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

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

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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)

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SLIDE 1

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

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SLIDE 2

Introduction

Calcium imaging: following neuronal activity

scale bar: 40 µm

with courtesy of R. Franconville

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 2 / 18

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SLIDE 3

Introduction

Fura-2, a ratiometric calcium indicator

250 300 350 400 450 500 550 600 650 20 40 60 80 100 Normalized fluorescence

Fura−2 spectra

Wavelength (nm) Ca2+ free form (Exc.) Ca2+ free form (Em.) Ca2+ bound form (Exc.) Ca2+ bound form (Em.)

source: www.invitrogen.com

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 3 / 18

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SLIDE 4

Introduction

Experimental protocol

80000 85000 90000 95000 100000

adu340 (photons)

0 ton 2 4 6 8 10 12

Time (s)

145000 155000 165000 175000

adu380 (photons)

Fluorescence transient evoked in an olfactory neuron

  • f the cockroach Periplaneta Americana

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 4 / 18

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SLIDE 5

Fluorescence model

Expression of the fluorescence intensity

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 5 / 18

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SLIDE 6

Fluorescence model

Expression of the fluorescence intensity

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calibration parameters

Rmin, Rmax, Keff and Kd are calibrated using a dedicated set of experiments

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 5 / 18

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SLIDE 7

The ratiometric transformation

Getting the intracellular calcium concentration ?

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

R = F340 − FB,340 F380 − FB,380 · T380 T340

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

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SLIDE 8

The ratiometric transformation

Getting the intracellular calcium concentration ?

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

R = F340 − FB,340 F380 − FB,380 · T380 T340 = Rmin · Keff + Rmax · [Ca2+] Keff + [Ca2+]

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

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SLIDE 9

The ratiometric transformation

Getting the intracellular calcium concentration ?

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

R = F340 − FB,340 F380 − FB,380 · T380 T340 = Rmin · Keff + Rmax · [Ca2+] Keff + [Ca2+] ≫ [Ca2+] = Keff · R − Rmin Rmax − R

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

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SLIDE 10

The ratiometric transformation

Getting the intracellular calcium concentration ?

F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

R = F340 − FB,340 F380 − FB,380 · T380 T340 = Rmin · Keff + Rmax · [Ca2+] Keff + [Ca2+] ≫ [Ca2+] = Keff · R − Rmin Rmax − R

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 6 / 18

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SLIDE 11

The ratiometric transformation

Bias on the absolute calcium concentration

  • −3

−2 −1 1 2 3

(Keff − Keff) / σ(Keff)

−50 50 100 150

Normalized bias on [Ca2+]

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 7 / 18

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SLIDE 12

The “direct” approach

Embedding a calcium model into the fluorescence model

FB,340 = sB,340 · Te,340 · P, F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

FB,380 = sB,380 · Te,340 · P, F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calcium model

[Ca2+](t) = Ca0 + ∆Ca · exp

  • − (t − ton)/τ
  • Joucla et al. (CNRS, Univ. Paris)

CalciOMatic July 9, 2009 8 / 18

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SLIDE 13

The “direct” approach

Embedding a calcium model into the fluorescence model

FB,340 = sB,340 · Te,340 · P, F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

FB,380 = sB,380 · Te,340 · P, F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calcium model

[Ca2+](t) = Ca0 + ∆Ca · exp

  • − (t − ton)/τ
  • Joucla et al. (CNRS, Univ. Paris)

CalciOMatic July 9, 2009 8 / 18

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SLIDE 14

The “direct” approach

Embedding a calcium model into the fluorescence model

FB,340 = sB,340 · Te,340 · P, F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

FB,380 = sB,380 · Te,340 · P, F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calcium model

[Ca2+](t) = Ca0 + ∆Ca · exp

  • − (t − ton)/τ
  • Joucla et al. (CNRS, Univ. Paris)

