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

  • Melis Arslan (a1), Mary C. Boyce (a2), Hang J. Qi (a3) and Christine Ortiz (a4)

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.

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Keywords

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

  • Melis Arslan (a1), Mary C. Boyce (a2), Hang J. Qi (a3) and Christine Ortiz (a4)

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