An Algorithm for Reconstructing the Dynamics of Supercoiled DNA

Abstract

The level and distribution of DNA supercoiling changes continuously in response to thermal fluctuations and important cellular processes (e.g., transcription). Interestingly, such processes are sensitive to the level of supercoiling such that topoisomerases are required to regulate the level of supercoiling. Clearly, we must characterize and understand supercoil dynamics to better understand cellular processes. Unfortunately, previous experimental and computational techniques offer only limited access to these dynamics. We believe the marriage of next generation imaging systems with novel computational algorithms will alleviate these limitations. Therefore, our long term research objective is to develop computational algorithms to facilitate this marriage. We present an algorithm intended to be paired with experiments in which several identical fluorescent labels are distributed around supercoiled circular DNA molecules. The 3-dimensional trajectory through time of each fluorophore could be obtained by a next generation super-resolution fluorescent imaging system. Given these trajectories, our algorithm reconstructs the arrangement of fluorophores around circular DNA much like a game of connect the dots. However, this isn’t an easy game because the ‘dots’ aren’t numbered (the fluorophores are indistinguishable), the ‘dots’ are spaced several persistence lengths apart along the DNA, and supercoiling implies the connections cross in 3-dimensions. Our approach maps reconstruction into the well-known traveling salesman problem for which there are efficient solvers. To demonstrate the utility of our algorithm, we simulate fluorophore trajectories with our discrete wormlike chain model for DNA. We show that (i) our algorithm converges to the correct arrangement as observation time increases, (ii) increasing the number of fluorophores on a supercoiled DNA reduces the observation time required for correct reconstruction, and (iii) the required observation time increases with the level of supercoiling.