Towards inferring circuits from calcium imaging

                                                 Joshua Vogelstein
      ...
The Most important slide of the talk




   Acknowledgments
       Eric D. Young
           Liam Paninski
           Adam ...
Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
          Inverting the model
...
Introduction

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
          In...
Introduction

    What is our goal?

   Inferring a microcircuit




Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring ...
Introduction

    Everybody wants it



   List of Publications
        [Smetters et al., 1999, Ikegaya et al., 2004, Aaro...
Introduction

    Why is this a hard problem?




   Many reasons. . .
           Too many spike trains (2T ) to search th...
Introduction

    What are we going to do?



   Our strategy
       Write down a generative model, explaining the causal ...
Introduction

    What are we going to do?



   Our strategy
       Write down a generative model, explaining the causal ...
Single Neuron

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
          I...
Single Neuron    Generative Model

    Outline


        Introduction
   1


        Single Neuron
   2
          Generati...
Single Neuron    Generative Model

    Generative Model for a single neuron



   Equations


                            ...
Single Neuron    Generative Model

    Generative Model for a single neuron

   Simulation




Joshua Vogelstein Yuriy Mis...
Single Neuron    Generative Model

    Generative Model for a single neuron
   Simulation

                    Spatially
 ...
Single Neuron    Inverting the model

    Outline


        Introduction
   1


        Single Neuron
   2
          Gener...
Single Neuron    Inverting the model

    Inverting the model




   How do we do it?
      Our model is a hidden markov m...
Single Neuron    Inverting the model

    Inverting the model



   How do we do it?
      We use anexpectation-maximizati...
Single Neuron    Inverting the model

    Approximating the E step
    Using the tridiagonal non-negative deconvolution


...
Single Neuron    Inverting the model

    Approximating the E step
    Using sequential monte carlo




   How we do it
  ...
Single Neuron    Results

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
...
Single Neuron    Results

    Results

   Four cells simulated according to our generative model




Joshua Vogelstein Yur...
Single Neuron    Results

    Matlab Demo




Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium i...
Single Neuron    Results

    Results
   Tridiagonal non-negative deconvolution results

                 Cell 1




     ...
Single Neuron    Results

    Results
   Sequential monte carlo results

                 Cell 1




                 Cell...
Population of Neurons

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
   ...
Population of Neurons   Generative Model

    Outline


        Introduction
   1


        Single Neuron
   2
          G...
Population of Neurons   Generative Model




Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium im...
Population of Neurons   Algorithm for inferring connectivity

    Outline


        Introduction
   1


        Single Neu...
Population of Neurons   Algorithm for inferring connectivity




Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circ...
Population of Neurons   Results

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative...
Population of Neurons   Results




Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging   M...
Discussion

    Outline


        Introduction
   1


        Single Neuron
   2
          Generative Model
          Inve...
Discussion

    Discussion


   Conclusions
       We have developed optimal inference algorithms for inferring spike
    ...
Discussion

    Ideal data sets


   Calibration data
     1 Movies with high frame rates (∼ 67 Hz), many neurons (> 50), ...
Discussion

    Ideal data sets


   Calibration data
     1 Movies with high frame rates (∼ 67 Hz), many neurons (> 50), ...
Discussion


          Aaron, G. and Yuste, R. (2006).
          Reverse optical probing (roping) of neocortical circuits....
Discussion


          Shepherd, G., Stepanyants, A., Bureau, I., Chklovskii, D., and
          Svoboda, K. (2005).
      ...
Discussion

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




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  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 22. Single Neuron Results Matlab Demo Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 22 / 34
  23. 23. Single Neuron Results 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) Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 23 / 34
  24. 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. 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. 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. 27. Population of Neurons Generative Model Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 27 / 34
  28. 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. 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. 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. 31. Population of Neurons Results Joshua Vogelstein Yuriy Mishchenko (JHU/CU)Inferring circuits from calcium imaging March 24, 2009 31 / 34
  32. 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. 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. 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. 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. 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. 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. 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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