| Mineralized Collagen Fibrils: A Mechanical Model with a Staggered Arrangement of Mineral Particles Biophysical Journal, Volume 79, Issue 4, 1 October 2000, Pages 1737-1746 Ingomar Jäger and Peter Fratzl Abstract Both elastic modulus and fracture stress are known to increase with the amount of mineral deposited within collagen fibrils. Current mechanical models of mineralized fibrils, where mineral platelets are arranged in parallel arrays, reproduce the first effect but fail to predict an increase in fracture stress. Here, we propose a model with a staggered array of platelets that is in better agreement with results on molecular packing in collagen fibrils and that accounts for an increase of both elastic modulus and fracture stress with the amount of mineral in the fibril. Finally, we explore the dependence of the mechanical properties within the model, when the degree of mineralization and the thickness of the platelets as well as their distance varies. Abstract | Full Text | PDF (285 kb) |
| Hierarchical Modeling of the Elastic Properties of Bone at Submicron Scales: The Role of Extrafibrillar Mineralization Biophysical Journal, Volume 94, Issue 11, 1 June 2008, Pages 4220-4232 Svetoslav Nikolov and Dierk Raabe Abstract We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils’ shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature. Abstract | Full Text | PDF (893 kb) |
| Atomic Force and Total Internal Reflection Fluorescence Microscopy for the Study of Force Transmission in Endothelial Cells Biophysical Journal, Volume 78, Issue 4, 1 April 2000, Pages 1725-1735 Anshu Bagga Mathur, George A. Truskey and W. Monty Reichert Abstract This paper describes the combined use of atomic force microscopy (AFM) and total internal reflection fluorescence microscopy (TIRFM) to examine the transmission of force from the apical cell membrane to the basal cell membrane. A Bioscope AFM was mounted on an inverted microscope, the stage of which was configured for TIRFM imaging of fluorescently labeled human umbilical vein endothelial cells (HUVECs). Variable-angle TIRFM experiments were conducted to calibrate the coupling angle with the depth of penetration of the evanescent wave. A measure of cellular mechanical properties was obtained by collecting a set of force curves over the entire apical cell surface. A linear regression fit of the force-indentation curves to an elastic model yields an elastic modulus of 7.22±0.46kPa over the nucleus, 2.97±0.79kPa over the cell body in proximity to the nucleus, and 1.27±0.36kPa on the cell body near the edge. Stress transmission was investigated by imaging the response of the basal surface to localized force application over the apical surface. The focal contacts changed in position and contact area when forces of 0.3–0.5nN were applied. There was a significant increase in focal contact area when the force was removed (<0.01) from the nucleus as compared to the contact area before force application. There was no significant change in focal contact coverage area before and after force application over the edge. The results suggest that cells transfer localized stress from the apical to the basal surface globally, resulting in rearrangement of contacts on the basal surface. Abstract | Full Text | PDF (613 kb) |
Copyright © 1996 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 70, Issue 1, 556-567, 1 January 1996
doi:10.1016/S0006-3495(96)79602-9
Research Article
M. Radmacher, M. Fritz, C.M. Kacher, J.P. Cleveland and P.K. Hansma
Department of Physics, University of California, Santa Barbara 93106, USA. manfred@physics.ucsb.edu
We have measured force curves as a function of the lateral position on top of human platelets with the atomic force microscope. These force curves show the indentation of the cell as the tip loads the sample. By analyzing these force curves we were able to determine the elastic modulus of the platelet with a lateral resolution of approximately 100 nm. The elastic moduli were in a range of 1–50 kPa measured in the frequency range of 1–50 Hz. Loading forces could be controlled with a resolution of 80 pN and indentations of the platelet could be determined with a resolution of 20 nm.