Single-particle tracking: Brownian dynamics of viscoelastic materials.

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identified as the dashpots in the latter. In elementary terms, the intimate correspondence between time-correlation of the fluctuation measurements and transient relaxation kinetics after perturbation is discussed, and the central role of the fluctuation-dissipation relation is emphasized. The work presented here provides a bridge between the microscopic and the macroscopic views of linear viscoelastic biological materials, and is applicable to membrane protein diffusion, linear DNA chain dynamics, and mechanics of intracellular cytoskeletal networks.

[1]  Mason,et al.  Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. , 1995, Physical review letters.

[2]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[3]  J. M. Fernández.  Cellular and molecular mechanics by atomic force microscopy: capturing the exocytotic fusion pore in vivo? , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[4]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[5]  Robert Zwanzig,et al.  Memory Effects in Irreversible Thermodynamics , 1961 .

[6]  M. M. Carroll,et al.  Foundations of Solid Mechanics , 1985 .

[7]  H. Qian,et al.  Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. , 1991, Biophysical journal.

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

[9]  M B Jackson,et al.  Single‐Channel Recording , 1998, Current protocols in neuroscience.

[10]  B. Zimm.  Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss , 1956 .

[11]  Hong Qian,et al.  Vector Field Formalism and Analysis for a Class of Thermal Ratchets , 1998 .

[12]  M. Huggins.  Viscoelastic Properties of Polymers. , 1961 .

[13]  A Kusumi,et al.  Cell surface organization by the membrane skeleton. , 1996, Current opinion in cell biology.

[14]  H. Qian,et al.  Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads. , 1992, Biophysical journal.

[15]  H. Qian,et al.  Remarks on discrete and continuous large-scale models of DNA dynamics. , 1998, Biophysical journal.

[16]  K. Jacobson,et al.  Single-particle tracking: applications to membrane dynamics. , 1997, Annual review of biophysics and biomolecular structure.

[17]  E. Elson,et al.  Cellular mechanics as an indicator of cytoskeletal structure and function. , 1988, Annual review of biophysics and biophysical chemistry.

[18]  L. Finzi,et al.  Measurement of lactose repressor-mediated loop formation and breakdown in single DNA molecules , 1995, Science.

[19]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[20]  G. Fredrickson.  The theory of polymer dynamics , 1996 .

[21]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[22]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[23]  Christoph F. Schmidt,et al.  Chain dynamics, mesh size, and diffusive transport in networks of polymerized actin. A quasielastic light scattering and microfluorescence study , 1989 .

[24]  Leslie M. Loew,et al.  Spectroscopic Membrane Probes , 1988 .

[25]  H. Geerts,et al.  Nanovid tracking: a new automatic method for the study of mobility in living cells based on colloidal gold and video microscopy. , 1987, Biophysical journal.

[26]  M. Sheetz,et al.  Tracking kinesin-driven movements with nanometre-scale precision , 1988, Nature.

[27]  G. Weiss.  TIME-REVERSIBILITY OF LINEAR STOCHASTIC PROCESSES , 1975 .

[28]  Maggs,et al.  Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. , 1996, Physical review letters.

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

[30]  Denis Wirtz,et al.  Particle Tracking Microrheology of Complex Fluids , 1997 .

[31]  Toyoichi Tanaka,et al.  Spectrum of light scattered from a viscoelastic gel , 1973 .

[32]  E. Mizraji,et al.  Viscoelastic models for enzymes with multiple conformational states. , 1987, Journal of theoretical biology.

[33]  H. Qian,et al.  Quantitative study of polymer conformation and dynamics by single-particle tracking. , 1999, Biophysical journal.

[34]  R. Fox,et al.  Gaussian stochastic processes in physics , 1978 .

[35]  B. S,et al.  Hysteresis in Force Probe Measurements : a Dynamical Systems Perspective , 1998 .

[36]  J. Mellema,et al.  Singular behavior of Rouse-like spectra , 1999 .

[37]  S. J. Webb,et al.  Evidence for non-thermal excitation of energy levels in active biological systems , 1977 .

[38]  H. Qian,et al.  A quantitative analysis of single protein-ligand complex separation with the atomic force microscope. , 1997, Biophysical chemistry.

[39]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[40]  Jan Greve,et al.  Three dimensional single-particle tracking with nanometer resolution , 1998 .

[41]  R. Kubo.  Brownian Motion and Nonequilibrium Statistical Mechanics , 1986, Science.

[42]  R. Donnelly,et al.  Nonequilibrium Thermodynamics, Variational Techniques, and Stability. , 1965, Science.

[43]  H. Qian,et al.  Graphical method for force analysis: Macromolecular mechanics with atomic force microscopy , 1999, Proteins.

[44]  Bruno H. Zimm,et al.  Theory of twisting and bending of chain macromolecules; analysis of the fluorescence depolarization of DNA , 1979 .