Abstract
Given a theoretical model for a self-propelled particle or micro-organism, how does one optimally determine the parameters of the model from experimental data in the form of a time-lapse recorded trajectory? For very long trajectories, one has very good statistics, and optimality may matter little. However, for biological micro-organisms, one may not control the duration of recordings, and then optimality can matter. This is especially the case if one is interested in individuality and hence cannot improve statistics by taking population averages over many trajectories. One can learn much about this problem by studying its simplest case, pure diffusion with no self-propagation. This is an interesting problem also in its own right for the very same reasons: interest in individuality and short trajectories. We summarize our recent results on this latter issue here and speculate about the extent to which similar results may be obtained also for self-propelled particles.
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References
C.L. Vestergaard, P.C. Blainey, H. Flyvbjerg, Phys. Rev. E 89, 022726 (2014)
K.I. Mortensen, L.S. Churchman, J.A. Spudich, H. Flyvbjerg, Nat. Methods 7, 377 (2010)
L. Li, E.C. Cox, H. Flyvbjerg, Phys. Biol. 8, 046006 (2011)
D. Selmeczi, S. Mosler, P.H. Hagedorn, N.B. Larsen, H. Flyvbjerg, Biophys. J. 89, 912 (2005)
D. Selmeczi, L. Li, L.I.I. Pedersen, S.F. Nørrelykke, P.H. Hagedorn, S. Mosler, N.B. Larsen, E.C. Cox, H. Flyvbjerg, Eur. Phys. J. Special Topics 157, 1 (2008)
C.L. Vestergaard, Optimizing experimental parameters for tracking of diffusing particles [arXiv:1504.05462v1] (2015)
A. Tafvizi, L.A. Mirny, A.M. van Oijen, Chem. Phys. Chem. 12, 1481 (2011)
J. Gorman, E.C. Greene, Nat. Struct. Mol. Biol. 15, 768 (2008)
R.D. Vale, D.R. Soll, I.R. Gibbons, Cell 59, 915 (1989)
J. Helenius, G. Brouhard, Y. Kalaidzidis, S. Diez, J. Howard, Nature 441, 115 (2006)
I. Minoura, E. Katayama, K. Sekimoto, E. Muto, Biophys. J. 98, 1589 (2010)
A.W. Sonesson, U.M. Elofsson, T.H. Callisen, H. Brismar, Langmuir 23, 8352 (2007)
S. Wieser, G.J. Schütz, Methods 46, 131 (2008)
D. Lasne, G.A. Blab, S. Berciaud, M. Heine, L. Groc, D. Choquet, L. Cognet, B. Lounis, Biophys. J. 91, 4598 (2006)
S.Y. Nishimura, S.J. Lord, L.O. Klein, K.A. Willets, M. He, Z. Lu, R.J. Twieg, W.E. Moerner, J. Phys. Chem. B 110, 8151 (2006)
M.B. Smith, E. Karatekin, A. Gohlke, H. Mizuno, N. Watanabe, D. Vavylonis, Biophys. J. 101, 1794 (2011)
H. Bornfleth, P. Edelmann, D. Zink, T. Cremer, Biophys. J. 77, 2871 (1999)
M. Goulian, S.M. Simon, Biophys. J. 79, 2188 (2000)
P.C. Blainey, A.M. van Oijen, A. Banerjee, G.L. Verdine, X.S. Xie, Proc. Natl. Acad. Sci. (USA) 103, 5752 (2006)
P.C. Blainey, G. Luo, S.C. Kou, W.F. Mangel, G.L. Verdine, B. Bagchi, X.S. Xie, Nat. Struct. Mol. Biol. 16, 1224 (2009)
J. Elf, G.-W. Li, X.S. Xie, Science 316, 1191 (2007)
A.J. Berglund, Phys. Rev. E 82, 011917 (2010)
A. Graneli, C.C. Yeykal, R.B. Robertson, E.C. Greene, Proc. Natl. Acad. Sci. (USA) 103, 1221 (2006)
M. Vrljic, S.Y. Nishimura, S. Brasselet, W.E. Moerner, H.M. McConnell, Biophys. J. 83, 2681 (2002)
C.R. Rao, Linear Statistical Inference and its Applications, 2nd edition (Wiley Eastern, 1973)
A. Einstein, Annal. Phys. 17, 549 (1905)
X. Michalet, Phys. Rev. E 82, 041914 (2010)
H. Qian, M.P. Sheetz, E.L. Elson, Biophys. J. 60, 910 (1991)
