Brain Rhythms

Question 1

Why did Umberto say he was not going to talk about studies such as gamma oscillations and meditation?

Answer 1

While important, most of this evidence (identification of a cognitive task with fluctuations in gamma) is phenomenological. It precludes what are the mechanisms of oscillations and what are the neuronal computations modulated by oscillations.

Question 2

What is the focus of this lecture instead?

Answer 2

More mechanistic questions:
*What are Brain Oscillations? (and what are the metrics that we use to
measure brain oscillations)
*What are the mechanisms underlying brain oscillations?
*What are the functions of oscillations?

Question 3

What function is used as a representation of a rhythm?

Answer 3

A sinusoidal function; may not be super accurate but a sinusoidal function is the best way to represent a rhythm

Question 4

Describe a sinusoidal function mathematically and explain the parameters

Answer 4

f(t) = A x sin( ωt + ø)
where
ω = 2π f; angular speed; equation like clock
A = amplitude; how big is the oscillation
t = time
f = frequency; how long a cycle lasts in time; period = 1 / frequency
ø = phase; when the peak is in the oscillation

Question 5

Describe a study which demonstrates the influence of oscillations on the LFP signal

Answer 5

Researchers recorded neuronal activity with an electrocorticographic (ECoG) grid covering large parts of the left hemisphere of 2 macaque monkeys, and recorded eye movements using a tracker while they freely viewed natural images. They found that natural viewing led to pronounced gamma-band activity in the visual cortex. Amplitude increase and changes in frequency were observed after saccades. This demonstrates that oscillations are an essential part of the LFP signal

Question 6

What is a PSTH and can it depict the contribution of a neuron to an oscillation?

Answer 6

Cross-correlograms or peristimulus time histograms are functions which plot the activity of one electrode relative to another. The cross-correlogram plots a count of the spikes in certain time bins in the target neuron following a spike in the reference neuron. Therefore, the graph plots a dependence of one neuron on the other neuron; If there is no dependence of the target neuron on the reference neuron, then the activity plotted should be relatively constant or flat. Peaks in the cross-correlogram indicate an increase in activity of the target neuron following an increase of activity in the reference neuron. Conversely, dips in the graph would indicate a decrease in the rate of activity in the target neuron following an increase of activity in the reference neuron. This can be observed in an interneuron – pyramidal cell pair, where an increase in activity of the interneuron results in a decrease in activation of the pyramidal cell. It shows increase of spiking activity after t = 0. The rhythmic nature observed neurons is not visible in a PSTH. The PSTH (counting spikes) does not
show the oscillatory behaviour of this
neuron

Question 7

How can we measure the oscillation of a sigle isolated neuron?

Answer 7

Autocorrelation function:
* The spike interval distribution measures the distribution of times between successive AP in a train
* The distribution of times between any two spikes on a train is called the spike-train autocorrelation function of a neuron:
Qpp(τ) = 1/Τ ∫(Τ,0) dt<(p(t) - <r>)(p(t+τ) - <r>)></r></r>

Question 8

Describe what this equation does intuitively

Answer 8

Takes a spike train and duplicates it and overlays the two trains. It then slightly shifts the original to the right and the duplicate to the left so they’re no longer exactly overlaying but are still the same pattern. The graph in docs labeled D is an autocorrelation histogram measuring how much the two spike trains overlay at gradual increments at T=0. Autocorrelation measures the relationship between a variable’s current value and its past values. An autocorrelation of +1 represents a perfect positive correlation, while an autocorrelation of negative 1 represents a perfect negative correlation. If spike train is periodical, at some point, you will see an oscillatory component/rhythm. You can calculate the distance between peaks to get the period.

Question 9

How can a fourier based analysis help with EEG/ LFP recordings?

Answer 9

It can tell you what the presence of a particular signal is in the overall signal. It can decompose the signal into multiple sine functions and determine the weight of it. A stronger signal indicates a higher power.

