Executive Summary : | In order to accomplish essential cell processes, such as cell division and DNA transcription, DNA twists, turns, and folds itself into knots. DNA deformation contributes, for example, to the expression of genes, and, therefore, understanding it is vital to genomics and other associated fields. Measuring geometric properties and mechanical parameters in a continuum mathematical model of DNA is a crucial step towards this understanding. Furthermore, simulation of the mathematical model corroborates experimental data and predicts other DNA properties and deformations that may not be observable in an experimental setup. PIs will predominantly concentrate on these aspects in this project: high-dimensional parameter and configuration spaces, stiff dynamics, and drift in the conserved quantities of DNA's mathematical model. These aspects will be investigated from the standpoint of various mathematical fields, such as structure-preserving computational methods and high-dimensional deterministic and stochastic differential equations. |