Abstract

Ratiometric fluorescent indicators are becoming increasingly prevalent in many areas of biology. They are used for making quantitative measurements of intracellular free calcium both in vitro and in vivo, as well as measuring membrane potentials, pH, and other important physiological variables of interest to researchers in many subfields. Often, functional changes in the fluorescent yield of ratiometric indicators are small, and the signal-to-noise ratio (SNR) is of order unity or less. In particular, variability in the denominator of the ratio can lead to very poor ratio estimates. We present a statistical optimization method for objectively detecting and estimating ratiometric signals in dual-wavelength measurements of fluorescent, ratiometric indicators that improves on standard methods. With the use of an appropriate statistical model for ratiometric signals and by taking the pixel–pixel covariance of an imaging dataset into account, we are able to extract user-independent spatiotemporal information that retains high resolution in both space and time.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
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    [CrossRef] [PubMed]
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  18. M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
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  19. J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. F. Campbell and J. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).
  28. J. Hanks, "Hanks' balanced salt solution and pH control," Tissue Culture Association Manual 3, 3-5 (1976).
  29. A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
    [CrossRef] [PubMed]
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  34. A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
    [PubMed]
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    [CrossRef] [PubMed]
  36. R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

2007 (1)

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

2005 (2)

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

2004 (1)

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

2003 (1)

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

2002 (1)

A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
[CrossRef] [PubMed]

2001 (3)

T. Yokoo, B. Knight, and L. Sirovich, "An optimization approach to signal extraction from noisy multivariate data," Neuroimage 14, 1309-1326 (2001).
[CrossRef] [PubMed]

T. Gomez, E. Robles, M. Poo, and N. Spitzer, "Filopodial calcium transients promote substrate-dependent growth cone turning," Science 291, 1983-1987 (2001).
[CrossRef] [PubMed]

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

2000 (3)

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
[CrossRef] [PubMed]

A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
[PubMed]

1999 (2)

K. Cheng, J. Virtanen, and P. Somerharju, "Fluorescence studies of dehydroergosterol in phosphatidylethanolamine/phosphatidylcholine bilayers," Biophys. J. 77, 3108-3119 (1999).
[CrossRef] [PubMed]

A. Takahashi, P. Camacho, J. Lechleiter, and B. Herman, "Measurement of intracellular calcium," Physiol. Rev. 79, 1089-1125 (1999).
[PubMed]

1998 (1)

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

1997 (3)

J. Gonzalez and R. Tsien, "Improved indicators of cell membrane potential that use fluorescence resonance energy transfer," Chem. Biol. 4, 269-277 (1997).
[CrossRef] [PubMed]

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

M. Siegel and E. Isacoff, "A genetically encoded optical probe of membrane voltage," Neuron 19, 735-741 (1997).
[CrossRef] [PubMed]

1995 (2)

J. Gonzalez and R. Tsien, "Voltage sensing by fluorescence resonance energy transfer in single cells," Biophys. J. 69, 1272-1280 (1995).
[CrossRef] [PubMed]

J. Bischofberger and D. Schild, "Different spatial patterns of [Ca2+] increase caused by N- and L-type Ca2+ channel activation in frog olfactory bulb neurones," J. Physiol. (London) 487(Pt 2), 305-317 (1995).

1994 (1)

J. Kao, "Practical aspects of measuring [Ca2+] with fluorescent indicators," Methods Cell Biol. 40, 155-181 (1994).
[CrossRef] [PubMed]

1993 (2)

S. Wang, "Modeling the apparent diffusion constant of calcium ions emanating from a channel: Implications for calcium wave propagation," Biol. Bull. 185, 297-298 (1993).

P. Lipp and E. Niggli, "Ratiometric confocal Ca2+-measurements with visible wavelength indicators in isolated cardiac myocytes," Cell Calcium 14, 359-372 (1993).
[CrossRef] [PubMed]

1992 (2)

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

C. Schlatterer, G. Knoll, and D. Malchow, "Intracellular calcium during chemo-taxis of Dictyostelium discoideum: a new Fura-2 derivative avoids sequestration of the indicator and allows long-term calcium measurements," Entomol. News 58, 172-181 (1992).

