All children, having Lego bricks or pieces of a jigsaw puzzle in their hands, have tried at least once to build something or to reassemble the image hidden in the tiles.

Being able to assemble DNA molecules, like Lego bricks or pieces of a jigsaw puzzle, to make complex structures like crystals, is the latest frontier in physics.

DNA lends itself to being used for this purpose due to the complementarity of the four nitrogenous bases, which makes it very versatile and suitable for joining into compounds. Through a mechanism known as 'self-assembly', the molecules themselves, even in enormous numbers, form an organised structure as a consequence of specific and local interactions between the constituents, without external actions. However, achieving and controlling the self-assembly of particles is not easy. Given a specific structure, the challenge is to be able to synthesise it correctly and efficiently, reducing the number of different components required as much as possible.

An international collaboration has attempted to investigate the problem in depth in a study published in Science. Among the experts involved were Lorenzo Rovigatti, Francesco Sciortino and John Russo from the Physics Department of Sapienza University, together with colleagues from Ca' Foscari, Columbia and Arizona State University.

Going back to the previous example, Lego bricks and puzzle pieces are actually two alternative and different construction processes. The former are all similar to each other and are designed in such a way that they can be combined with any other brick to create infinite shapes. The latter, on the other hand, are all different and only bond to their corresponding one, in a very specific position, to form a predefined design.

The scientists' choice therefore lies in the middle: not bricks that are all the same to have infinite structures, nor pieces that are all different to achieve the desired result, but the minimum number of different elements to create exactly and only the desired conformation.

The key to the solution was to translate this theoretical problem, and thus the desired structure, into a set of simple logical clauses. These can then be solved numerically, giving an optimal and efficient solution for any shape.

To demonstrate the validity of the method, the authors decided to experimentally realise the self-assembly of a crystal chosen for its nanoscale photonic properties, pyrochlore, "a crystal that does not exist in nature and was considered impossible to realise experimentally", says John Russo, of the Department of Physics. To create it, particles entirely composed of DNA (in jargon "DNA origami") were used. In this way, it was possible to demonstrate that the required structure forms precisely as expected, in a kind of jigsaw puzzle of only four types of pieces that infallibly assembles itself.

"The work is based on the idea of using a mathematical tool called "Boolean satisfiability", also known as SAT, to solve the problem of self-assembling ordered structures from a limited number of bricks. The advantage of using SAT is that, in addition to obtaining a solution that assembles the desired ordered structure, it also allows us to refine the solution so that any structures that compete with the target structure are disfavoured", says Lorenzo Rovigatti of the Department of Physics. "In this work we apply this sophisticated technique to design on the computer and then obtain in the laboratory a crystalline material that has never been assembled before, clearly demonstrating the potential of our method, which we have dubbed "SAT-assembly"."

This innovative approach to the spontaneous formation of structures offers a new perspective for the design of nanomaterials, enabling the construction of structures made up of billions of components arranged with absolute precision and paving the way for applications in fields such as photonics and nanoelectronics.