Question 10

What sacrifice do you make through this fourier analysis?

Answer 10

You lose the time variable; it tells you the power as a function of frequency.

Question 11

How can you keep the time variable in the fourier analysis?

Answer 11

Sliding window analysis: you carry out this analysis part by part and achieve a sort of heat map shown in the docs (saccades)

Question 12

Describe the oscillitary nature of the LFP/ EEG signal

Answer 12

The LFP can be modeled as a sum of dampened oscillators driven by a tonic excitatory drive. By dampened it means that the amplitude gradually decreases like a swing being pushed and neglected. The oscillations aren’t actually sinusoids, they aren’t fixed at a certain Hz. Local circuits change frequency as well as amplitude due to tonic excitatory drive.

Question 13

What equation is therefore used to model this oscillation?

Answer 13

General equation:
x(t) = (Ae^-bt/2m)(sin(w’t+ø))
where w’= sqrt(k/m - b^2/4m^2); angular frequency
k/m is regarding the mass and drive in the oscillator

Sinusoidal function for comparison:
f(t) = A x sin( ωt + ø)

Question 14

Give the following oscillation classes in order of increasing frequencies:
gamma
theta
beta
delta

Answer 14

Delta: 1.5-4Hz
Theta: 4-10 Hz
Beta: 10-30 Hz
gamma: 30-80Hz

Question 15

What can be observed when plotting frequency and power (power analysis)?

Answer 15

There is a near-linear decrease of log power with increasing log frequency from 0.5 to 100 Hz. This demonstrates that that there are low-frequency perturbations cause a cascade of high-
frequency energy dissipation

Question 16

What signals are true oscillators and which are not in this power spectrum?

Answer 16

Only periodical signals are true oscillators, this relative power shows oscillations and is a periodic component we’d like to study. The aperiodical component reflects power energy (in all frequencies) without oscillations. The aperiodic component also reflects important physiological properties (criticality)

Question 17

When should you remove periodic components from the power spectrum and when should you keep them?

Answer 17

Remove it when: focusing on fast-time-scale dynamics –> things that are changing in the brain on a time-scale (specific brain responses to let’s say visual stimuli)

Embrace it: when focusing on long time-scale traits or dynamics

Question 18

What is meant by neuronal synchrony?

Answer 18

Synchrony is a widespread concept in physics and biology (e.g., Huygens’ observation on synchronous clocks). In neural systems, synchrony is a measure of relationship between two neural signals (Spike-Spike, LFP-LFP, Spike-LFP). It measures the dependence of the firing of one neuronal group respecting another neuronal group.

Question 19

What model is used to describe synchronisation phenomena in natural systems?

Answer 19

The Kuramoto Model describes the behaviour of a system of coupled oscillators. This model is used to describe synchronization phenomena in natural systems. (website with adjustable parameters)

Question 20

Describe the Kuramoto model

Answer 20

The model defines the rate of change of state variables θn(t) according to:

θn = wn + K/N sum(sin(θm-θn)

Parameter K represents the coupling strength of the oscillators
Models each member of the population as a phase oscillator and manually changes the coupling between them

Question 21

backtracking a little
What is meant by pink noise?

Answer 21

Noise in electronics which is not flat but observed at lower frequencies which then dissipates

Question 22

What causes coupling in oscillations?

Answer 22

Coupling can be any joining factor such as the cans under metronomes. The brain has some kind of force that causes the coupling which allows us to observe oscillations.

Question 23

Name two ways we can observe coupling/ synchrony between two neurons (from looking at spike trains)

Answer 23

Simultaneous firing: zero-time lag
Consistent delay: XX ms time lag (coupling is slightly weaker)

Question 24

How can we use a function to investigate neuronal synchrony in the time domain

Answer 24

Cross-correlation function: is analogous to the autocorrelation but with spike trains from different neurons

Question 25

How can we use a function to investigate neuronal synchrony in the frequency domain?

