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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

The Most important slide of the talk

Acknowledgments
Eric D. Young
Liam Paninski
Adam M. Packer


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


Introduction

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Introduction

What is our goal?

Inferring a microcircuit


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


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


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


Single Neuron

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Single Neuron Generative Model

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4



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




Simulation



Simulation

Spatially
Filtered
Fluorescence

Calcium

Spike
Train

3 6 9
Time (sec)

Single Neuron Inverting the model

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4



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



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)



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



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


Single Neuron Results

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4



Results

Four cells simulated according to our generative model



Matlab Demo



Results
Tridiagonal non-negative deconvolution 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)



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)



Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Population of Neurons Generative Model

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Population of Neurons Generative Model


Population of Neurons Algorithm for inferring connectivity

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Population of Neurons Algorithm for inferring connectivity


Population of Neurons Results

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


Population of Neurons Results


Discussion

Outline

Introduction
1

Single Neuron
2
Generative Model
Inverting the model
Results

3
Generative Model
Results

Discussion
4


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


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


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


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.

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).

Discussion

Excitatory cortical neurons form ﬁne-scale functional networks.
Nature, 433:868–873.


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