The investigator develops a computational method for estimating local, sequence-dependent curvature parameters for DNA from hydrodynamic data on short, relatively stiff fragments. The method consists of minimizing a least-squares functional which quantifies the difference between theoretical and experimental sedimentation speeds for a given collection of fragments, and its numerical implementation requires the repeated solution of an exterior Stokes-type problem around various slender, three-dimensional domains. The research effort is centered on three areas: (1) the study of the theoretical sedimentation speed of a stiff polymer in a Stokes-type fluid with thermal fluctuations in different asymptotic limits, (2) the design and analysis of fast, provably convergent boundary element methods for computing the theoretical sedimentation speed based on the novel idea of a kernel-adapted Nystrom method, and (3) the design and analysis of fast, reliable methods for minimizing a least-squares sedimentation functional over a space of sequence-dependent curvature parameters.
The sequence-dependent curvature and flexibility of DNA is critical for its packaging into the cell, recognition by other molecules, and conformational changes during biochemically important processes. However, few experimental methods are available for probing these properties at the basepair level. The objective of this project is to exploit the stiffness of DNA at short length scales and develop a method for estimating local, sequence-dependent curvature parameters from hydrodynamic data on short fragments. The method is based on the observation that small, relatively stiff fragments of different shape typically travel at different speeds when forced through a viscous fluid or through a dilute gel. The investigator seeks to develop a sufficiently refined mathematical relation between shape and speed and further use this relation to develop a computational method to estimate shape parameters from measurements of speed. Results from this research lead to new tools for quantifying the intrinsic sequence-dependent curvature of DNA, which in turn may lead to an enhanced understanding of important genomic regions and of how DNA interacts with other molecules.
