A semi-analytical approach and theoretical investigation to multi-dimensional DNA models.

IF 1.4 4区 生物学 Q3 BIOLOGY
Khalid K Ali, Mohamed S Mohamed, M Maneea, Monica Botros
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引用次数: 0

Abstract

The dynamics of DNA molecules play a crucial role in understanding genetic information storage, replication, and transmission. This study investigates the nonlinear dynamics of double-chain DNA systems using fractional-order differential equations, addressing the need for accurate mathematical models to capture the complex, non-local interactions inherent in biological systems. Traditional integer-order models often fail to account for memory effects and anomalous diffusion observed in DNA behavior. By employing fractional calculus, we develop a more realistic framework to model longitudinal and transverse displacements in DNA strands. The Laplace Residual Power Series Method (L-RPSM) is utilized to derive analytical solutions for (2+1)- and (3+1)-dimensional fractional DNA models, validated through numerical and graphical comparisons with exact solutions. Numerical experiments demonstrate that the method achieves absolute errors up to 10 - 18 compared with exact solutions. Our results demonstrate the efficacy of fractional calculus in capturing the nuanced dynamics of DNA, offering insights into soliton propagation and structural analysis, which are vital for applications in biophysics and genetic engineering.

多维DNA模型的半解析方法及理论研究。
DNA分子的动力学在理解遗传信息的储存、复制和传递中起着至关重要的作用。本研究利用分数阶微分方程研究了双链DNA系统的非线性动力学,解决了对精确数学模型的需求,以捕捉生物系统中固有的复杂的非局部相互作用。传统的整阶模型往往不能解释记忆效应和DNA行为中观察到的异常扩散。通过采用分数微积分,我们开发了一个更现实的框架来模拟DNA链的纵向和横向位移。利用拉普拉斯残差幂级数法(L-RPSM)推导出(2+1)维和(3+1)维分数阶DNA模型的解析解,并通过与精确解的数值和图形比较进行验证。数值实验表明,与精确解相比,该方法的绝对误差可达10 ~ 18。我们的研究结果证明了分数微积分在捕捉DNA细微动态方面的有效性,为孤子传播和结构分析提供了见解,这对生物物理学和基因工程的应用至关重要。
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来源期刊
Theory in Biosciences
Theory in Biosciences 生物-生物学
CiteScore
2.70
自引率
9.10%
发文量
21
审稿时长
3 months
期刊介绍: Theory in Biosciences focuses on new concepts in theoretical biology. It also includes analytical and modelling approaches as well as philosophical and historical issues. Central topics are: Artificial Life; Bioinformatics with a focus on novel methods, phenomena, and interpretations; Bioinspired Modeling; Complexity, Robustness, and Resilience; Embodied Cognition; Evolutionary Biology; Evo-Devo; Game Theoretic Modeling; Genetics; History of Biology; Language Evolution; Mathematical Biology; Origin of Life; Philosophy of Biology; Population Biology; Systems Biology; Theoretical Ecology; Theoretical Molecular Biology; Theoretical Neuroscience & Cognition.
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