Optimal kinematics of supercoiled filaments
Seminar Room 1, Newton Institute
In this talk we propose kinematics of supercoiling of closed filaments as solutions of the elastic energy minimization . The analysis is based on the thin rod approximation of linear elastic theory, under conservation of self-linking number with elastic energy evaluated by means of bending and torsional influence. Time evolution functions are described by means of piecewise polynomial transformations based on cubic spline functions. In contrast with traditional interpolation, the parameters defining the cubic splines representing the evolution functions are considered as the unknowns in a non-linear optimization problem. We show how the coiling process is associated with conversion of mean twist energy into bending energy through the passage by an inflexional configuration  in relation to geometric characteristics of the filament evolution. Geometric models for chromatin fibre folding are finally presented, compared in terms of geometric quantities and tested on ChIP Data (Chromatin ImmunoPrecipitation) generated from human pluripotent embryonic stem cells. These results provide new insights on the folding mechanism  and associated energy contents and may find useful applications in folding of macromolecules and DNA packing in cell biology .
References:  F. Maggioni & R.L. Ricca (2006) Writhing and coiling of closed filaments. Proc. R. Soc. A 462, 3151-3166.  Maggioni, F., Potra, F. & Bertocchi, M. Optimal kinematics of a looped filament (under referee reviewing).  H.K. Moffatt & R.L. Ricca (1992) Helicity and the C?lug?reanu invariant. Proc. R. Soc. Lond A 439, 411- 429.  R.L. Ricca & F. Maggioni (2008) Multiple folding and packing in DNA Computer & Mathematics with Applications, 55, 1044-1053