Answer 25

A coherence spectrum: Coherence is the normalised cross-spectrum, it quantifies linear coupling between 2 signals; how consistent is the phase difference between 2 signals.

C1(f) = S1^XY (f) / sqrt(S1^XX (f) S1^XY (f))
aka cross-spectrum of 2 signals / auto spectrum of 2 signals

The cross-spectrum is kinda like cross correlation for LFPs, The auto-spectrum is kinda like auto correlation for LFPs.

From the raw EEG/LFP recordings, first, do Fourier analysis to get amplitude and phase information. Then normalise by amplitude to find the phase relationship.

Question 26

How can the phase difference be interpretted?

Answer 26

As the phase difference across signals; the angle shows you the difference in phase; is phase difference consistent? Then it is periodic

Question 27

Why can we rely on EEG or MEG studies to find neuronal (oscillatory) correlates across of different cognitive functions? What must we be aware of when doing this?

Answer 27

Oscillations are scalable measurements across different spatial recordings. That is the reason why we can rely on EEG or MEG studies to find neuronal (oscillatory) correlates across of different cognitive functions. BUT we must be aware that oscillations are coordinating the activity of neuronal circuits to different low-level computational operations. Conrado’s opinion is that oscillations don’t really represent things or cognition, but shows low-level operations at microcircuit level and that engages representations.

Question 28

On a superficial level, what are the mechanisms underlying cortical oscillations?

Answer 28

Single neurons are the building blocks of network oscillations; Oscillations properties depend on channel conductances of Na+ and K+

Question 29

What are relaxation type of oscillators?

Answer 29

Relaxation types of oscillators are non-lineal, their “phase response curve” depends on the ‘timing’ of the input pulse.

Question 30

Why are action potentials and membrane potentials relaxation type oscillators?

Answer 30

Relaxation type of oscillators - we can delay or prolong the relative refractory period of neurons. If you give an input during refractory period, you’ll see it much more delayed. If you give it near the end of the refractory period, you’ll see the response immediately, so this way it is non-linear. (?; unsure)

Question 31

Describe an example of ‘chattering cells’

Answer 31

Recorded from intracellular recordings in striate cortex (V1) of anesthetised cats; Cells located in superficial layers of V1 cortex.
*Intrinsically generate 20- to 70-hertz repetitive bursting firing in response to suprathreshold depolarizing current injection
*Chattering cells exhibit pronounced oscillations in membrane potential during visual stimulation

Question 32

Describe the results of a recent study which re-studied cells in V1 with similar properties as Chattering Cells

Answer 32

Narrow-waveform (Bursting) cells (putative chattering cells) seems to be a new and specific type of excitatory cells; These cells show strong phase-locking to the LFP gamma rhythm (very strong lateral inhibition; phase is consistent at a given frequency) and are very selective to image orientation. Also, they appear to be specific of primates (Rhesus, Capuchin monkeys) and carnivores (cats); not clearly observed in rodents.

Usually, Narrow waveform (NW) spikes come from Interneurons, and Broad waveform (BW) from excitatory cells, but this study found a bigger number of NW in primate V1. Analysis of these cells show a non-overlapped population of NW cells (Burst and non-Burst). The bursting population resembles the previously found Chattering Cells.

Question 33

How has gamma activation been causally achieved?

Answer 33

Researchers targeted particular parvalbumin interneurons and excitatory neurons and excited them via optogenetics (PV-Cre, aCamKII-Cre). Immediately the LFP oscillates and resonates at high freq. Found that light-driven activation of fast-spiking interneurons at varied frequencies (8-200 Hz) selectively amplifies gamma oscillations. In contrast, pyramidal neuron activation amplifies only lower frequency oscillations, a cell-type-specific double dissociation. Parvalbumin interneuron cells are therefore important in the generation of this gamma rhythm

Using cell-type-specific optogenetic manipulations in behaving animals, other researchers showed that dendrite-targeting somatostatin (SOM) interneurons are critical for a visually induced, context-dependent gamma rhythm in visual cortex. This was verified with a computational model. SOM-mediated oscillations may expand the computational power of gamma rhythms.

