Computer simulation of DNA supercoiling

Major goals of this research are to comprehend and visualize the detailed three-dimensional arrangements of supercoiled DNA. Attention has been focused in the initial stages on mathematical procedures to generate the spatial coordinates of the B-DNA double helix constrained to specific spatial pathways and on simple energy models of chain conformation. The new treatment of superhelical DNA in terms of parametric curves is an important first step in being able to generate and examine tertiary structure systematically. The location of every residue is implicitly determined by the equation of the closed curve, with the number of computational variables sharply reduced compared to the number required for explicit specification of all chain units. Furthermore, the constraints of ring closure in cyclic chains and/or the end-to-end limitations on constrained open chains are automatically satisfied by the formulations (cubic B-splines and finite Fourier series) chosen in this work. The predicted conformations of elastic DNA do not appear to be tied to either the form of chain representation or the computer simulation method. Significantly, two very different minimization and modeling approaches come to the same structural conclusions. The most stable configurations of the closed circular elastic DNA model are found to be interwound superhelices that are critically dependent on the specified linking number difference. The total elastic energy is proportional to the imposed linking number difference, and beyond the critical linking number difference separating the circular and figure-eight forms, the writhing number of the DNA superhelices is directly proportional to delta Lk. The measured proportionality constant between Wr and delta Lk, however, is somewhat greater than that deduced from experimental observations of plectonemically interwound DNA chains and an assumed structural model. Furthermore, at large delta Lk, the interwound structures appear to curve. The treatment of the DNA double helix as an ideal elastic rod is clearly incorrect. The chain cannot bend with the same ease in all directions. The degree of bending observed in atomic level models is also tied to the angular twist so that the presumed partitioning of bending and twisting components is in error. Furthermore, the local chain bending and twisting are base sequence dependent, with certain residues able to flex more symmetrically than others. The polyelectrolyte character of the DNA is additionally expected to govern the overall folding of the chain and to influence the local secondary structure. The next step in this work is to compare the properties of such "real" DNA with conventional elastic models.(ABSTRACT TRUNCATED AT 400 WORDS)