The neural code�Oscillations

Kenneth D Harris, UCL

Local field potential

• Oscillations are generated by rhythmic firing of action potentials in populations of neurons

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• But they are often measured by the local field potential (LFP), measured inside the brain

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• Or the electroencephalogram (EEG), measured outside the skull
• Where they were first discovered

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• These potentials reflect synaptic activity

Physical basis of the LFP signal

Power spectrum

White noise, pink noise, narrow- and broadband oscillations

LFP power spectra

• Typical “1/f” shape (pink noise). Can multiply by f to normalize
• Oscillations seen as modulations around this
• Usually small, broad peaks
• Ocassionally narrowband

Two types of oscillation

• “Inactive” oscillations
• When the brain is resting/idling/sleeping
• Alpha (eyes closed, visual cortex)
• Beta (immobility, motor system)
• Slow, delta, spindle (sleep, thalamus/cortex)

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• “Active” oscillations
• When the brain is in an active state
• Theta (spatial exploration, rodent hippocampus)
• Gamma (Cortex/hippocampus, active states)

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Two types of oscillation

• “Inactive” oscillations
• When the brain is resting/idling/sleeping
• Alpha (eyes closed, visual cortex)
• Beta (immobility, motor system)
• Slow, delta, spindle (sleep, thalamus/cortex)

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• “Active” oscillations
• When the brain is in an active state
• Theta (spatial exploration, rodent hippocampus)
• Gamma (Cortex/hippocampus, active states)

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Visual cortical Alpha rhythm

• 8-12 Hz oscillation over visual cortex of humans
• Particularly when the eyes are closed or during rest (but not sleep)

Beta rhythm in motor system during immobility

Human globus pallidus and substantia nigra

Off L-DOPA

On L-DOPA

Sleep: delta, slow, and spindle oscillations

Two types of oscillation

• “Inactive” oscillations
• When the brain is resting/idling/sleeping
• Alpha (eyes closed, visual cortex)
• Beta (immobility, motor system)
• Slow, delta, spindle (sleep, thalamus/cortex)

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• “Active” oscillations
• When the brain is in an active state
• Theta (spatial exploration, rodent hippocampus)
• Gamma (Cortex/hippocampus, active states)

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Theta oscillation: locomotion

Gamma oscillation: multifarious high-frequency oscillations

High-gamma correlates with firing rate

• High-frequency broadband power usually correlates with firing rate
• Sometimes called high-gamma or epsilon
• Is it an oscillation?

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Attention reduces low-frequency power in V1

Different cells and cell types fire on different phases

• Hypothesis: different theta phases reflect different steps in a computation cycle
• Inputs from different regions arrive in different phases
• Different inhibitory classes are active

Phase of firing can encode information

How do you measure phase?

• Hilbert transform estimates instantaneous phase and amplitude of a narrowband oscillation
• Doesn’t work for broadband signals! So you might need to filter your data.

Phase histogram

• Different cells prefer different phases

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• How do we compute each cell’s mean phase?

Linear mean doesn’t work

Circular mean

How does phase depend on another variable?

• Don’t use linear regression!

Nadaraya-Watson smoothing for phase

Phase field

• Local likelihood estimation for von Mises

Confirmatory statistics:

• How to test that phase is independent of place?

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• Shuffling method?

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• Test statistic?

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Interpretation of phase precession

• Three types of temporal coding:

1. Following the timing of an external stimulus

2. Sequence of activity reflecting steps in a serial computation

3. Generating new temporal structure that encodes non-temporal information

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• Phase precession is not type 1.
• Could it be type 2? Or both 2 and 3?

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