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Simulation of 3D-AFM images for non-equilibrium systems

KANAZAWA, Japan, June 16, 2022 /PRNewswire/ — Researchers from Kanazawa University report in The Journal of Physical Chemistry Letters how to simulate 3D atomic force microscopy images of non-equilibrium systems involving biomolecules. The approach uses a famous thermodynamic equation applicable to non-equilibrium situations.

Three-dimensional atomic force microscopy (3D-AFM) is a technique used to probe the distribution of solvent molecules at solid-liquid interfaces. Initially applied to study situations where the solvent is water, the method is now also used for other molecules. A recent development is to use 3D-AFM to solve the organization of biopolymers such as chromosomes or proteins in cells. Due to the complexity of these systems, however, simulations of the 3D-AFM imaging process are needed to aid in its interpretation. The simulation methods developed so far have assumed that the probed system is in equilibrium during the AFM scan cycle. This limits their validity to situations where the solvent molecules are moving much faster than the scanning probe. Now, Takeshi Fukuma from Kanazawa University and colleagues have developed a 3D-AFM simulation approach that works for non-equilibrium systems, applicable to situations where molecular motion occurs on timescales comparable to or greater than the probing cycle AFM.

The basic principle of AFM is to have a very small tip, attached to a cantilever, scan the surface of a sample. The response of the tip to height differences in the scanned surface provides structural information about the sample. In 3D-AFM, the tip is made to penetrate the sample, and the force experienced by the tip is the result of interactions with (parts of) nearby molecules. For a given horizontal (xy) position of the tip, the dependence of the force F on the vertical of the tip (z) the position as it enters the sample is captured in a force-distance (F according to the curve z). By combining all the force-distance curves obtained during the xy scan gives the 3D-AFM image.

Fukuma and colleagues examined the situation where an AFM tip probes a globular biopolymer and modeled both the tip and the molecule as beads connected by springs (2000 beads for the molecule, 50 beads for the tip). They calculated the force-distance curves using the so-called Jarzynski equality, an equation that relates the difference in free energy between two states of a system at work (proportional to the force) required to go from one state to the other. It is important to note that the equality holds for non-equilibrium situations.

The researchers were able to show that the simulations reproduced the internal structure of the biopolymer, with certain characteristics of the fibers being clearly observable. They also looked at how sweep speed affects simulation results and found that there is an optimal speed range for vertical (z) to analyse. Finally, Fukuma and colleagues simulated 3D-AFM images of cytoskeletal fibers for which experimentally obtained 3D-AFM images exist, and found that the simulations agreed well with experiment. The scientists therefore concluded that their method “is applicable to various fibers in cells such as DNA and so on by modifying parameters such as stiffness, providing an important theoretical basis for such experimental measurements.”


3D Atomic Force Microscopy (3D-AFM)

The general principle of atomic force microscopy (AFM) is to have a very small tip scan the surface of a sample. During this horizontal (xy) scan, the tip, which is attached to a small cantilever, follows the vertical of the sample (z) profile, inducing a force on the cantilever that can be measured. The magnitude of the force at xy position can be related to the z assess; the X Y Z the data generated during a scan then translates into a height map providing structural information about the sample being studied.

In 3D-AFM, the sample is penetrated by the (oscillating) scanning tip, so that not only the surface, but also the interior of a sample can be probed. To correctly interpret the images obtained by means of 3D-AFM, it is important to perform simulations which, based on a structural model, calculate the expected 3D-AFM images, which can then be compared with what has been recorded experimentally.

Takeshi Fukuma from Kanazawa University and his colleagues have now developed a simulation approach that applies to non-equilibrium situations – important for studying biologically relevant systems such as biomolecules in a cell.


Takashi Sumikama, Filippo Federici Canova, David Z. Gao, Marcos Penedo, Keisuke Miyazawa, Adam S. Fosterand Takeshi Fukuma. Computed three-dimensional atomic force microscopy images of biopolymers using Jarzynski’s equality, The Journal of Physical Chemistry Letters June 9, 2022.


Related Movies
Movie 1.
Penetration of the probe into the biopolymer. The biopolymer is a single fiber colored red to blue from end to end. 🄫Takashi Sumikama
Movie 2.
A 3D-AFM image. This movie shows a series of xy slices from top to bottom z. 🄫Takashi Sumikama

Hiroe Yoneda
Deputy Director of Public Affairs
WPI Nano Life Sciences Institute (WPI-NanoLSI)
Kanazawa University
Kakuma-machi, Kanazawa 920-1192, Japan
E-mail: [email protected]
Tel: +81 (76) 234-4550

About the Nano Life Science Institute (WPI-NanoLSI)

The Nano Life Science Institute (NanoLSI) at Kanazawa University is a research center established in 2017 under the World Premier International Research Center Initiative of the Ministry of Education, Culture, Sports, Science and Technology. The objective of this initiative is to create world-class research centres. NanoLSI combines the most advanced knowledge of biological probe microscopy to establish “nano-endoscopic techniques” to directly image, analyze and manipulate biomolecules to better understand the mechanisms governing life phenomena such as diseases.

About Kanazawa University

As the leading comprehensive university in the sea of Japan coast, Kanazawa University has contributed greatly to higher education and academic research in Japan since its inception in 1949. The University has three colleges and 17 schools offering courses in subjects including medicine, computer engineering, and humanities.

The University is located on the sea coast of Japan in Kanazawa – a city rich in history and culture. The city of Kanazawa has had a highly respected intellectual profile since the time of the feud (1598-1867). The University of Kanazawa is divided into two main campuses: Kakuma and Takaramachi for its approximately 10,200 students, including 600 foreigners.

SOURCE Kanazawa University

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