nano technology, nanomaterials, nanophysics, nanotechnology, science, technology, self-organization of complex structures
Time complexity. (A–C) The minimal assembly time Tmin90in in the four scenarios in dependence of the size S of the target structure as obtained from stochastic simulations for different dimensionalities of the structures: (A) 1D, (B) 2D, and (C) 3D. The reactive timescale (Cν)−1 defines the basic timescale in the system, which depends on the initial concentration C of monomers per species. Hence, the minimal assembly time is measured in units of (Cν)−1. Each data point represents an average over several independent realizations of the stochastic simulation for the same (optimal) parameter value, determined by a parameter sweep (SI Appendix, section 1). We find power-law dependencies of the minimal assembly time on the size of the target structure. The corresponding time complexity exponents θsim resulting from the simulations are summarized in the tables in A–C together with their theoretic estimates θth (which we derive in SI Appendix, section 3). We indicate the scenarios as rev, reversible binding; act, activation; jis, just-in-sequence; and dim, dimerization. Credit: DOI: 10.1073/pnas.2116373119

Ludwig Maximilian University of Munich researchers have developed a new strategy for manufacturing nanoscale structures in a time- and resource-efficient manner.

Macromolecules such as cellular structures or virus capsids can emerge from small building blocks without external control to form complex spatial structures. This self-organization is a central feature of biological systems. But such self-organized processes are also becoming increasingly important for the building of complex nanoparticles in nanotechnological applications. In DNA origami, for instance, larger structures are created out of individual bases.

But how can these reactions be optimized? This is the question that LMU physicist Prof. Erwin Frey and his team are investigating. The researchers have now developed an approach based on the concept of time complexity, which allows new strategies to be created for the more efficient synthesizing of complex structures, as they report in the journal PNAS.

A concept from the computer sciences

Time complexity originally describes problems from the field of informatics. It involves investigating how the amount of time needed by an algorithm increases when there is more data to process. When the volume of data doubles, for example, the time required could double, quadruple, or increase to an even higher power. In the worst case, the running time of the algorithm increases so much that a result can no longer be output within a reasonable timeframe.

“We applied this concept to self-organization,” explains Frey. “Our approach was: How does the time required to build large structures change when the number of individual building blocks increases?” If we assume—analogously to the case in computing—that the requisite period of time increases by a very high power as the number of components increases, this would practically render syntheses of large structures impossible. “As such, people want to develop methods in which the time depends as little as possible on the number of components,” explains Frey.

The LMU researchers have now carried out such time complexity analyses using computer simulations and mathematical analysis and developed a new method for manufacturing complex structures. Their theory shows that different strategies for building complex molecules have completely different time complexities—and thus also different efficiencies. Some methods are more, and others less, suitable for synthesizing complex structures in nanotechnology. “Our time complexity analysis leads to a simple but informative description of self-assembly processes in order to precisely predict how the parameters of a system must be controlled to achieve optimum efficiency,” explains Florian Gartner, a member of Frey’s group and lead author of the paper.

The team demonstrated the practicability of the new approach using a well-known example from the field of nanotechnology: The scientists analyzed how to efficiently manufacture a highly symmetrical viral envelope. Computer simulations showed that two different assembly protocols led to high yields in a short window of time.

A new strategy for self-organization

When carrying out such experiments before now, scientists have relied on an experimentally complicated method that involves modifying the bond strengths between individual building blocks. “By contrast, our model is based exclusively on controlling the availability of the individual building blocks, thus offering a simpler and more effective option for regulating artificial self-organization processes,” explains Gartner. With regard to its time efficiency, the new technique is comparable, and in some cases better, than established methods. “Most of all, this schema promises to be more versatile and practical than conventional assembly strategies,” says the physicist.

“Our work presents a new conceptual approach to self-organization, which we are convinced will be of great interest for physics, chemistry, and biology,” says Frey. “In addition, it puts forward concrete practical suggestions for new experimental protocols in nanotechnology and synthetic and molecular biology.” More information: Florian M. Gartner et al, The time complexity of self-assembly, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2116373119 Journal information: Proceedings of the National Academy of Sciences

Provided by Ludwig Maximilian University of Munich Citation: Self-organization of complex structures (2022, January 19) retrieved 19 January 2022 from This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.


