Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

Long-range correlations in pinned athermal networks

We derive exact results for displacement fields that develop as a response to external pinning forces in two-dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a Green's function formalism which we use to derive exact results for displacement fields produced by localized external forces. We show that in the continuum limit the displacement fields decay as 1/r at large distances r away from a force dipole. Finally, we extend our formulation to study correlations in the displacement fields produced by the external pinning forces. We show that uncorrelated pinned forces at each vertex give rise to long-range correlations in displacements in athermal systems, with a nontrivial system size dependence. We verify our predictions with numerical simulations of athermal networks in two dimensions.

Nuclear Stiffness Decreases with Disruption of the Extracellular Matrix in Living Tissues

Reciprocal interactions between the cell nucleus and the extracellular matrix lead to macroscale tissue phenotype changes. However, little is known about how the extracellular matrix environment affects gene expression and cellular phenotype in the native tissue environment. Here, it is hypothesized that enzymatic disruption of the tissue matrix results in a softer tissue, affecting the stiffness of embedded cell and nuclear structures. The aim is to directly measure nuclear mechanics without perturbing the native tissue structure to better understand nuclear interplay with the cell and tissue microenvironments. To accomplish this, an atomic force microscopy needle-tip probe technique that probes nuclear stiffness in cultured cells to measure the nuclear envelope and cell membrane stiffness within native tissue is expanded. This technique is validated by imaging needle penetration and subsequent repair of the plasma and nuclear membranes of HeLa cells stably expressing the membrane repair protein CHMP4B-GFP. In the native tissue environment ex vivo, it is found that while enzymatic degradation of viable cartilage tissues with collagenase 3 (MMP-13) and aggrecanase-1 (ADAMTS-4) decreased tissue matrix stiffness, cell and nuclear membrane stiffness is also decreased. Finally, the capability for cell and nucleus elastography using the AFM needle-tip technique is demonstrated. These results demonstrate disruption of the native tissue environment that propagates to the plasma membrane and interior nuclear envelope structures of viable cells.