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HERDIN Record #: R07-USC-13071011202763 Submitted: 10 July 2013 Modified: 13 September 2013

Local viscoelasiticity of living mammalian cells

The ability of cells to deform or resist deformation affects several important factors of cell function. Most studies infer the elastic modulus of a living cells from the simultaneous measurements of forces and deformations exerted on the cell, based on Hertz model. However, the force-distance curves are affected by indenter-cell adhesion forces, and neglecting this effect may result in systematic errors in the determination of the Young's modulus of elasticity.

For the first time, the Hertz model was extended to include the effect of adhesion in the description of contact stiffness by using the Lennard-Jones potential to model the inter-molecular interaction between the probe surface and a living cell sample. The adhesion force derived from the potential gradient was incorporated to the Hertz relation, from which the value of the elastic modulus of the sample is obtained.

Our results show that during indentation of the intact cell, the adhesion force increases in proportion to the indentation depth. The increase in the slope of the force-indentation curves predicts a higher Young's modulus than the value obtained by the Hertz model neglecting adhesion force by up to 25% for decreasing size of molecules coating the probe. The model predicts the Young's modulus of a cell based on the radius of the probe, and the size and concentration of the molecules coating the surface. Thus, our approach provides precision on cell mechanics measurements without neglecting surface interactions that could be incorrectly neglected.

Publication Type
Thesis Degree
Publication Date
October 2011
1. Kirmizis, D. , Logothetidis, S. . "Atomic force microscopy probing in the measurement of cell mechanics" , 137-145,
2. Ragsdale, G. K., Phelps, J. , Luby-Phelps, K. . "Viscoelastic response of fibroblasts to tension transmitted through adherens junctions" , 2798-2808,
3. Mizuno, D. . "High resolution probing of cellular force transmission" , 168102-168,
4. Bacabac, R. G.. "Round versus flat: Bone cell morphology, elasticity and mechanosensing" , 1590-1598,
5. Neumann, T. . "Determining the elastic modulus of biological samples using atomic force microscopy" ,
6. Ashkin, A. . "Optical trapping and manipulation of viruses and bacteria" 235,
7. Ashkin, A. . "Optical trapping and manipulation of neutral particles using lasers" 94, 4853-4860,
8. Harada, Y. . "Manipulation of primary cilia using optical tweezers" , 1-4,
9. Nishimura, Y. . "The active digestion of uninparental chloroplast DNA in a single zygote of Chlamydomonas reinhardtii is revealed by using the optical tweezers" 96,
10. Zhang, H. . "Optical tweezers for single cells" 5, 671-690,
11. Sleep, J. . "Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezer study" , 3085-3095,
12. Huruta, R. R.. "Mechanical properties of stored red blood cells using optical tweezers" , 2975-2977,
13. Felgner, H. . "Flexural rigidity of microtubules measured with the use of optical tweezer" , 509-516,
14. Asbury, C. . "Kenesin moves by an asymmetric hand-over-hand mechanics" , 2130-2134,
15. Block, S. . "Probing the kenesin reaction cycle with a 2D optical force clamp" , 2351-2356,
16. Malik, R. . "Cytoplasmic dynein functions as a gear in response to load" , 649-652,
17. Knight, A. E.. "Analysis of single-molecule mechanical recordings: application to acto-myosin interactions" , 45-72,
18. Ryu, W. S.. "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio" , 444-447,
19. Bustamante, C. . "Ten years of tension: single-molecule DNA mechanics" , 423-427,
20. Cecconi, C. . "Direct observation of the three-state folding of a single protein molecules" , 2057-2060,
21. Ashkin, A. . "Optical trapping and manipulation of viruses and bacteria" , 1517-1520,
22. Johnson, K. L., Kendall, K. , Roberts, A. D.. "Surface enegy and the contacts of elastic solids" , 301-303,
23. Derjaguin, B. V.. "Effects of contact deformations on the adhesion of particles" , 314-326,
24. Maugis, G. D.. "JKR-DMT transition in the presence of liquid meniscus" , 1311-1322,
25. Zhang, H. . "Effects of Nanoparticle coverage on the Adhesion properties of Emulsion aggregation toner particles" , 020501-7,
26. Emerson, J. A.. "Surface contamination on adhesive forces as measured by contact mechanics" ,
27. Robbins, B. . "Contact of single asperities with varying adhesion: comparing continnum mechanics to atomistic simulation" , 02611,
28. Robbins, B. . "The breakdown of continnum models for mechanical contact" , 929-932,
29. Shoeson, B. . "Evidence and implications of inhomogeneity in tectoral membrance elasticity" , 2768-2777,
30. Johnson, K. J.. "Contact Mechanics" ,
31. Timoshenko, S. P.. "Theory of Elasticity" ,
32. Mahaffy, R. E.. Scanning Probe-Based frequency-dependent microrheology of polymer gels and biological cells. 880-883
33. Zhao, Y. P.. "Effects of work of adhesion on nanoindentation" , 348-353,
34. Lennard-Jones, J. E.. "On the determination of molecular field" , 463-477,
35. Larson, R. G.. "The structure and rheology of Complex fluid" ,
36. Paci, I. . "Structural behavior and self-assembly of Lennard-Jones on rigid surfaces" , 12935-1294,
37. Zhankadamova, Z. A.. "Molecular dynamics calculation of the sticking coeffecient of gases to surface" , 145-146,