1990 (2)

M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
[CrossRef] [PubMed]

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

1987 (2)

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

1985 (2)

G. Grynkiewicz, M. Poenie, and R. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Biol. Chem. 260, 3440-3450 (1985).
[PubMed]

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

1976 (1)

J. Hanks, "Hanks' balanced salt solution and pH control," Tissue Culture Association Manual 3, 3-5 (1976).

1968 (1)

F. Campbell and J. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

Adams, J.

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

Anderson, T.

T. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley, 1984).

Ando, J.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Antic, S.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Ashley, C.

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

Bagshaw, C.

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

Bajer, A.

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

Bischofberger, J.

J. Bischofberger and D. Schild, "Different spatial patterns of [Ca2+] increase caused by N- and L-type Ca2+ channel activation in frog olfactory bulb neurones," J. Physiol. (London) 487(Pt 2), 305-317 (1995).

Borgdorff, A.

A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
[PubMed]

Brandes, R.

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Bright, G.

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

Brown, K.

A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
[CrossRef] [PubMed]

Camacho, P.

A. Takahashi, P. Camacho, J. Lechleiter, and B. Herman, "Measurement of intracellular calcium," Physiol. Rev. 79, 1089-1125 (1999).
[PubMed]

Camacho, S.

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Campbell, F.

F. Campbell and J. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

Cheng, K.

K. Cheng, J. Virtanen, and P. Somerharju, "Fluorescence studies of dehydroergosterol in phosphatidylethanolamine/phosphatidylcholine bilayers," Biophys. J. 77, 3108-3119 (1999).
[CrossRef] [PubMed]

Cohen, L.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Davies, M.

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

Delorme, A.

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

Falk, C.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Fan, X.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Fetcho, J.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

Figueredo, V.

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Fisher, G.

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

Friedrich, R.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Fujimoto, T.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Fujita, T.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Gomez, T.

T. Gomez, E. Robles, M. Poo, and N. Spitzer, "Filopodial calcium transients promote substrate-dependent growth cone turning," Science 291, 1983-1987 (2001).
[CrossRef] [PubMed]

Gonzalez, J.

J. Gonzalez and R. Tsien, "Improved indicators of cell membrane potential that use fluorescence resonance energy transfer," Chem. Biol. 4, 269-277 (1997).
[CrossRef] [PubMed]

J. Gonzalez and R. Tsien, "Voltage sensing by fluorescence resonance energy transfer in single cells," Biophys. J. 69, 1272-1280 (1995).
[CrossRef] [PubMed]

Grynkiewicz, G.

G. Grynkiewicz, M. Poenie, and R. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Biol. Chem. 260, 3440-3450 (1985).
[PubMed]

Hama, H.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Hanks, J.

J. Hanks, "Hanks' balanced salt solution and pH control," Tissue Culture Association Manual 3, 3-5 (1976).

Heim, R.

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

Herman, B.

A. Takahashi, P. Camacho, J. Lechleiter, and B. Herman, "Measurement of intracellular calcium," Physiol. Rev. 79, 1089-1125 (1999).
[PubMed]

M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
[CrossRef] [PubMed]

Higashijima, S.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

Ikura, M.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

Isacoff, E.

M. Siegel and E. Isacoff, "A genetically encoded optical probe of membrane voltage," Neuron 19, 735-741 (1997).
[CrossRef] [PubMed]

Isshiki, M.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Jackson, A.

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

Kamiya, A.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Kao, J.

J. Kao, "Practical aspects of measuring [Ca2+] with fluorescent indicators," Methods Cell Biol. 40, 155-181 (1994).
[CrossRef] [PubMed]

Kaplan, E.

L. Sirovich and E. Kaplan, "Analysis Methods for Optical Imaging," in Optical Imaging: CRC Reviews, R.Frostig, ed. (CRC Press, 2002).

Keith, C.

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

Keith, C. H.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
[CrossRef] [PubMed]

Knight, B.

