Deciphering the scaling of single-molecule interactions using Jarzynski's equality

Area of Science:

• Physical Chemistry
• Biophysics
• Materials Science

Background:

• Understanding macroscopic properties requires knowledge of how single-molecule interactions scale.
• Jarzynski's equality provides a theoretical link between non-equilibrium work and equilibrium free energy.

Purpose of the Study:

• To demonstrate the scaling of single acid-amine interactions to macroscopic properties.
• To validate Jarzynski's equality in correlating single-molecule and macroscopic measurements.
• To establish a scaling strategy for predicting large-scale properties from single-molecule data.

Main Methods:

• Synergistic experimental approach combining macroscopic surface forces apparatus (SFA) and single-molecule force spectroscopy (SMFS).
• Utilizing SFA for equilibrium measurements of acid-amine interactions.
• Employing SMFS to probe non-equilibrium dynamics and test Jarzynski's equality.

Main Results:

• Macroscopic equilibrium measurements showed linear scaling with interfacial bond density, yielding acid-amine interaction energies of 10.9 ± 0.2 kT.
• Jarzynski's free energy calculated from non-equilibrium SMFS experiments converged to 11 ± 1 kT.
• Experimental results validated the applicability of Jarzynski's equality across different scales.

Conclusions:

• Jarzynski's equality effectively bridges non-equilibrium single-molecule dynamics with equilibrium macroscopic behavior.
• The developed scaling strategy enables prediction of bulk properties (e.g., adhesion, cell interactions) from single-molecule measurements.
• This work provides a robust framework for understanding molecular interactions at different scales.