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Many genetic processes are mediated by proteins that bind at separate, often widely spaced, sites on the double helix, tethering the intervening DNA into a loop. Examples of these processes include gene expression and its control, DNA replication, genetic rearrangements, multi-site cutting by restriction enzymes, and DNA packaging. A DNA loop stabilized by such long-range protein-protein contacts constitutes a discrete topological unit. As long as the ends of the DNA stay in place and the duplex remains unbroken, the linking number, Lk, or number of times the two strands of the double helix wrap around one another, is conserved. This constraint in Lk underlies the well known supercoiling of DNA: the stress induced by positioning the ends of the polymer in locations other than the natural (relaxed) state perturbs the overall coiling of the chain axis and/or the twisting of successive base-pairs in the intervening parts of the chain. As a first step in understanding the effects of specific proteins and drugs on DNA looping, we propose to study the imposed bending and twisting of neighboring base pairs in known complexes of proteins and drugs with double helical DNA stored in the Nucleic Acid Database. By subjecting a DNA segment of the same chain length as that found in a given complex to the observed orientation, displacement, and superhelical stress and setting the elastic moduli to sufficiently high values, we can use existing programs, to simulate the presence of a rigidly bound molecule at arbitrary positions on circular DNA molecules or to model specific systems in which DNA looping plays an important role, e.g., the lac repressor-operator assembly in Escherichia coli.
Week 1: Since both Dr. Olson and Nicolas were out of town, I met with Andrew and did some background reading on DNA topology as well as looking at some of Nicolas's papers that are still in progress.
Week 2: Finally met Dr. Olson this week. I was introduced to Mathematica's application of what I'll be doing this summer, and then spent the rest of this week preparing my first presentation and this website. Also, gave the introductory presentation on Friday. (Introductory Presentation (ppt))
Week 3: Began playing around with Mathematica and PDB files in order to figure out what the commands Nicolas's examples give are exactly doing with the data. Also working with the PDB data in order to isolate the DNA information from the protein information. Finally met Nicolas, who (thankfully) is a Mathematica expert and is going to help to teach me everything I'll need to know for this summer.
Week 4: Working some more with Mathematica to extract some basic geometric information (distances between specific atoms, angles, etc.) from some ideal DNA as a basis for exploring the topology of more complicated DNA structures.
Week 5: Began applying the Mathematica program to DNA bubble structures both before and after the structures are affected by melting to see how the melted portion affects the geometric characteristics of the DNA.
Week 6: Worked with four specific DNA structures: a nucleosome core particle (PDB ID:1KX5) and three bubble structures which were the same 65 base pair sequence with changing linking numbers 5, 6, and 7. I gathered all necessary geometric information and put the data into line plots and histograms in order to compare the melted structures with the "regular" nucleosome structure to see any correlations between the data and the locations of bubbles.
Week 7: Finished up working with the A DNA, B DNA, nucleosome, and the three bubble structures data by compiling all my information into some tables and graphs in order to see it much more easily. Then began to work on my final presentation and delivered it on Friday morning. (Final Presentation (ppt))
Week 8: Worked on two structures that resemble both A and B DNA as the last part of my project. And wrapped up a great summer at DIMACS.
Calladine, Drew, Luisi, and Travers. Understanding DNA: the molecule and how it works (Third edition)
Vologodskii. Topology and Physics of Circular DNA
Clauvelin, Olson, and Tobias. "DNA topology at the strand level" (Still in progress)
Britton, Olson, and Tobias. "Two perspectives on the twist of DNA"
Fogg, Catanese, Randall, Swick, and Zechiedrich. "Differences between positively and negatively supercoiled DNA that topoisomerases may distinguish"
Hofstra Mathematics Department
Hofstra Biology Department
Hofstra Honors College
BioMaPS Institute for Quantitative Biology
Rutgers Chemistry Department
Nucleic Acid Database
Protein Data Bank