T. Yokoo, B. Knight, and L. Sirovich, "An optimization approach to signal extraction from noisy multivariate data," Neuroimage 14, 1309-1326 (2001).
[CrossRef] [PubMed]

Knoll, G.

C. Schlatterer, G. Knoll, and D. Malchow, "Intracellular calcium during chemo-taxis of Dictyostelium discoideum: a new Fura-2 derivative avoids sequestration of the indicator and allows long-term calcium measurements," Entomol. News 58, 172-181 (1992).

Kogo, H.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Korenaga, R.

M. Isshiki, J. Ando, R. Korenaga, H. Kogo, T. Fujimoto, T. Fujita, and A. Kamiya, "Endothelial Ca2+ waves preferentially originate at specific loci in caveolin-rich cell edges," Proc. Natl. Acad. Sci. USA 95, 5009-5014 (1998).
[CrossRef] [PubMed]

Lam, Y.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Lauderdale, J. D.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Lechleiter, J.

A. Takahashi, P. Camacho, J. Lechleiter, and B. Herman, "Measurement of intracellular calcium," Physiol. Rev. 79, 1089-1125 (1999).
[PubMed]

Lemasters, J.

M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
[CrossRef] [PubMed]

Li, J.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Lipp, P.

P. Lipp and E. Niggli, "Ratiometric confocal Ca2+-measurements with visible wavelength indicators in isolated cardiac myocytes," Cell Calcium 14, 359-372 (1993).
[CrossRef] [PubMed]

Llopis, J.

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

Mack, J.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Magalhaes, P. J.

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

Majumder, A.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Mal, T.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Malchow, D.

C. Schlatterer, G. Knoll, and D. Malchow, "Intracellular calcium during chemo-taxis of Dictyostelium discoideum: a new Fura-2 derivative avoids sequestration of the indicator and allows long-term calcium measurements," Entomol. News 58, 172-181 (1992).

Mandel, G.

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

Masino, M.

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

Massie, B.

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Maxfield, F.

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

McCaffery, J.

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

McCarthy, S.

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

McDougall, A.

A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
[CrossRef] [PubMed]

Merritt, J.

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

Mione, M.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Miyawaki, A.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

Mizuno, A.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Mongillo, M.

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

Moores, K.

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

Murnane, A. C.

A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
[CrossRef] [PubMed]

Niggli, E.

P. Lipp and E. Niggli, "Ratiometric confocal Ca2+-measurements with visible wavelength indicators in isolated cardiac myocytes," Cell Calcium 14, 359-372 (1993).
[CrossRef] [PubMed]

Poenie, M.

G. Grynkiewicz, M. Poenie, and R. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Biol. Chem. 260, 3440-3450 (1985).
[PubMed]

Poo, M.

T. Gomez, E. Robles, M. Poo, and N. Spitzer, "Filopodial calcium transients promote substrate-dependent growth cone turning," Science 291, 1983-1987 (2001).
[CrossRef] [PubMed]

Porter, E. L.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Pozzan, T.

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

Ratan, R.

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

Reagin, S. S.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Robles, E.

T. Gomez, E. Robles, M. Poo, and N. Spitzer, "Filopodial calcium transients promote substrate-dependent growth cone turning," Science 291, 1983-1987 (2001).
[CrossRef] [PubMed]

Robson, J.

F. Campbell and J. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

Roe, M.

M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
[CrossRef] [PubMed]

Rogowska, J.

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

Rudolf, R.

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

Russ, J. C.

J. C. Russ, The Image Processing Handbook, 5th ed. (CRC Press, 2006).
[CrossRef]

Sailstad, C.

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

Sawano, A.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Schild, D.

J. Bischofberger and D. Schild, "Different spatial patterns of [Ca2+] increase caused by N- and L-type Ca2+ channel activation in frog olfactory bulb neurones," J. Physiol. (London) 487(Pt 2), 305-317 (1995).

Schlatterer, C.

C. Schlatterer, G. Knoll, and D. Malchow, "Intracellular calcium during chemo-taxis of Dictyostelium discoideum: a new Fura-2 derivative avoids sequestration of the indicator and allows long-term calcium measurements," Entomol. News 58, 172-181 (1992).

