High-dimensional geometry of cortical population activity Marius - PowerPoint PPT Presentation

High-dimensional geometry of cortical population activity Marius Pachitariu University College London

• Part I: introduction to “the brave new world of large - scale neuroscience” • Part II: large-scale data preprocessing with Suite2p • Part III: large-scale data analysis • Visual stimulus responses • Ongoing spontaneous activity • Behaviorally-related activity

The brave new world of large-scale neuroscience* However, we are accelerating!!! 2017 prediction: ∼ 200 neurons Stevenson & Kording, 2011 *Gao and Ganguli, Current Opinion in Neurobiology 2015

“Standard”, ∼ 200 cell recordings https://www.youtube.com/watch?v=xr-flH2Ow2Y

“Zoomed out”, multiplane imaging, ∼ 10,000 cell recordings 10x real time https://www.youtube.com/watch?v=xr-flH2Ow2Y Conventional resonant 2p scope 12 planes @ 2.5 Hz / plane GCaMP6s in excitatory neurons (Ai94, EMX-Cre) Layers 2/3 and 4

2016, year of the mesoscopes Sofroniew et al, 2016, eLife Chen et al, 2016, eLife Stirman et al, 2016 , Nature Methods Nadella et al, 2016, Nature Methods

2016, year of the mesoscopes 2017, year of the high-density probes Neuropixels probe 70 μ m 384 channels digitized 960 sites 1 cm

Right now, we can record 1,000 neurons with electrodes 10,000 neurons with two-photon But why do we need to record so many neurons? Is it really necessary?

How do we make sense of this kind of data? • dimensionality reduction • measure tuning to stimuli stimuli • relate to behavior, neurons 10,000 decision-making, data perception • etc. • then do statistics x B number of dimensions

Is cortical activity: Low dim Lo dimensio ional? l? • good for us we only need to record a subset of all neurons • bad for the e brain no room for complex computations, wasted neurons High gh dim dimensio ional? • bad for us we need to record a LOT of neurons • good for the e brain complex computations, like object recognition in deep networks

Classical theories of visual cortex MOUNTCASTLE • All neurons in a column encode the same quantity, redundantly Bosking et al, 1997, J Neurosci BARLOW • Cortex recodes into a high dimensional sparse code Nonlinear Expansion transformation Low dimensional Low dimensional High dimensional input in few dense code in sparse code neurons many neurons Cortical membrane Thalamocortical inputs Cortical spiking potentials Barlow, Possible principles underlying the transformations of sensory messages, 1961

Is cortical activity low or high dimensional? Gao and Ganguli, Curr. Op. Neuro. 2015

Is cortical activity low or high dimensional? 100 trials neurons Gao,…, Ganguli, CoSyNe 2014 data 100 • we cannot really know yet • not enough recorded neurons, stimuli 2,800 stimuli Our study neurons • we recorded ∼ 10,000 neurons 10,000 • we showed ∼ 3,000 stimuli data • long periods of spontaneous activity (2 hours)

Multiplane imaging in visual cortex of awake mice 10x real time https://www.youtube.com/watch?v=xr-flH2Ow2Y Conventional resonant 2p scope 12 planes @ 2.5 Hz / plane GCaMP6s in excitatory neurons (Ai94, EMX-Cre) Layers 2/3 and 4

Suite2p pipeline

Cell detection model 𝑠 𝑙 = ෍ Λ 𝑙𝑗 𝒈 𝑗 + 𝛽 𝑙 ෍ 𝐶 𝑙𝑘 𝒐 𝑘 + 𝜃 𝑗 𝑘 • 𝑠 𝑙 is the timecourse of pixel 𝑙 • Λ 𝑙𝑗 is the weight of the ROI 𝑗 onto pixel 𝑙 • 𝒈 𝑗 is the timecourse of ROI 𝑗 • B 𝑙𝑘 is the weight of the background component 𝑘 onto pixel 𝑙 • 𝒐 𝑘 is the timecourse of background component 𝑘 • 𝜃 is some noise, which we’re going to model as Gaussian

12,392 neurons Processed in 2 hours on a GPU by Suite2p

Registration

Th The effect of of the the ba background sign signal l on on fluo fluorescence at t the the som soma

Mo Model elli ling the the ba background sig signal is is rea eall lly im impo portant!!!

Graphical user interface for quality control

Comparing with the other major pipeline (Pnevmatikakis et al) …we find more cells!

The activity of boutons (pre-synaptic terminals)

The activity of dendrites and spines (post-synaptic terminals)

Spike deconvolution 𝐆 − 𝐭 ∗ 𝐥 2 + 𝜇 ⋅ 𝑀(𝐭 ሻ 𝑫 𝐭 = 𝐆 is the fluorescence of one cell 𝐥 is the calcium response kernel 𝐭 is the actual spike train 𝜇𝑀 𝒕 is a regularization penalty

We have >10,000 cells, now what?

