Equilibrium structure and deformation response of 2D kinetoplast sheets.

The considerable interest in two-dimensional (2D) materials and complex molecular topologies calls for a robust experimental system for single-molecule studies. In this work, we study the equilibrium properties and deformation response of a complex DNA structure called a kinetoplast, a 2D network of thousands of linked rings akin to molecular chainmail. Examined in good solvent conditions, kinetoplasts appear as a wrinkled hemispherical sheet. The conformation of each kinetoplast is dictated by its network topology, giving it a unique shape, which undergoes small-amplitude thermal fluctuations at subsecond timescales, with a wide separation between fluctuation and diffusion timescales. They deform elastically when weakly confined and swell to their equilibrium dimensions when the confinement is released. We hope that, in the same way that linear DNA became a canonical model system on the first investigations of its polymer-like behavior, kinetoplasts can serve that role for 2D and catenated polymer systems.

Long-Lived Self-Entanglements in Ring Polymers.

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

Motion of Knots in DNA Stretched by Elongational Fields.

Knots in DNA occur in biological systems, serve as a model system for polymer entanglement, and affect the efficacy of modern genomics technologies. We study the motion of complex knots in DNA by stretching molecules with a divergent electric field that provides an elongational force. We demonstrate that the motion of knots is nonisotropic and driven towards the closest end of the molecule. We show for the first time experimentally that knots can go from a mobile to a jammed state by varying an applied strain rate, and that this jamming is reversible. We measure the mobility of knots as a function of strain rate, demonstrating the conditions under which knots can be driven towards the ends of the molecule and untied.

Knots modify the coil-stretch transition in linear DNA polymers.

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Constructing custom thermodynamics using deep learning.

One of the most exciting applications of artificial intelligence is automated scientific discovery based on previously amassed data, coupled with restrictions provided by known physical principles, including symmetries and conservation laws. Such automated hypothesis creation and verification can assist scientists in studying complex phenomena, where traditional physical intuition may fail. Here we develop a platform based on a generalized Onsager principle to learn macroscopic dynamical descriptions of arbitrary stochastic dissipative systems directly from observations of their microscopic trajectories. Our method simultaneously constructs reduced thermodynamic coordinates and interprets the dynamics on these coordinates. We demonstrate its effectiveness by studying theoretically and validating experimentally the stretching of long polymer chains in an externally applied field. Specifically, we learn three interpretable thermodynamic coordinates and build a dynamical landscape of polymer stretching, including the identification of stable and transition states and the control of the stretching rate. Our general methodology can be used to address a wide range of scientific and technological applications.

Automated electrokinetic stretcher for manipulating nanomaterials.

In this work, we present an automated platform for trapping and stretching individual micro- and nanoscale objects in solution using electrokinetic forces. The platform can trap objects at the stagnation point of a planar elongational electrokinetic field for long time scales, as demonstrated by the trapping of <100 nm polystyrene beads and DNA molecules for minutes, with a standard deviation in displacement from the trap center <1 µm. This capability enables the stretching of deformable nanoscale objects in a high-throughput fashion, as illustrated by the stretching of more than 400 DNA molecules within ∼4 hours. The flexibility of the electrokinetic stretcher opens up numerous possibilities for complex manipulation, with sequential stretching of a molecule at different voltages and multiple stretch-relaxation cycles of the same molecule as examples. The platform described provides an automated, high-throughput method to track and manipulate objects for real-time studies of micro- and nanoscale systems.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement.

A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.

Phase Transition of Catenated DNA Networks in Poly(ethylene glycol) Solutions.

Conformational phase transitions of macromolecules are an important class of problems in fundamental polymer physics. While the conformational phase transitions of linear DNA have been extensively studied, this feature of topologically complex DNA remains unexplored. We report herein the polymer-and-salt-induced (Ψ) phase transition of 2D catenated DNA networks, called kinetoplasts, using single-molecule fluorescence microscopy. We observe that kinetoplasts can undergo a reversible transition from the flat phase to the collapsed phase in the presence of NaCl as a function of the crowding agent poly(ethylene glycol). The nature of this phase transition is tunable through varying ionic strengths. For linear DNA, the coexistence of coil and globule phases was attributed to a first order phase transition associated with a double well potential in the transition regime. Kinetoplasts, however, navigate from the flat to the collapsed phase by passing through an intermediate regime, characterized by the coexistence of a multipopulation with varying shapes and sizes. Conformations of individual molecules in the multipopulation are long-lived, which suggests a rugged energy landscape.

Deformation Response of Catenated DNA Networks in a Planar Elongational Field.

A kinetoplast is a complex catenated DNA network that bears resemblance to a two-dimensional polymeric system. In this work, we use single-molecule experiments to study the transient and steady-state deformation of kinetoplasts in a planar elongational field. We demonstrate that kinetoplasts deform in a stagewise manner and undergo transient deformation at large strains, due to conformational rearrangements from an intermediate metastable state. Kinetoplasts in an elongational field achieve a steady-state deformation that depends on strain rate, akin to the deformation of linear polymers. We do not observe an abrupt transition between the nondeformed and deformed states of a kinetoplast, in contrast to the coil-stretch transition for a linear polymer.

Conformational State Hopping of Knots in Tensioned Polymer Chains.

We use Brownian dynamics simulations to study the conformational states of knots on tensioned chains. Focusing specifically on the 81 knot, we observe knot conformational state hopping and show that the process can be described by a two-state kinetic model in the presence of an external force. The distribution of knot conformational states depends on the applied chain tension, which leads to a force-dependent distribution of knot untying pathways. We generalize our findings by considering the untying pathways of other knots and find that the way knots untie is generally governed by the force applied to the chain. From a broader perspective, being able to influence how a knot unties via external force can potentially be useful for applications of single-molecule techniques in which knots are unwanted.