Loops versus lines and the compression stiffening of cells

Tissues exhibit a nonlinear phenomenon known as compression stiffening: an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer cytoskeletal network maintains the mechanical integrity of the cell. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen. To understand this finding, we uncover potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks. We find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. We make comparisons of these models with fibrin network experiments interlaced with beads.