Shearer, J.

A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
[CrossRef] [PubMed]

Shelanski, M.

C. Keith, R. Ratan, F. Maxfield, A. Bajer, and M. Shelanski, "Microscopic observations of local cytoplasmic calcium gradients in living mitotic cells," Nature 316, 848-850 (1985).
[CrossRef] [PubMed]

Siegel, M.

M. Siegel and E. Isacoff, "A genetically encoded optical probe of membrane voltage," Neuron 19, 735-741 (1997).
[CrossRef] [PubMed]

Sirovich, L.

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

T. Yokoo, B. Knight, and L. Sirovich, "An optimization approach to signal extraction from noisy multivariate data," Neuroimage 14, 1309-1326 (2001).
[CrossRef] [PubMed]

L. Sirovich and E. Kaplan, "Analysis Methods for Optical Imaging," in Optical Imaging: CRC Reviews, R.Frostig, ed. (CRC Press, 2002).

Somerharju, P.

K. Cheng, J. Virtanen, and P. Somerharju, "Fluorescence studies of dehydroergosterol in phosphatidylethanolamine/phosphatidylcholine bilayers," Biophys. J. 77, 3108-3119 (1999).
[CrossRef] [PubMed]

Somjen, G.

A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
[PubMed]

Sornborger, A.

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

Sornborger, A. T.

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

Souren, M.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Spitzer, N.

T. Gomez, E. Robles, M. Poo, and N. Spitzer, "Filopodial calcium transients promote substrate-dependent growth cone turning," Science 291, 1983-1987 (2001).
[CrossRef] [PubMed]

Takahashi, A.

A. Takahashi, P. Camacho, J. Lechleiter, and B. Herman, "Measurement of intracellular calcium," Physiol. Rev. 79, 1089-1125 (1999).
[PubMed]

Taylor, D.

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

Timmerman, M.

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

Tong, K.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Truong, K.

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Tsien, R.

A. Miyawaki, J. Llopis, R. Heim, J. McCaffery, J. Adams, M. Ikura, and R. Tsien, "Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin," Nature 388, 882-887 (1997).
[CrossRef] [PubMed]

J. Gonzalez and R. Tsien, "Improved indicators of cell membrane potential that use fluorescence resonance energy transfer," Chem. Biol. 4, 269-277 (1997).
[CrossRef] [PubMed]

J. Gonzalez and R. Tsien, "Voltage sensing by fluorescence resonance energy transfer in single cells," Biophys. J. 69, 1272-1280 (1995).
[CrossRef] [PubMed]

G. Grynkiewicz, M. Poenie, and R. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Biol. Chem. 260, 3440-3450 (1985).
[PubMed]

Virtanen, J.

K. Cheng, J. Virtanen, and P. Somerharju, "Fluorescence studies of dehydroergosterol in phosphatidylethanolamine/phosphatidylcholine bilayers," Biophys. J. 77, 3108-3119 (1999).
[CrossRef] [PubMed]

Wachowiak, M.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Wadman, W.

A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
[PubMed]

Wang, S.

S. Wang, "Modeling the apparent diffusion constant of calcium ions emanating from a channel: Implications for calcium wave propagation," Biol. Bull. 185, 297-298 (1993).

Weiner, M.

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Whitaker, M.

A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
[CrossRef] [PubMed]

Yaksi, E.

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

Yokoo, T.

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

T. Yokoo, B. Knight, and L. Sirovich, "An optimization approach to signal extraction from noisy multivariate data," Neuroimage 14, 1309-1326 (2001).
[CrossRef] [PubMed]

Zecevic, D.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Zochowsky, M.

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

Am. J. Physiol. Heart Circ. Physiol. (1)

R. Brandes, V. Figueredo, S. Camacho, B. Massie, and M. Weiner, "Suppression of motion artifacts in fluorescence spectroscopy of perfused hearts," Am. J. Physiol. Heart Circ. Physiol. 263, H972-H980 (1992).

