The CalciOMatic package: a new tool for quantitative calcium imaging - PowerPoint PPT Presentation

The CalciOMatic package: a new tool for quantitative calcium imaging analysis S´ ebastien Joucla ∗ , Andreas Pippow, Peter Kloppenburg and Christophe Pouzat CNRS, University Paris-Descartes July 9, 2009 Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 1 / 18

Introduction Calcium imaging: following neuronal activity scale bar: 40 µ m with courtesy of R. Franconville Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 2 / 18

Introduction Fura-2, a ratiometric calcium indicator Fura−2 spectra 100 Ca2+ free form (Exc.) Ca2+ free form (Em.) 80 Normalized fluorescence Ca2+ bound form (Exc.) Ca2+ bound form (Em.) 60 40 20 0 250 300 350 400 450 500 550 600 650 Wavelength (nm) source: www.invitrogen.com Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 3 / 18

Introduction Experimental protocol 100000 adu 340 (photons) 95000 90000 85000 80000 175000 adu 380 (photons) 165000 155000 145000 0 t on 2 4 6 8 10 12 Time (s) Fluorescence transient evoked in an olfactory neuron of the cockroach Periplaneta Americana Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 4 / 18

Fluorescence model Expression of the fluorescence intensity φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � F 380 = · T e , 380 · P . Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 5 / 18

Fluorescence model Expression of the fluorescence intensity φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � F 380 = · T e , 380 · P . Calibration parameters R min , R max , K eff and K d are calibrated using a dedicated set of experiments Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 5 / 18

The ratiometric transformation Getting the intracellular calcium concentration ? φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 R = F 340 − F B , 340 · T 380 F 380 − F B , 380 T 340 Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

The ratiometric transformation Getting the intracellular calcium concentration ? φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 = R min · K eff + R max · [ Ca 2+ ] R = F 340 − F B , 340 · T 380 K eff + [ Ca 2+ ] F 380 − F B , 380 T 340 Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

The ratiometric transformation Getting the intracellular calcium concentration ? φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 = R min · K eff + R max · [ Ca 2+ ] R = F 340 − F B , 340 · T 380 K eff + [ Ca 2+ ] F 380 − F B , 380 T 340 ≫ [ Ca 2+ ] = K eff · R − R min R max − R Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

The ratiometric transformation Getting the intracellular calcium concentration ? φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � = · T e , 340 · P , F 340 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 = R min · K eff + R max · [ Ca 2+ ] R = F 340 − F B , 340 · T 380 K eff + [ Ca 2+ ] F 380 − F B , 380 T 340 ≫ [ Ca 2+ ] = K eff · R − R min R max − R Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

The ratiometric transformation Bias on the absolute calcium concentration Normalized bias on [Ca 2 + ] 150 ● ● 100 ● ● ● ● 50 ● ● ● ● ● ● 0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● −50 −3 −2 −1 0 1 2 3 (K eff − K eff ) / σ ( K eff ) Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 7 / 18

The “direct” approach Embedding a calcium model into the fluorescence model = s B , 340 · T e , 340 · P , F B , 340 φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � F 340 = · T e , 340 · P , = s B , 380 · T e , 340 · P , F B , 380 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 Calcium model [ Ca 2+ ]( t ) = Ca 0 + ∆ Ca · exp � � − ( t − t on ) /τ Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 8 / 18

The “direct” approach Embedding a calcium model into the fluorescence model = s B , 340 · T e , 340 · P , F B , 340 φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � F 340 = · T e , 340 · P , = s B , 380 · T e , 340 · P , F B , 380 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 Calcium model [ Ca 2+ ]( t ) = Ca 0 + ∆ Ca · exp � � − ( t − t on ) /τ Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 8 / 18

The “direct” approach Embedding a calcium model into the fluorescence model = s B , 340 · T e , 340 · P , F B , 340 φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � F 340 = · T e , 340 · P , = s B , 380 · T e , 340 · P , F B , 380 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 Calcium model [ Ca 2+ ]( t ) = Ca 0 + ∆ Ca · exp � � − ( t − t on ) /τ Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 8 / 18

The “direct” approach Embedding a calcium model into the fluorescence model = s B , 340 · T e , 340 · P , F B , 340 φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � F 340 = · T e , 340 · P , = s B , 380 · T e , 340 · P , F B , 380 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 Calcium model [ Ca 2+ ]( t ) = Ca 0 + ∆ Ca · exp � � − ( t − t on ) /τ Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 8 / 18

The “direct” approach Embedding a calcium model into the fluorescence model = s B , 340 · T e , 340 · P , F B , 340 φ · [ B T ] K d + [ Ca 2+ ]( R min · K eff + R max · [ Ca 2+ ]) + s B , 340 � � F 340 = · T e , 340 · P , = s B , 380 · T e , 340 · P , F B , 380 φ · [ B T ] K d + [ Ca 2+ ]( K eff + [ Ca 2+ ]) + s B , 380 � � = · T e , 380 · P . F 380 Calcium model [ Ca 2+ ]( t ) = Ca 0 + ∆ Ca · exp � � − ( t − t on ) /τ Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 8 / 18

The “direct” approach A CCD camera model The fluorescence signals acquisition, with a CCD camera, induces a Poisson noise. At high photon counts, the Poisson distribution can be well approximated by a Gaussian with variance equal to the mean. Expected adu and adu distributions at selected times 800 adu 400 0 0 2 4 6 8 10 adu "noise" distributions at selected times adu − µ −100 0 2 4 6 8 10 Time (s) Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 9 / 18

The “direct” approach The square root transformation Taking the square root of the fluorescence signals stabilizes the noise variance, which becomes equal to 1 / 4 independently of the mean. Expected adu and adu distributions at selected times 30 20 adu 10 0 0 2 4 6 8 10 adu "noise" distributions at selected times adu − µ 1 −2 0 2 4 6 8 10 Time (s) Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 10 / 18

The “direct” approach Fitting simultaneously both fluorescence transients �� � � � � � adu B , 340 , adu 340 , adu B , 380 , c adu 380 nls �� � � � � � ∼ c F B , 340 , F 340 , F B , 380 , F 380 Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 11 / 18

The “direct” approach Fitting simultaneously both fluorescence transients �� � � � � � adu B , 340 , adu 340 , adu B , 380 , c adu 380 nls �� � � � � � ∼ c F B , 340 , F 340 , F B , 380 , F 380 Estimated parameters Ca 0 , ∆ Ca , τ, φ, s B , 340 , s B , 380 Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 11 / 18

The “direct” approach Fitting simultaneously both fluorescence transients and actual values of the calibration parameters �� � � � � � c adu B , 340 , adu 340 , adu B , 380 , adu 380 , R min , R max , K eff , K d nls �� � � � � F B , 340 , F 340 , F B , 380 , F 380 , R min , R max , K eff , K d , ∼ c � 1 1 1 1 � � weights = c 4 , 4 , 4 , 4 , , , , σ 2 σ 2 σ 2 σ 2 Rmin Rmax Keff Kd Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 12 / 18