Inference of the 3D pressure field exerted by a single cell from a thin membrane transverse deformation

TL;DR

This paper presents a method to infer the three-dimensional pressure exerted by a cell on its environment from one-dimensional membrane deformation measurements obtained via atomic force microscopy, addressing a complex inverse problem.

Contribution

It introduces a novel approach to reconstruct 3D cell pressure fields from limited AFM data, expanding the capabilities of traction force microscopy techniques.

Findings

Successfully reconstructs 3D pressure fields from 1D AFM data

Defines the regime of applicability for the proposed inverse method

Enhances understanding of cell-environment mechanical interactions

Abstract

Numerous cell types relate to their immediate environment by exerting a three-dimensional pressure field on their environment, with components both longitudinal and transverse to the cell membrane. This pressure field can in principle be measured by traction force microscopy experiments. Compared to other approaches, the technique of Protrusion Force Microscopy gives access with high spatial resolution to the pressure field by measuring the deformation of a thin elastic membrane using atomic force microscopy (AFM). However, while the pressure field under interest is three-dimensional, the height profile measured by AFM is only one-dimensional. We propose a solution to this inverse problem and we explore its regime of applicability in the experimental context.