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Spectrin-Level Modeling of the Cytoskeleton and Optical Tweezers Stretching of the Erythrocyte

J. Li ^*, M. Dao , C. T. Lim  and S. Suresh  

^* Department of Materials Science and Engineering, Ohio State University, Columbus, Ohio; Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts; Division of Bioengineering and Department of Mechanical Engineering, The National University of Singapore, Republic of Singapore; and Division of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts

Correspondence: Address reprint requests to Dr. Subra Suresh, Dept. of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. E-mail: ssuresh{at}mit.edu.

We present a three-dimensional computational study of whole-cell equilibrium shape and deformation of human red blood cell (RBC) using spectrin-level energetics. Random network models consisting of degree-2, 3, ..., 9 junction complexes and spectrin links are used to populate spherical and biconcave surfaces and intermediate shapes, and coarse-grained molecular dynamics simulations are then performed with spectrin connectivities fixed. A sphere is first filled with cytosol and gradually deflated while preserving its total surface area, until cytosol volume consistent with the real RBC is reached. The equilibrium shape is determined through energy minimization by assuming that the spectrin tetramer links satisfy the worm-like chain free-energy model. Subsequently, direct stretching by optical tweezers of the initial equilibrium shape is simulated to extract the variation of axial and transverse diameters with the stretch force. At persistence length p = 7.5 nm for the spectrin tetramer molecule and corresponding in-plane shear modulus µ₀ 8.3 µN/m, our models show reasonable agreement with recent experimental measurements on the large deformation of RBC with optical tweezers. We find that the choice of the reference state used for the in-plane elastic energy is critical for determining the equilibrium shape. If a position-independent material reference state such as a full sphere is used in defining the in-plane energy, then the bending modulus needs to be at least a decade larger than the widely accepted value of 2 x 10^–19 J to stabilize the biconcave shape against the cup shape. We demonstrate through detailed computations that this paradox can be avoided by invoking the physical hypothesis that the spectrin network undergoes constant remodeling to always relax the in-plane shear elastic energy to zero at any macroscopic shape, at some slow characteristic timescale. We have devised and implemented a liquefied network structure evolution algorithm that relaxes shear stress everywhere in the network and generates cytoskeleton structures that mimic experimental observations.

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