The first microscopic knots have been created inside a liquid crystal. This miniature 鈥渒not laboratory鈥� could help mathematicians study the intricacies of knot theory and even help us understand how DNA is unravelled.
While knots may conjure up images of sailors and boy scouts, their potential for complexity poses problems throughout science, from the more esoteric reaches of mathematics to biology. For instance, biologists know that enzymes untie double-stranded DNA so that proteins can be produced. 鈥淏ut it鈥檚 still not very clear how this actually works,鈥� says of the Jo啪ef Stefan Institute in Ljubljana, Slovenia.
To see if they could create microscopic knots, he and his colleagues turned to the kind of liquid crystal used in laptop displays and TVs. These materials flow like fluids but their constituent molecules are aligned in the same direction, more like a solid crystal.
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The researchers added silica particles about 4.72 micrometres across to a liquid crystal and sandwiched the mixture between two glass plates.
Star of David
Each silica particle was coated with a surfactant, making its surface hydrophobic. This disrupted the crystal鈥檚 highly ordered structure 鈥� any liquid crystal molecule adjacent to a silica particle aligned itself perpendicular to the curved surface of the particle and these 鈥渄isordered鈥� molecules formed a three-dimensional Saturn鈥檚 ring around the surface. 鈥淚t鈥檚 visible like a black ring around the particle,鈥� says Tkalec.
When the team trapped the loops with a laser and brought them close together, they immediately joined up to form a bigger, twisted loop around both the particles. A similar thing happened with three particles. By bringing just the right combination of twisted loops into contact, these arrays could be made to unknot and then re-knot to form loops that aren鈥檛 just twisted, but are intertwined.
And by using a series of moves known as Reidemeister moves, which define how one knot can be turned into another equivalent knot, the team identified a range of well-known knots, from the simple Hopf link (two interlocked loops) to the Star of David to Borromean rings (see diagram). 鈥淸With 16 particles] you can achieve up to 80 topologically different structures,鈥� says Tkalec.
Topological bond
, an expert on liquid crystals at the University of Pennsylvania in Philadelphia, says, 鈥淸The work] opens up the possibility of doing experimental knot theory.鈥� He imagines robotic machines manipulating arrays of loops inside a liquid crystal. 鈥淚n principle, you can make a grid of 10,000 knots and study them in a data-intensive way,鈥� he says.
Besides exploring the more esoteric extremes of knot theory, there may be practical applications, for instance, for understanding DNA knotting. 鈥淲e don鈥檛 have other systems where we can control knot formation on microscopic scale. [Now], you have a fully controllable reconfiguration of arbitrary microscopic knots and links,鈥� says Tkalec.
The technique might also lead to a new kind of biomarker. If biologists want to study a given protein, they usually 鈥渢ag鈥� it with a marker molecule, which binds itself to the protein, potentially altering its properties. But what if you created a loop of a biomarker material around a protein that could be tracked under a microscope? 鈥淚magine [tying] little things, or tracers, onto big molecules,鈥� says Kamien. 鈥淚t鈥檚 a topological bond, not a chemical bond.鈥�
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