The Annals of Applied Statistics

Tracking rapid intracellular movements: A Bayesian random set approach

Vasileios Maroulas and Andreas Nebenführ

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We focus on the biological problem of tracking organelles as they move through cells. In the past, most intracellular movements were recorded manually, however, the results are too incomplete to capture the full complexity of organelle motions. An automated tracking algorithm promises to provide a complete analysis of noisy microscopy data. In this paper, we adopt statistical techniques from a Bayesian random set point of view. Instead of considering each individual organelle, we examine a random set whose members are the organelle states and we establish a Bayesian filtering algorithm involving such set states. The propagated multi-object densities are approximated using a Gaussian mixture scheme. Our algorithm is applied to synthetic and experimental data.

Article information

Ann. Appl. Stat. Volume 9, Number 2 (2015), 926-949.

Received: September 2013
Revised: December 2014
First available in Project Euclid: 20 July 2015

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Multi-object Bayesian filtering cardinalized probability hypothesis density Gaussian mixture implementation monitoring intracellular movements random finite set theory finite set statistics


Maroulas, Vasileios; Nebenführ, Andreas. Tracking rapid intracellular movements: A Bayesian random set approach. Ann. Appl. Stat. 9 (2015), no. 2, 926--949. doi:10.1214/15-AOAS819.