Biochem. J. (1)

J. Merritt, S. McCarthy, M. Davies, and K. Moores, "Use of fluo-3 to measure cytosolic Ca2+ in platelets and neutrophils. Loading cells with the dye, calibration of traces, measurements in the presence of plasma, and buffering of cytosolic Ca2+," Biochem. J. 269, 513-519 (1990).
[PubMed]

Biol. Bull. (2)

M. Zochowsky, M. Wachowiak, C. Falk, L. Cohen, Y. Lam, S. Antic, and D. Zecevic, "Imaging membrane potential with voltage-sensitive dyes," Biol. Bull. 198, 1-21 (2000).
[CrossRef]

S. Wang, "Modeling the apparent diffusion constant of calcium ions emanating from a channel: Implications for calcium wave propagation," Biol. Bull. 185, 297-298 (1993).

Biol. Cell (1)

A. McDougall, J. Shearer, and M. Whitaker, "The initiation and propagation of the fertilization wave in sea urchin eggs," Biol. Cell 92, 205-214 (2000).
[CrossRef] [PubMed]

Biophys. J. (2)

K. Cheng, J. Virtanen, and P. Somerharju, "Fluorescence studies of dehydroergosterol in phosphatidylethanolamine/phosphatidylcholine bilayers," Biophys. J. 77, 3108-3119 (1999).
[CrossRef] [PubMed]

J. Gonzalez and R. Tsien, "Voltage sensing by fluorescence resonance energy transfer in single cells," Biophys. J. 69, 1272-1280 (1995).
[CrossRef] [PubMed]

Cell Calcium (2)

P. Lipp and E. Niggli, "Ratiometric confocal Ca2+-measurements with visible wavelength indicators in isolated cardiac myocytes," Cell Calcium 14, 359-372 (1993).
[CrossRef] [PubMed]

M. Roe, J. Lemasters, and B. Herman, "Assessment of Fura-2 for measurements of cytosolic free calcium," Cell Calcium 11, 63-73 (1990).
[CrossRef] [PubMed]

Chem. Biol. (1)

J. Gonzalez and R. Tsien, "Improved indicators of cell membrane potential that use fluorescence resonance energy transfer," Chem. Biol. 4, 269-277 (1997).
[CrossRef] [PubMed]

Entomol. News (1)

C. Schlatterer, G. Knoll, and D. Malchow, "Intracellular calcium during chemo-taxis of Dictyostelium discoideum: a new Fura-2 derivative avoids sequestration of the indicator and allows long-term calcium measurements," Entomol. News 58, 172-181 (1992).

FEBS Lett. (1)

A. Jackson, M. Timmerman, C. Bagshaw, and C. Ashley, "The kinetics of calcium binding to Fura-2 and indo-1," FEBS Lett. 216, 35-39 (1987).
[CrossRef] [PubMed]

J. Biol. Chem. (1)

G. Grynkiewicz, M. Poenie, and R. Tsien, "A new generation of Ca2+ indicators with greatly improved fluorescence properties," J. Biol. Chem. 260, 3440-3450 (1985).
[PubMed]

J. Biomed. Opt. (1)

X. Fan, A. Majumder, S. S. Reagin, E. L. Porter, A. T. Sornborger, C. H. Keith, and J. D. Lauderdale, "New statistical methods enhance imaging of cameleon fluorescence resonance energy transfer in cultured zebrafish spinal neurons," J. Biomed. Opt. 12034017 (2007).
[CrossRef] [PubMed]

J. Cell Biol. (2)

R. Rudolf, M. Mongillo, P. J. Magalhaes, and T. Pozzan, "In vivo monitoring of Ca2+ uptake into mitochondria of mouse skeletal muscle during contraction," J. Cell Biol. 166, 527-536 (2004).
[CrossRef] [PubMed]

G. Bright, G. Fisher, J. Rogowska, and D. Taylor, "Fluorescence ratio imaging microscopy: temporal and spatial measurements of cytoplasmic pH," J. Cell Biol. 104, 1019-1033 (1987).
[CrossRef] [PubMed]

