Topological Interaction by Entangled DNA Loops

We have discovered a new type of interaction between micro- or nanoscale particles that results from the entanglement of strands attached to their surfaces. Self-complementary DNA single strands on a particle can hybridize to form loops. A similar proximal particle can have its loops catenate with those of the first. Unlike conventional thermodynamic interparticle interactions, the catenation interaction is strongly history and protocol dependent, allowing for nonequilibrium particle assembly. The interactions can be controlled by an interesting combination of forces, temperature, light sensitive cross-linking and enzymatic unwinding of the topological links. This novel topological interaction may lead to new materials and phenomena such as particles strung on necklaces, confined motions on designed contours and surfaces, and colloidal Olympic gels.

Figure 1

The model system with direct binding and entanglement binding. Four different sequences of DNA sticky ends $P1$, $P2$, C, D are shown on top. (a) Direct binding $P1\mathrm{\text{−}}P1$ and topological entanglement binding $P1\mathrm{\text{−}}P2$ schemes. (b) Random mixture of Watson-Crick chain system (C-D) gives binding fraction $P=50\%$ from CD direct bindings; $P1$ chain system gives $P=100\%$ from $P1P1$ direct bindings; Random mixture of $P1$ and $P2$, if $P1P1$ and $P2P2$ will bond but not $P1P2$ or $P2P1$ then $P=50\%$; if there are entanglements for $P1P2$ and $P2P1$, $P$ will increase to 100%.

Figure 2

Typical measurements of “number of objects” in the system. We use an evenly mixed $P1$ and $P2$ particle system. Initial soup ($52°\mathrm{C}$): particles are chained up with a magnetic field $\sim 2\mathrm{mT}$, followed by a temperature quench to $T_{\mathrm{quench}}$ (refer to different shapes in the right column), and then released from the magnetic field. Bottom 3 pictures show the microscope images at different stages of the protocol. Scale bar is $20\mu \mathrm{m}$ in all images.

Figure 3

Experimental data compared with model prediction. (a) Experimental data: binding fraction vs temperature in 4 different experiments. The 2 transitions on the square curve show direct binding (higher $T$) and entanglement binding (lower $T$) in the $P1$ and $P2$ mixed system. Triangle or circle transition curves show direct binding of $P1$ or $P2$. The flipped triangle transition curve shows direct binding of the C and D mixed system, there is no entanglement possibility in this system, the binding fraction remains at 50% at low temperature. (b) Model prediction for entanglement binding transition and direct binding transition with effective entangled area $A=100{\mathrm{nm}}^2$. (c) Direct $P1$ and $P2$ binding curves are rescaled to 50% for easy comparison to square curve model system. After using a fitting parameter $\Delta S_p$ set by the pure $P1$ or $P2$ melting transition [7], we can predict the entanglement melting transition by $P(T)=P_{\mathrm{entangle}}(T)/2+P_{\mathrm{direct}}(T)/2$. Dashed lines and grey zone show prediction with uncertainty in $A$ from $50{\mathrm{nm}}^2$ to $130{\mathrm{nm}}^2$. The error bars result from statistics on several experimental runs and an estimate of error in analyzing the number of independent objects from each image.

Figure 4

Topoisomerase unlinking experiments. (a) a typical image for particles chained together: $P1$ and $P2$ mixed system with only 1x NE and BSA buffer, $P1$ system with topoisomerase I ($1\mathrm{unit}/25\mu \mathrm{L}$), 1x NE and BSA buffer; (b) $P1$ and $P2$ mixed system with topoisomerase, 1x NE and BSA buffer. Breaking of the chains proves our entanglement interaction is topological. (c) $P1$ (bright) and $P2$ (dark) mixed system at $40°\mathrm{C}$ forms separate $P1$ and $P2$ clusters. (d) at low temperature $\sim 37°\mathrm{C}$, $P1$ and $P2$ clusters are connected by entanglement and catenation. (e) and (f) $P1$ and $P2$ clusters separate after adding topoisomerase. The scale bar indicates $20\mu \mathrm{m}$ in all images.