This project combines mathematical techniques with molecular biology to
investigate the way in which DNA folds and twists under the influence
of various types of forces to produce a hierarchy of structures. These
eventually enable DNA to be neatly compacted into the nucleus. No consistent
theory has been developed to describe how this folding of DNA affects
a hierarchy
of time, energy and length scales that enable molecular interactions at
the atomic level to be integrated into a coherent mechanism that orchestrates
largescale biological processes such as the cell cycle. The goal of the
project is not only to describe a final state in the hierarchy but to
model the transformation from an initial configuration to the final one.
Computationally, this is done by dividing the DNA into small segments
and deriving a complex set of differential equations that describes the
motion of one segment relative to neighboring ones. The computations are
done in mathematically convenient coordinates, which must be converted
to position coordinates for visualization. The entire response of DNA
to different stimuli can then be analyzed. The final states are very complex
structures that require imaging techniques such as slicing, shading and
projecting (onto planes) in order to understand the configurations and
the way they affect the energy of the system.

The result will be a powerful
tool that scientists will be able to use to formulate and test hypotheses,
and to construct, analyze and visualize the dynamics of DNA in a variety
of cellular mechanisms.
The investigators leading this project are Dr. Thomas Bishop (Environmental
Health Sciences), Dr.Ricardo
Cortez (Mathematics) and postdoctoral researcher Dr. Oleksandr Zhmudsky.
Dr. Bishop's expertise is in proteinDNA interactions and he is one of
the investigators who have developed the elastic rod model for DNA, which
is at the core of the project. Dr. Cortez is an expert in computational
methods for differential equations and oversees the numerical aspects
of the project. Dr. Zhmudsky has extensive experience in mathematical
physics, scientific computation and the elastic rod model developed by
Dr. Bishop from previous collaborations.
