A tethered adhesive particle model of two-dimensional elasticity and its application to the erythrocyte membrane

A new model of two-dimensional elasticity with application to the erythrocyte membrane is proposed. The system consists of a planar array of self-adhesive particles attached to nearest neighbors with flexible tethers. Stretching from the equilibrium dimension is resisted because force is required to dissociate the particle clusters and to decrease the distribution entropy. Release of the external force is accompanied by a contraction as thermal diffusion randomizes the particles and allows interparticle attachments to form again. Analysis of membrane thermodynamics and mechanics under the two-state particle assumption results in a shear softening stress-strain relation. The shear modulus is found proportional to the square root of the surface density of particles, the interparticle adhesive energy, and is inversely proportional to the tether length. Applied to the erythrocyte membrane under the assumption that band 3 tetramer represents the particle and spectrin the tether, the shear modulus predicted corresponds to the measured value when the interparticle adhesive energy is approximately 4.0-5.9 kT, where kT is the Boltzmann constant multiplied by the temperature. This model suggests a mechanism wherein erythrocyte membrane deformability depends on integral protein homomultimeric interactions and can be modulated from the external surface.