J. Neurophysiol. (2)

S. Higashijima, M. Masino, G. Mandel, and J. Fetcho, "Imaging neuronal activity during zebrafish behavior with a genetically encoded calcium indicator," J. Neurophysiol. 90, 3986-3997 (2003).
[CrossRef] [PubMed]

A. Borgdorff, G. Somjen, and W. Wadman, "Two mechanisms that raise free intracellular calcium in rat hippocampal neurons during hypoosmotic and low NaCl treatment," J. Neurophysiol. 83, 81-9 (2000).
[PubMed]

J. Neurosci. (1)

J. Li, J. Mack, M. Souren, E. Yaksi, S. Higashijima, M. Mione, J. Fetcho, and R. Friedrich, "Early development of functional spatial maps in the zebrafish olfactory bulb," J. Neurosci. 25, 5784-5795 (2005).
[CrossRef] [PubMed]

J. Neurosci. Methods (1)

A. Sornborger, T. Yokoo, A. Delorme, C. Sailstad, and L. Sirovich, "Extraction of average and differential dynamical responses in stimulus-locked experimental data," J. Neurosci. Methods 141, 223-229 (2005).
[CrossRef] [PubMed]

J. Neurosci. Res. (1)

A. C. Murnane, K. Brown, and C. H. Keith, "Preferential initiation of PC12 neurites in directions of changing substrate adhesivity," J. Neurosci. Res. 67, 321-328 (2002).
[CrossRef] [PubMed]

J. Physiol. (London) (2)

F. Campbell and J. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

J. Bischofberger and D. Schild, "Different spatial patterns of [Ca2+] increase caused by N- and L-type Ca2+ channel activation in frog olfactory bulb neurones," J. Physiol. (London) 487(Pt 2), 305-317 (1995).

Methods Cell Biol. (1)

J. Kao, "Practical aspects of measuring [Ca2+] with fluorescent indicators," Methods Cell Biol. 40, 155-181 (1994).
[CrossRef] [PubMed]

Nat. Struct. Biol. (1)

K. Truong, A. Sawano, A. Mizuno, H. Hama, K. Tong, T. Mal, A. Miyawaki, and M. Ikura, "FRET-based in vivoCa2+ imaging by a new calmodulin-GFP fusion molecule," Nat. Struct. Biol. 8, 1069-1073 (2001).
[CrossRef] [PubMed]

Nature (2)

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Figures (6)

Fig. 1
Fig. 1

Analysis of the fluorescence of PC12 cells loaded with fluo-4 and Fura-Red in response to depolarization with 50 mM KCl . A, Transmitted light image of three loaded cells. A , Fluo-4 fluorescence of the same cells. Note that some dye is compartmentalized, but there is a significant amount of dye in the cytoplasm. A , Fura-Red fluorescence of the same three loaded cells; scale bar, 20 μ m . B, Time courses of fluo-4 and Fura-Red fluorescence in response to 10 cycles of stimulation ( 2 min on, 2 min off) with 50 mM K + solution, followed by 5 min with ionomycin + EGTA (low calcium clamp), followed by 5 min ionomycin + saturating Ca + + . C, Switching profile (black trace) and concentration profile of 0.0005 % fluorescein flowing through the Dvorak–Stotler chamber (blue trace online).

Fig. 2
Fig. 2

Standard ROI analysis of ratiometric calcium imaging data. PC12 cells were loaded with fluo-4 and Fura-Red. Fluorescence measurements of the response to periodic stimulation with a high-potassium medium followed by a low calcium clamp ( ionomycin + EGTA ) were made in the fluo-4 and Fura-red emission bands. A, Transmitted light image of a field of neurites. A , Fluo-4 mean fluorescence with ROI indicated (red-bordered region online); scale bar A, A , 40 μ m . B, Time course of fluorescence ratio in ROI depicted in A and A . Although a periodic change in the ratio is visible initially, as its amplitude decreases, it becomes invisible in the noise.

