A novel strain energy relationship for red blood cell membrane skeleton based on spectrin stiffness and its application to micropipette deformation

Abstract

Red blood cell (RBC) membrane skeleton is a closed two-dimensional elastic network of spectrin tetramers with nodes formed by short actin filaments. Its three-dimensional shape conforms to the shape of the bilayer, to which it is connected through vertical linkages to integral membrane proteins. Numerous methods have been devised over the years to predict the response of the RBC membrane to applied forces and determine the corresponding increase in the skeleton elastic energy arising either directly from continuum descriptions of its deformation, or seeking to relate the macroscopic behavior of the membrane to its molecular constituents. In the current work, we present a novel continuum formulation rooted in the molecular structure of the membrane and apply it to analyze model deformations similar to those that occur during aspiration of RBCs into micropipettes. The microscopic elastic properties of the skeleton are derived by treating spectrin tetramers as simple linear springs. For a given local deformation of the skeleton, we determine the average bond energy and define the corresponding strain energy function and stress–strain relationships. The lateral redistribution of the skeleton is determined variationally to correspond to the minimum of its total energy. The predicted dependence of the length of the aspirated tongue on the aspiration pressure is shown to describe the experimentally observed system behavior in a quantitative manner by taking into account in addition to the skeleton energy an energy of attraction between RBC membrane and the micropipette surface.

Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

“…Experimental tests probing whether NMIIA activity is non-uniform along the RBC membrane will also give insight into NMIIA density distribution versus activity distribution along the membrane. Second, we assumed that the contributions from thermal fluctuations and the deformation of the membrane skeleton are negligible compared to the bending energy [55,114] . However, for a more general quantitative model, these effects should be considered [103] .…”

Meaning of the Solid and Liquid Fascia to Reconsider the Model of Biotensegrity

“…These proteins connect the membrane with the cytoplasm, with a short actin filament, creating a complex net that reaches the DNA. The erythrocyte deforms according to the calibre of the vessel or according to the speed and direction of blood flow; the membrane changes its shape just like the cytoskeleton and, probably, thanks to the elastic accumulation of spectrins, the erythrocyte is restored to its original shape [ 23 - 24 ]. Its biotensegretive organization allows it to absorb the mechanical force it endures, to distribute it inside the cell, and to restore its shape, carrying out its function [ 15 ].…”

On Eulerian versus Lagrangian models of mechanical blood damage and the linearized damage function

“…However, problems have been recognized with this extension . There is also another class of more mechanistic hemolysis prediction models based on cell membrane strain . With advances in computer technology, computational fluid dynamics (CFD) simulations have been extensively used in analysis of hemolysis, including recent direct numerical simulations of flows containing deformable erythrocytes .…”

“…6,7 There is also another class of more mechanistic hemolysis prediction models based on cell membrane strain. [8][9][10][11] With advances in computer technology, computational fluid dynamics (CFD) simulations have (1) D = CT Eulerian method as reported is valid only for steady, uniaxial flow in which velocity is constant along streamlines. The second issue is related to linearization, which involves distributing an exponent across an integral.…”