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  • Avisar, D., Prokhnevsky, A. I., Makarova, K. S., Koonin, E. V. and Dolja, V. V. (2008). Myosin XI-K is required for rapid trafficking of Golgi stacks, peroxisomes, and mitochondria in leaf cells of Nicotiana benthamiana. Plant Physiol. 146 1098–1108.
  • Bar-Shalom, Y. and Blair, W. D. (2000). Multitarget-Multisensor Tracking: Applications and Advances. Norwood, MA, Artech House.
  • Blackman, S. and Popoli, R. (1999). Design and Analysis of Modern Tracking Systems. Artech House, Norwood, MA.
  • Brémaud, P. (1981). Point Processes and Queues: Martingale Dynamics. Springer, New York.
  • Clark, D. E., Panta, K. and Vo, B.-N. (2006). The GM-PHD filter multiple target tracker. In 9th International Conference on Information Fusion 1–8. IEEE.
  • Collings, D. A., Harper, J. D. I., Marc, J., Overall, R. and Mullen, L. R. T. (2002). Life in the fast lane: Actin-based motility of plant peroxisomes. Canadian Journal of Botany 80 430–441.
  • Corti, B. (1774). Osservazioni microscopiche sulla tremella e sulla circolazione del fluido in una pianta acquajuola. Lucca.
  • Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
  • Danuser, G. (2011). Computer vision in cell biology. Cell 147 973–978.
  • Doucet, A., de Freitas, N. and Gordon, N., eds. (2001). Sequential Monte Carlo Methods in Practice. Springer, New York.
  • Fortmann, T. E., Bar-Shalom, Y. and Scheffe, M. (1983). Sonar tracking of multiple targets using joint probabilistic data association. Oceanic Engineering, IEEE Journal of 8 173–184.
  • Gilks, W. R. and Berzuini, C. (2001). Following a moving target—Monte Carlo inference for dynamic Bayesian models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 127–146.
  • Goodman, I. R., Mahler, R. P. S. and Nguyen, H. T. (1997). Mathematics of Data Fusion. Theory and Decision Library. Series B: Mathematical and Statistical Methods 37. Kluwer Academic, Dordrecht.
  • Gordon, N. J., Salmond, D. J. and Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar and Signal Processing, IEE Proceedings F 140 107–113.
  • Gutierrez, R., Lindeboom, J. J., Paredez, A. R., Emons, A. M. C. and Ehrhardt, D. W. (2009). Arabidopsis cortical microtubules position cellulose synthase delivery to the plasma membrane and interact with cellulose synthase trafficking compartments. Nature Cell Biology 11 797–806.
  • Hamada, T., Tominaga, M., Fukaya, T., Nakamura, M., Nakano, A., Watanabe, Y., Hashimoto, T. and Baskin, T. I. (2012). RNA processing bodies, peroxisomes, golgi bodies, mitochondria, and endoplasmic reticulum tubule junctions frequently pause at cortical microtubules. Plant and Cell Physiology 53 699–798.
  • Hoffman, J. R. and Mahler, R. P. S. (2002). Multitarget miss distance and its applications. In Proceedings of the Fifth International Conference on Information Fusion 1 149–155. IEEE.
  • Hughes, J. and Fricks, J. (2011). A mixture model for quantum dot images of kinesin motor assays. Biometrics 67 588–595.
  • Hughes, J., Fricks, J. and Hancock, W. (2010). Likelihood inference for particle location in fluorescence microscopy. Ann. Appl. Stat. 4 830–848.
  • Jaqaman, K., Loerke, D., Mettlen, M., Kuwata, H., Grinstein, S., Schmidt, S. L. and Danuser, G. (2008). Robust single-particle tracking in live-cell time-lapse sequences. Nat. Methods 5 695–702.
  • Kang, K. and Maroulas, V. (2013). Drift homotopy methods for a nonGaussian filter. In 16th International Conference on Information Fusion (FUSION) 1088–1094. IEEE, Istanbul.
  • Kang, K., Maroulas, V. and Schizas, I. D. (2014). Drift homotopy particle filter for non-Gaussian multi-target tracking. In 17th International Conference on Information Fusion (FUSION) 1–7. IEEE, Salamanca.
  • Klaus, A. and Heribert, H. (2004). Reactive oxygen species: Metabolism, oxidative stress, and signal transduction. Annual Review of Plant Biology 55 373–399.
  • Liu, J. S. (2008). Monte Carlo Strategies in Scientific Computing. Springer, New York.
  • Liu, J. S. and Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. J. Amer. Statist. Assoc. 93 1032–1044.
  • Logan, D. C. and Leaver, C. J. (2000). Mitochondria-targeted GFP highlights the heterogeneity of mitochondrial shape, size and movement within living plant cells. J. Experimental Botany 51 865–871.
  • Madison, S. L. and Nebenführ, A. (2013). Understanding myosin functions in plants: Are we there yet? Preprint.
  • Mahler, R. P. S. (2003). Multitarget Bayes filtering via first-order multitarget moments. Aerospace and Electronic Systems, IEEE Transactions on 39 1152–1178.
  • Mahler, R. P. S. (2007). Statistical Multisource-Multitarget Information Fusion. Artech House, Norwood, MA.
  • Mahler, R. P. S. and Maroulas, V. (2013). Tracking spawning objects. Radar, Sonar Navigation, IET 7 321–331.
  • Maroulas, V. and Stinis, P. (2012). Improved particle filters for multi-target tracking. J. Comput. Phys. 231 602–611.
  • Møller, J. and Waagepetersen, R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes. Monographs on Statistics and Applied Probability 100. Chapman & Hall/CRC, Boca Raton, FL.
  • Nebenführ, A., Gallagher, L. A., Dunahay, T. G., Frohlick, J. A., Mazurkiewicz, A. M., Meehl, J. B. and Staehelin, L. A. (1999). Stop-and-go movements of plant Golgi stacks are mediated by the actomyosin system. Plant Physiol. 121 1127–1141.
  • Nelson, B. K., Cai, X. and Nebenführ, A. (2007). A multi-color set of in vivo organelle markers for colocalization studies in Arabidopsis and other plants. Plant Journal 51 1126–1136.
  • Ojangu, E.-L., Tanner, K., Pata, P., Järve, K., Holweg, C. L., Truve, E. and Paves, H. (2012). Myosins XI-K, XI-1, and XI-2 are required for development of pavement cells, trichomes, and stigmatic papillae in Arabidopsis. BMC Plant Biol. 12 81.
  • Paredez, A. R., Somerville, C. R. and Ehrhardt, D. W. (2006). Visualization of cellulose synthase demonstrates functional association with microtubules. Science 311 1491–1495.
  • Peremyslov, V. V., Prokhnevsky, A. I., Avisar, D. and Dolja, V. V. (2008). Two class XI myosins function in organelle trafficking and root hair development in Arabidopsis. Plant Physiol. 146 1009–1116.
  • Sbalzarini, I. F. and Koumoutsakos, P. (2005). Feature point tracking and trajectory analysis for video imaging in cell biology. J. Struct. Biol. 151 182–195.
  • Schneider, C. A., Rasband, W. S. and Eliceiri, K. W. (2012). NIH image to ImageJ: 25 years of image analysis. Nat. Methods 9 671–675.
  • Schuhmacher, D., Vo, B.-T. and Vo, B.-N. (2008). A consistent metric for performance evaluation of multi-object filters. IEEE Trans. Signal Process. 56 3447–3457.
  • Schuhmacher, D. and Xia, A. (2008). A new metric between distributions of point processes. Adv. in Appl. Probab. 40 651–672.
  • Shimmen, T. (2007). The sliding theory of cytoplasmic streaming: Fifty years of progress. J. Plant Res. 120 31–43.
  • Shimmen, T. and Yokota, E. (1994). Physiological and biochemical aspects of cytoplasmic streaming. International Review of Cytology 155 97–139.
  • Smal, I. (2009). Particle filtering methods for subcellular motion analysis. Ph.D. thesis, Erasmus Univ. Rotterdam, Rotterdam, The Netherlands.
  • Smal, I., Niessen, W. and Meijering, E. (2006). Particle filtering for multiple object tracking in molecular cell biology. In IEEE Nonlinear Statistical Signal Processing Workshop 129–132. IEEE.
  • Smal, I., Draegestein, K., Galjart, N., Niessen, W. and Meijering, E. (2008). Particle filtering for multiple object tracking in dynamic fluorescence microscopy images: Application to microtubule growth analysis. Medical Imaging, IEEE Transactions on 27 789–804.
  • Snyder, C., Bengtsson, T., Bickel, P. and Anderson, J. (2008). Obstacles to high-dimensional particle filtering. Mon. Wea. Rev. 136 4629–4640.
  • Tominaga, M., Kojima, H., Yokota, E., Orii, H., Nakamori, R., Katayama, E., Nason, M., Shimmen, T. and Oiwa, K. (2003). Higher plant myosin XI moves processively on actin with 35 nm steps at high velocity. EMBO Journal 22 1263–1272.
  • Van Gestel, K., Köhler, R. H. and Verbelen, J.-P. (2002). Plant mitochondria move on F-actin, but their positioning in the cortical cytoplasm depends on both F-actin and microtubules. J. Experimental Botany 53 659–667.
  • Vick, J. K. and Nebenführ, A. (2012). Putting on the breaks: Regulation of organelle movements in plant cellst. Journal of Integrative Plant Biology 54 868–874.
  • Vo, B.-T., Vo, B.-N. and Cantoni, A. (2007). Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Trans. Signal Process. 55 3553–3567.
  • Weare, J. (2009). Particle filtering with path sampling and an application to a bimodal ocean current model. J. Comput. Phys. 228 4312–4331.