Torsion affects the calculation of DNA twisting number

The topological properties of DNA have long been a focal point in biophysics. In the 1970s, White proposed that the topology of closed DNA double helix follows White's formula: Lk = Wr + Tw. However, there has been controversy in the calculation of DNA twisting number, partly due to discrepancies in the definition of torsion in differential geometry. In this paper, we delved into a detailed study of torsion, revealing that the calculation of DNA twisting number should use the curve's geodesic torsion. Furthermore, we found that the discrepancy in DNA twisting numbers calculated using different torsion is N. This study elucidated the impact of torsion on the calculation of DNA twisting numbers, aiming to resolve controversies in the calculation of DNA topology and provided accurate computational methods and theoretical foundations for related research.