Diffusion in a fluid membrane with a flexible cortical cytoskeleton.

We calculate the influence of a flexible network of long-chain proteins, which is anchored to a fluid membrane, on protein diffusion in this membrane. This is a model for the cortical cytoskeleton and the lipid bilayer of the red blood cell, which we apply to predict the influence of the cytoskeleton on the diffusion coefficient of a mobile band 3 protein. Using the pressure field that the cytoskeleton exerts on the membrane, from the steric repulsion between the diffusing protein and the cytoskeletal filaments, we define a potential landscape for the diffusion within the bilayer. We study the changes to the diffusion coefficient on removal of one type of anchor proteins, e.g., in several hemolytic anemias, as well as for isotropic and anisotropic stretching of the cytoskeleton. We predict an overall increase of the diffusion for a smaller number of anchor proteins and increased diffusion for anisotropic stretching in the direction of the stretch, because of the decrease in the spatial frequency as well as in the height of the potential barriers.

[1]  D. W. Knowles,et al.  Membrane dynamics of the water transport protein aquaporin-1 in intact human red cells. , 1999, Biophysical journal.

[2]  V. M. Kenkre,et al.  Molecular motion in cell membranes: analytic study of fence-hindered random walks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M. Saxton,et al.  Single-particle tracking: effects of corrals. , 1995, Biophysical journal.

[4]  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.

[5]  M. Sheetz,et al.  Lateral mobility of integral membrane proteins is increased in spherocytic erythrocytes , 1980, Nature.

[6]  H. Noguchi,et al.  Shape transitions of fluid vesicles and red blood cells in capillary flows. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[7]  J. Enderlein,et al.  Surface sticking and lateral diffusion of lipids in supported bilayers. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[8]  G. Klose.  Biomembranes, Physical Aspects , 1996 .

[9]  M. Saxton.  Gaps in the erythrocyte membrane skeleton: a stretched net model. , 1992, Journal of theoretical biology.

[10]  Nicolas Destainville,et al.  Confined diffusion without fences of a g-protein-coupled receptor as revealed by single particle tracking. , 2003, Biophysical journal.

[11]  W. Kühlbrandt,et al.  Three‐dimensional map of the dimeric membrane domain of the human erythrocyte anion exchanger, Band 3. , 1994, The EMBO journal.

[12]  G. Gompper,et al.  Self-avoiding linear and star polymers anchored to membranes. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. B. D. Monvel,et al.  Lateral diffusion anisotropy and membrane lipid/skeleton interaction in outer hair cells. , 2006, Biophysical journal.

[14]  T. Lamb,et al.  Gain and kinetics of activation in the G-protein cascade of phototransduction. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Thorsten Auth,et al.  Fluctuations of coupled fluid and solid membranes with application to red blood cells. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Akihiro Kusumi,et al.  Regulation Mechanism of the Lateral Diffusion of Band 3 in Erythrocyte Membranes by the Membrane Skeleton , 1998, The Journal of cell biology.

[17]  D W Tank,et al.  Enhanced molecular diffusibility in muscle membrane blebs: release of lateral constraints , 1982, The Journal of cell biology.

[18]  Nir S Gov,et al.  Diffusion in curved fluid membranes. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. Sheetz.  Membrane skeletal dynamics: role in modulation of red cell deformability, mobility of transmembrane proteins, and shape. , 1983, Seminars in hematology.

[20]  D. Branton,et al.  Lateral mobility of human erythrocyte integral membrane proteins , 1977, Nature.

[21]  N. Mohandas,et al.  Shear-Response of the Spectrin Dimer-Tetramer Equilibrium in the Red Blood Cell Membrane* , 2002, The Journal of Biological Chemistry.

[22]  P. Low,et al.  Crystallographic structure and functional interpretation of the cytoplasmic domain of erythrocyte membrane band 3. , 2000, Blood.

[23]  J. Lyklema,et al.  Diffusion in a disordered medium , 1982 .

[24]  N. Mohandas,et al.  Disorders of red cell membrane , 2008, British journal of haematology.

[25]  Udo Seifert,et al.  Hybrid simulations of lateral diffusion in fluctuating membranes. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Paul W Wiseman,et al.  Membrane lateral diffusion and capture of CFTR within transient confinement zones. , 2006, Biophysical journal.

[27]  J. Wade,et al.  Ultrastructure of the human erythrocyte cytoskeleton and its attachment to the membrane. , 1991, Cell motility and the cytoskeleton.

