Precise determination of elastic modulus of cell using conical AFM probe

Area of Science:

• Biophysics
• Materials Science
• Computational Mechanics

Background:

• The Sneddon formula is standard for determining cell elastic modulus via atomic force microscopy (AFM).
• This formula's assumptions are often violated, leading to inaccuracies in elastic modulus calculations.
• Accurate cell mechanics are crucial for understanding cellular functions and disease states.

Purpose of the Study:

• To investigate the errors associated with the Sneddon formula in AFM experiments on cells.
• To develop a modified Sneddon formula for enhanced accuracy in elastic modulus determination.
• To validate the improved formula against experimental data for cells and hydrogels.

Main Methods:

• Finite element analysis using ABAQUS software to simulate AFM conical probe compression of cells.
• Systematic variation of probe geometry (cone half-angle, tip radius) and compression depth.
• Development of a correction factor based on simulated error data.
• Experimental validation using AFM to measure elastic moduli of cells and hydrogels.

Main Results:

• The Sneddon formula exhibits relative errors ranging from 0.094 to 1.455 folds.
• Error magnitude is dependent on cone half-angle, tip curvature radius, and compression depth.
• A correction factor was derived and integrated into the Sneddon formula.
• The modified formula significantly improves the accuracy of elastic modulus measurements.

Conclusions:

• The proposed modified Sneddon formula provides more accurate cell elastic modulus values compared to the conventional formula.
• The correction factor effectively addresses the limitations of the original Sneddon formula under AFM conditions.
• Experimental results for cells and hydrogels align well with predictions from the modified formula, confirming its utility.