Calibrating the Young’s modulus of soft materials with surface tilt angle measured by atomic force microscopy

We investigated the apparent Young’s modulus, Em, of soft materials with the surface tilt angle, as measured by colloidal probe atomic force microscopy (AFM). The AFM measurements of soft polymer hydrogels and natural unfertilized eggs showed a clear universal behavior of Em as a function of the tilt angle, θ, of the sample surface at the local contact area. We found that the observed θ dependence of Em was well fitted with a simple modified Hertz contact model, in which the pressure distribution in the contact area follows the conventional Hertz contact model, the vertical component of the net force balances the loading force, and the remaining lateral component of the net force is approximately ignored. We demonstrated how a simple analytical formula derived from the modified Hertz contact model can calibrate the Em values for single cells in a spherical embryo and for single isolated cells and a confluent cell monolayer adhered on flat substrates.