[28]  D. Leitner,et al.  Regulation of protein mobility in cell membranes: a dynamic corral model. , 2000, Biophysical journal.

[29]  A. Kusumi,et al.  Regulation of band 3 mobilities in erythrocyte ghost membranes by protein association and cytoskeletal meshwork. , 1988, Biochemistry.

[30]  D. Boal.  Two-Dimensional Cytoskeletons Under Stress , 1998 .

[31]  M. Saxton.  A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics. , 2008, Biophysical journal.

[32]  Michael J Saxton,et al.  A biological interpretation of transient anomalous subdiffusion. I. Qualitative model. , 2007, Biophysical journal.

[33]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[34]  Udo Seifert,et al.  Curvature coupling dependence of membrane protein diffusion coefficients. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[35]  R. Winkler,et al.  Finite size distribution and partition functions of Gaussian chains: maximum entropy approach , 1992 .

[36]  Michael J. Saxton,et al.  Chapter 8 Lateral Diffusion of Lipids and Proteins , 1999 .

[37]  Hai-Tao He,et al.  Dynamics in the plasma membrane: how to combine fluidity and order , 2006, The EMBO journal.

[38]  M. Blaustein,et al.  Plasma Membrane-Cytoskeleton-Endoplasmic Reticulum Complexes in Neurons and Astrocytes* , 2004, Journal of Biological Chemistry.

[39]  M Edidin,et al.  Lateral movements of membrane glycoproteins restricted by dynamic cytoplasmic barriers. , 1991, Science.

[40]  M. Saxton,et al.  The membrane skeleton of erythrocytes. A percolation model. , 1990, Biophysical journal.

[41]  J. Käs,et al.  Attractive membrane domains control lateral diffusion. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  A. Cumano,et al.  Forced Unfolding of Proteins Within Cells , 2007 .

[43]  M. Sheetz,et al.  2,3-Diphosphoglycerate and ATP dissociate erythrocyte membrane skeletons. , 1980, The Journal of biological chemistry.

[44]  Akihiro Kusumi,et al.  Rapid hop diffusion of a G-protein-coupled receptor in the plasma membrane as revealed by single-molecule techniques. , 2005, Biophysical journal.

[45]  E. Evans,et al.  Structure and deformation properties of red blood cells: concepts and quantitative methods. , 1989, Methods in enzymology.

[46]  Barrier-free paths of directed protein motion in the erythrocyte plasma membrane. , 1995, Biophysical journal.

[47]  M. Poo,et al.  Rates of membrane-associated reactions: reduction of dimensionality revisited , 1986, The Journal of cell biology.

[48]  Akihiro Kusumi,et al.  Three-dimensional reconstruction of the membrane skeleton at the plasma membrane interface by electron tomography , 2006, The Journal of cell biology.

[49]  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.

[50]  R. Winkler.  Deformation of semiflexible chains , 2003 .

[51]  Combination of random-barrier and random-trap models , 1996, cond-mat/9610191.

[52]  Akihiro Kusumi,et al.  Single-molecule tracking of membrane molecules: plasma membrane compartmentalization and dynamic assembly of raft-philic signaling molecules. , 2005, Seminars in immunology.

[53]  Nir S Gov,et al.  Active elastic network: cytoskeleton of the red blood cell. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  G. Schütz,et al.  Diffusion of Particles on Lattices , 2005 .

[55]  L. Lin,et al.  Dynamics of pinned membranes with application to protein diffusion on the surface of red blood cells. , 2004, Biophysical journal.

[56]  N. Gov,et al.  Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. , 2005, Biophysical journal.

[57]  Levi A. Gheber,et al.  A model for membrane patchiness: lateral diffusion in the presence of barriers and vesicle traffic. , 1999, Biophysical journal.

[58]  A. Benda,et al.  Lipid diffusion in giant unilamellar vesicles is more than 2 times faster than in supported phospholipid bilayers under identical conditions. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[59]  S. Lux,et al.  Red cell membrane skeletal defects in hereditary and acquired hemolytic anemias. , 1983, Seminars in hematology.

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

[61]  M. Saxton,et al.  The spectrin network as a barrier to lateral diffusion in erythrocytes. A percolation analysis. , 1989, Biophysical journal.

