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Hysteresis in force probe measurements: a dynamical systems perspective

B E Shapiro1, H Qian

  • 1Department of Biomathematics, UCLA School of Medicine, AV-155 CHS, 10833 Le Conte Ave, Los Angeles, CA, 90095-1766, USA. bshapiro@ucla.edu

Journal of Theoretical Biology
|October 29, 1998
PubMed
Summary

Atomic Force Microscope (AFM) experiments reveal hysteresis in macromolecular binding forces. This occurs because bond rupture ("jumping-off") and formation ("jumping-on") involve different energy pathways due to cusp catastrophes.

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Area of Science:

  • Biophysics
  • Surface Science
  • Materials Science

Background:

  • Macromolecular binding forces are crucial for biological processes.
  • Direct measurement of single protein-ligand interactions is essential for understanding molecular mechanisms.
  • Atomic Force Microscopy (AFM) enables precise force measurements at the single-molecule level.

Purpose of the Study:

  • To investigate the phenomenon of hysteresis in macromolecular binding forces measured by AFM.
  • To explain the underlying physical mechanisms causing differences in rupture and formation forces.
  • To analyze the role of probe position and cantilever stiffness in binding force measurements.

Main Methods:

  • Utilizing Atomic Force Microscope (AFM) to measure single protein-ligand binding forces.

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  • Performing experiments involving controlled approach and withdrawal of the AFM probe to the substrate.
  • Analyzing cantilever deflection to determine rupture forces ('jumping-off') and formation forces ('jumping-on').

    • Main Results:

    • Observed distinct force measurements for bond rupture ('jumping-off') and bond formation ('jumping-on'), indicating hysteresis.
    • Identified that hysteresis arises from a cusp catastrophe in the probe position and cantilever stiffness space.
    • Demonstrated that the system passes through a saddle-node bifurcation during probe movement, leading to different post-bifurcation equilibria.

    Conclusions:

    • Hysteresis in macromolecular binding forces is a consequence of the system's dynamics and energy landscape.
    • The observed 'jumping' phenomena are explained by bifurcations in the force-distance curves.
    • Understanding these force measurement discrepancies is vital for accurate characterization of molecular interactions.