Next-generation weather models cross the divide to real-world impact

The NOAA Hazardous Weather Testbed provides a conceptual framework and a physical space to foster collaboration between research and operations to test and evaluate emerging technologies and science for NWS operations. Here, a scene from the 2020 Spring Experiment. Credit: NOAA Each winter, spring, and summer, extreme weather forecasters ...

View more: Next-generation weather models cross the divide to real-world impact

Build new data science skills with this A-to-Z training bundle deal

Data science is becoming one of the core drivers of not just IT but a wide range of industries it serves. The A to Z Data Science & Machine Learning Bundle grants valuable insight into how data is recorded, sorted, managed, and analyzed to draw important insights from huge ...

View more: Build new data science skills with this A-to-Z training bundle deal

Two-step molecular process rewires nutrient transport in wild thale cress

Thale cress (Arabidopsis thaliana), botanic school of the Jardin des Plantes of Paris, France. Credit: Marie-Lan Nguyen/Wikimedia Commons, CC BY 2.5 New research in plants that colonized the base of an active stratovolcano reveals that two simple molecular steps rewired nutrient transport, enabling adaptation. An international team led by ...

View more: Two-step molecular process rewires nutrient transport in wild thale cress

Graphene-wrapped zeolite membranes for fast hydrogen separation

Figure 1. Transmission electron micrograph of graphene-wrapped zeolite. Credit: The Authors The effects of global warming are becoming more serious, and there is a strong demand for technological advances to reduce carbon dioxide emissions. Hydrogen is an ideal clean energy which produces water when burned. To promote the use ...

View more: Graphene-wrapped zeolite membranes for fast hydrogen separation

For wetland plants, sea-level rise stamps out benefits of higher carbon dioxide

Sunrise at the Global Change Research Wetland, a site of futuristic climate research at the Smithsonian Environmental Research Center in Edgewater, Maryland. These chambers have been growing plants with extra CO2 since 1987. Credit: Tom Mozdzer Wetlands across the globe are in danger of drowning from rising seas. But ...

View more: For wetland plants, sea-level rise stamps out benefits of higher carbon dioxide

Solar Orbiter: Striking new imagery of our Sun has been released

The spacecraft’s closest approach to the Sun, known as perihelion, took place on March 26, taking it inside the orbit of Mercury, at about one-third the distance from the Sun to the Earth.

View more: Solar Orbiter: Striking new imagery of our Sun has been released

Fintech unicorn Slice wants to diversify beyond its credit card offering

ETtechBengaluru: Fintech unicorn Slice is shifting its focus to unified payments interface (UPI) and other payment methods on its app, as it looks to diversify from just being a card-based credit line business, according to company founder and chief executive Rajan Bajaj.Along with diversification into UPI, Slice will also push ...

View more: Fintech unicorn Slice wants to diversify beyond its credit card offering

5 Best Accessories For Your RGB Gaming PC

If you want an RGB gaming PC that stands out, spruce things out with RGB accessories. Accessorizing your PC to your preference makes it unique and allows you to get the best out of each gaming session. There are many RWB gaming PC accessories in the market to choose ...

View more: 5 Best Accessories For Your RGB Gaming PC

Best Cases for the 2018 and 2017 9.7-inch iPad 2022

People Counting Systems in 2022: how they work and why they’re important.

Product review: We test SMS Storetraffic’s 2022 people counting system.

Make Your First Android App For The Google Play Store - How And Why You Should Do It Now

PCIe 4.0? Naw, We Want The Phison PCIe 5.0 Redriver IC PS7101

Building and Maintaining Your Resume to Improve Job Success

New advances for reducing defects in multimaterials using directed energy deposition

Report evaluates food diversity in 10 Mediterranean countries

Study shows a '15-minute city' within reach for Vancouver

Energy-efficient AI hardware technology via a brain-inspired stashing system

Developing a better diagnostic nano-probe

DHS orders federal agencies to patch VMware bugs within 5 days