Moran's I quantifies spatio-temporal pattern formation in neural imaging data

C. Schmal, J. Myung, H. Herzel, G. Bordyugov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Motivation Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus. Results We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion.
Original languageEnglish
Pages (from-to)3072-3079
Number of pages8
JournalBioinformatics
Volume33
Issue number19
DOIs
Publication statusPublished - 2017
Externally publishedYes

Fingerprint

Spatio-temporal Patterns
Pattern Formation
Suprachiasmatic Nucleus
Quantify
Imaging
Imaging techniques
Order Parameter
Nucleus
Circadian Clocks
Spatial Analysis
Spatial Autocorrelation
Autocorrelation
Hypothalamus
Significance level
Clocks
Time series
Brain
Statistical Significance
Spatial Correlation
Length Scale

Keywords

  • animal
  • brain
  • image processing
  • male
  • mouse
  • physiology
  • spatial analysis
  • suprachiasmatic nucleus
  • Animals
  • Brain
  • Image Processing, Computer-Assisted
  • Male
  • Mice
  • Spatial Analysis
  • Suprachiasmatic Nucleus

Cite this

Moran's I quantifies spatio-temporal pattern formation in neural imaging data. / Schmal, C.; Myung, J.; Herzel, H.; Bordyugov, G.

In: Bioinformatics, Vol. 33, No. 19, 2017, p. 3072-3079.

