Spike Sorting I: Bijan Pesaran New York University

Acknowledgements Ken Harris and Samar Mehta at Neuroinformatics course Woods Hole.

Aims We would like to … Monitor the activity of large numbers of neurons simultaneously Know which neuron fired when Know which neuron is of which type Estimate our errors

Primate retinal ganglion cells, courtesy of the lab of Dr. E.J. Chichilnisky THE PROBLEM: Multiple Neural Signals 3 msec Time (sec) Voltage (A/D Levels) Time (sec) Voltage (A/D Levels)

THE GOAL: Spike Times of Single Neurons Time (sec) Spike Detector Neuron #1 Spikes Neuron #2 Spikes Raw Data Region from previous slide

THE ‘GRADUATE STUDENT’ ALGORITHM Time (sec) Voltage (A/D Levels) Raw Data Threshold detector at 3  2 Time (msec) Voltage (A/D Levels) Candidate Waveforms Spike Height vs. Width Plot Width (msec) Height (A/D Levels) # of Intervals Time (msec) Interspike Interval Histogram

A GENERAL FRAMEWORK Locate Spikes Preprocess Waveforms Density Estimation Spike Classification Quality Measures

Extracellular Recording Hardware You can buy two types of hardware, allowing Wide-band continuous recordings Filtered, spike-triggered recordings

The Tetrode Four microwires twisted into a bundle Different neurons will have different amplitudes on the four wires

Raw Data Spikes

High Pass Filtering Local field potential is primarily at low frequencies. Spikes are at higher frequencies. So use a high pass filter. 800hz cutoff is good.

Filtered Data Cell 1 Cell 2

Spike Detection Locate spikes at times of maximum extracellular negativity Exact alignment is important: is it on peak of largest channel or summed channels?

Data Reduction We now have a waveform for each spike, for each channel. Still too much information! Before assigning individual spikes to cells, we must reduce further.

Principal Component Analysis Create “feature vector” for each spike. Typically takes first 3 PCs for each channel. Do you use canonical principal components, or new ones for each file?

“Feature Space”

Cluster Cutting Which spikes belong to which neuron? Assume a single cluster of spikes in feature space corresponds to a single cell Automatic or manual clustering?

Cluster Cutting Methods Purely manual – time consuming, leads to high error rates. Purely automatic – untrustworthy. Hybrid – less time consuming, lowest error rates.

Semi-automatic Clustering

How Do You Know It Works? We can split waveforms into clusters, but are we sure they correspond to single cells? Simultaneous intra- and extra-cellular recordings allow us to estimate errors. Quality measures allow us to guess errors even without simultaneous intracellular recording.

Intra-extra Recording Simultaneous recording with a wire tetrode and glass micropipette.

Intra-extra Recording Extracellular waveform is almost minus derivative of intracellular

Bizarre Extracellular Waveshapes ModelExperiment

Two Types of Error Type I error (false positive) –Incorrect inclusion of noise, or spikes of other cells Type II error (false negative) –Omission of true spikes from cluster Which is worse? Depends on application…

Manual Clustering Contest

Best Ellipsoid Error Rates Find ellipsoid that minimizes weighted sum of Type I and Type II errors. Must evaluate using cross-validation!

Humans vs. B.E.E.R.

Waveshape Helps Separation

Why were human errors higher? To understand this, try to understand why clusters have the shape they do Simplest possibility: spike waveform is constant, cluster spread comes from background noise Are clusters multivariate normal?

Problem: Overlapping Spikes

Problem: Cellular Synchrony

Problem: Bursting

Problem: Misalignment When you have a spike whose peak occurs at different times on different channels, it can align on either. This causes the cluster to be split in two.

Problem: Dimensionality Manual clustering only uses 2 dimensions at a time BEER measure can use all of them

“Semi-Automatic” Clustering Uses all dimensions at once Errors should be lower Still requires human input

Semi-automatic Performance

Software: KlustaKwik Mixture of Gaussians, unconstrained covariance matrices Speed is crucial CEM Algorithm – faster than EM Most probabilities not calculated Local maxima result in over- and under- clustering Split and merge features to tunnel out of local maxima Still requires supercomputer resources. klustakwik.sourceforge.net

Software: Klusters Recluster Feature Ergonomic Design Auto/Cross correlograms Grouping Assistant Waveforms Timecourse klusters.sourceforge.net

Cluster Quality Measures Would like to automatically detect which cells are well isolated. BEER measure needs intracellular data, which we don’t have in general. Will define two measures that only use extracellular data.

Isolation Distance Size of ellipsoid within which as many spikes belong to our cluster as not

L_ratio

False Positives and Negatives

Which Measure to Use? Isolation distance correlates with false positive error rates –Measures distance to other clusters L_ratio correlates with false negative error rates –Measures number of spikes near cluster boundary

Conclusions Automatic clustering will save time and reduce errors. Errors can be as low as ~5%. Quality measures give you a feeling of how bad your errors are.

Room for Improvement Make it faster Improved spike detection and alignment Quality measures that estimate % error Fully automatic sorting Resolve overlapping spikes Easy Hard