Rosenbluth, Crow, Shaevitz, and Fletcher 2008
Supplementary Documents for: Slow stress propagation in adherent cells
Michael J. Rosenbluth*#§, Ailey Crow*#¶, Joshua W. Shaevitz||, Daniel A. Fletcher#§¶
*Both authors contributed equally to this work
#Department of Bioengineering, §University of California San Francisco/University of California Berkeley Joint Graduate Group in Bioengineering, Berkeley, CA 94720
¶Biophysics Graduate Group, University of California, Berkeley, CA 94720
||Department of Physics and Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
Distance-dependent decay of displacement magnitude on a polyacrylamide gel
As a proof of concept of our system, a 10 mm thick polyacrylamide film was indented with an AFM cantilever at several locations and the surface displacement was quantified by tracking a 500 nm fluorescent particle bound to the surface. Surface displacement decayed as cantilever-particle distance increased, as expected for elastic half-space or thin film models (Fig. S1).
Acrylamide thin films were made by coating (3-Aminopropyl)trimethylsiloxane for 5 minutes onto glass coverslips, washing, incubating with 0.5% glutaraldyhyde for 30 minutes, and then washing again. 8% polyacrylamide solution with dilute 10 mm polystyrene beads (Polysciences) was sandwiched between the coated coverslip and a clean coverslip to ensure a 10 mm thickness. Once gelled, the coverslip was removed.
Figure S1. Particle displacement magnitude decays in a distance-dependent manner on a thin acrylamide gel.
The out of plane displacement of a single particle on a cell was quantified as a function of cantilever-particle distance as an AFM tip was stepped into the cell at distances ranging between 0-13 mm from the particle. Particle displacement decayed towards zero as distance increased. Displacement magnitude was measured after particle relaxation. Error bars represent the fitting error. The dark grey curve is the predicted surface for a semi-infinite elastic halfspace. The light grey shaded area represents the cantilever tip.
Figure S2. Voigt-Kelvin model of the cell. (A) To test if a simple viscoelastic model of the cell could explain the observed distance-dependent equilibration, we modeled the cell as a series of viscoelastic materials, with the first material being a simple elastic component and the second two materials being viscoelastic. All elastic constants (represented by springs) are assumed to be equal. To simulate the cantilever indenting the cell, a step compression of the material is induced at time = 0 s, and the relaxation of the different nodes (a-c) is observed over time to evaluate how points away from the indentation will move. Each material in this model is assumed to be of equal length. (B) In the first case, the viscosity of dashpots 1 and 2 are set to be equal and a step compression strain of 20% is induced in the material at point (a). Point (a) immediately moves 20% of the total material length and remains there. Points (b) and (c) compress to their final positions with the same equilibration time, as expected, since both dashpots are the same viscosity. (C) In the second case, dashpot 2 is set to a viscosity three times that of dashpot 1. As a result, the equilibration time of point (b) is much faster than that of point (c), demonstrating that placing viscous elements of increasing viscosities further away from the step indentation could result in an increasing equilibration time at distances further from indentation. (D) In this example, the viscosity of dashpot 1 is set to three times that of dashpot 2, and the reverse situation from (C) is observed—point (c), the point furthest away from the indentation, equilibrates in a shorter time than point (b). This example demonstrates that a Voigt-Kelvin model of the cell cannot explain the experimental observations observed, even when material properties are spatially varied. While it can produce different equilibration times at different points away from indentation, it cannot produce a consistently increasing equilibration time as distance from indentation increases, unless viscous elements are very specifically rearranged.