Cell force microscopy on elastic layers of finite thickness.

Forces applied by cells to substrates can be measured using soft substrates with embedded displacement markers. Traction forces are retrieved from microscopic images by determining the displacements of these markers and fitting the generating forces. Here we show that using elastic films of 5-10-microm thickness one can improve the spatial resolution of the technique. To this end we derived explicit equations for the mechanical response of an elastic layer of finite thickness to point forces. Moreover, these equations allow highly accurate force measurements on eukaryotic cells on films where finite thickness effects are relevant (below approximately 60 microm).

[1]  J. Pawley,et al.  Handbook of Biological Confocal Microscopy , 1990, Springer US.

[2]  L. Addadi,et al.  Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates , 2001, Nature Cell Biology.

[3]  Ben Fabry,et al.  Traction fields, moments, and strain energy that cells exert on their surroundings. , 2002, American journal of physiology. Cell physiology.

[4]  Zhong Qi Yue,et al.  On generalized Kelvin solutions in a multilayered elastic medium , 1995 .

[5]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[6]  D. Burmister,et al.  The General Theory of Stresses and Displacements in Layered Soil Systems. II , 1945 .

[7]  M. Dembo,et al.  Stresses at the cell-to-substrate interface during locomotion of fibroblasts. , 1999, Biophysical journal.

[8]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[9]  S. Lo,et al.  Focal adhesions: what's new inside. , 2006, Developmental biology.

[10]  K. Jacobson,et al.  Imaging the traction stresses exerted by locomoting cells with the elastic substratum method. , 1996, Biophysical journal.

[11]  N. Schwarzer,et al.  Arbitrary Load Distribution on a Layered Half Space , 2000 .

[12]  A. Harris,et al.  Silicone rubber substrata: a new wrinkle in the study of cell locomotion. , 1980, Science.

[13]  N. Balaban,et al.  Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization. , 2002, Biophysical journal.

[14]  K. Jacobson,et al.  Traction forces in locomoting cells. , 1995, Cell motility and the cytoskeleton.

[15]  Kenneth M. Yamada,et al.  Transmembrane crosstalk between the extracellular matrix and the cytoskeleton , 2001, Nature Reviews Molecular Cell Biology.

[16]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[17]  W. Press,et al.  Numerical Recipes in C++: The Art of Scientific Computing (2nd edn)1 Numerical Recipes Example Book (C++) (2nd edn)2 Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version3 , 2003 .

[18]  A. Sonnenberg,et al.  Current insights into the formation and breakdown of hemidesmosomes. , 2006, Trends in cell biology.

[19]  Zhong Qi Yue,et al.  On elastostatics of multilayered solids subjected to general surface traction , 1996 .

[20]  Dirk Mayer,et al.  Micropatterned silicone elastomer substrates for high resolution analysis of cellular force patterns. , 2007, The Review of scientific instruments.

[21]  Z. Yue,et al.  Extended Sneddon and Muki solutions for multilayered elastic materials , 2002 .

[22]  M. Dembo,et al.  Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. , 2001, Biophysical journal.

[23]  Z. Yue,et al.  Computation of point load solutions for geo-materials exhibiting elastic non-homogeneity with depth , 1999 .

[24]  M. Aepfelbacher,et al.  Podosomes: adhesion hot-spots of invasive cells. , 2003, Trends in cell biology.