“DNA is not only an information carrier but also a mechanical structure, and transcription can drive mechanical and topological excitations in DNA,” said Iso Lomso fellow Ishmael Takyi. “Our model identifies a critical frequency at which energy can be transferred into internal modes, providing a possible physical explanation for why DNA requires different topological management mechanisms at different transcriptional rates.”
Takyi is one of the seventh cohort of Iso Lomso fellows currently in his second residence. He is a mathematical physicist and lecturer in the Department of Mathematics at Kwame Nkrumah University of Science and Technology in Ghana. His academic path has included a PhD at the Institute of Theoretical Physics at Stellenbosch University, being the recipient of the Stephen Hawking Scholarship for his studies at the African Institute for Mathematical Science in Cape Town, and winning the Vice-Chancellor’s Award for the best graduating student in mathematics at the University of Ghana. His research interests are theoretical particle and nuclear physics, particularly in the areas of non-linear field theory, quantum field theory, baryons as solitons and quantum energies of solitons. Takyi has received STIAS support for his work from the PhD level.
In his first STIAS seminar in 2024, Takyi explained his work to develop a mathematical model to study how matter interacts at the subatomic level by modelling solitons and how he hopes that one day his work could have practical application in helping to explain mathematically exactly what happens when a disease interacts with a human cell. After that presentation, he was encouraged by another Fellow, Dieter Ebert of the Department of Environmental Sciences at the University of Basel, to investigate in more detail whether some of the principles and modelling he studies could be applied to DNA supercoiling. This discussion has led to his latest research endeavours.
Takyi started by explaining his modelling work on solitons. “Solitons are classical solutions of non-linear field theory. They have a permanent form, and their energy density moves undistorted with a constant velocity,” he said. “They were first discovered by John Scott Russell in 1834 while observing the motion of a boat on the Edinburgh-Glasgow canal. The wave that developed as a result of the boat's quick stop maintained its shape as it travelled. He referred to these waves as the Great Waves of Translation.”
Because of their unique features, solitons are used in many areas of physics including condensed matter and nuclear and particle physics, as well as in biophysics for studying DNA dynamics.
Takyi also gave a brief overview of our expanded understanding of DNA over the past 150 years – from the work of Swiss physician and biologist Fredrich Miescher who was the first to isolate nucleic acid in 1869 to Martha Chase and Alfred Hershey who helped confirm than DNA is genetic material, and to the work of Watson, Crick and Franklin in the 1950s that proposed the double helix structure of DNA and expanded of our understanding of how genetic information stored in DNA undergoes transcription, translation and replication, and in the process experiences torsional stress and can form supercoiled structures.
Using a belt to model the supercoiling process, Takyi explained that as messenger RNA moves along DNA, it causes the structure to twist, creating supercoiled structures. “The challenge is that transcription is not purely an informational process but also has mechanical consequences. As transcription proceeds, torsional stress can accumulate, which can lead to bulking, stalling and even bursting.”
“There are two forms of supercoiling,” he added, “– plectonemic supercoils and toroidal supercoils. My research is focused on plectonemic.”
Needing to retain cell integrity, there are enzymes in the DNA structure that manage the supercoiling process to reduce torsional stress. These come in two types – Type I topoisomerases, which break one strand of the DNA and allow the other strand to wind around it, and don’t use the energy-carrying enzyme adenosine triphosphate (ATP). Type II topoisomerases, by contrast, break the double strand, requiring a lot of enzymes, including ATP and energy to seal this break.
“We are trying to answer under what conditions or at what mechanical level these enzymes respond. As well as asking whether there is a critical frequency associated with the internal dynamics of the DNA structure upon which the topoisomerases act?” said Takyi.
“To investigate this, I apply a relativistic collective coordinate method to the generalised sine–Gordon equation to model the dynamics of a DNA plectoneme (topological kink) under an external, oscillatory transcriptional drive,” he explained. “Building on this approach, I derive the topological integrity condition, which identifies a critical structural gap frequency, Ωgap, that separates the adiabatic and non-adiabatic regimes of plectoneme motion.”
“The simulated results confirm that driving the system near this resonance leads to energy transfer into radiative (internal structural) modes, causing structural instability,” he continued. “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.”
“Basically, we have found the critical frequency at which plectonemes respond,” he said. “Below the critical level it behaves as a coherent structure, physically protected, but once the critical frequency is approached, the external drive is stronger, and the system transfers energy into structural deformation. At greater frequency, resonance results in rapid energy transfer and plectonemes become chaotic, motion disrupts, and biological repair requires Type II topoisomerases.”
“This means we have developed a model equation for transcriptional drive. The model allows us to represent a localised topological structure as something that can move, respond to forces and interact with its environment. This means that physics provides an additional language for studying how the DNA structure responds to forcing, motion, energy transfer and instability.”
However, Takyi was quick to point out the limitations of the study. “This is a simplified representation of a highly complex biological system,” he said. “The value of the model is that it identifies a possible mechanism and provides quantitative conditions under which different behaviours emerge. Experimental and biological validation would be needed to determine how directly these predictions apply in particular cellular contexts.”
Takyi hopes to find collaborators from other fields to take this work further.
Article: Michelle Galloway
Picture: Curt Ruiters, Quickclick Productions