細胞牽引力顯微術是藉由擷取包埋於在彈性平面基質中的標定粒子影像得到基質形變，並藉數學方法解出基質形變與表面應力的關係，而將基質形變計算得應力。細胞牽引力顯微術的測量增進了人們在細胞黏著及細胞遷移的了解。在過去大多的細胞牽引力顯微術只考慮牽引力中剪應力分量，但近年來少數研究顯示細胞在平面基質上造成的牽引力中正向應力仍不應被忽略。本論文發展了一新式三維細胞牽引力顯微術。我們測試兩種不同包埋標定粒子方式的細胞牽引力顯微術基質：一為聚丙烯醯胺，為目前最常使用的一種基質；一為在聚丙烯醯胺中加入另一含羧基的單體，使蛋白質可以與基質鍵結。我們意外發現新基質材料可將標定粒子集中於基質表面，而形成一單層。這近乎二維分佈的單層標定粒子在細胞牽引力顯微術上提供了額外的優勢，使得在擷取以及分析資料上更加簡化。基於這新式牽引力顯微術，我們成功觀測到在點狀黏著附近細胞牽引力細部上的分佈。

Traction force microscopy (TFM) on a flat elastic substrate was carried out by imaging the deformation of elastic substrate through imaging marker particles embedded inside the substrate. The deformation was later converted into stress through some mathematical techniques to solve the relationship between surface stress and deformation of an elastic substrate. In the past, most TFM only considers shear traction stress. TFM measurement has advanced people knowledge on cell adhesions and migrations. Recently a handful of groups showed that the normal traction stress exerted by a cell on a flat substrate is not negligible compared with the shear traction stress. In this thesis, we also developed a novel three-dimensional traction force microscopy (TFM). I tested two kinds of TFM substrates embedded with marker particles for image: one is the mostly commonly used polyacrylamide substrate and the other is to incorporate additional monomer containing acrylic acid group for the purpose to improve protein conjugation. Surprisingly we found the new substrate offers additional advantage – a concentrated monolayer of marker particles near the surface. The almost two-dimensional distribution of marker particles simplify data acquisition and analysis. Based on the novel TFM, I successfully observed detailed traction stress pattern around cellular focal adhesions.

1. Balaban, N.Q., Schwarz, U.S., Riveline, D., Goichberg, P., Tzur, G., Sabanay, I., Mahalu, D., Safran, S., Bershadsky, A., Addadi, L., et al. (2001). Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nature Cell Biology 3, 466-472.
2. Kumar, S., Maxwell, I.Z., Heisterkamp, A., Polte, T.R., Lele, T.P., Salanga, M., Mazur, E., and Ingber, D.E. (2006). Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys. J. 90, 3762-3773.
3. Beningo, K.A., Dembo, M., Kaverina, I., Small, J.V., and Wang, Y.L. (2001). Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts. J. Cell Biol. 153, 881-887.
4. Lauffenburger, D.A., and Horwitz, A.F. (1996). Cell Migration: A Physically Integrated Molecular Process. Cell 84, 359-369.
5. Lemmon, C.A., Chen, C.S., and Romer, L.H. (2009). Cell Traction Forces Direct Fibronectin Matrix Assembly. Biophysical Journal 96, 729-738.
6. Odde, D.J., Ma, L., Briggs, A.H., DeMarco, A., and Kirschner, M.W. (1999). Microtubule bending and breaking in living fibroblast cells. J. Cell Sci. 112, 3283-3288.
7. Bischofs, I.B., Klein, F., Lehnert, D., Bastmeyer, M., and Schwarz, U.S. (2008). Filamentous Network Mechanics and Active Contractility Determine Cell and Tissue Shape. Biophysical Journal 95, 3488-3496.
8. Harris, A.K., Wild, P., and Stopak, D. (1980). SILICONE-RUBBER SUBSTRATA - NEW WRINKLE IN THE STUDY OF CELL LOCOMOTION. Science 208, 177-179.
9. Hur, S.S., Zhao, Y.H., Li, Y.S., Botvinick, E., and Chien, S. (2009). Live Cells Exert 3-Dimensional Traction Forces on Their Substrata. Cellular and Molecular Bioengineering 2, 425-436.
10. Li, Y., Hu, Z., and Li, C. (1993). New method for measuring poisson's ratio in polymer gels. Journal of Applied Polymer Science 50, 1107-1111.
11. Maskarinec, S.A., Franck, C., Tirrell, D.A., and Ravichandran, G. (2009). Quantifying cellular traction forces in three dimensions. Proceedings of the National Academy of Sciences 106, 22108-22113.
12. Franck, C., Hong, S., Maskarinec, S.A., Tirrell, D.A., and Ravichandran, G. (2007). Three-dimensional Full-field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation. Exp Mech 47, 427-438.
13. Delanoe-Ayari, H., Rieu, J.P., and Sano, M. (2010). 4D Traction Force Microscopy Reveals Asymmetric Cortical Forces in Migrating Dictyostelium Cells. Phys. Rev. Lett. 105.
14. Legant, W.R., Choi, C.K., Miller, J.S., Shao, L., Gao, L., Betzig, E., and Chen, C.S. (2013). Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions. Proc. Natl. Acad. Sci. U. S. A. 110, 881-886.
15. del Alamo, J.C., Meili, R., Alvarez-Gonzalez, B., Alonso-Latorre, B., Bastounis, E., Firtel, R., and Lasheras, J.C. (2013). Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy. Plos One 8.
16. Guizar-Sicairos, M., Thurman, S.T., and Fienup, J.R. (2008). Efficient subpixel image registration algorithms. Opt. Lett. 33, 156-158.
17. Stricker, J., Aratyn-Schaus, Y., Oakes, Patrick W., and Gardel, Margaret L. (2011). Spatiotemporal Constraints on the Force-Dependent Growth of Focal Adhesions. Biophysical Journal 100, 2883-2893.
18. Legant, W.R., Choi, C.K., Miller, J.S., Shao, L., Gao, L., Betzig, E., and Chen, C.S. (2013). Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions. Proceedings of the National Academy of Sciences 110, 881-886