Speaker
Description
Qualitative and quantitative variations in mechanobiological markers, such as extracellular matrix stiffness, cell adhesion, and cellular Young’s modulus, are strongly correlated with physiological state and frequently associated with pathological conditions. Atomic force microscopy (AFM) enables mechanical testing at the single-cell level, but interpreting indentation data is challenging due to contact nonlinearity and complex cell surface structure.
We develop a heuristic variational framework for unilateral indentation in AFM probing of living cells. Interpreting the augmented Lagrangian formulation of quasi-variational inequalities as a Winkler-type compliant coating, we propose a variational model for the indentation of an elastic substrate covered by a nonlinearly deforming, brush-like layer that represents the pericellular coat. Its compressive response follows the Alexander–de Gennes model, capturing strong nonlinearity. Building on Itou, Kovtunenko, and Rajagopal’s general solution for viscoelastic substrates with non-increasing contact area, we derive explicit displacement–force relations for monomial (axisymmetric) and self-similar (non-axisymmetric, e.g., Berkovich pyramidal) indenters.
The proposed formulation provides a mathematically consistent route to separating bulk cellular mechanics from pericellular coat effects, thereby improving the interpretation of AFM measurements in mechanobiology.
