert a knot to the unknot, is equal to one for any twist knot. Each crossing reversal performed by a type II topoisomerase requires energy. Within the cell, DNA knots might be pulled tight by forces such as those which accompany transcription, replication and segregation, thus increasing the likelihood of DNA damage. Therefore, it would be advantageous for type II topoisomerases to act on a crossing in the clasp region of a DNA twist knot, thus, resolving the DNA knot in a single step. The mathematical unknotting number corresponds to the smallest number of topoisomerase strand passage events needed to untie a DNA knot. In order to study unknotting of DNA knots by a type II topoisomerase, I used site-specific recombination systems and a bench-top fermentor to isolate large quantities of knotted DNA. My data show that purified five- and seven-noded twist knots are converted to the unknot by human topoisomerase IIá with no appearance of either trefoils or five-noded twist knots which are possible intermediates if the enzyme acted on one of the interwound nodes. Consequently, these data suggest that type II topoisomerase may preferentially act upon the clasp region of a twist knot. We have uniquely combined biology, chemistry, physics and mathematics to gain insight into the mechanism of type II topoisomerases, which are an important class of drug targets. Our results suggest that DNA knotting alters DNA structure in a way that may drive type II topoisomerase resolution of DNA knots. Ultimately, the knowledge gained about type II topoisomerases and their unknotting mechanism may lead to the development of new drugs and treatments of human infectious diseases and cancer.