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<p>The efficient management of DNA supercoiling generated by processive enzymes is essential for maintaining genomic integrity. To investigate this, we apply a relativistic collective coordinate method to the generalized sine–Gordon equation to model the dynamics of a DNA plectoneme (topological kink) under an external, oscillatory transcriptional drive. Building on this approach, we derive the topological integrity condition, which identifies a critical structural gap frequency, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega _{\text {gap}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Ω</mi> <mtext>gap</mtext> </msub> </math></EquationSource> </InlineEquation>, that separates the adiabatic and non-adiabatic regimes of plectoneme motion. Our simulation results further confirm that driving the system near this resonance leads to energy transfer into radiative (internal structural) modes, causing structural instability. Taken together, these findings provide a novel, physics-based explanation for the necessity of ATP-dependent (Type II) topoisomerases at high transcriptional rates, while slower drives are efficiently resolved by passive (Type I) enzymes.</p>

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Nonlinear dynamics and topological transitions in DNA supercoiling

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Mordecai Opoku Ohemeng,
  • Joseph Ackora-Prah,
  • Benedict Barnes,
  • Ishmael Takyi

摘要

The efficient management of DNA supercoiling generated by processive enzymes is essential for maintaining genomic integrity. To investigate this, we apply a relativistic collective coordinate method to the generalized sine–Gordon equation to model the dynamics of a DNA plectoneme (topological kink) under an external, oscillatory transcriptional drive. Building on this approach, we derive the topological integrity condition, which identifies a critical structural gap frequency, \(\Omega _{\text {gap}}\) Ω gap , that separates the adiabatic and non-adiabatic regimes of plectoneme motion. Our simulation results further confirm that driving the system near this resonance leads to energy transfer into radiative (internal structural) modes, causing structural instability. Taken together, these findings provide a novel, physics-based explanation for the necessity of ATP-dependent (Type II) topoisomerases at high transcriptional rates, while slower drives are efficiently resolved by passive (Type I) enzymes.