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Sub-femtonewton force sensing in solution by super-resolved photonic force microscopy

Nature Photonics volume 18, pages 913–921 (2024)Cite this article

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An Author Correction to this article was published on 15 August 2024

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Abstract

Precise force measurement is critical to probe biological events and physics processes, spanning from molecular motor’s motion to the Casimir effect, as well as the detection of gravitational waves. Yet, despite extensive technological developments, the three-dimensional nanoscale measurement of weak forces in aqueous solutions still faces major challenges. Techniques that rely on optically trapped nanoprobes are of significant potential but are beset with limitations, including probe heating induced by high trapping power, undetectable scattering signals and localization errors. Here we report the measurement of the long-distance interaction force in aqueous solutions with a minimum detected force value of 108.2 ± 510.0 attonewton. To achieve this, we develop a super-resolved photonic force microscope based on optically trapped lanthanide-doped nanoparticles coupled with nanoscale three-dimensional tracking-based force sensing. The tracking method leverages neural-network-empowered super-resolution localization, where the position of the force probe is extracted from the optical-astigmatism-modified point spread function. We achieve a force sensitivity down to 1.8 fN Hz–1/2, which approaches the nanoscale thermal limit. We experimentally measure electrophoresis forces acting on single nanoparticles as well as the surface-induced interaction force on a single nanoparticle. This work opens the avenue of nanoscale thermally limited force sensing and offers new opportunities for detecting sub-femtonewton forces over long distances and biomechanical forces at the single-molecule level.

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Fig. 1: Nanoscale thermally limited force sensing by an SRPFM.
Fig. 2: Monte Carlo trapping simulation was used to analyse the force sensitivity.
Fig. 3: DNN-empowered optical astigmatism optical tweezers for 3D trapping.
Fig. 4: Thermally limited force sensing on single Ln-NP.
Fig. 5: Nanoscale interaction force sensing between Ln-NC and Au surface.

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Data availability

The data that support the findings of this study are available within the Article and its Supplementary Information. Other relevant data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

All the custom codes are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank the experimental assistance from M. Maddahfar, J. Liao and X. He; equipment support from C. Jagadish and the Analysis & Testing Center in Beihang University; and DNN assistance from P. Nie. We acknowledge financial support from the National Natural Science Foundation of China (U23A20481, 62275010 and 52073006), the Beijing Natural Science Foundation (1232027) and the fellowship of China Postdoctoral Science Foundation (2022TQ0020).

Author information

Author notes

  1. These authors contributed equally: Xuchen Shan, Lei Ding, Dajing Wang.

Authors and Affiliations

  1. School of Physics, Beihang University, Beijing, People’s Republic of China

    Xuchen Shan, Dajing Wang, Jinlong Shi, Hongyan Zhu, Xiaolan Zhong, Baolei Liu, Weichang Hao & Fan Wang

  2. School of Biomedical Engineering, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, New South Wales, Australia

    Lei Ding & Qian Peter Su

  3. Centre for Atomaterials and Nanomanufacturing, School of Science, RMIT University, Melbourne, Victoria, Australia

    Lei Ding

  4. Institute for Biomedical Materials and Devices (IBMD), School of Mathematical and Physical Sciences, Faculty of Science, University of Technology Sydney, Sydney, New South Wales, Australia

    Shihui Wen, Dayong Jin & Lei Jiang

  5. Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, Australian Capital Territory, Australia

    Chaohao Chen

  6. Key Laboratory of Biomechanics and Mechanobiology (Ministry of Education), Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical Engineering, Beihang University, Beijing, People’s Republic of China

    Yang Wang, Zhaocun Huang & Lingqian Chang

  7. Computing and Information Systems Department, Melbourne School of Engineering, University of Melbourne, Melbourne, Victoria, Australia

    Shen S. J. Wang

  8. School of Physics, The University of New South Wales, Sydney, New South Wales, Australia

    Peter John Reece

  9. School of Chemistry & Chemical Engineering, Shaanxi Normal University, Xi’an, People’s Republic of China

    Wei Ren

  10. Particles and Catalysis Research Laboratory, School of Chemical Engineering, The University of New South Wales, Sydney, New South Wales, Australia

    Xunyu Lu

  11. Australian Artificial Intelligence Institute, Faculty of Engineering and IT, University of Technology Sydney, Sydney, New South Wales, Australia

    Jie Lu

  12. Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Rare Earth Materials Chemistry and Applications, PKU-HKU Joint Laboratory in Rare Earth Materials and Bioinorganic Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, People’s Republic of China

    Lingdong Sun

  13. Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo, People’s Republic of China

    Dayong Jin

  14. Key Laboratory of Bio-Inspired Materials and Interfaces Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Lei Jiang

  15. Science and Technology Center for Quantum Biology, National Institute of Extremely-Weak Magnetic Field Infrastructure, Hangzhou, People’s Republic of China

    Fan Wang

Authors
  1. Xuchen Shan
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Contributions

F.W. conceived and supervised the project. L.D., X.S. and F.W. constructed the optical setup. F.W. and S.S.J.W. built the theoretical simulation and analytical model. X.S. and P.N. built the deep-learning model. S.W. and J.S. synthesized the nanoparticles. L.D. and H.Z. built the analysis of the net charge of the nanoparticles. L.D., X.S. and D.W. performed all the experiments. L.D., X.S. and F.W. analysed the results, prepared the figures and wrote the manuscript in consultation with all authors.

Corresponding authors

Correspondence to Xiaolan Zhong, Lingqian Chang or Fan Wang.

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Supplementary Sections 1–8, Equations (1)–(31), Tables 1–6 and Figs. 1–12.

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Shan, X., Ding, L., Wang, D. et al. Sub-femtonewton force sensing in solution by super-resolved photonic force microscopy. Nat. Photon. 18, 913–921 (2024). https://doi.org/10.1038/s41566-024-01462-7

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