Altogether: Inhibitory interneurons have a critical role in the generation of oscillations

Question 34

Describe the I-I models of gamma oscillations

Answer 34

Only three requirements are needed for gamma oscillations to emerge, as illustrated by a
“stripped-down” network model consisting of only inhibitory interneurons (see docs; a). mutually connected inhibitory interneurons, a time constant provided by GABA_A receptors, and sufficient drive to induce spiking in the interneurons. Gamma oscillations in inhibitory-inhibitory (I-I) neuron models can emerge in two different ways: When the input drive is relatively tonic, neurons can fire spikes with a well-defined periodicity (a). By contrast, when neurons receive stochastic inputs and fire spikes irregularly, sufficiently strong recurrent synaptic interactions will make the asynchronous state unstable against random fluctuations, and oscillations emerge. In both cases, the emerging synchrony is caused when a subset of the interneurons begins to discharge together and generates synchronous IPSPs in the partner neurons. In turn, the inhibited neurons will spike again with increased probability
when GABA_A receptor–mediated hyperpolarisation has decayed, and the cycle repeats.

Question 35

Describe the E-I models of gamma oscillations

Answer 35

These models are based on the reciprocal connections between pools of excitatory pyramidal (E) and inhibitory (I) neurons. In these models, fast excitation and the delayed feedback inhibition alternate, and with appropriate strength of excitation and inhibition, cyclic behaviour may persist for a while. They describe reciprocally connected E-I network where pyramidal cells send fast excitation via AMPA receptors to interneurons, which in turn provide inhibition via GABA_A receptors, leading to coherent oscillations in the gamma-frequency range.

Question 36

Therefore what does Conrado describe is required for gamma generation?

Answer 36

1. Mutually connected inhibitory interneurons
2. Time constant provided by GABA type A receptors
3. Excitatory drive to induce spiking in interneurons

The combination of these mechanisms make gamma oscillations a robust and heritable phenotype

Question 37

Name two models of gamma generation proposed by the bossman himself

Answer 37

Pyramidal-Interneuron Gamma generation (PING)

Interneuron-Interneuron Gamma generation (ING)

Question 38

describe the PING model

Answer 38

Pyramidal-Interneuron Gamma generation (PING): Upper panel (see docs) shows an E pyramidal neuron and an inhibitory I with reciprocal connections. Lower panel shows the spike rate fluctuations between I and E cell populations. I stimulation by E cells causes an increase in the I firing rate which, in turn, inhibits E neurons. When the firing rate of I neurons decays, E neurons increase their activity, producing an oscillatory response. Excitatory and Inhibitory cells are phase-locked to the rhythm of gamma.

Question 39

What research supports the PING model?

Answer 39

Recordings of prefrontal cortex in anaesthetised ferrets:
Excitatory and Inhibitory cells are phase-locked to the rhythm of gamma RS (excitatory) cells spike before then FS (inhibitory); they are responsible for different parts of the cycle.

Question 40

Describe the ING model

Answer 40

Upper panel (docs) shows a simplified version of two Is reciprocally connected. These interneurons, under proper excitatory drive (red arrows on the left), exert rhythmic inhibition on the adjacent population of pyramidal E neurons. Lower panel shows the expected spike-rate relationships between the two neuronal populations (I in blue and E in red). Excitation of I neurons produces volleys of activity that will reciprocally inhibit themselves. This releases the inhibition exerted over the E cells, rendering a synchronous increase in the firing rate at the E population. The period is determined by the recovery of the I cells.

Question 41

What evidence has been found for the PING theory?

Answer 41

• PV cells fire unconditionally lock to gamma activity when power is separated into quantiles
• Pyramidal cells are phase locked during visually evokes gamma bursts; only when stimulated

Question 42

Give two opposing (extreme) views of the following question:
What are the functions of neuronal oscillations?