A. Biebricher, W. Wende, C. Escude, A. Pingoud, P. Desbiolles, Biophys. J. 96, L50 (2009)
S.F. Nørrelykke, H. Flyvbjerg, Rev. Sci. Instrum. 81, 075103 (2010)
K. Berg-Sørensen, H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004)
B. Lukic, S. Jeney, C. Tischer, A.J. Kulik, L. Forro, E.L. Florin, Phys. Rev. Lett. 95, 160601 (2005)
K. Berg-Sørensen, H. Flyvbjerg, New J. Phys. 7, 38 (2005)
Th. Franosch, M. Grimm, M. Belushkin, F. Mor, G. Foffi, L. Forro, S. Jeney, Nature 478, 85 (2011)
A. Jannasch, M. Mahamdeh, E. Schäffer, Phys. Rev. Lett. 107, 22830 (2011)
G.E. Uhlenbeck, L.S. Ornstein, Phys. Rev. 36, 823 (1930)
G.L. de Haas-Lorentz, Over de theorie der Brown’sche beweging (Dissertation, Leyden, 1912)
G.L. de Haas-Lorentz, Die Brownsche Bewegung (Braunschweig, 1913)
G.L. de Haas-Lorentz, Die Wissenshaft, B. 52 (Vieweg, 1913)
M. Smoluchowski, Phys. Z. 27, 557 (1916)
R. Fürth, Z. Phys. 2, 244 (1920)
R. Fürth, Pflügers Arch. Physiol. 184, 294 (1920)
K. Przibram, Pflügers Arch. Physiol. 153, 401 (1913)
D. Selmeczi, S. Tolic-Nørrelykke, E. Schäffer, P.H. Hagedorn, S. Mosler, K. Berg-Sørensen, N.B. Larsen, H. Flyvbjerg, Brownian Motion after Einstein: Some new applications and new experiments, edited by H. Linke, A. Månsson, Controlled Nanoscale Motion in Biological and Artificial Systems, Vol. 711, Springer Lecture Notes in Physics, Nobel Symposium 131, Bäckaskog Castle, Sweden (Springer-Verlag, 2007), p. 181
D. Selmeczi, S.F. Tolic-Nørrelykke, E. Schäffer, P.H. Hagedorn, S. Mosler, K. Berg-Sørensen, N.B. Larsen, H. Flyvbjerg, Acta Phys. Pol. B38, 2407 (2007)
http://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics)
N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edition (Elsevier, 2007)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, 1999)
J.N. Pedersen, L. Li, C. Gradinaru, R.H. Austin, E.C. Cox, H. Flyvbjerg, Time-Lapse Recorded Trajectories of Motile Micro-Organisms: How to connect discrete data with continuous models (unpublished) (2015)
K.D. Girard, S.C. Kuo, D.N. Robinson, Proc. Natl. Acad. Sci. (USA), 103(7), 2103 (2006)
S. Huet, E. Karatekin, V.S. Tran, I. Fanget, S. Cribier, J.-P. Henry, Biophys. J. 91, 3542 (2006)
K. de Bruin, N. Ruthardt, K. von Gersdorff, R. Bausinger, E. Wagner, M. Ogris, C. Braeuchle, Mol. Therap. 15, 1297 (2007)
D. Arcizet, B. Meier, E. Sackmann, J.O. Rädler, D. Heinrich, Phys. Rev. Lett. 101, 248103 (2008)
M. Otten, A. Nandi, D. Arcizet, M. Gorelashvili, B. Lindner, Biophys. J. 102, 758 (2012)
A. Nandi, D. Heinrich, B. Lindner, Phys. Rev. E 86, 021926 (2012)
R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)
R. Metzler, J. Klafter, J. Phys. A: Math. Gen. 37, R161 (2004)
Y. Meroz, I.M. Sokolov, Phys. Rep. 573, 1 (2015)
D. Boyer, D.S. Dean, C. Mejía-Monasterio, G. Oshanin, J. Stat. Mech. Theory Exp. 2013, P04017 (2013)
E. Kepten, I. Bronshtein, Y. Ganini, Phys. Rev. E 87, 052713 (2013)
E. Kepten, A. Weron, G. Sikora, K. Burnecki, Y. Garini, PLoS ONE 10, e0117722 (2015)
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Vestergaard, C.L., Pedersen, J.N., Mortensen, K.I. et al. Estimation of motility parameters from trajectory data. Eur. Phys. J. Spec. Top. 224, 1151–1168 (2015). https://doi.org/10.1140/epjst/e2015-02452-5
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DOI: https://doi.org/10.1140/epjst/e2015-02452-5