THE FIBROBLAST-POPULATED COLLAGEN MICROSPHERE ASSAY OF CELL TRACTION FORCE .2. MEASUREMENT OF THE CELL TRACTION PARAMETER

In Part I of this work, we formulated and analyzed a mathematical mode l for our fibroblast-populated collagen microsphere (FPCM) assay of ce ll traction forces (Moon and Tranquillo, 1993). In this assay, the FPC M diameter decreases with time as the cells compact the gel by exertin g traction on collagen fibrils. In Part I we demonstrated that the dia meter reduction profiles for varied initial cell concentration and var ied initial FPCM diameter are qualitatively consistent with the model predictions. We show here in Part 2 how predictions of a model similar to that of Part 2, along with the determination of the growth paramet ers of the cells and the viscoelastic parameters of the gel, allow us to estimate the magnitude of a cell traction parameter, the desired ob jective index of cell traction forces. The model is based on a monopha sic continuum-mechanical theory of cell-extracellular matrix (ECM) mec hanical interactions, with a species conservation equation for cells ( 2), a mass conservation equation for ECM (2), and a mechanical force b alance for the cell/ECM composite (3). Using a constant-stress rheomet er and a fluids spectrometer in creep and oscillatory shear modes, res pectively we establish and characterize the linear viscoelastic regime for the reconstituted type I collagen gel used in our FPCM fraction a ssay and in other assays of cell-collagen mechanical interactions. Cre ep tests are performed on collagen gel specimens in a state resembling that in our FPCM fraction assay (initially uncompacted, and therefore nearly isotropic and at a relatively low collagen concentration of 2. 1 mg/ml), yielding measurements of the zero shear viscosity mu(0) (7.4 x 106 Poise), and the steady-state creep compliance, J(e)(0). The she ar modulus, G (155 dynes/cm(2)), is then determined from the inverse o f J(e)(0) in the linear viscoelastic regime. Oscillatory shear tests a re performed in strain sweep mode, indicating linear viscoelastic beha vior up to shear strains of approximately 10 percent. We discuss the e stimation of Poisson's ratio, nu, which along with G and mu(0) specifi es the assumed isotropic, linear viscoelastic stress tensor for the ce ll/collagen gel composite which appears in (3). The proliferation rate of fibroblasts in free floating collagen gel (appealing in (1)) is ch aracterized by direct cell counting, yielding an estimate of the first -order growth rate constant k (5.3 x 10(-6) s(-1)). These independentl y measured and estimated parameter values allow us to estimate that th e cell traction parameter, tau(0), defined in the active stress tensor which also appeals in (3), is in the range of 0.00007-0.0002 dyne . c m(4)/mg collagen . cell This value is in agreement with a reported mea sure of fraction obtained directly via isometric force measurement acr oss a slab of fibroblast-containing collagen gel.