What if a complex material could reshape itself in response to a simple chemical signal? A team of physicists from the University of Vienna and the University of Edinburgh has shown that even small changes in pH value and thus in electric charge can shift the spatial arrangement of closed ring-shaped polymers (molecular chains) – by altering the balance between twist and writhe, two distinct modes of spatial deformation. Their findings, published in Physical Review Letters, demonstrate how electric charge can be used to reshape polymers in a reversible and controllable way – opening up new possibilities for programmable, responsive materials. With such materials, permeability and mechanical properties such as elasticity, yield stress and viscosity could be better controlled and precisely 'programmed'.

Imagine taking a ribbon and twisting it by half before connecting its ends: you create the famous Möbius band – a loop with a single twist and a continuous surface. Add more twists before closing the ribbon, and the structure becomes so called supercoiled. Such shapes are common in biology and materials science, especially in circular DNA and synthetic (artificially produced) ring polymers. Whether and how the balance between twist– the local rotation of the ribbon around its axis – and writhe – the large-scale coiling of the ribbon in space could be tuned in a controlled and reversible way is still unclear. The research team set out to investigate this question using a model system of ring-shaped polymers, where electric charge – introduced via pH-dependent ionization – serves as an external tuning parameter.

From writhe to twist

To explore the tunability of this topological balance, the researchers combined computer simulations and analytical theory to study how charge affects the conformation of supercoiled ring polymers. In their model, each monomeric unit acts as a weak acid, gaining or losing charge depending on the pH value (specifies the acidity or basicity of aqueous solutions) of the surrounding solution. This setup enabled a gradual buildup of charge and revealed how the molecule reshapes in response.

The results: Neutral polymers adopt writhe-rich, compact shapes. As charge increases, electrostatic repulsion grows – driving the molecule toward more extended conformations and shifting the internal distribution from writhe to twist. These transitions are smooth at low supercoiling. At higher levels, however, the model predicts a striking feature: the polymer can split into coexisting twist- and writhe-rich domains – a kind of topologically constrained microphase separation. This hidden form of phase coexistence had not been observed in such systems before.

To capture these mechanisms, the researchers developed a Landau-type mean-field theory. This simplified mathematical model accurately predicts when a polymer will undergo a continuous or abrupt conformational change – depending on its degree of supercoiling and charge.

Topology as a design tool

The idea of tuning not just molecular structure, but topology itself, opens up new ways to control responsive systems. "By adjusting the local charge, we can shift the balance between twist and writhe – and that gives us a handle on the shape of the whole molecule," says first author Roman Staňo from the Faculty of Physics at the University of Vienna (currently at Cambrigde Univesrity). Because each monomer can gain or lose charge, the polymer gradually reshapes itself – a behavior that resembles real polyelectrolytes, such as chemically modified DNA. The team suggests that synthetic DNA rings with pH-sensitive side chains – not yet realized experimentally, but now feasible thanks to recent advances in nucleotide chemistry – could display this kind of controllable shape-shifting behavior. These molecules would act as topologically constrained scaffolds, adjusting their form in response to local chemical conditions.

Responsive shapes, programmable function

Polymer shape isn't just geometry – it governs flow, function, and interaction. The ability to reversibly shift between twist- and writhe-dominated states offers a powerful strategy for designing adaptive materials. Ring polymers that respond to subtle changes in pH could one day be used in microfluidic devices, where local conditions trigger controlled changes in shape and flow behavior. "What's remarkable," says co-author Christos Likos, Faculty of Physics at the University of Vienna, "is that the transition from compact to extended shapes happens gradually, can be controlled via pH – and doesn’t require any changes to the molecule’s topology."

This effect, the team notes, could be realized experimentally in synthetic DNA rings – a possibility enabled by recent advances in nucleotide chemistry. Their results also offer predictive insight: they show how function can be encoded not only in chemical composition, but also in topological state – pointing toward a new generation of shape-adaptive materials.

Likos-group, Soft Matter Theory and Simulation, University of Vienna

Michieletto-group, Topologically active polymers Lab, University of Edinburgh