Tempered processes in modelling of single-particle tracking experiments

• Autorzy: Burnecki Krzysztof , Rogalska Aleksandra

Identyfikatory

DOI

10.14708/ma.v52i1.7247

Warianty tytułu

PL

Temperowane procesy w modelowaniu danych z eksperymentów śledzenia pojedynczych cząstek w komórkach biologicznych

• Języki publikacji: EN

Abstrakty

EN

In this paper, we check the usefulness of the autoregressive tempered fractionally integrated moving average (ARTFIMA) processes to modelling of single-particle tracking (SPT) experiments. We illustrate the main properties of the discrete-time tempered model and compare them to the non-tempered ARFIMA. The main part of the paper is devoted to an extensive statistical analysis of the ARTFIMA and ARFIMA processes fitted to single-particle tracking data from different biological experiments. The results show that there are experiments where tempering provides a significant improvement over the classical approach.

PL

W niniejszej pracy zbadano przydatność temperowanych procesów ARTFIMA (ang. autoregressive tempered fractionally integrated moving average) do modelowania danych z eksperymentów śledzenia pojedynczych cząstek (ang. single-particle tracking, SPT) w komórkach biologicznych. Przedstawiono główne właściwości modelu ARTFIMA oraz porównano je z właściwościami nietemperowanego modelu ARFIMA. Główna część pracy jest poświęcona rozbudowanej analizie statystycznej procesów ARTFIMA i ARFIMA w kontekście modelowania danych SPT z różnych eksperymentów biologicznych. Wyniki pokazują, że w niektórych eksperymentach temperowanie zapewnia znaczną poprawę w porównaniu do podejścia klasycznego. W niniejszej pracy sprawdzono przydatność temperowanych procesów ARTFIMA (ang. autoregressive tempered fractionally integrated moving average) do modelowania danych z eksperymentów śledzenia pojedynczych cząstek (ang. single-particle tracking, SPT) w komórkach biologicznych. Zilustrowano główne własności modelu ARTFIMA i porównano je z własnościami nietemperowanego modelu ARFIMA. Główna część pracy poświęca jest rozbudowanej analizie statystycznej procesów ARTFIMA i ARFIMA w kontekście modelowania danych SPT z różnych eksperymentów biologicznych. Wyniki pokazują, że istnieją eksperymenty, w których temperowanie zapewnia znaczną poprawę w porównaniu z podejściem klasycznym.

Słowa kluczowe

EN

ARTFIMA process; tempered fractional Brownian motion; single-particle tracking

PL

temperowany ułamkowy ruch Browna; eksperyment śledzenia pojedynczych cząstek; proces ARTFIMA

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2024
• Tom: Vol. 52, no. 1
• Strony: 27--84
• Opis fizyczny: Bibliogr. 33 poz., wykr.

Twórcy

autor

Burnecki Krzysztof

• Wrocław University of Science and Technology Faculty of Pure and Applied Mathematics Hugo Steinhaus Center Wybrzeże Wyspiańskiego 27, 50–370 Wrocław

• https://orcid.org/0000-0002-1754-4472

autor

Rogalska Aleksandra

• Wrocław University of Science and Technology Faculty of Pure and Applied Mathematics Wybrzeże Wyspiańskiego 27, 50–370 Wrocław