Neural tuning to drifting gratings example neuron mean (12,392 neurons) responses ( t est da t a) Gaussian fit 0.6 sd = 11.4 deg 0.4 0.2 more examples 0 -200 -100 0 100 200 degrees from preferred direction

Responses to visual stimuli 100 of 3,000 stimuli 9 of 3,000 stimuli data 300 of 10,000 neurons (presented twice – over 2 hours)

Dimensionality estimation Stimuli Dimensions Stimuli ≈ x Neurons Neurons Linear model B data

more diverse stimuli Model (linear) = more dimensions data x B 32 32 directions nat scenes 1 1 explained variance fraction 0.5 0.5 0 0 1 4 8 12 16 1 4 8 12 16 number of dimensions number of dimensions

Dimensionality of thousands of stimuli Model (linear) repeat 1 data x repeat 2 B 1 ex pl a in e d va ri a n ce • compute signal variance fraction • fit model to each repeat upper 0.5 bound • unexplained variance ~1,000 = signal variance of residuals of model fit 0 16 128 1024 number of dimensions

Nonli linear dimensionality reduction Hypothetical scenario 50 Dimensionality is • 2 --- linear 40 • 1 --- nonlinear neuron 2 30 20 10 0 0 10 20 30 40 neuron 1

Defining nonlinear dimensionality Ambient dimension: 3 Linear dimension: 2 Nonlinear dimension: 1

Nonli linear dimensionality reduction linear nonlinear Model (linear) Model (nonlinear) data f x B data = f(Bx)

~ 4x fewer dimensions in nonlinear model linear nonlinear 32 16 32 nat scenes orientations directions

2,800 na 2, natural l im images, , rep epeated tw twic ice, , ~ 4x fewer dimensions in nonlinear model Linear model Nonlinear model 100 95% 95% Explained variance (%) 50 0 4 16 128 1024 4 16 128 1024 Number of dimensions Number of dimensions

How can the nonlinear dimensionality be so much lower? 16 orientations basis functions B threshold rectified linear response fit nonlinear recorded basis function neuron #3943 reconstruction 0 45 90 135 0 45 90 135 0 45 90 135 orientation (deg) orientation (deg) orientation (deg) Number of dimensions

Dimensionality is higher than predicted by filtering images Linear model Nonlinear model 100 95% 95% Explained variance (%) Gabor Gabor filters filters 50 0 4 16 128 1024 4 16 128 1024 Number of dimensions Number of dimensions

Did we present enough stim timuli? Linear model Nonlinear model 100 95% Explained variance (%) Dimensions to explain 900 more 95% variance more stimuli stimuli 600 50 300 0 0 4 16 128 1024 4 16 128 1024 1,000 2,000 3,000 0 Number of dimensions Number of dimensions Number of stimuli Nope. No sign of saturation.

Did we record enough ne neurons? Linear model Nonlinear model 100 95% Explained variance (%) Dimensions to explain 900 more 95% variance more neurons neurons 50 600 300 0 0 4 16 128 1024 4 16 128 1024 4,000 6,000 0 2,000 Number of dimensions Number of dimensions Number of neurons Nope. No sign of saturation.

The sensory cortex

What about spontaneous activity?

1,500 of 13,451 neurons during spontaneous activity 1,500 neurons 30 minutes

Top principal component Time Dimensions Time x ≈ Neurons Neurons Linear model B data Top principal component

Same neurons, reordered by first principal component 1,500 neurons PC1

The first principal component is… the the pu pupil il 1,500 neurons Pupil area PC1

Non-negative matrix factorization (is kind of like clustering) Time Dimensions Time ≈ x Neurons Neurons Non-negative constraints B data B>0 X>0

Same neurons, organized into clusters 1,500 neurons

Pairwise spontaneous correlations are consistent Correlation matrices (10 out of 12,384 neurons) 1 st half of data 2 nd half of data How many dim Ho dimensions s of f sp spontaneous act ctivity y acc ccount for th the correlation matrix? • similarity of matrices: 90.34% common variance

Decomposing the correlation matrix Neurons Neurons Dimensions Dimensions B 𝑈 ≈ Neurons Neurons Correlation B matrix Two different time periods Time Dimensions Time Dimensions Time ≈ 𝑦 1 𝑦 2 Neurons Neurons Neurons Z-score B B (data)

Spontaneous activity: dimensionality 20,000 timepoints of the correlation matrix neurons 10,000 explained variance data variance explained x B number of dimensions

Have we recorded enough neurons? Yes! increasing number of neurons

Does spontaneous activity resemble stimulus responses? Can we visualize them together? Kenet et al, Nature , 2003 Ringach, Curr Op Neurobiol 2009 Berkes et al, Science 2011 (and many more)