Analysis of nanoindentation of soft materials with an atomic force microscope

Nanoindentation is a popular experimental technique for characterization of the mechanical properties of soft and biological materials. With its force resolution of tens of pico-Newtons, the atomic force microscope (AFM) is well-suited for performing indentation experiments on soft materials. However, nonlinear contact and adhesion complicate such experiments. This paper critically examines the application of the Johnson-Kendall-Roberts (JKR) adhesion model to nanoindentation data collected with an AFM. The use of a nonlinear least-square error-fitting algorithm to calculate reduced modulus from the nanoindentation data using the JKR model is discussed. It is found that the JKR model fits the data during loading but does not fit the data during unloading. A fracture stability analysis shows that the JKR model does not fit the data collected during unloading because of the increased stability provided by the AFM cantilever

Tractions and stress fibers control cell shape and rearrangements in collective cell migration

Key to collective cell migration is the ability of cells to rearrange their position with respect to their neighbors. Recent theory and experiments demonstrated that cellular rearrangements are facilitated by cell shape, with cells having more elongated shapes and greater perimeters more easily sliding past their neighbors within the cell layer. Though it is thought that cell perimeter is controlled primarily by cortical tension and adhesion at each cell's periphery, experimental testing of this hypothesis has produced conflicting results. Here we studied collective cell migration in an epithelial monolayer by measuring forces, cell perimeters, and motion, and found all three to decrease with either increased cell density or inhibition of cell contraction. In contrast to previous understanding, the data suggest that cell shape and rearrangements are controlled not by cortical tension or adhesion at the cell periphery but rather by the stress fibers that produce tractions at the cell-substrate interface. This finding is confirmed by an experiment showing that increasing tractions reverses the effect of density on cell shape and rearrangements. Our study therefore reduces the focus on the cell periphery by establishing cell-substrate traction as a major physical factor controlling cell shape and motion in collective cell migration.Comment: 39 pages, 6 figure

A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells

We construct a homogeneous, nonlinear elastic constitutive law, that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material, than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.Comment: 18 pages, 2 figure

A finite loop space not rationally equivalent to a compact Lie group

We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.Comment: 8 page