1.
Towards inferring circuits from calcium imaging
Joshua Vogelstein
Yuriy Mishchenko
JHU/CU
March 24, 2009
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 1 / 34
2.
The Most important slide of the talk
Acknowledgments
Eric D. Young
Liam Paninski
Adam M. Packer
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 2 / 34
3.
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 3 / 34
4.
Introduction
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 4 / 34
5.
Introduction
What is our goal?
Inferring a microcircuit
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 5 / 34
6.
Introduction
Everybody wants it
List of Publications
[Smetters et al., 1999, Ikegaya et al., 2004, Aaron and Yuste, 2006,
Nikolenko et al., 2007]
[Shepherd et al., 2005, Shepherd and Svoboda, 2005,
Stepanyants and Chklovskii, 2005]
[Yoshimura et al., 2005, Kerr et al., 2007]
Pubmed: > 100 articles using the word microcircuit
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 6 / 34
7.
Introduction
Why is this a hard problem?
Many reasons. . .
Too many spike trains (2T ) to search through them all
1
Noise is non-Gaussian
2
Observation are non-linear
3
Parameters are unknown
4
...
5
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 7 / 34
8.
Introduction
What are we going to do?
Our strategy
Write down a generative model, explaining the causal relationship
between spikes and movies
Develop an algorithm to invert that model, to obtain spike trains and
microcircuits from the movies
Test our approach on real data
Answer neurobiological questions that were previously intractable
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 8 / 34
9.
Introduction
What are we going to do?
Our strategy
Write down a generative model, explaining the causal relationship
between spikes and movies
Develop an algorithm to invert that model, to obtain spike trains and
microcircuits from the movies
Test our approach on real data
Answer neurobiological questions that were previously intractable
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 9 / 34
10.
Single Neuron
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 10 / 34
11.
Single Neuron Generative Model
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 11 / 34
12.
Single Neuron Generative Model
Generative Model for a single neuron
Equations
n(t) ∼ Poisson(λ∆)
√
C (t) − C (t − 1)
= C (t − 1) + Cb + An(t − 1) + σc ∆ε
∆
C (t)
F (x, t) ∼ Poisson α(x) +β
C (t) + kd
I (x, t) = ξF (x, t) + η + σI ε
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 12 / 34
13.
Single Neuron Generative Model
Generative Model for a single neuron
Simulation
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 13 / 34
14.
Single Neuron Generative Model
Generative Model for a single neuron
Simulation
Spatially
Filtered
Fluorescence
Calcium
Spike
Train
3 6 9
Time (sec)
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 14 / 34
15.
Single Neuron Inverting the model
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 15 / 34
16.
Single Neuron Inverting the model
Inverting the model
How do we do it?
Our model is a hidden markov model (HMM)
We adapt tools for HMMs to our model
This yields both an estimate of the spike train and the parameters
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 16 / 34
17.
Single Neuron Inverting the model
Inverting the model
How do we do it?
We use anexpectation-maximization (EM) algorithm to iterate
between
Computing the expected spike train
Maximizing the parameters, given our guess of the spike train
We approximate the E step in 3 ways:
tridiagonal non-negative deconvolution
sequential monte carlo (or particle ﬁlter) (SMC or PF)
markov chain monte carlo relaxation of PF
We use gradient ascent to perform the M step (which is concave)
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 17 / 34
18.
Single Neuron Inverting the model
Approximating the E step
Using the tridiagonal non-negative deconvolution
How we do it
Try to maximize P(n|F )
Constrain it to be non-negative
Approximate integer spikes with spikes of any (non-negative) size
Why is it good
Super fast
Gives us an optimal spatial ﬁlter
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 18 / 34
19.
Single Neuron Inverting the model
Approximating the E step
Using sequential monte carlo
How we do it
Try to maximize P(nt |F ) at each time step
At each time, we sample a spike or no spike, and see which performs
better
We do this many times, and compute the average
Why is it good
Incorporates saturating function
Better SNR than non-negative method
Can incorporate refractoriness and stimulus dependence
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 19 / 34
20.
Single Neuron Results
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 20 / 34
21.
