Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding.

To assess local elasticity in the red cell's spectrin-actin network, nano-particles were tethered to actin nodes and their constrained thermal motions were tracked. Cells were both immobilized and controllably deformed by aspiration into a micropipette. Since the network is well-appreciated as soft, thermal fluctuations even in an unstressed portion of network were expected to be many tens of nanometers based on simple equipartition ideas. Real-time particle tracking indeed reveals such root-mean-squared motions for 40-nm fluorescent beads either tethered to actin directly within a cell ghost or connected to actin from outside a cell via glycophorin. Moreover, the elastically constrained displacements are significant on the scale of the network's internodal distance of approximately 60-80 nm. Surprisingly, along the aspirated projection-where the network is axially extended by as much as twofold or more-fluctuations in the axial direction are increased by almost twofold relative to motions in the unstressed network. The molecular basis for such strain softening is discussed broadly in terms of force-driven transitions. Specific considerations are given to 1) protein dissociations that reduce network connectivity, and 2) unfolding kinetics of a localized few of the red cell's approximately 10(7) spectrin repeats.

[1]  S Chien,et al.  Influence of network topology on the elasticity of the red blood cell membrane skeleton. , 1997, Biophysical journal.

[2]  Evans,et al.  Entropy-driven tension and bending elasticity in condensed-fluid membranes. , 1990, Physical review letters.

[3]  E. Evans,et al.  Strength of a weak bond connecting flexible polymer chains. , 1999, Biophysical journal.

[4]  C. Steele,et al.  Mechanical properties of the lateral cortex of mammalian auditory outer hair cells. , 1996, Biophysical journal.

[5]  A. Kusumi,et al.  Compartmentalization of the erythrocyte membrane by the membrane skeleton: intercompartmental hop diffusion of band 3. , 1999, Molecular biology of the cell.

[6]  R Skalak,et al.  Mechanics and thermodynamics of biomembranes: part 1. , 1979, CRC critical reviews in bioengineering.

[7]  D. Boal,et al.  Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration. , 1998, Biophysical journal.

[8]  Shechao Feng,et al.  Percolation on Elastic Networks: New Exponent and Threshold , 1984 .

[9]  E. Sackmann,et al.  Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. , 1995, Biophysical journal.

[10]  D. Wirtz,et al.  Mechanics of living cells measured by laser tracking microrheology. , 2000, Biophysical journal.

[11]  W. H. Reid,et al.  The Theory of Elasticity , 1960 .

[12]  J. Conboy,et al.  Mechanochemistry of protein 4.1's spectrin-actin-binding domain: ternary complex interactions, membrane binding, network integration, structural strengthening , 1995, The Journal of cell biology.

[13]  M. Lieber,et al.  Hemolytic holes in human erythrocyte membrane ghosts. , 1989, Methods in enzymology.

[14]  D. Discher,et al.  Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton. , 1999, Biophysical journal.

[15]  N. Mohandas,et al.  Red blood cell glycophorins. , 1992, Blood.

[16]  D. Discher,et al.  Actin protofilament orientation at the erythrocyte membrane. , 1999, Biophysical journal.

[17]  F. Ziemann,et al.  Micropipet-based pico force transducer: in depth analysis and experimental verification. , 1998, Biophysical journal.

[18]  S. Hénon,et al.  A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. , 1999, Biophysical journal.

[19]  Dennis E. Discher,et al.  PHASE TRANSITIONS AND ANISOTROPIC RESPONSES OF PLANAR TRIANGULAR NETS UNDER LARGE DEFORMATION , 1997 .

[20]  D. Golan,et al.  Lateral mobility of band 3 in the human erythrocyte membrane studied by fluorescence photobleaching recovery: evidence for control by cytoskeletal interactions. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[21]  M. Saraste,et al.  States and transitions during forced unfolding of a single spectrin repeat , 2000, FEBS letters.

[22]  D. Speicher,et al.  Analysis of human red cell spectrin tetramer (head-to-head) assembly using complementary univalent peptides. , 1992, Biochemistry.

[23]  A Leung,et al.  Static and dynamic rigidities of normal and sickle erythrocytes. Major influence of cell hemoglobin concentration. , 1984, The Journal of clinical investigation.

