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Over the past decade, experts in the field of nanotechnology and materials science have been trying to devise architectures composed of small structures that spontaneously arrange themselves following specific patterns. Some of these architectures are based on so-called icosahedral shells, structures with 20 different triangular phases that are symmetrically organized.

The reliable assembly of these programmable shells has proved challenging, as the resulting structures often differ from the design, forming alternative, less stable structures. This essentially means that their organization into desired architectures is prone to "missing the target." Identifying strategies to enable the assembly of icosahedral shells or other programmable nanostructures could be advantageous for various real-world applications.

Researchers at BabeÅŸ-Bolyai University, Brandeis University and the University of Massachusetts recently developed a new algorithm for the high-fidelity assembly of programmable shells at a minimal cost. Their proposed method, outlined in a paper in Â鶹ÒùÔºical Review Letters, could enable the scalable creation of nanostructures that could serve as a basis for various medical and consumer-facing technologies.

"Recent advancements in DNA nanotechnology and de novo protein design allow for the detailed design of building blocks which self-assemble into precisely defined target structures," Gregory M. Grason and Michael F. Hagan, co-senior authors of the paper, told Â鶹ÒùÔº. "A specific vexing design goal is to program these assemblies to 'stop' their subunit-by-subunit growth at a particular finite size (the 'target' size)."

While conducting earlier studies focusing on the realization of self-assembling programmable nanostructures, Grason, Hagan and their colleagues encountered various challenges. Most notably, they found that these synthetic self-assembled platforms often misassemble into off-target or defective structures, and this tendency becomes increasingly pronounced as they grow larger.

"For example, in a recent collaboration with our group, Hendrick Dietz and Seth Fraden developed triangular DNA origami subunits that assemble into icosahedral capsids with programmable sizes," said Grason and Hagan. "While this effort was spectacularly successful and demonstrated assembly of target capsids up to 180 triangular subunits, it was observed that the yield of target structures decreased significantly as the size increased."

When they started planning their new study, the researchers knew that increasing the complexity of a programmable nanostructure's design, or in other words, using a greater variety and number of underlying building blocks, led to a greater fraction of assembled subunits assembling into desired structures. However, their earlier works and those of other teams showed that a greater design complexity is also linked to higher material synthesis costs and longer assembly times.

"There is a trade-off between high fidelity (high yields of the target structure and low yields of competing structures) and economy (limiting the number of building blocks that need to be designed)," said Grason and Hagan. "In this context, more required species are more 'costly' in the sense that experimentalists have more types of subunits to design, synthesize and purify."

The main goal of the team's study was to identify optimal design strategies for the assembly of programmable nanostructures, which are both economical and reliably eliminate defective structures. First, they used symmetry-related principles to develop an algorithm that could identify optimum complexity designs. These are designs that would produce target structures with the highest possible yield at the lowest possible "cost."

"The designs avoid the specific symmetry elements that enable defects to easily form as shells are assembling," explained Grason and Hagan. "Those defects are places where the 'lock-and-key' type interactions between the subunit can form, but in the wrong geometry, for example, a smaller than intended shell. We demonstrate the algorithm on icosahedral shells, such as formed by natural viruses, and show that the principle generalizes to other types of structures."

To validate the potential of their newly developed algorithm, Grason, Hagan and their colleagues ran a series of dynamical computer simulations, known as Monte Carlo and Brownian Dynamics simulations. They found that their algorithm enabled the high-fidelity assembly of programmable shells, while keeping the design simple enough to enable their scalable realization.

"This contribution is enabled by identifying a selection rule, based on the overlap of the complete structure's symmetry axis with its vertices," said Grason and Hagan. "Whenever any symmetry axis overlaps with a vertex (point where multiple triangular subunits meet in an assembling structure), defects can form, and the assembly is likely to result in non-target structures. The optimal design for a given size is the lowest complexity design that does not have any symmetry axis overlapping with the vertex."

Interestingly, the researchers' simulations led to the identification of various "magic sizes" that allow for a particularly low complexity due to their symmetry. In structures with these sizes, symmetry axes cross a shell face (i.e., one of the flat triangular panels) instead of a vertex (i.e., corner points where the triangular shells meet).

"These magic sizes require 12-fold fewer subunit types than the most complex assemblies," explained Grason and Hagan. "Our optimal algorithm opens the door to nanomaterials applications in which structures composed of thousands of subunits assemble without external intervention, while also shedding new light on how biological structures such as viruses assemble so reliably."

In the future, the algorithm developed by Grason, Hagan and their colleagues could be used to conduct research, for instance to study the assembly of biological structures or living organisms, as well as to engineer programmable nanostructures tailored for specific applications. In their next studies, the researchers plan to implement and test their designs for the assembly of nanostructures based on strands of DNA.

"In addition, we would like to extend the concepts underlying this algorithm to identify other strategies for optimizing self-assembly," added Grason and Hagan. "For instance, can we identify other types of symmetry principles or other approaches that reduce the design complexity while also directing assembly pathways away from defects that caused mis-assembly?

"This sort of question might be applied to address what type of subunit symmetry—triangular, square, or some other polygon—gives us the 'cheapest' way to make size-scalable structures of various shapes, well beyond simple spherical shells."

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