Fig. 3
Fig. 3

Standard temporal averaging analysis of ratiometric calcium imaging data. The PC12 cells were loaded with fluo-4 and Fura-Red. Fluorescence measurements of the response to periodic stimulation with a high-potassium medium followed by a low calcium clamp ( ionomycin + EGTA ) were made in the fluo-4 and Fura-Red emission bands. A, Transmitted light image of a field of neurites. B–F, Ratio estimates at 20 , 40 , 60 , 80 and 100 s after stimulus onset (timing of onset was based on the fluorescein time course shown in Fig. 2D). These frames show baseline-to-peak response to stimulus. Obvious neuritic structures start to become evident by 60 s after stimulus onset. For temporal averaging, a boxcar window of 100 frames was used.

Fig. 4
Fig. 4

Comparison of ROI, temporal averaging, and SOARS analyses of ratiometric data. The first column shows spatial information: A–C, Three different ROIs superimposed on the mean fluorescence image from the fluo-4 channel: A, Single pixel ROI; B, ROI around region of bright fluorescence; C, ROI along a neurite. D, Eigenimage arising from a SOARS analysis of the data. The next three columns show temporal information: E–G, Time courses of the ratio calculated with the three different ROIs. H, Time course from a SOARS analysis. Because SOARS is a multivariate analysis technique, the ratio reconstruction has information from across the entire imaging region. For comparison with the ROI analyses, we plot the time course of the pixel depicted in D (inset). I–L, As with E–H, except temporally filtered (before ratioing) with a 10-frame boxcar average. M–P, As with E–H, except filtered with a 100-frame boxcar average.

Fig. 5
Fig. 5

Results from a SOARS analysis of measurements of the Ca 2 + response in a cluster of PC12 cells imaged. A, Optical image of PC12 cells showing cell bodies and neurites. B, First image of reconstructed ratio. The Ca 2 + response was stronger in the cytoplasm. The dark areas are cell nuclei. Numbers in A and B denote pixels whose time courses are depicted in C. The numbered pixels start in the cell body and extend along a neurite. The periodic response is seen to be strongest in the cell body and to become increasingly weaker along the neurite.

Fig. 6
Fig. 6

Conducting a SOARS analysis: Intermediate results from the SOARS analysis in Fig. 4 are shown here. A–E, Eigenimages (scale bar, 40 μ m ). F–J, Standardized time courses of the eigenimages. K–O, Time courses of eigenimages in fluo-4 and Fura-Red bands. Note the obvious periodic anticorrelation in panels K and L, which correspond to the eigenimages with evident cellular and neuritic structures in panels A and B. P–T, Histogram estimate of the distribution of standardized time courses. Normal distribution based on mean and standard deviation of time course plotted in a thin solid curve (red online). An eigenimage is taken to represent anticorrelated information in the data if its distribution is nonnormal. U–Y, Joint probability of the time courses of the eigenimage on the standardized fluo-4 and Fura-Red datasets. An alternative measure of statistical significance is deviation of the joint probability from the diagonal axis.

Equations (10)

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X t a ( t ) = 1 n t = n 2 n 2 X ( t ) .
X 1 ( t ) = α b ( t ) [ 1 f ( t ) ] + η 1 ( t ) ,
X 2 ( t ) = β b ( t ) [ 1 + f ( t ) ] + η 2 ( t ) .
X 1 ( t ) X 2 ( t ) = α β 1 f ( t ) 1 + f ( t )
X i ( t ) = X i ( t ) X ¯ i V ¯ i ,
E { ε ( t ) } E { X 1 ( t ) X 2 ( t ) } = 0 ,
ϕ T X N ( ϕ T μ , ϕ T Σ ϕ ) .
X 1 d e n o i s e ( t ) : = i n o n n o r m a l [ ψ i , X 1 ( t ) ] ψ i ,
X 2 d e n o i s e ( t ) : = i n o n n o r m a l [ ψ i , X 2 ( t ) ] ψ i .
R j e s t i m a t e ( t ) : = V ¯ ̂ 1 , j X 1 , j d e n o i s e ( t ) + X ¯ ̂ 1 , j V ¯ ̂ 2 , j X 2 , j d e n o i s e ( t ) + X ¯ ̂ 2 , j ,

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