Effects of non-linearity on cell-ECM interactions

Abstract

Filamentous biopolymers such as F-actin, vimentin, fibrin and collagen that form networks within the cytoskeleton or the extracellular matrix have unusual rheological properties not present in most synthetic soft materials that are used as cell substrates or scaffolds for tissue engineering. Gels formed by purified filamentous biopolymers are often strain stiffening, with an elastic modulus that can increase an order of magnitude at moderate strains that are relevant to cell and tissue deformation in vivo. This review summarizes some experimental studies of non-linear rheology in biopolymer gels, discusses possible molecular mechanisms that account for strain stiffening, and explores the possible relevance of non-linear rheology to the interactions between cell and extracellular matrices.

Keywords: cell; cell-ECM interaction; extracellular matrix; non-linear elasticity; strain-stiffening.

Figure 1

Stiffness and structure of cytoskeleton filaments. Microtubule, F-actin and intermediate filaments of 10 micrometers are drawn on the same scale. Stiffer filaments with larger persistence length appear to be straighter. In comparison, a 10μm flexible synthetic polyethylene chain is a random coil with a much smaller projeted length.

Figure 2

Shear storage modulus measurements of F-actin crosslinked by filamin (A), vimentin (B) colalgen (C), fibrin (D), Matrigel (E), and polyacrylamide (F) measured at frequencies near 1Hz and a range of stain magnitudes. The solid symbols in C show results for G, the static shear moduls for a colalgen gel of the same compsotion as used for oscillaotry measuremnt of storage modulus. Data for A-E from [29], Data for E unpublished results, and F from [56].

Figure 3

Entropic and enthalpic model for strain-stiffening. (a) Semiflexible polymers in the entropic under shear deformation. The red filament is stretched and resist to the shear stress; the yellow filament is being compressed with negligible contribution to the gel stiffness. (b) Stiff polymers in the enthalpic model under shear deformation. At small deformations, the red polymer is bent and contributes mainly to the gel stiffness at small deformations; the yellow filament rotates without contribution to the network stiffness. At large deformations, the red polymer buckles and the yellow filament is enthalpically stretched.

Figure 4

Elastic moduli of aortae from different species as a function of inflation pressure. The data are normalized to the mean blood pressure for each species. Adapted from [2].

Figure 5

Effect of platelets on shear modulus of fibrin gels. Purified fibrinogen (3 mg.ml) was polymerized by addition of U/ml thrombin in solutions without (open circles) or with (closed symbols) platelets at a density approximately 50% that in blood plasma. Rheological measurements were done at 1 rad/s over range of strains. Data from [57].

Figure 6

Comparison of strain-dependent shear moduli of polyacrylamide and fibrin gels, two commonly used soft substrates constructed to have comparable stiffness in the limit of small strains. Cells that apply little force on the matrix, such as neurons, would detect similar levels or resistance from both substrates, but cells such as mesenchymal stem cells that pull harder would deform the substrates so that fibrin would provide a lager resistance to additional stress than would polyacrylamide gels at large strains. Adapted from [9].

Figure 7

Cell generated traction fields in fibrin gels, and the resulting effect on cell alignment. The left panel shows the direction and relative magnitude of strains generated by a single cell on the fibrin matrix surrounding it. The right panel shows that when cells are plated sparsely on fibrin gels, the long axes of spontaneously polarized cells are significantly oriented toward each other when cells are within 400 to 600 microns of each other, and a random orientation of cell direction occurs only at distances greater than 600 μm. Adapted from [9].