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Measuring Spatiotemporal Dependencies in Bivariate Temporal Random Sets with Applications to Cell Biology
September 2008 (vol. 30 no. 9)
pp. 1659-1671
Analyzing spatio-temporal dependencies between different types of events is highly relevant to numerous biological phenomena (e.g. signalling and trafficking) especially as advances in probes and microscopy have facilitated imaging of dynamic processes in living cells. For many types of events, the segmented areas can overlap spatially and temporally forming random clumps. In this paper, we model binary image sequences of two different event types as a realization of a bivariate temporal random set and propose a non-parametric approach to quantify spatial and spatio-temporal interrelations using the pair-correlation, cross-covariance and the Ripley ${\mathbb K}$ functions. Based on these summary statistics we propose a randomization procedure to test independence between event types by applying random toroidal shifts and Monte Carlo tests. A simulation study assessed the performance of the proposed estimators and showed that these statistics capture the spatio-temporal dependencies accurately. The estimation of the spatio-temporal interval of interactions was also obtained. The method was successfully applied to analyze the interdependencies of several endocytic proteins using image sequences of living cells and validated the procedure as a new way to automatically quantify dependencies between proteins in a formal and robust manner.

[1] G. Ayala, J. Ferrandiz, and F. Montes, “Boolean Models: Maximum Likelihood Estimation from Circular Clumps,” Biometrical J., vol. 32, pp. 73-78, 1990.
[2] G. Ayala, R. Sebastian, M.E. Díaz, E. Díaz, R. Zoncu, and D. Toomre, “Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, pp. 1707-1712, 2006.
[3] K.D. Bellve, D. Leonard, C. Standley, L.M. Lifshitz, R.A. Tuft, A. Hayakawa, S. Corvera, and K.E. Fogarty, “Plasma Membrane Domains Specialized for Clathrin-Mediated Endocytosis in Primary Cells,” The J. Biological Chemistry, vol. 281, no. 23, pp.16139-16146, 2006.
[4] T.J. Brett and L.M. Traub, “Molecular Structures of Coat and Coat-Associated Proteins: Function Follows Form,” Current Opinion in Cell Biology, vol. 18, no. 4, pp. 395-406, 2006.
[5] F.M. Brodsky, C.Y. Chen, C. Knuehl, M.C. Towler, and D.E. Wakeham, “Biological Basket Weaving: Formation and Function of Clathrin-Coated Vesicles,” Ann. Rev. Cell and Developmental Biology, vol. 17, pp. 517-568, 2001.
[6] H. Chen, S. Fre, V.I. Slepnev, M.R. Capua, K. Takei, M.H. Butler, P.P. Di Fiore, and P. De Camilli, “Epsin Is an EH-Domain-Binding Protein Implicated in Clathrin-Mediated Endocytosis,” Nature, vol. 394, no. 6695, pp. 793-797, 1998.
[7] N.A.C. Cressie, Statistics for Spatial Data, revised ed. John Wiley & Sons, 1993.
[8] P.J. Diggle, Statistical Analysis of Spatial Point Patterns, second ed. Ar nold, 2003.
[9] M.A. Edeling et al., “Life of a Clathrin Coat: Insights from Clathrin and AP Structures,” Nature Reviews Molecular Cellular Biology, vol. 7, no. 1, pp. 32-44, 2006.
[10] M. Ehrlich, W. Boll, A. van Oijen, R. Hariharan, K. Chandran, M.L. Nibert, and T. Kirchhausen, “Endocytosis by Random Initiation and Stabilization of Clathrin-Coated Pits,” Cell, vol. 118, pp. 591-605, 2004.
[11] A.E. Engqvist-Goldstein, R.A. Warren, M.M. Kessels, J.H. Keen, J. Heuser, and D.G. Drubin, “The Actin-Binding Protein HIP1r Associates with Clathrin During Early Stages of Endocytosis and Promotes Clathrin Assembly In Vitro,” The J. Cell Biology, vol. 154, no. 6, pp. 1209-1223, 2001.
[12] I. Epifanio and G. Ayala, “A Random Set View of Texture Classification,” IEEE Trans. Image Processing, vol. 11, no. 8, pp. 859-867, 2002.
[13] M.G. Ford et al., “Curvature of Clathrin-Coated Pits Driven by Epsin,” Nature, vol. 419, no. 6905, pp. 361-366, 2002.
[14] R. Foxall and A.J. Baddeley, “Nonparametric Measures of Association between a Spatial Point Process and a Random Set with Geological Applications Part 2,” Applied Statistics, vol. 51, pp.165-182, 2002.
