Analytical description of extension, torque, and supercoiling radius of a stretched twisted DNA

Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...

Topoisomerases are enzymes that relax overwound DNA molecules during various cell processes, including DNA replication and transcription. These enzymes regulate positive and negative DNA supercoiling without changing the nucleotide sequence. DNA overwinding in a clockwise direction results in positively supercoiled DNA, whereas underwinding in a counterclockwise direction produces negatively supercoiled DNA.
Types and Mechanism of action
Topoisomerases are divided into two main types.  Type I...

Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...

Strain energy is a fundamental concept in the field of materials science and structural engineering, describing the energy absorbed by a material or structure when it is deformed under load.
Consider a rod that is fixed at one end and subjected to an axial force at the free end. This axial force induces stress within the rod, leading to its elongation. As the axial force increases, so does the elongation of the rod, illustrating a direct relationship between the force applied and the resulting...

Each human somatic cell contains 6 billion base pairs of DNA. Each base pair is 0.34 nm long, meaning each diploid cell contains a staggering 2 meters of DNA. This long DNA strand is packed inside a nucleus measuring only 10-20 microns in diameter with the help of specialized DNA-binding proteins called histones. Together they form a compact DNA-protein complex called chromatin. The chromatin is further compacted into higher-order structures. The highest level of compaction is achieved during...

Each human somatic cell contains 6 billion base-pairs of DNA. Each base-pair is 0.34 nm long, which means that each diploid cell contains a staggering 2 meters of DNA. How is such a long DNA strand packed inside a nucleus measuring only 10 - 20 microns in diameter? 
The chromatin
In combination with specialized DNA binding protein called Histones, the DNA double helix forms a compact DNA: protein complex called chromatin. The chromatin itself is further compacted into higher-order structures.