Anomalous Diffusion: Single Particle Trajectory Analysis

  • A. Brodin National Technical University of Ukraine “KPI”
  • T. Turiv Institute of Physics, Nat. Acad. of Sci. of Ukraine
  • V. Nazarenko Institute of Physics, Nat. Acad. of Sci. of Ukraine
Keywords: Brownian motion, anomalous diffusion, single particle tracking, mean square displacement, velocity autocorrelation function

Abstract

Single particle tracking data are usually analyzed in terms of the mean square displacement (MSD) which exhibits, in the case of Brownian particles undergoing the anomalous diffusion, a time dependence that is slower (subdiffusion) or faster (superdiffusion) than a linear one. The particle velocity autocorrelation function (VAF), which is directly related to the underlying dynamics of the host medium that brings about the anomalous diffusion, can then be obtained as the second time derivative of MSD. We examine the possibility to obtain the mean velocity autocorrelation function (MVAF) directly from the particle trace data and analyze its relation to the true VAF for an instantaneous velocity. So long as the sampling time interval is much shorter than the correlation time, MVAF gives an accurate estimate of VAF. Data analysis procedures are illustrated, by using the data generated within a simple stochastic model of superdiffusion.

References

J. Gelles, B.J. Schnapp, and M.P. Sheetz, Nature 331, 450 (1988).

https://doi.org/10.1038/331450a0

J.C. Crocker and D.G. Grier, J. Colloid Interface Sci. 179, 298 (1996).

https://doi.org/10.1006/jcis.1996.0217

P. Habdas and E.R. Weeks, Curr. Opin. Colloid Interface Sci. 7, 196 (2002).

https://doi.org/10.1016/S1359-0294(02)00049-3

A. Pertsinidis, Y. Zhang, and S. Chu, Nature 466, 647 (2010).

https://doi.org/10.1038/nature09163

O. Otto, F. Czerwinski, J.L. Gornall, G. Stober, L.B. Oddershede, R. Seidel, and U.F. Keyser, Opt. Express 18, 22722 (2010).

https://doi.org/10.1364/OE.18.022722

C.D. Saunter, Biophys. J. 98, 1566 (2010).

https://doi.org/10.1016/j.bpj.2009.12.4297

E. Toprak, C. Kural, and P.R. Selvin, Methods Enzymol. 475, 1 (2010).

https://doi.org/10.1016/S0076-6879(10)75001-1

O. Otto, J.L. Gornall, G. Stober, F. Czerwinski, R. Seidel, and U.F. Keyser, J. Opt. 13, 044011 (2011).

https://doi.org/10.1088/2040-8978/13/4/044011

A. Einstein, Ann. Phys. (Leipzig) 17, 549 (1905).

https://doi.org/10.1002/andp.19053220806

M. von Smoluchowski, Ann. Phys. (Leipzig) 21, 756 (1906).

https://doi.org/10.1002/andp.19063261405

P. Langevin, C. R. Acad. Sci. (Paris) 146, 530 (1908).

I.Y. Wong, M.L. Gardel, D.R. Reichman, E.R. Weeks, M.T. Valentine, A.R. Bausch, and D.A. Weitz, Phys. Rev. Lett. 92, 178101 (2004).

https://doi.org/10.1103/PhysRevLett.92.178101

M.M. Alam and R. Mezzenga, Langmuir 27, 6171 (2011).

https://doi.org/10.1021/la200116e

D.S. Banks and C.Fradin, Biophys. J. 89, 2960 (2005).

https://doi.org/10.1529/biophysj.104.051078

J. Sprakel, J. van der Gucht, M.A.C. Stuart, and N.A.M. Besseling, Phys. Rev. E 77, 061502 (2008).

https://doi.org/10.1103/PhysRevE.77.061502

T.V. Ratto and M.L. Longo, Langmuir 19, 1788 (2003).

https://doi.org/10.1021/la0261803

J. Sprakel, J. van der Gucht, M. A. C. Stuart, and N. A. M. Besseling, Phys. Rev. Lett. 99, 208301 (2007).

https://doi.org/10.1103/PhysRevLett.99.208301

S.C. Weber, A.J. Spakowitz, and J.A. Theriot, Phys. Rev. Lett. 104, 238102 (2010).

https://doi.org/10.1103/PhysRevLett.104.238102

A. Ott, J.P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 65, 2201 (1990).

https://doi.org/10.1103/PhysRevLett.65.2201

Y. Gambin, G. Massiera, L. Ramos, C. Ligoure, and W. Urbach, Phys. Rev. Lett. 94, 110602 (2005).

https://doi.org/10.1103/PhysRevLett.94.110602

R. Ganapathy, A.K. Sood, and S. Ramaswamy, Europhys. Lett. 77, 18007 (2007).

https://doi.org/10.1209/0295-5075/77/18007

R. Angelico, A. Ceglie, U. Olsson, G. Palazzo, and L. Ambrosone, Phys. Rev. E 74, 031403 (2006).

https://doi.org/10.1103/PhysRevE.74.031403

X.-L. Wu and A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000); Ibid. 86, 557 (2001).

https://doi.org/10.1103/PhysRevLett.86.557

G.L. Paul and P.N. Pusey, J. Phys. A: Math. Gen. 14, 3301 (1981).

https://doi.org/10.1088/0305-4470/14/12/025

T. Turiv, I. Lazo, A. Brodin, B.I. Lev, V. Reiffenrath, V.G. Nazarenko, and O.D. Lavrentovich, Science 342, 1351 (2013).

https://doi.org/10.1126/science.1240591

A. Brodin, Ukr. J. Phys. 58, 237 (2013).

https://doi.org/10.15407/ujpe58.03.0237

X. Michalet, Phys. Rev. E 82, 041914 (2010).

https://doi.org/10.1103/PhysRevE.82.041914

H. Scher and M. Lax, Phys. Rev. B 7, 4491 (1973).

https://doi.org/10.1103/PhysRevB.7.4491

V.M. Kenkre, R. K¨uhne, and P. Reineker, Z. Phys. B 41, 177 (1981).

https://doi.org/10.1007/BF01293416

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

L.E. Reichel, A Modern Course in Statistical Physics (Wiley, New York, 1998).

Published
2018-10-24
How to Cite
Brodin, A., Turiv, T., & Nazarenko, V. (2018). Anomalous Diffusion: Single Particle Trajectory Analysis. Ukrainian Journal of Physics, 59(8), 775. https://doi.org/10.15407/ujpe59.08.0775
Section
Soft matter