Answer 42

The “functions” of oscillations are not clearly defined, some authors consider oscillations as an epiphenomenon of neuronal activity. Merely, a reflection of the excitatory/inhibitory balance within neuronal circuits (e.g., Roelfsema)

Other authors consider brain rhythms as a brain-wide coordinator of activity (integration of many distributed processed into globally ordered states).

Question 43

How does Conrado view neuronal oscillations?

Answer 43

“Brain Rhythms provide a framework for a neural syntax “

Question 44

Historically, what two functions of gamma oscillations have been defined

Answer 44

1. Binding
2. Flexible routing

Question 45

What is meant by the function ‘binding’?

Answer 45

Temporal binding has been suggested as a remedy to the problem of how to define dynamic functional relations between neurons in distributed sensorimotor networks e.g if you have very distant cells processing small visual fields, how do they know a particular area is a table and not a chair? The binding solution posits that neurons in assemblies can communicate for a cohesive presentation.

Question 46

How can binding by synchronisation (BBS) explain certain illusions?

Answer 46

Say in the example of an perceptual illusion of a face and a candle, the perception of either a face or a candle could be dependent on which cells are in synchrony;

These perceptual situations mutually exclude each other, and most observers flip back and forth between the two. In this case, the temporal binding model predicts that neurons should dynamically switch between assemblies and, hence, that temporal correlations should differ for the two perceptual states. Consider four visual cortical neurons with receptive fields (positions 1–4 in a) over image components, the grouping of which changes with the transition from one percept to the other. As shown in part d of the figure, neurons 1 and 2 should synchronise if the respective contours are part of the one background face, and the same should hold for neurons 3 and 4, which represent contours of the candlestick. When the image is segmented into two opposing faces, the temporal coalition switches to synchrony between 1–3 and 2–4, respectively (e).

Question 47

What problems are there to this BBS solution? (3)

Answer 47

Oscillations are not invariant to stimulus properties. The bigger the stimulus,  there will be an increase in oscillations (see docs) and a decrease in the total number of spikes.

A plaid (instead of a grating) destroys the synchrony, so binding doesn’t seem consistent with the theory. Because plaid if it’s seen by the same two cells, they theoretically should be in synchrony.

Also, noise doesn’t evoke synchrony although it is consciously perceived. So is gamma just a by-product of the circuit activity instead of having a role in perception?

Question 48

What is meant by the function of flexible routing?

Answer 48

Lower areas will compete to send info to higher areas. Fries proposes that gamma oscillations reflect this flexible data transmission across brain areas.

Question 49

What is this flexible routing hypothesis called?

Answer 49

Communication through Coherence (CTC) hypothesis

Question 50

What evidence has been found through communication through coherence (CTC) hypothesis

Answer 50

When animals focused their attention on one of the displayed stimuli, increased gamma-band coherence was observed between the V4 site and the target V1 that conveyed the relevant information. Concomitantly, gamma synchronisation between the unattended V1 site and V4 was reduced. Therefore, top-down attentional signals can exert control over the establishment of coherent relationships between specific regions of primary visual cortex by gamma-synchronising the activity of the neuronal populations involved in visual processing; Gamma synchronization can selectively route relevant (attended) information
through different brain regions

Question 51

What is the ‘behavioural impact’ of gamma synchronisation

Answer 51

According to the referenced article: V1-V4 gamma coherence before stimulus change predicts the speed of change detection of an attended stimulus. Deviations from the phase relation of gamma synchronisation increase reaction times. V1-V4 gamma phase relations explain reaction time differences of 13 to 31 ms. Effects are specific to the attended stimulus and not due to local phase or power

Question 52

What does it mean to say the gamma frequency peak depends on contrast?