CalciOMatic July 9, 2009 8 / 18

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SLIDE 15

The “direct” approach

Embedding a calcium model into the fluorescence model

FB,340 = sB,340 · Te,340 · P, F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

FB,380 = sB,380 · Te,340 · P, F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calcium model

[Ca2+](t) = Ca0 + ∆Ca · exp

  • − (t − ton)/τ
  • Joucla et al. (CNRS, Univ. Paris)

CalciOMatic July 9, 2009 8 / 18

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SLIDE 16

The “direct” approach

Embedding a calcium model into the fluorescence model

FB,340 = sB,340 · Te,340 · P, F340 =

  • φ · [BT]

Kd + [Ca2+](Rmin · Keff + Rmax · [Ca2+]) + sB,340

  • · Te,340 · P,

FB,380 = sB,380 · Te,340 · P, F380 =

  • φ · [BT]

Kd + [Ca2+](Keff + [Ca2+]) + sB,380

  • · Te,380 · P.

Calcium model

[Ca2+](t) = Ca0 + ∆Ca · exp

  • − (t − ton)/τ
  • Joucla et al. (CNRS, Univ. Paris)

CalciOMatic July 9, 2009 8 / 18

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SLIDE 17

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.

2 4 6 8 10 400 800

Expected adu and adu distributions at selected times adu

2 4 6 8 10 −100

Time (s) adu "noise" distributions at selected times adu − µ

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 9 / 18

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SLIDE 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.

2 4 6 8 10 10 20 30

Expected adu and adu distributions at selected times adu adu "noise" distributions at selected times

2 4 6 8 10

Time (s)

−2 1

adu − µ

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 10 / 18

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SLIDE 19

The “direct” approach

Fitting simultaneously both fluorescence transients

nls

  • c
  • aduB,340,
  • adu340,
  • aduB,380,
  • adu380
  • ∼c
  • FB,340,
  • F340,
  • FB,380,
  • F380

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 11 / 18

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SLIDE 20

The “direct” approach

Fitting simultaneously both fluorescence transients

nls

  • c
  • aduB,340,
  • adu340,
  • aduB,380,
  • adu380
  • ∼c
  • FB,340,
  • F340,
  • FB,380,
  • F380

Estimated parameters

Ca0, ∆Ca, τ, φ, sB,340, sB,380

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 11 / 18

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SLIDE 21

The “direct” approach

Fitting simultaneously both fluorescence transients and actual values of the calibration parameters

nls

  • c
  • aduB,340,
  • adu340,
  • aduB,380,
  • adu380, Rmin, Rmax, Keff , Kd
  • ∼c
  • FB,340,
  • F340,
  • FB,380,
  • F380, Rmin, Rmax, Keff , Kd
  • ,

weights = c

  • 4, 4, 4, 4,

1 σ2

Rmin

, 1 σ2

Rmax

, 1 σ2

Keff

, 1 σ2

Kd

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 12 / 18

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SLIDE 22

The “direct” approach

Fitting simultaneously both fluorescence transients and actual values of the calibration parameters

nls

  • c
  • aduB,340,
  • adu340,
  • aduB,380,
  • adu380, Rmin, Rmax, Keff , Kd
  • ∼c
  • FB,340,
  • F340,
  • FB,380,
  • F380, Rmin, Rmax, Keff , Kd
  • ,

weights = c

  • 4, 4, 4, 4,

1 σ2

Rmin

, 1 σ2

Rmax

, 1 σ2

Keff

, 1 σ2

Kd

Estimated parameters

Ca0, ∆Ca, τ, φ, sB,340, sB,380, Rmin, Rmax, Keff , Kd

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 12 / 18

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SLIDE 23

Results

Monte-Carlo simulations

Simulate data

1 Choose values for [Ca2+] and experiment-specific parameters Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 13 / 18

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SLIDE 24

Results

Monte-Carlo simulations

Simulate data

1 Choose values for [Ca2+] and experiment-specific parameters 2 Draw calibrated parameters from Gaussian distributions Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 13 / 18

