Exploring dynamical patterns and optical solutions of space-time fractional-order double-chain deoxyribonucleic acid...

DNA, or deoxyribonucleic acid, exists in every human cell, including hair, blood, and skin, carrying the genetic blueprint for all living organisms. Comprised of two strands with four nucleotides-adenine (A), thymine (T), cytosine (C), and guanine (G)-DNA forms a double-helix structure that encodes species-specific traits. Its ability to store data and perform logical operations makes it crucial for biological research, particularly in genome sequencing, which involves complex nonlinear mathematical models. To address these challenges, nonlinear partial differential equations (NPDEs) effectively model DNA's dynamic behavior. The Atangana's conformable derivative accommodates memory effects and nonlocal properties, which are crucial in describing the viscoelastic and hereditary nature of biological systems such as DNA. Unlike integer-order derivatives, this approach captures the complexity of the molecular interactions and relaxation phenomena observed in DNA dynamics. Recent literature has supported the use of fractional models for DNA due to their ability to reflect real-world phenomena more accurately (e.g., base pair opening and long-range interactions). In this study, we explore fractional-order derivatives using Atangana's conformable derivative, applying the $\left(\psi -\varphi \right)$ -expansion method to investigate double-chain DNA dynamical patterns. This method provides precise soliton solutions, such as one-soliton kinks, multiple-soliton solutions, and periodic waves, crucial for understanding DNA's optical properties. Solitons represent localized, stable wave packets that maintain their shape while propagating. In the context of DNA, these structures can model energy transmission along the chain without dispersion. This directly corresponds to base pair openings during transcription, where localized energy must be delivered and preserved to break hydrogen bonds selectively. Hence, solitons offer a feasible mathematical abstraction of physical mechanisms observed in transcription and DNA breathing. The visualized soliton solutions from the space-time fractional-order double-chain DNA model underscore the system's biological importance. The findings have potential applications in evaluating systems and refining scientific insights into DNA dynamics.