Answer 52

One study found that changes in stimulus contrast over time leads to a reliable gamma frequency modulation on a fast timescale. Further, large stimuli whose contrast varies across space generate gamma rhythms at significantly different frequencies in simultaneously recorded neuronal assemblies separated by as little as 400 mm, making the gamma rhythm a poor candidate for binding or communication, at least in V1.

Question 53

What cautionary note does Corando leave about interpreting gamma synchronisation as coherence between areas?

Answer 53

Don’t forget the mechanisms by which the LFP signal is generated: It shows that areas connect dynamically, but it’s not necessary a mechanism there, only connections - input output. Gamma synchronisation (coherence) between areas might be different depending the targeted compartment during electrophysiological recordings.

Question 54

What visual stimuli induce unusually large gamma oscillations in V1? What question does this raise?

Answer 54

Long-wavelength (reddish) hues induce unusually large gamma oscillations in the primate primary visual cortex. Is this the explanation why the study on natural images (Brunet et al. 2013; first study) show an increase of gamma after the presentation of the orange? Is a gamma a mechanism for specific colour relationships ? Could explain why monkeys have such high gamma when looking at a highly uniform (no gratings etc) stimulus.

Question 55

What is the behavioural link between gamma and predictions?

Answer 55

The strength of gamma-synchronisation reflects the extent to which the visual input in the Classical Receptive Field (CRF) can be accurately predicted. Populations with non-overlapping CRFs will gamma-synchronise to the degree that they accurately predict each other’s visual input. Therefore Gamma synchronised networks dynamics facilitate the integration of surround with CRF data

Question 56

What are the likely physiological underpinnings of this relationship with gamma and predictions

Answer 56

The strength of gamma synchronisation reflects the extent to which the visual input in the Classical Receptive Field can be accurately predicted. Neurons that predict surround synchronise better. If there is nothing to predict in the surrounding, you see a decrease in gamma and an increase in the spiking rate. If there is a big area that can be predicted from the receptive field, then you’ll see higher gamma oscillations. When there’s a match between stimulus and surroundings, there is high gamma. When we refer to a receptive field, we usually refer to a whole cortical column, so the increase in gamma oscillations when the surrounding area is predicted well happens within a cortical column. But there are also lateral connections between cortical columns so if we record at a distance, we see the sum of all these columns.

Question 57

Describe a study which demonstrates this relationship of gamma and predictions

Answer 57

When a bar stimulus was presented in a receptive field with bars in the surround field pointing in random directions, reflecting an inaccurate or no prediction by surround: irregular firing was found in that cell and asynchronous, irregular firing was found in surrounding cells which had receptive fields in line with the orientation of the main bar stimulus. This was said to reflect inaccurate predictions between columns.

When a bar stimulus was presented in a receptive field which was one continuous long bar, reflecting an accurate prediction by surround:gamma-rhythmic firing/ gamma-oscillation was found in that cell and gamma-synchronisation was found in surrounding cells which had receptive fields along the bar stimulus. This was said to reflect accurate predictions between columns.

Question 58

How does one study offer an alternative solution to why gamma oscillations were so strong for red hues?

Answer 58

Researchers showed that large uniform surfaces, which have high spatial predictability, strongly suppressed firing yet induced prominent gamma synchronisation in macaque V1, particularly when they were coloured. Yet, chromatic mismatches between centre and surround ( ‘blob mismatch’ group: the central 1 deg of the stimulus had a different (equiluminant) color than the rest of the stimulus; ‘annulus mismatch’ group: presented an annulus ring (of 0.25 deg) of another color on top of the uniform surface (at equiluminant intensity) around the inner one degree from the stimulus center), breaking predictability, strongly reduced gamma synchronisation while increasing firing rates. Differences between responses to different colours, including strong gamma-responses to red, arose from stimulus adaptation to a full-screen background, suggesting prominent differences in adaptation between M- and L-cone signalling pathways. Thus, synchrony signalled whether RF inputs were predicted from spatial context, while firing rates increased when stimuli were unpredicted from context.