[24]  D. Discher,et al.  Actin protofilament orientation in deformation of the erythrocyte membrane skeleton. , 2000, Biophysical journal.

[25]  E. Evans,et al.  Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects. , 1994, Annual review of biophysics and biomolecular structure.

[26]  J. Rudnick,et al.  Elasticity theory of the B-DNA to S-DNA transition. , 1998, Biophysical journal.

[27]  Hong Qian,et al.  Nanometre-level analysis demonstrates that lipid flow does not drive membrane glycoprotein movements , 1989, Nature.

[28]  M. Rief,et al.  Reversible unfolding of individual titin immunoglobulin domains by AFM. , 1997, Science.

[29]  J. Hartwig,et al.  The mechanics of F-actin microenvironments depend on the chemistry of probing surfaces. , 2000, Biophysical journal.

[30]  F. C. MacKintosh,et al.  Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations , 1997 .

[31]  R Josephs,et al.  Ultrastructure of the intact skeleton of the human erythrocyte membrane , 1986, The Journal of cell biology.

[32]  T. L. Hill Cooperativity Theory in Biochemistry: Steady-State and Equilibrium Systems , 2011 .

[33]  A. Mikkelsen,et al.  The human erythrocyte membrane skeleton may be an ionic gel , 1986, European Biophysics Journal.

[34]  D. Discher,et al.  Kinematics of red cell aspiration by fluorescence-imaged microdeformation. , 1996, Biophysical journal.

[35]  D. Boal,et al.  Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models. , 1998, Biophysical journal.

[36]  A. Oberhauser,et al.  Atomic force microscopy captures length phenotypes in single proteins. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[37]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[38]  R. Hochmuth,et al.  Force relaxation and permanent deformation of erythrocyte membrane. , 1983, Biophysical journal.

[39]  V. Ohanian,et al.  Analysis of the ternary interaction of the red cell membrane skeletal proteins spectrin, actin, and 4.1. , 1984, Biochemistry.

[40]  D. Branton,et al.  Visualization of the protein associations in the erythrocyte membrane skeleton. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[41]  R. Waugh,et al.  Thermoelasticity of red blood cell membrane. , 1979, Biophysical journal.

[42]  R. Waugh,et al.  Reductions of erythrocyte membrane viscoelastic coefficients reflect spectrin deficiencies in hereditary spherocytosis. , 1988, The Journal of clinical investigation.

[43]  F. MacKintosh,et al.  Microrheology of biopolymer-membrane complexes. , 2000, Physical review letters.

[44]  Evan Evans,et al.  Chemically distinct transition states govern rapid dissociation of single L-selectin bonds under force , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[45]  N. Mohandas,et al.  Restoration of normal membrane stability to unstable protein 4.1-deficient erythrocyte membranes by incorporation of purified protein 4.1. , 1986, The Journal of clinical investigation.

[46]  V. Fowler,et al.  Immunolocalization of tropomodulin, tropomyosin and actin in spread human erythrocyte skeletons. , 1994, Journal of cell science.

[47]  M. Rief,et al.  Single molecule force spectroscopy of spectrin repeats: low unfolding forces in helix bundles. , 1999, Journal of molecular biology.

[48]  D. Speicher,et al.  Forced unfolding modulated by disulfide bonds in the Ig domains of a cell adhesion molecule. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[49]  A. Kusumi,et al.  Structure of the erythrocyte membrane skeleton as observed by atomic force microscopy. , 1998, Biophysical journal.

[50]  J. Liphardt,et al.  Reversible Unfolding of Single RNA Molecules by Mechanical Force , 2001, Science.

[51]  E. Evans,et al.  Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. , 1994, Science.

[52]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[53]  R M Hochmuth,et al.  Erythrocyte membrane elasticity and viscosity. , 1987, Annual review of physiology.

[54]  S. Lowen The Biophysical Journal , 1960, Nature.

[55]  Matthias Rief,et al.  Elastically Coupled Two-Level Systems as a Model for Biopolymer Extensibility , 1998 .

[56]  E. Evans A new material concept for the red cell membrane. , 1973, Biophysical journal.