DNA Model

In the effort to construct a comprehensive mathematical model for DNA, it is essential to represent not only the quasi-helical geometry of the molecule but also its non-linear and sequence-dependent energetic behavior. A valid model must remain consistent under symmetry-preserving transformations and account for global topological constraints. The Mobius weight energy function (MWEF) is introduced as a scalar descriptor for capturing the intertwined effects of structural topology and torsional energy distribution. The Mobiusweight function, adapted from continuous mapping principles in differential topology, assigns a signed curvature weight to local torsional segments of the DNA. This weighting incorporates a parity-sensitive inversion property, enabling the detection of torsional phasediscontinuities that conventional helical twist measures often overlook. In this framework, DNA is represented as a sequence of discrete base-pair states embedded in a ribbon-like manifold with non-trivial topological properties. The MWEF aggregates the Mobius weights across the DNA contour while incorporating local bending resistance and torsional flexibility parameters. This approach produces an energy landscape sensitive to both the base sequence variations and higher-order structural deformations such as supercoiling or localized kinking. One of the strengths of this model is its ability to combine mechanical deformation characteristics with electronic interaction potentials between base pairs, while preserving global topological invariants. Computational studies using this method show that energy minima emerge near specific Mobius phase transitions, which correlate with experimentally observed loop-closure points and structural kinks in constrained DNA samples.