Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer– couple hypothesis from membrane mechanics

doi:10.1073/pnas.202617299

Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer– couple hypothesis from membrane mechanics

^*Department of Physics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6; and ^‡NEC Research Institute, 4 Independence Way, Princeton, NJ 08540

Communicated by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA (received for review August 19, 2002)

Abstract

Red-cell shape is encoded in the mechanical properties of the membrane. The plasma membrane contributes bending rigidity; the protein-based membrane skeleton contributes stretch and shear elasticity. When both effects are included, membrane mechanics can reproduce in detail the full stomatocyte–discocyte–echinocyte sequence by variation of a single parameter related to the bilayer couple originally introduced by Sheetz and Singer [Sheetz, M. P. & Singer, S. J. (1974) Proc. Natl. Acad. Sci. USA 71, 4457–4461].

Footnotes

↵ † To whom correspondence should be addressed. E-mail: wortis{at}sfu.ca.
↵ § Volume is controlled osmotically and can be maintained constant by keeping the tonicity of the suspending medium constant.
↵ ¶ ΔA (see Eq. 1) is measurable, because it depends on the observable shape only; however, ΔA ₀ cannot be deduced from ΔA without resorting to theory.
↵ ∥ More precisely, D is the separation between the neutral surfaces of the two bilayer leaflets and is assumed independent of bending. The neutral surface of the leaflet is the plane about which the net bending moment caused by the stress profile vanishes.
↵ ** The energy scale is set by κ_b, which for the RBC has a value around 48 k _B T _room (18–20), so the effects of thermal fluctuations are normally small.
↵ †† These values are neither experimental nor unique. They have been chosen to provide a modest hardening of the elasticity for α and β in the range 0.3–0.5. Such large strains occur only for the echinocyte II and III and the stomatocyte III. These nonlinearities affect only the details of spicule shape and other highly strained configurations.
↵ ‡‡ For example, the area difference for the echinocyte III has been estimated to be 1.7 ± 0.6% (9). Note that a single measurement is not really meaningful, because C ₀ and ΔA ₀ enter together into determining $\text{[math]}$ ₀.
↵ §§ Shapes with $\text{[math]}$ ₀ below that for stomatocyte III require global self-avoidance of S. Because we implemented only local self-avoidance, we are presently unable to obtain more extreme stomatocytes.
↵ ¶¶ This process involves treating osmotically swelled RBCs with diamide and then shrinking them back to the normal volume (27). The diamide treatment has the effect of fixing S ₀ at or close to a sphere while also increasing K _α and μ. Although the latter prevents a direct comparison with our results, the fact that we obtained a nonaxisymmetric discocyte for a nearly spherical S ₀ with lower, normal values of K _α and μ suggests that the change in S ₀ has a nonnegligible role in the production of a stable nonaxisymmetric discocyte.
Abbreviations:
1. ADE, area–difference–elasticity
2. MS, membrane skeleton