Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking

Diffusion in the plasma membrane of living cells is often found to display anomalous dynamics. However, the mechanism underlying this diffusion pattern remains highly controversial. Here, we study the physical mechanism underlying Kv2.1 potassium channel anomalous dynamics using single-molecule tracking. Our analysis includes both time series of individual trajectories and ensemble averages. We show that an ergodic and a nonergodic process coexist in the plasma membrane. The ergodic process resembles a fractal structure with its origin in macromolecular crowding in the cell membrane. The nonergodic process is found to be regulated by transient binding to the actin cytoskeleton and can be accurately modeled by a continuous-time random walk. When the cell is treated with drugs that inhibit actin polymerization, the diffusion pattern of Kv2.1 channels recovers ergodicity. However, the fractal structure that induces anomalous diffusion remains unaltered. These results have direct implications on the regulation of membrane receptor trafficking and signaling.

[1]  R. Metzler,et al.  In vivo anomalous diffusion and weak ergodicity breaking of lipid granules. , 2010, Physical review letters.

[2]  J. Klafter,et al.  Detecting origins of subdiffusion: P-variation test for confined systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Gaudenz Danuser,et al.  Cargo- and adaptor-specific mechanisms regulate clathrin-mediated endocytosis , 2010, The Journal of cell biology.

[4]  T. Franosch,et al.  Development of anomalous diffusion among crowding proteins , 2010, 1003.3748.

[5]  Ralf Jungmann,et al.  Quantitative analysis of single particle trajectories: mean maximal excursion method. , 2010, Biophysical journal.

[6]  J. Klafter,et al.  Subdiffusion of mixed origins: when ergodicity and nonergodicity coexist. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. Klafter,et al.  Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics. , 2009, Physical review letters.

[8]  M. Weiss,et al.  Elucidating the origin of anomalous diffusion in crowded fluids. , 2009, Physical review letters.

[9]  Y. Garini,et al.  Transient anomalous diffusion of telomeres in the nucleus of mammalian cells. , 2009, Physical review letters.

[10]  H. McMahon,et al.  Mechanisms of endocytosis. , 2009, Annual review of biochemistry.

[11]  S. Hell,et al.  Direct observation of the nanoscale dynamics of membrane lipids in a living cell , 2009, Nature.

[12]  Ludovico Silvestri,et al.  Event-driven power-law relaxation in weak turbulence. , 2009, Physical review letters.

[13]  R. Metzler,et al.  Random time-scale invariant diffusion and transport coefficients. , 2008, Physical review letters.

[14]  J. Klafter,et al.  Nonergodicity mimics inhomogeneity in single particle tracking. , 2008, Physical review letters.

[15]  J. Klafter,et al.  Probing microscopic origins of confined subdiffusion by first-passage observables , 2008, Proceedings of the National Academy of Sciences.

[16]  B. Sung,et al.  Lateral diffusion of proteins in the plasma membrane: spatial tessellation and percolation theory. , 2008, The journal of physical chemistry. B.

[17]  M. Tamkun,et al.  A cytoskeletal-based perimeter fence selectively corrals a sub-population of cell surface Kv2.1 channels , 2007, Journal of Cell Science.

[18]  E. Isacoff,et al.  Subunit counting in membrane-bound proteins , 2007, Nature Methods.

[19]  Jennifer D. Whitesell,et al.  Kv2.1 Potassium Channels Are Retained within Dynamic Cell Surface Microdomains That Are Defined by a Perimeter Fence , 2006, The Journal of Neuroscience.

[20]  M. Tamkun,et al.  Targeting of voltage-gated potassium channel isoforms to distinct cell surface microdomains , 2005, Journal of Cell Science.

[21]  J. Trejo Internal PDZ Ligands: Novel Endocytic Recycling Motifs for G Protein-Coupled Receptors , 2005, Molecular Pharmacology.

[22]  Paul R Selvin,et al.  Fluorescence imaging with one nanometer accuracy: application to molecular motors. , 2005, Accounts of chemical research.

[23]  M. Saxton,et al.  Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level. , 2005, Biophysical journal.

[24]  Golan Bel,et al.  Weak Ergodicity Breaking in the Continuous-Time Random Walk , 2005 .

[25]  P. Evans,et al.  Adaptors for clathrin coats: structure and function. , 2004, Annual review of cell and developmental biology.

[26]  D. Reichman,et al.  Anomalous diffusion probes microstructure dynamics of entangled F-actin networks. , 2004, Physical review letters.

[27]  E. Barkai Aging in subdiffusion generated by a deterministic dynamical system. , 2003, Physical review letters.

[28]  W E Moerner,et al.  Translational diffusion of individual class II MHC membrane proteins in cells. , 2002, Biophysical journal.

[29]  J. Klafter,et al.  The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times , 2001, cond-mat/0202326.

[30]  M K Cheezum,et al.  Quantitative comparison of algorithms for tracking single fluorescent particles. , 2001, Biophysical journal.

[31]  J. Martens,et al.  Isoform-specific Localization of Voltage-gated K+Channels to Distinct Lipid Raft Populations , 2001, The Journal of Biological Chemistry.

[32]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[33]  Karl Heinz Hoffmann,et al.  The similarity group and anomalous diffusion equations , 2000 .

[34]  J. Hörber,et al.  Sphingolipid–Cholesterol Rafts Diffuse as Small Entities in the Plasma Membrane of Mammalian Cells , 2000, The Journal of cell biology.

[35]  Gerald Kada,et al.  Properties of lipid microdomains in a muscle cell membrane visualized by single molecule microscopy , 2000, The EMBO journal.

[36]  K. Jacobson,et al.  Transient confinement of a glycosylphosphatidylinositol-anchored protein in the plasma membrane. , 1997, Biochemistry.

[37]  H Schindler,et al.  Single-molecule microscopy on model membranes reveals anomalous diffusion. , 1997, Biophysical journal.

[38]  M. Saxton Single-particle tracking: the distribution of diffusion coefficients. , 1997, Biophysical journal.

[39]  A. Bershadsky,et al.  Swinholide A Is a Microfilament Disrupting Marine Toxin That Stabilizes Actin Dimers and Severs Actin Filaments (*) , 1995, The Journal of Biological Chemistry.

[40]  M. Saxton Anomalous diffusion due to obstacles: a Monte Carlo study. , 1994, Biophysical journal.

[41]  Solomon,et al.  Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow. , 1993, Physical review letters.

[42]  A. Kusumi,et al.  Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells. , 1993, Biophysical journal.

[43]  J. Bouchaud Weak ergodicity breaking and aging in disordered systems , 1992 .

[44]  M. Shlesinger,et al.  Stochastic pathway to anomalous diffusion. , 1987, Physical review. A, General physics.

[45]  I. Procaccia,et al.  Analytical solutions for diffusion on fractal objects. , 1985, Physical review letters.

[46]  J. Klafter,et al.  Continuous-Time Random Walks on Fractals , 1984 .

[47]  E. Montroll,et al.  Anomalous transit-time dispersion in amorphous solids , 1975 .

[48]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[49]  W. Coffey,et al.  Diffusion and Reactions in Fractals and Disordered Systems , 2002 .

[50]  W. Wilson,et al.  Simulating Ecological and Evolutionary Systems in C: Diffusion and Reactions , 2000 .

[51]  J. Quastel Diffusion in Disordered Media , 1996 .

[52]  A. Minton,et al.  Macromolecular crowding: biochemical, biophysical, and physiological consequences. , 1993, Annual review of biophysics and biomolecular structure.