[62]  R. Josephs,et al.  On the structure of erythrocyte spectrin in partially expanded membrane skeletons. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[63]  E. Sackmann,et al.  Coupling of spectrin and polylysine to phospholipid monolayers studied by specular reflection of neutrons. , 1991, Biophysical journal.

[64]  Bridget S. Wilson,et al.  Plasma membrane-associated proteins are clustered into islands attached to the cytoskeleton , 2006, Proceedings of the National Academy of Sciences.

[65]  Akihiro Kusumi,et al.  Detection of non-Brownian diffusion in the cell membrane in single molecule tracking. , 2005, Biophysical journal.

[66]  Akihiro Kusumi,et al.  Ultrafine membrane compartments for molecular diffusion as revealed by single molecule techniques. , 2004, Biophysical journal.

[67]  F. Brown.  Regulation of protein mobility via thermal membrane undulations. , 2003, Biophysical journal.

[68]  Hiroshi Watanabe,et al.  Metropolis Monte Carlo method as a numerical technique to solve the Fokker-Planck equation , 1991 .

[69]  D. Koch,et al.  Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes. , 1995, Biophysical journal.

[70]  L. Lin,et al.  Dynamic simulations of membranes with cytoskeletal interactions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  M. Saxton.  The membrane skeleton of erythrocytes: models of its effect on lateral diffusion. , 1990, International Journal of Biochemistry.

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

[73]  M. Rosa,et al.  Bounding fluid viscosity and translational diffusion in a fluid lipid bilayer , 1987, European Biophysics Journal.

[74]  N. Gov,et al.  Filament networks attached to membranes: cytoskeletal pressure and local bilayer deformation , 2007 .

[75]  J. Wade,et al.  Ultrastructure and immunocytochemistry of the isolated human erythrocyte membrane skeleton. , 1993, Cell motility and the cytoskeleton.

[76]  D. Golan,et al.  Regulation of band 3 rotational mobility by ankyrin in intact human red cells. , 1998, Biochemistry.

[77]  J. Morrow,et al.  Spectrin tethers and mesh in the biosynthetic pathway. , 2000, Journal of cell science.

[78]  Leah Edelstein-Keshet,et al.  Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a one-dimensional model of a motile cell. , 2007, Biophysical journal.

[79]  M. Sheetz,et al.  Matrix control of protein diffusion in biological membranes. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[80]  K R Wilson,et al.  Lateral diffusion of membrane proteins in the presence of static and dynamic corrals: suggestions for appropriate observables. , 2000, Biophysical journal.

[81]  V. Fowler,et al.  Association of spectrin with its membrane attachment site restricts lateral mobility of human erythrocyte integral membrane proteins , 1978 .

[82]  E. Evans,et al.  Molecular friction and epitactic coupling between monolayers in supported bilayers , 1989 .

[83]  T. Fujiwara,et al.  Application of laser tweezers to studies of the fences and tethers of the membrane skeleton that regulate the movements of plasma membrane proteins. , 1998, Methods in cell biology.

[84]  Local entropic effects of polymers grafted to soft interfaces , 2000, cond-mat/0006082.

[85]  Gerhard J Schütz,et al.  (Un)confined diffusion of CD59 in the plasma membrane determined by high-resolution single molecule microscopy. , 2007, Biophysical journal.

[86]  S. Ohnishi,et al.  Restriction of the lateral motion of band 3 in the erythrocyte membrane by the cytoskeletal network: dependence on spectrin association state. , 1986, Biochemistry.

[87]  G. Schwarzmann,et al.  Minor effects of bulk viscosity on lipid translational diffusion measured by the excimer formation technique , 2004, European Biophysics Journal.

[88]  P. Saffman,et al.  Brownian motion in biological membranes. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[89]  D. Golan,et al.  Differential control of band 3 lateral and rotational mobility in intact red cells. , 1994, The Journal of clinical investigation.

[90]  E. Nigg,et al.  Anchorage of a band 3 population at the erythrocyte cytoplasmic membrane surface: protein rotational diffusion measurements. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[91]  P. Heitjans,et al.  Diffusion in Condensed Matter , 2005 .

[92]  Akihiro Kusumi,et al.  Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: high-speed single-molecule tracking of membrane molecules. , 2005, Annual review of biophysics and biomolecular structure.

[93]  R. S. Hodges,et al.  Lateral mobility of proteins in liquid membranes revisited , 2006, Proceedings of the National Academy of Sciences of the United States of America.