Research output: Contribution to journalArticle

Schmal, C. ; Myung, J. ; Herzel, H. ; Bordyugov, G. / Moran's I quantifies spatio-temporal pattern formation in neural imaging data. In: Bioinformatics. 2017 ; Vol. 33, No. 19. pp. 3072-3079.
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title = "Moran's I quantifies spatio-temporal pattern formation in neural imaging data",
abstract = "Motivation Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus. Results We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion.",
keywords = "animal, brain, image processing, male, mouse, physiology, spatial analysis, suprachiasmatic nucleus, Animals, Brain, Image Processing, Computer-Assisted, Male, Mice, Spatial Analysis, Suprachiasmatic Nucleus",
author = "C. Schmal and J. Myung and H. Herzel and G. Bordyugov",
note = "引用次數:2 Export Date: 18 September 2018 CODEN: BOINF 通訊地址: Schmal, C.; Institute for Theoretical Biology, Charit{\'e} Universit{\"a}tsmedizin and Humboldt Universit{\"a}tGermany; 電子郵件: christoph.schmal@charite.de 出資詳情: 16H01652 出資詳情: 16K08538 出資詳情: BAK-F1-2017 出資詳情: BO 3612/2-1, DFG, Deutsche Forschungsgemeinschaft 出資詳情: Joachim Herz Stiftung 出資正文: This work has been supported by the Deutsche Forschungsgemeinschaft [grant number BO 3612/2-1]. CS acknowledges support from the Joachim Herz Stiftung. JM acknowledges support from JSPS for KAKENHI grants [grant numbers 16H01652 and 16K08538] and Berliner Antike-Kolleg [BAK-F1-2017]. 參考文獻: Abel, J.H., Functional network inference of the suprachiasmatic nucleus (2016) Proc. Natl. Acad. Sci. USA, 113, pp. 4512-4517; Acebr{\'o}n, J.A., The kuramoto model: A simple paradigm for synchronization phenomena (2005) Rev. Mod. Phys, 77, pp. 137-185; Aton, S.J., Herzog, E.D., Come together right now: Synchronization of rhythms in a mammalian circadian clock (2005) Neuron, 48, pp. 531-534; Aton, S.J., Vasoactive intestinal polypeptide mediates circadian rhythmicity and synchrony in mammalian clock neurons (2005) Nat. Neurosci, 8, pp. 476-483; Azzi, A., Network dynamics mediate circadian clock plasticity (2017) Neuron, 93, pp. 1-10; Bloch, G., Socially synchronized circadian oscillators (2013) Proc. R. Soc. B, 280, p. 20130035; Cliff, A.D., Ord, K., Evaluating the percentage points of a spatial autocorrelation coefficient (1971) Geogr. Anal, 3, pp. 51-62; Cliff, A.D., Ord, K., (1981) Spatial Processes: Models & Applications, , Pion Limited, London; Cohen, J.D., Computational approaches to fMRI analysis (2017) Nat. Neurosci, 20, pp. 304-313; Ermentrout, B., Neural networks as spatio-temporal pattern-forming systems (1998) Rep. Prog. Phys, 61, p. 353; Ermentrout, B., Ko, T.-W., Delays and weakly coupled neuronal oscillators (2009) Phil. Trans. R. Soc. A, 367, pp. 1097-1115; Ermentrout, G.B., Kopell, N., Frequency plateaus in a chain of weakly coupled oscillators i (1984) SIAM J Math. Anal, 15, pp. 215-237; Evans, J., Dynamic interactions mediated by nonredundant signaling mechanisms couple circadian clock neurons (2013) Neuron, 80, pp. 973-983; Evans, J.A., Intrinsic regulation of spatiotemporal organization within the suprachiasmatic nucleus (2011) Plos One, 6, p. e15869; Foley, N.C., Characterization of orderly spatiotemporal patterns of clock gene activation in mammalian suprachiasmatic nucleus (2011) Eur. J. Neurosci, 33, pp. 1851-1865; Fukuda, H., Quantitative analysis of phase wave of gene expression in the mammalian central circadian clock network (2011) Plos One, 6, p. e23568; Getis, A., Reflections on spatial autocorrelation (2007) Reg. Sci. Urban Econ, 37, pp. 491-496; Goodchild, M.F., (1986) Spatial Autocorrelation: Concepts and Techniques in Modern Geography, , Geo Books, Norwich; Herzog, E.D., Temporal precision in the mammalian circadian system: A reliable clock from less reliable neurons (2004) J. Biol. Rhythms, 19, pp. 35-46; Horikawa, K., Noise-resistant and synchronized oscillation of the segmentation clock (2006) Nature, 441, pp. 719-723; Iannella, N.L., Spike timing-dependent plasticity as the origin of the