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SLIDE 25

Results

Monte-Carlo simulations

Simulate data

1 Choose values for [Ca2+] and experiment-specific parameters 2 Draw calibrated parameters from Gaussian distributions 3 Create ideal background and transient fluorescence signals Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 13 / 18

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SLIDE 26

Results

Monte-Carlo simulations

Simulate data

1 Choose values for [Ca2+] and experiment-specific parameters 2 Draw calibrated parameters from Gaussian distributions 3 Create ideal background and transient fluorescence signals 4 Simulate noisy signals according to the Poisson distribution Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 13 / 18

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SLIDE 27

Results

Monte-Carlo simulations

Simulate data Fit data

Ratiometric approach Compute an equivalent [Ca2+] transient and fit a monoexponential model

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 14 / 18

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SLIDE 28

Results

Monte-Carlo simulations

Simulate data Fit data

Ratiometric approach Compute an equivalent [Ca2+] transient and fit a monoexponential model Direct approach Fit the whole fluorescence model on the square-rooted signals and the calibrated parameters

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 14 / 18

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SLIDE 29

Results

Monte-Carlo simulations

Simulate data / Fit data Test the reliability of the confidence intervals - Procedure

1 Test if the true value of each parameter is within the 95% confidence

interval returned by nls (TRUE / FALSE)

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 15 / 18

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SLIDE 30

Results

Monte-Carlo simulations

Simulate data / Fit data Test the reliability of the confidence intervals - Procedure

1 Test if the true value of each parameter is within the 95% confidence

interval returned by nls (TRUE / FALSE)

2 Repeat the Simulation and Fitting steps 1000 times Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 15 / 18

slide-31
SLIDE 31

Results

Monte-Carlo simulations

Simulate data / Fit data Test the reliability of the confidence intervals - Procedure

1 Test if the true value of each parameter is within the 95% confidence

interval returned by nls (TRUE / FALSE)

2 Repeat the Simulation and Fitting steps 1000 times 3 Count the number of TRUE Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 15 / 18

slide-32
SLIDE 32

Results

Monte-Carlo simulations

Simulate data / Fit data Test the reliability of the confidence intervals - Procedure

1 Test if the true value of each parameter is within the 95% confidence

interval returned by nls (TRUE / FALSE)

2 Repeat the Simulation and Fitting steps 1000 times 3 Count the number of TRUE 4 Compare these values with the 2.5% and 97.5% quantiles of the

Binomial distribution with probability p = 0.95.

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 15 / 18

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SLIDE 33

Results

Monte-Carlo simulations

  • Ca0 ∆Ca

τ φ sB,340sB,380 Rmin Rmax Keff Kd

900 936 950 963 1000 128 297

# of successes

  • Ratiometric

Direct

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 16 / 18

slide-34
SLIDE 34

Results

Fitting cockroach’s data

285 290 295 300 305 310 315

adu340

A

−0.6 0.0 0.6

res340

380 385 390 395 400 405 410 415

adu380

B

2 4 6 8 10 12 tON

Time (s)

−0.6 0.0 0.6

res380

5 10 15 20 25

Lag

−0.2 0.0 0.2 0.4 0.6 0.8 1.0

ACF

C

  • ●●●
  • ●●●
  • −3

−2 −1 1 2 3

Theoretical quantiles

−0.6 −0.3 0.0 0.3 0.6

Sample quant.

D Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 17 / 18

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SLIDE 35

Summary

Data generation model including a probabilistic model of the CCD camera The“ratiometric”transformation gives wrong confidence intervals The“direct”approach, combined with the square root transformation, gives meaningful confidence intervals We can take into account the uncertainty of calibration measurements The latter feature has been shown to improve the fits of physiological data The“direct”method is available from the CRAN website ≫ look for CalciOMatic

Joucla et al. (CNRS, Univ. Paris) CalciOMatic July 9, 2009 18 / 18