Extracting Quantitative Data from AFM Indentations on Soft, Heterogeneous Biomaterials

Abstract

Atomic force microscopy (AFM) is a commonly used method for extracting mechanical information about samples ranging from soft biological matter to rigid semiconductors. AFM and other force spectroscopy techniques have been recently employed to examine how the elastic properties of metastatic cancer cells differ from their healthy counterparts and to study the contractile forces that cancer cells exert during the process of invasion through an extracellular matrix (ECM). As the samples being studied with AFM become more complex, novel analysis methods must be developed to produce meaningful and quantitative data, thus new strategies for fitting force-indentation data beyond the standard Hertz model are essential. We present a method of raw data fitting which determines the apparent Young's modulus as a function of indentation depth, providing sensitivity to sample heterogeneities such as subsurface elasticity effects. An improved AFM tip shape model is derived for a spherical apex with a smooth transition to a cone to provide a realistic representation of the experimental AFM tips used. A bonded two-layered elastic model is created to include the perturbations caused by a heterogeneous material, such as a cell embedded in ECM. This model allows for understanding the signal generated from subsurface components as well as the theoretical limits for determining the elastic properties of the underlying second layer. To validate this, we performed finite element analysis simulations and AFM indentations on polyacrylamide. We also show specific examples of how these analysis methods and finite element analysis can be employed to extract more information regarding the mechanical basis of cancer cell invasion into an ECM.