formation of clustered synaptic efficacy engrams (2010) Front. Comput. Neurosci, 4, p. 21; Kang, K., Mexican hats and pinwheels in visual cortex (2003) Proc. Natl. Acad. Sci. USA, 100, pp. 2848-2853; Kuhlman, S.J., GFP fluorescence reports Period 1 circadian gene regulation in the mammalian biological clock (2000) Neuroreport, 11, pp. 1479-1482; Kuramoto, Y., Self-entrainment of a population of coupled non-linear oscillators (1975) International Symposium on Mathematical Problems in Theoretical Physics Number 39 in Lecture Notes in Physics, pp. 420-422. , ArakiP.H. (ed Springer, Berlin, Heidelberg; Kuramoto, Y., Chemical oscillations (1984) Waves, and Turbulence, 19. , Springer Science & Business Media, Berlin-Heidelberg-New York-Tokyo; Lee, Y.-H., (2015) Spatial and Temporal Analysis of Glutamate Receptor Localisation at the Drosophila Neuromuscular Junction, , Dissertation. Humboldt-Universit{\"a}t zu Berlin, Lebenswissenschaftliche Fakult{\"a}t, Berlin, Germany; Liu, A.C., Intercellular coupling confers robustness against mutations in the SCN circadian clock network (2007) Cell, 129, pp. 605-616; Massimini, M., The sleep slow oscillation as a traveling wave (2004) J. Neurosci, 24, pp. 6862-6870; Moore, E.F., Machine models of self-reproduction (1962) Math. Problems Biol. Sci. Proc. Syrup. Appl. Math, 14, pp. 17-33; Moran, P.A., Notes on continuous stochastic phenomena (1950) Biometrika, 37, pp. 17-23; Muldoon, S.F., Spatially clustered neuronal assemblies comprise the microstructure of synchrony in chronically epileptic networks (2013) Proc. Natl. Acad. Sci. USA, 110, pp. 3567-3572; Myung, J., Period coding of Bmal1 oscillators in the suprachiasmatic nucleus (2012) J. Neurosci, 32, pp. 8900-8918; Myung, J., GABA-mediated repulsive coupling between circadian clock neurons in the SCN encodes seasonal time (2015) Proc. Natl. Acad. Sci. USA, 112, pp. E3920-E3929; Reppert, S.M., Weaver, D.R., Coordination of circadian timing in mammals (2002) Nature, 418, pp. 935-941; Robinson, B., Stochastic subcellular organization of dense-core vesicles revealed by point pattern analysis (2016) Biophys. J., 111, pp. 852-863; Shinohara, K., Effects of gap junction blocker on vasopressin and vasoactive intestinal polypeptide rhythms in the rat suprachiasmatic nucleus in vitro (2000) Neurosci. Res, 38, pp. 43-47; Sokal, R.R., Oden, N.L., Spatial autocorrelation in: Biology 1 methodology (1978) Biol. J. Linn. Soc, 10, pp. 199-228; Sokal, R.R., Oden, N.L., (1978) Spatial Autocorrelation in Biology, 2; Some biological implications and four applications of evolutionary and ecological interest Biol. J. Linn. Soc, 10, pp. 229-249; St. John, P.C., Doyle, F.J., Quantifying stochastic noise in cultured circadian reporter cells (2015) Plos Comput. Biol, 11, p. e1004451; Steyn-Ross, M.L., Interacting turing-hopf instabilities drive symmetry-breaking transitions in a mean-field model of the cortex: A mechanism for the slow oscillation (2013) Phys. Rev, 10 (3), p. 021005; Taylor, S.R., Resynchronization dynamics reveal that the ventral entrains the dorsal suprachiasmatic nucleus (2016) J. Biol. Rhythms, 32, pp. 35-47; Tsiairis, C., Aulehla, A., Self-organization of embryonic genetic oscillators into spatiotemporal wave patterns (2016) Cell, 164, pp. 656-667; VanderLeest, H.T., Seasonal encoding by the circadian pacemaker of the SCN (2007) Curr. Biol, 17, pp. 468-473; Webb, A.B., Intrinsic nondeterministic circadian rhythm generation in identified mammalian neurons (2009) Proc. Natl. Acad. Sci. USA, 106, pp. 16493-16498; Yamaguchi, S., Synchronization of cellular clocks in the suprachiasmatic nucleus (2003) Science, 302, pp. 1408-1412; Yoo, S.-H., Period2: Luciferase real-time reporting of circadian dynamics reveals persistent circadian oscillations in mouse peripheral tissues (2004) Proc. Natl. Acad. Sci. USA, 101, pp. 5339-5346",
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pages = "3072--3079",
journal = "Bioinformatics",
issn = "1367-4803",
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}

