One-Step Calibration of AFM in Liquid

Fidan Sumbul,Felix Rico,Jorge Rodriguez-Ramos,Nahid Hassanpour

doi:10.3389/fphy.2020.00301

Abstract

Nanomechanical measurements of cells and single molecules with atomic force microscopy (AFM) require accurate calibration of two parameters: the spring constant of the cantilever (k) and the inverse of the optical lever sensitivity (InvOLS). The most established calibration approach in liquid consists in determining the InvOLS from force–distance curves on a stiff surface, k being calculated using the thermal spectrum (PSD) of the cantilever via the equipartition theorem. Recent works proposed using cantilevers with calibrated k and then determining the InvOLS from the PSD. These non-contact approaches improve the precision of nanomechanical measurements compared to conventional contact-based approaches. The Sader method or the recent global calibration initiative (GCI) are accurate approaches and do not require knowledge of the InvOLS to determine k, thus they would allow one-step calibration of AFM in liquid. However, both methods assume high quality factor cantilevers, not the case for most cantilevers in liquid. Here we assess the accuracy and precision of the Sader and GCI methods in liquid on two types of cantilevers with low Q-factor using two different PSD fitting models (SHO and Pirzer). We evaluate the two approaches using only the PSD in liquid to calibrate both k and the InvOLS. While both methods led to similar results, the GCI approach is less prone to systematic uncertainties and, using the SHO model, provides higher accuracy in k and the InvOLS. Therefore, the proposed SHO, GCI-based approach utilizing only the thermal spectrum in liquid is precise and accurate and allows one-step calibration of AFM.

Highlights

Force measurements using atomic force microscopy (AFM) are becoming a standard and robust method to probe the mechanical properties of living cells, protein unfolding, and receptor-ligand bonds [1]
The standard deviation across cantilevers for f R and Q was of ∼10%, and for kair it was of ∼16% using either Sader or global calibration initiative (GCI) methods
We have assessed two different approaches that allow the one-step calibration of AFM in liquid. These two approaches were based on the Sader and GCI methods to determine both kliq and InvOLSliq from the thermal spectrum in liquid using the parameters f R, Q and B extracted from the first flexural mode using either simple harmonic oscillator (SHO) or Pirzer’s model

Summary

Introduction

Force measurements using atomic force microscopy (AFM) are becoming a standard and robust method to probe the mechanical properties of living cells, protein unfolding, and receptor-ligand bonds [1]. The first steps before any force measurement require the calibration of the spring constant of the cantilever (k) and the inverse of the optical lever sensitivity (InvOLS) and are crucial for accurate quantification of the measured and applied forces. The spring constant is calculated using the thermal method, acquiring the thermal noise spectrum of the cantilever deflection (d) of the fundamental mode of oscillation in liquid and invoking the equipartition theorem [2] 1 2 kB T = 1 2 k1 d2 (1). The actual value of the mean square deflection of the fundamental mode () is commonly calculated analytically, from the fit to the power spectral density (PSD) of the thermal fluctuations of the simple harmonic oscillator (SHO) or a related model, like the one developed by Pirzer and Huger for cantilevers in liquid [4,5,6]

Methods

Results

Conclusion