Bibliografia

• [1] E.J. Akin, L. Solé, B. Johnson, M. el Beheiry, J.-B. Masson, D. Krapf, and M.M. Tamkun, Single-molecule imaging of nav1.6 on the surface of hippocampal neurons reveals somatic nanoclusters, Biophysical Journal 111 (2016), no. 6, 1235-1247. Cited on p. 33.
• [2] E. Azmoodeh, Y. Mishura, and F. Sabzikar, How does tempering affect the local and global properties of fractional Brownian motion?, Journal of Theoretical Probability 35 (2022), 1-44. Cited on p. 32.
• [3] M. Balcerek, H. Loch-Olszewska, J.A. Torreno-Pina, M.F. Garcia-Parajo, A. Weron, C. Manzo, and K. Burnecki, Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model, Phys. Chem. Chem. Phys. 21 (2019), 3114-3121. Cited on p. 28.
• [4] G.E.P. Box and D.A. Pierce, Distribution of residual autocorrelations in autoregressive-integrated moving average time series models, Journal of the American Statistical Association 65 (1970), 1509-1526. Cited on p. 33.
• [5] I. Bronstein, Y. Israel, E. Kepten, S. Mai, Y. Shav-Tal, E. Barkai, and Y. Garini, Transient anomalous diffusion of telomeres in the nucleus of mammalian cells, Phys. Rev. Lett. 103 (2009), 018102. Cited on p. 33.
• [6] K. Burnecki, FARIMA processes with application to biophysical data, Journal of Statistical Mechanics: Theory and Experiment 2012 (2012), no. 05, P05015. Cited on p. 28.
• [7] K. Burnecki, M. Muszkieta, G. Sikora, and A. Weron, Statistical modelling of subdiffusive dynamics in the cytoplasm of living cells: A FARIMA approach, Europhysics Letters 98 (2012), no. 1, 10004. Cited on p. 28.
• [8] K. Burnecki, G. Sikora, and A. Weron, Fractional process as a unified model for subdiffusive dynamics in experimental data., Phys. Rev. E 86 (2012), 041912. Cited on p. 28.
• [9] K. Burnecki, G. Sikora, A. Weron, M.M. Tamkun, and D. Krapf, Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models, Physical Review E 99 (2019), 012101. Cited on p. 28.
• [10] K. Burnecki and A. Weron, Fractional Lévy stable motion can model subdiffusive dynamics, Phys. Rev. E 82 (2010), no. 2, 021130. Cited on p. 28.
• [11] I. Golding and E.C. Cox, Physical nature of bacterial cytoplasm, Physical Review Letters 96 (2006), 098102. Cited on p. 33.
• [12] J.-H. Jeon, H.M.-S. Monne, M. Javanainen, and R. Metzler, Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins, Phys. Rev. Lett. 109 (2012), 188103. Cited on p. 28.
• [13] J.S. Kabala, K. Burnecki, and F. Sabzikar, Tempered linear and nonlinear time series models and their application to heavy-tailed solar flare data, Chaos 31 (2021), 113124. Cited on pp. 28 and 41.
• [14] G.M. Ljung and G.E.P. Box, On a measure of lack of fit in time series models, Biometrika 65 (1978), 297-303. Cited on p. 33.
• [15] M. Magdziarz and A. Weron, Fractional Langevin equation with alphastable noise. A link to fractional ARIMA time series, Studia Math. 181 (2007), 47-60. Cited on p. 28.
• [16] B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968), no. 4, 422-437. Cited on p. 28.
• [17] C. Manzo and M.F. Garcia-Parajo, A review of progress in single particle tracking: from methods to biophysical insights, Reports on Progress in Physics 78 (2015), no. 12, 124601. Cited on p. 27.
• [18] Y. Mardoukhi, J.-H. Jeon, A.V. Chechkin, and R. Metzler, Fluctuations of random walks in critical random environments, Phys. Chem. Chem. Phys. 20 (2018), no. 31, 20427-20438. Cited on p. 28.
• [19] A.I. McLeod and W.K. Li, Diagnostic checking ARMA time series models using squared-residual autocorrelations, Journal of Time Series Analysis 4 (1983), 269-273. Cited on p. 34.
• [20] M.M. Meerschaert, F. Sabzikar, M.S. Phanikumar, and A. Zeleke, Tempered fractional time series model for turbulence in geophysical flows, J. Stat. Mech. 2014 (2014), no. 9, P09023. Cited on p. 28.
• [21] R. Metzler, J.-H.Jeon, A.G. Cherstvy, and E. Barkai, Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Phys. Chem. Chem. Phys. 16 (2014), no. 44, 24128-24164. Cited on p. 27.
• [22] R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep. 339 (2000), no. 1, 1-77. Cited on p. 27.
• [23] D. Molina-Garcia, T. Sandev, H. Safdari, G. Pagnini, A. Chechkin, and R. Metzler, Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers, New J. Phys. 20 (2018), 10327. Cited on p. 28.
• [24] F. Sabzikar, J. Kabala, and K. Burnecki, Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model, Journal of Physics A: Mathematical and Theoretical 55 (2022), no. 17, 174002. Cited on pp. 28, 32, and 41.
• [25] F. Sabzikar, A.I. McLeod, and M.M. Meerschaert, Parameter estimation for ARTFIMA time series, J. Statist. Plann. Inference 200 (2019), 129-145. Cited on pp. 28, 29, 30, and 31.
• [26] F. Sabzikar, M.M. Meerschaert, and J. Chen, Tempered fractional calculus, J. Comput. Phys. 293 (2015), 14-28. Cited on p. 28.
• [27] F. Sabzikar and D. Surgailis, Invariance principles for tempered fractionally integrated processes, Stochastic Process. Appl. 128 (2018), 3419-3438. Cited on p. 28.
• [28] F. Sabzikar and D. Surgailis, Tempered fractional Brownian and stable motions of second kind, Statistics & Probability Letters 132 (2018), 17-27. Cited on p. 32.
• [29] S. Sadegh, J.L. Higgins, P.C. Mannion, M.M. Tamkun, and D. Krapf, Plasma membrane is compartmentalized by a self-similar cortical actin meshwork, Physical Review X 7 (2017), 011031. Cited on p. 33.
• [30] E. Said and D. A. Dickey, Testing for unit roots in autoregressive-moving average models of unknown order, Biometrika 71 (1984), 599-607. Cited on p. 33.
• [31] S.S. Shapiro and M.B. Wilk, An analysis of variance test for normality (complete samples), Biometrika 52 (1965), no. 3-4, 591-611. Cited on p. 34.
• [32] J. Ślęzak, K. Burnecki, and R. Metzler, Random coefficient autoregressive processes describe brownian yet non-Gaussian diffusion in heterogeneous systems, New J. Phys. 21 (2019), no. 7, 073056. Cited on p. 28.
• [33] S. Stoev and M.S. Taqqu, Simulation methods for linear fractional stable motion and FARIMA using the Fast Fourier Transform, Fractals 12 (2004), no. 01, 95-121. Cited on p. 28.