TY - JOUR

T1 - Moran's I quantifies spatio-temporal pattern formation in neural imaging data

AU - Schmal, C.

AU - Myung, J.

AU - Herzel, H.

AU - Bordyugov, G.

N1 - 引用次數:2 Export Date: 18 September 2018 CODEN: BOINF 通訊地址: Schmal, C.; Institute for Theoretical Biology, Charité Universitätsmedizin and Humboldt UniversitätGermany; 電子郵件: christoph.schmal@charite.de 出資詳情: 16H01652 出資詳情: 16K08538 出資詳情: BAK-F1-2017 出資詳情: BO 3612/2-1, DFG, Deutsche Forschungsgemeinschaft 出資詳情: Joachim Herz Stiftung 出資正文: This work has been supported by the Deutsche Forschungsgemeinschaft [grant number BO 3612/2-1]. CS acknowledges support from the Joachim Herz Stiftung. JM acknowledges support from JSPS for KAKENHI grants [grant numbers 16H01652 and 16K08538] and Berliner Antike-Kolleg [BAK-F1-2017]. 參考文獻: Abel, J.H., Functional network inference of the suprachiasmatic nucleus (2016) Proc. Natl. Acad. Sci. USA, 113, pp. 4512-4517; Acebrón, J.A., The kuramoto model: A simple paradigm for synchronization phenomena (2005) Rev. Mod. Phys, 77, pp. 137-185; Aton, S.J., Herzog, E.D., Come together right now: Synchronization of rhythms in a mammalian circadian clock (2005) Neuron, 48, pp. 531-534; Aton, S.J., Vasoactive intestinal polypeptide mediates circadian rhythmicity and synchrony in mammalian clock neurons (2005) Nat. Neurosci, 8, pp. 476-483; Azzi, A., Network dynamics mediate circadian clock plasticity (2017) Neuron, 93, pp. 1-10; Bloch, G., Socially synchronized circadian oscillators (2013) Proc. R. Soc. B, 280, p. 20130035; Cliff, A.D., Ord, K., Evaluating the percentage points of a spatial autocorrelation coefficient (1971) Geogr. Anal, 3, pp. 51-62; Cliff, A.D., Ord, K., (1981) Spatial Processes: Models & Applications, , Pion Limited, London; Cohen, J.D., Computational approaches to fMRI analysis (2017) Nat. Neurosci, 20, pp. 304-313; Ermentrout, B., Neural networks as spatio-temporal pattern-forming systems (1998) Rep. Prog. Phys, 61, p. 353; Ermentrout, B., Ko, T.-W., Delays and weakly coupled neuronal oscillators (2009) Phil. Trans. R. Soc. A, 367, pp. 1097-1115; Ermentrout, G.B., Kopell, N., Frequency plateaus in a chain of weakly coupled oscillators i (1984) SIAM J Math. Anal, 15, pp. 215-237; Evans, J., Dynamic interactions mediated by nonredundant signaling mechanisms couple circadian clock neurons (2013) Neuron, 80, pp. 973-983; Evans, J.A., Intrinsic regulation of spatiotemporal organization within the suprachiasmatic nucleus (2011) Plos One, 6, p. e15869; Foley, N.C., Characterization of orderly spatiotemporal patterns of clock gene activation in mammalian suprachiasmatic nucleus (2011) Eur. J. Neurosci, 33, pp. 1851-1865; Fukuda, H., Quantitative analysis of phase wave of gene expression in the mammalian central circadian clock network (2011) Plos One, 6, p. e23568; Getis, A., Reflections on spatial autocorrelation (2007) Reg. Sci. Urban Econ, 37, pp. 491-496; Goodchild, M.F., (1986) Spatial Autocorrelation: Concepts and Techniques in Modern Geography, , Geo Books, Norwich; Herzog, E.D., Temporal precision in the mammalian circadian system: A reliable clock from less reliable neurons (2004) J. Biol. Rhythms, 19, pp. 35-46; Horikawa, K., Noise-resistant and synchronized oscillation of the segmentation clock (2006) Nature, 441, pp. 719-723; Iannella, N.L., Spike timing-dependent plasticity as the origin of the formation of clustered synaptic efficacy engrams (2010) Front. Comput. Neurosci, 4, p. 21; Kang, K., Mexican hats and pinwheels in visual cortex (2003) Proc. Natl. Acad. Sci. USA, 100, pp. 2848-2853; Kuhlman, S.J., GFP fluorescence reports Period 1 circadian gene regulation in the mammalian biological clock (2000) Neuroreport, 11, pp. 1479-1482; Kuramoto, Y., Self-entrainment of a population of coupled non-linear oscillators (1975) International Symposium on Mathematical Problems in Theoretical Physics Number 39 in Lecture Notes in Physics, pp. 420-422. , ArakiP.H. (ed Springer, Berlin, Heidelberg; Kuramoto, Y., Chemical oscillations (1984) Waves, and Turbulence, 19. , Springer Science & Business Media, Berlin-Heidelberg-New York-Tokyo; Lee, Y.