Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-11T19:25:28.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Constitutive Modeling of the Stress-Stretch Behavior of Biological Membranes Containing Folded Domains

Published online by Cambridge University Press:  26 February 2011

Melis Arslan ,
Mary C. Boyce ,
Hang J. Qi  and
Christine Ortiz
Melis Arslan
Affiliation:
melis@mit.edu, Massachusetts Institute of Technology, Mechanical Engineering, 77 Massachusetts Avenue, Cambridge, MA, 02139, United States, (617)324-6444, (617)253-5859
Mary C. Boyce
Affiliation:
mcboyce@mit.edu, Massachusetts Institute of Technology, Mechanical Engineering, United States
Hang J. Qi
Affiliation:
Qih@colorado.edu, University of Colorado, Mechanical Engineering, United States
Christine Ortiz
Affiliation:
cortiz@mit.edu, Massachusetts Institute of Technology, Materials Science and Engineering, United States
Get access

Abstract

The mechanical behavior of the red blood cell membrane is governed by the lipid bilayer which resists changes in surface area and the underlying spectrin network which resists changes in shape. The spectrin network can be modeled as an idealized triangulated network. Each spectrin chain consists of folded domains along the length of the chain which can unfold during stretching of the chain. A domain will completely unfold under the application of a chain force of 20 to 35 pN depending on the rate of imposed chain stretch. During macroscopic stretch of a network, individual chains within the network will experience different levels of chain stretch since the network chains will collectively stretch and rotate to accommodate the imposed stretch. Hence, the stretch on any individual chain will depend on the magnitude and state of macroscopic strain. A microstructurally informed continuum level constitutive model is developed which tracks individual chain deformation behavior as a function of macroscopic strain and also determines the overall macroscopic network stress-strain behavior. Using the introduced continuum approach and statistical mechanics based models of individual chain force-extension behavior, the stress-stretch behavior of the membrane under uniaxial tension is simulated at large stretches and the behavior of the constituent chains is monitored. Domain unfolding occurs within constituent chains during network deformation and the effects of this domain unfolding on the overall macroscopic stress-strain behavior of the network subject to deformation at different strain rates is revealed.

Keywords

biologicalmicrostructurestress/strain relationship
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 898: Symposium L – Mechanical Behavior of Biological and Biomimetic Materials , 2005 , 0898-L14-05
Copyright
Copyright © Materials Research Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Rief, M., Pascual, J., Saraste, M. and Gaub, H.E. “Single Molecule Force Spectroscopy of Spectrin Repeats: Low Unfolding Forces in Helix Bundles”, J. Mol. Biol., 286, pp. 553–561 (1999).Google Scholar
[2] Law, R., Carl, P., Harper, S., Dalhaimer, P., Speicher, D., and Discher, D. E., “Cooperativity in Forced Unfolding of Tandem Spectrin Repeats”, Biophys. J., 84, pp. 533–544 (2003).Google Scholar
[3] Rief, M., Fernandez, J.M. and Gaub, H.E., “Elastically coupled two-level systems as a model for biopolymer extensibility”, Phys. Review Lett., 81, pp. 4764–4767 (1998).Google Scholar
[4] Qi, H.J., Ortiz, C., and Boyce, M.C., “Protein Forced Unfolding And Its Effect On The Finite Deformation Stress-Strain Behavior Of Biomacromolecular Solids”, Mater. Res. Soc. Symp. Proc., 874, pp L.4.3.1–L.4.3.6 (2005).Google Scholar
[5] Qi, H. J., Ortiz, C. and Boyce, M.C., “Constitutive Model for the Stress-Strain Behavior of Biomacromolecular Networks Containing Folded Domains”, submitted (2005).Google Scholar
[6] Arslan, M., and Boyce, M.C., “Constitutive Modeling of the Stress Stretch Behavior of embranes Possessing a Triangulated Network Microstructure”, Mater. Res. Soc. Symp., 874, L.6.8.1–L.6.8.6 (2005).Google Scholar
[7] Arslan, M., “Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Networked Microstructure”, Thesis, S.M., Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA (2005).Google Scholar
[8] Arslan, M., and Boyce, M. C., “Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Network Microstructure”, Jnl Appl. Mechanics, in press (2005).Google Scholar
[9] Treloar, L. R. G., The Physics of Rubber Elasticity, Oxford, Clarendon Press (1958).Google Scholar
[10] Eyring, H. “Viscosity, plasticity and diffusion as examples of absolute reaction rates” J. Chem. Physics, 4, pp. 283–291 (1936).Google Scholar