Single Neuron Results
Results
Four cells simulated according to our generative model
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 21 / 34
22.
Single Neuron Results
Matlab Demo
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 22 / 34
24.
Single Neuron Results
Results
Sequential monte carlo results
Cell 1
Cell 2
Cell 3
Cell 4
1.5 3 4.5 6 7.5 9 10.5 12 13.5 15
Time (sec)
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 24 / 34
25.
Population of Neurons
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 25 / 34
26.
Population of Neurons Generative Model
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 26 / 34
27.
Population of Neurons Generative Model
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 27 / 34
28.
Population of Neurons Algorithm for inferring connectivity
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 28 / 34
29.
Population of Neurons Algorithm for inferring connectivity
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 29 / 34
30.
Population of Neurons Results
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 30 / 34
31.
Population of Neurons Results
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 31 / 34
32.
Discussion
Outline
Introduction
1
Single Neuron
2
Generative Model
Inverting the model
Results
Population of Neurons
3
Generative Model
Algorithm for inferring connectivity
Results
Discussion
4
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 32 / 34
33.
Discussion
Discussion
Conclusions
We have developed optimal inference algorithms for inferring spike
trains from calcium movies
The code is easy to use and runs very quickly
Next steps
Conﬁrm simulated results with in vitro data
Generalized theory to account for novel scenarios (like genetic sensors)
Include optimal stimulation protocol to reduce variance of
connectivity error
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 33 / 34
34.
Discussion
Ideal data sets
Calibration data
1 Movies with high frame rates (∼ 67 Hz), many neurons (> 50), many
spikes/neuron (> 100), with ground truth from a few neurons
Include stimulation of neurons
2
Excitatory/inhibitory labeling of neurons using ﬂuorescent markers
3
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 / 34
35.
Discussion
Ideal data sets
Calibration data
1 Movies with high frame rates (∼ 67 Hz), many neurons (> 50), many
spikes/neuron (> 100), with ground truth from a few neurons
Include stimulation of neurons
2
Excitatory/inhibitory labeling of neurons using ﬂuorescent markers
3
Answering circuit questions
Impact of thalamic stimulation on subsets of observable neurons
1
Statistical properties of the network (eg, how common are reciprocal
2
connections)
Insert your experimental question here. . .
3
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 / 34
36.
Discussion
Aaron, G. and Yuste, R. (2006).
Reverse optical probing (roping) of neocortical circuits.
Synapse, 60(6):437–440.
Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D.,
and Yuste, R. (2004).
Synﬁre chains and cortical songs: temporal modules of cortical
activity.
Science, 304(5670):559–564.
Kerr, J., de Kock, C., Greenberg, D., Bruno, R., Sakmann, B., and
Helmchen, F. (2007).
Spatial organization of neuronal population responses in layer 2/3 of
rat barrel cortex.
Journal of Neuroscience, 27(48):13316.
Nikolenko, V., Poskanzer, K., and Yuste, R. (2007).
Two-photon photostimulation and imaging of neural circuits.
Nature Methods, 4:943–950.
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 / 34
37.
Discussion
Shepherd, G., Stepanyants, A., Bureau, I., Chklovskii, D., and
Svoboda, K. (2005).
Geometric and functional organization of cortical circuits.
Nature neuroscience, 8:782–790.
Shepherd, G. and Svoboda, K. (2005).
Laminar and columnar organization of ascending excitatory projections
to layer 2/3 pyramidal neurons in rat barrel cortex.
Journal of Neuroscience, 25(24):5670–5679.
Smetters, D., Majewska, A., and Yuste, R. (1999).
Detecting action potentials in neuronal populations with calcium
imaging.
Methods, 18(2):215–221.
Stepanyants, A. and Chklovskii, D. (2005).
Neurogeometry and potential synaptic connectivity.
TRENDS in Neurosciences, 28(7):387–394.
Yoshimura, Y., Dantzker, J., and Callaway, E. (2005).
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 / 34
38.
Discussion
Excitatory cortical neurons form ﬁne-scale functional networks.
Nature, 433:868–873.
Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 34 / 34
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