[15] D.R. Goucher, S.M. Wincovitch, S.H. Garfield, K.M. Carbone, and T.H. Malik, “A Quantitative Determination of Multi-Protein Interactions by the Analysis of Confocal Images Using a Pixel-by-Pixel Assessment Algorithm,” Bioinformatics, vol. 21, pp. 3248-3254, 2005.
[16] M. Kaksonen, C.P. Toret, and D.G. Drubin, “A Modular Design for the Clathrin- and Actin-Mediated Endocytosis Machinery,” Cell, vol. 123, pp. 305-320, 2005.
[17] G. Matheron, Random Sets and Integral Geometry. Wiley, 1975.
[18] C.J. Merrifield et al., “Coupling between Clathrin-Coated-Pit Invagination, Cortactin Recruitment, and Membrane Scission Observed in Live Cells,” Cell, vol. 121, no. 4, pp. 593-606, 2005.
[19] C.J. Merrifield, M.E. Feldman, L. Wan, and W. Almers, “Imaging Actin and Dynamin Recruitment During Invagination of Single Clathrin-Coated Pits,” Nature Cell Biology, vol. 4, pp. 691-698, 2002.
[20] M. Metzler, V. Legendre-Guillemin, L. Gan, V. Chopra, A. Kwok, P.S. McPherson, and M.R. Hayden, “Hip1 Functions in Clathrin-Mediated Endocytosis through Binding to Clathrin and Adaptor Protein 2,” The J. Biological Chemistry, vol. 276, no. 42, pp. 39271-39276, 2001.
[21] I. Molchanov, Theory of Random Sets (Probability and Its Applications). Springer, 2005.
[22] R.M. Perera, R. Zoncu, L. Lucast, P. De Camilli, and D. Toomre, “Two Synaptojanin 1 Isoforms Are Recruited to Clathrin-Coated Pits at Different Stages,” Proc. Nat'l Academy of Sciences, vol. 103, pp. 19332-19337, 2006.
[23] J.Z. Rappoport and S.M. Simon, “Real-Time Analysis of Clathrin-Mediated Endocytosis during Cell Migration,” J. Cell Science, vol. 116, no. 5, pp. 847-855, 2003.
[24] B.D. Ripley, Statistical Inference for Spatial Processes. Cambridge Univ. Press, 1988.
[25] R. Sebastian, E. Díaz, G. Ayala, M.E. Díaz, R. Zoncu, and D. Toomre, “Studying Endocytosis in Space and Time by Means of Temporal Boolean Models,” Pattern Recognition, vol. 39, pp. 2175-2185, 2006.
[26] J.P. Serra, Image Analysis and Mathematical Morphology, vol. 1. Academic Press, 1982.
[27] V.I. Slepnev and P. De Camilli, “Accessory Factors in Clathrin-Dependent Synaptic Vesicle Endocytosis,” Nature Reviews Neuroscience, vol. 1, no. 3, pp. 161-172, 2000.
[28] D. Stoyan, W.S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, second ed. Wiley, 1995.
[29] D. Stoyan and H. Stoyan, Fractals, Random Shapes, and Point Fields: Methods of Geometrical Statistics. Wiley, 1994.
[30] D. Toomre and D.J. Manstein, “Lighting Up the Cell Surface with Evanescent Wave Microscopy,” Trends in Cell Biology, vol. 11, pp.298-303, 2001.
[31] M.N.M. van Lieshout and A.J. Baddeley, “Indices of Dependence between Types in Multivariate Point Patterns,” Scandinavian J. Statistics, vol. 26, pp. 511-532, 1999.
[32] P.J. Yao, I. Bushlin, and R.S. Petralia, “Partially Overlapping Distribution of Epsin1 and Hip1 at the Synapse: Analysis by Immunoelectron Microscopy,” The J. Comparative Neurology, vol. 494, no. 2, pp. 368-379, 2006.
[33] R. Zoncu, R.M. Perera, R. Sebastian, F. Nakatsu, H. Chen, T. Balla, G. Ayala, D. Toomre, and P.V. De Camilli, “Loss of Endocytic Clathrin-Coated Pits upon Acute Depletion of Phosphatidylinositol 4, 5-Bisphosphate,” Proc. Nat'l Academy of Sciences, vol. 104, no. 10, pp. 3793-3798, 2007.

Index Terms:
Pattern analysis, Stochastic processes, Image models, Video analysis, Applications, Biology and genetics
Ester Díaz, Rafael Sebastian, Guillermo Ayala, María Elena Díaz, Roberto Zoncu, Derek Toomre, Stéphane Gasman, "Measuring Spatiotemporal Dependencies in Bivariate Temporal Random Sets with Applications to Cell Biology," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 9, pp. 1659-1671, Sept. 2008, doi:10.1109/TPAMI.2007.70821
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