-H., (2015) Spatial and Temporal Analysis of Glutamate Receptor Localisation at the Drosophila Neuromuscular Junction, , Dissertation. Humboldt-Universität zu Berlin, Lebenswissenschaftliche Fakultät, Berlin, Germany; Liu, A.C., Intercellular coupling confers robustness against mutations in the SCN circadian clock network (2007) Cell, 129, pp. 605-616; Massimini, M., The sleep slow oscillation as a traveling wave (2004) J. Neurosci, 24, pp. 6862-6870; Moore, E.F., Machine models of self-reproduction (1962) Math. Problems Biol. Sci. Proc. Syrup. Appl. Math, 14, pp. 17-33; Moran, P.A., Notes on continuous stochastic phenomena (1950) Biometrika, 37, pp. 17-23; Muldoon, S.F., Spatially clustered neuronal assemblies comprise the microstructure of synchrony in chronically epileptic networks (2013) Proc. Natl. Acad. Sci. USA, 110, pp. 3567-3572; Myung, J., Period coding of Bmal1 oscillators in the suprachiasmatic nucleus (2012) J. Neurosci, 32, pp. 8900-8918; Myung, J., GABA-mediated repulsive coupling between circadian clock neurons in the SCN encodes seasonal time (2015) Proc. Natl. Acad. Sci. USA, 112, pp. E3920-E3929; Reppert, S.M., Weaver, D.R., Coordination of circadian timing in mammals (2002) Nature, 418, pp. 935-941; Robinson, B., Stochastic subcellular organization of dense-core vesicles revealed by point pattern analysis (2016) Biophys. J., 111, pp. 852-863; Shinohara, K., Effects of gap junction blocker on vasopressin and vasoactive intestinal polypeptide rhythms in the rat suprachiasmatic nucleus in vitro (2000) Neurosci. Res, 38, pp. 43-47; Sokal, R.R., Oden, N.L., Spatial autocorrelation in: Biology 1 methodology (1978) Biol. J. Linn. Soc, 10, pp. 199-228; Sokal, R.R., Oden, N.L., (1978) Spatial Autocorrelation in Biology, 2; Some biological implications and four applications of evolutionary and ecological interest Biol. J. Linn. Soc, 10, pp. 229-249; St. John, P.C., Doyle, F.J., Quantifying stochastic noise in cultured circadian reporter cells (2015) Plos Comput. Biol, 11, p. e1004451; Steyn-Ross, M.L., Interacting turing-hopf instabilities drive symmetry-breaking transitions in a mean-field model of the cortex: A mechanism for the slow oscillation (2013) Phys. Rev, 10 (3), p. 021005; Taylor, S.R., Resynchronization dynamics reveal that the ventral entrains the dorsal suprachiasmatic nucleus (2016) J. Biol. Rhythms, 32, pp. 35-47; Tsiairis, C., Aulehla, A., Self-organization of embryonic genetic oscillators into spatiotemporal wave patterns (2016) Cell, 164, pp. 656-667; VanderLeest, H.T., Seasonal encoding by the circadian pacemaker of the SCN (2007) Curr. Biol, 17, pp. 468-473; Webb, A.B., Intrinsic nondeterministic circadian rhythm generation in identified mammalian neurons (2009) Proc. Natl. Acad. Sci. USA, 106, pp. 16493-16498; Yamaguchi, S., Synchronization of cellular clocks in the suprachiasmatic nucleus (2003) Science, 302, pp. 1408-1412; Yoo, S.-H., Period2: Luciferase real-time reporting of circadian dynamics reveals persistent circadian oscillations in mouse peripheral tissues (2004) Proc. Natl. Acad. Sci. USA, 101, pp. 5339-5346

PY - 2017

Y1 - 2017

N2 - Motivation Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus. Results We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion.

AB - Motivation Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus. Results We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion.

KW - animal

KW - brain

KW - image processing

KW - male

KW - mouse

KW - physiology

KW - spatial analysis

KW - suprachiasmatic nucleus

KW - Animals

KW - Brain

KW - Image Processing, Computer-Assisted

KW - Male

KW - Mice

KW - Spatial Analysis

KW - Suprachiasmatic Nucleus

U2 - 10.1093/bioinformatics/btx351

DO - 10.1093/bioinformatics/btx351

M3 - Article

VL - 33

SP - 3072

EP - 3079

JO - Bioinformatics

JF - Bioinformatics

SN - 1367-4803

IS - 19

ER -