Lecture 11.2: neurons, I (cont.)

A few more functions that neurons compute natively:

• DYNAMIC assemblies
• neurons as READOUT devices

many neurons acting together: cell assemblies and associative recall

Right: Donald Hebb's idea of cell assemblies.

For the cell assembly hypothesis to stand, key questions must be addressed:

• Why doesn't activity spread to the entire network and persist forever?
• How can a far-flung set of neurons be causally effective as a group?

how cell assemblies emerge: neurons as read-out devices (Buzsaki, 2010)

Three hypotheses regarding cell assemblies:

1. Cell assemblies are best understood in light of their output, as detected by "reader-actuator" mechanisms.
2. The hierarchical organization of cell assemblies may be regarded as a neural "syntax".
3. Constituents of the neural syntax are linked together by dynamically changing constellations of synaptic weights (ensembles of synapses, or "synapsembles").

---

[EXTRA: Note that the representations implemented by synapsembles are DUAL to those implemented by neural activities.]

cell assemblies and the problem of segmentation

(A) Hebb's reverberating cell assembly sequences ("assembly phases"). Arrows represent transitions between individual assemblies, numbered sequentially in order. The direction of activity flow across assemblies (edges) is determined by the stronger synaptic strengths among assembly members relative to other connections (not shown). The same assembly can participate in a sequence more than once (e.g., pathway 1, 4 indicates recurring transitions).

(B) Top: long sequence of two characters (e.g., dot and dash). Its embedded information is virtually impossible to recover. Bottom: same exact sequence as above after adding syntactic segmentation (space = stop-start punctuation) between the short strings of characters. The Morse code message reads: "segmentation of information is essence of coding." By analogy, segmentation or "chunking" of neuronal assemblies can be brought about by salient external stimulus sequences, brain-initiated, modality-specific synchronizing-blanking mechanisms (such as saccadic eye movement, sniffing, whisking, active touch, licking, contraction of middle ear muscles, etc.), internally generated oscillations, or other syntactical mechanisms.

reader-defined cell assemblies

(C) Neurons that fire within the integrating window of a reader mechanism (corresponding, e.g., to the ability of a reader neuron to integrate its inputs within the time frame of its membrane time constant) define an assembly (irrespective of whether or not assembly members are interconnected synaptically among themselves). Readers a, b, c ,and w may receive inputs from many neurons (1 to n) by way of synapses differing in strength but respond only to a combination of spiking neurons to which they are most strongly connected (e.g., reader a responds preferentially to cofiring of neurons 1, 5, and 9 at \(t_1\), even though it may be synaptically innervated by neurons 2, 6, and 10 as well; at \(t_2\), neuron b fires in response to the discharge of neurons 2, 6, and 10).

Synaptic strengths between neurons vary as a function of the spiking history of both postsynaptic and presynaptic neuron (short-term plasticity, to be discussed next week). The response of the reader neuron, therefore, depends on both the identity of the spiking upstream neurons and the constellation of current synaptic weights ("synapsembles"). Reader mechanism q has a longer time integrator and, therefore, can link together assemblies to neural "words," reading out a new quality not present in the individual representations of a, b, and c.

cell assembly: the fundamental unit of neural syntax

(A, B) Raster plot (A) of a subset of hippocampal pyramidal cells that were active during a 1 s period of spatial exploration on an open field out of a larger set of simultaneously recorded neurons, ordered by stochastic search over all possible orderings to highlight the temporal relationship between anatomically distributed neurons. Color-coded ticks (spikes) refer to recording locations shown in (B). Cell assembly organization is visible, with repeatedly synchronous firing of some subpopulations (circled).

Vertical lines indicate troughs of theta waves (bottom trace). Note that assemblies can alternate (top and bottom sets) rapidly across theta cycles. [MORE about BRAIN OSCILLATIONS later.]

(C) Spike timing is predictable from peer activity. [NOTE: this implies some very interesting collective dynamics, such as emergence and downward causation.] The histogram here shows the distribution of timescales at which peer activity optimally improved spike time prediction of a given cell, shown for all cells. The median optimal timescale is 23 ms (red line).

synchrony is only a small part of the story of TEMPORAL PATTERNS of neural activity

Summary of neuro-computational properties exhibited by Izhikevich's "simple model":

Eugene M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, 2005.

---

Re the next slide, note especially case (K), "resonator".

(K) an example in which input spike frequency is key: switching/steering a signal

Cell A can direct its output selectively:

• to cell B, by emitting 4 spikes at intervals of 12 ms,

or

• to cell C, by emitting 4 spikes at intervals of 18 ms.

Eugene M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, 2005.

a reality check: neurons are controlled by... (Buzsaki & Tingley, 2023)

Neurons are controlled by neurotransmitters, neuromodulators, hormones, immune factors, and other body-produced substances. In addition to receptors for GABA, glutamate, and canonical neuromodulators (Ach, DA, 5-HT), the average mouse cortical neuron expresses RNA transcripts for more than 60 receptors for metabolites, hormones, peptides (e.g., GPCR receptors), and immune-related molecules.

---

Directional climate change (global warming) is causing rapid alterations in animals’ environments. Because the nervous system is at the forefront of animals’ interactions with the environment, the neurobiological implications of climate change are central to understanding how individuals, and ultimately populations, will respond to global warming. Evidence is accumulating for individual level, mechanistic effects of climate change on nervous system development and performance. Climate change can also alter sensory stimuli, changing the effectiveness of sensory and cognitive systems for achieving biological fitness. At the population level, natural selection forces stemming from directional climate change may drive rapid evolutionary change in nervous system structure and function.

S. O'Donnell (2018). The neurobiology of climate change. The Science of Nature 105:11.

[back to Buzsaki] example of read-out: olfaction in the locust

(A) Wiring diagram of the early olfactory system of the locust. An odorant evokes an odor-specific temporal pattern in several of recurrently connected antennal lobe (AL) projection neurons (PNs), coordinated by a 20–30 Hz (gamma) oscillation. Kenyon cells (KC) of the mushroom body (MB) are the readers of the activity of AL projection neurons (PNs) and integrate their spikes.

(B) Firing patterns of 3 AL neurons (PN1-3) in response to 16 different odors. The activity of AL neurons defines the "population vector" or "state" of the network; the time-varying population vector (i.e., the shifting states) ascribes a trajectory. The state evolves over a few hundred milliseconds before relaxing back to baseline (illustrated by the curve in the inset in A).

(C) Activity of 3 KCs. Each KC carries out a pattern matching operation between its synaptic vector and the PN population activity vector. The AL output evokes a single burst in the reader KC ("sparse coding").

another example: birdsong

(D) Time-frequency spectrum of a zebra finch song and its amplitude envelope.

(E) Spike raster plot of eight projection neurons in area HVC (10 repeats). Each ensemble pattern ("state") in HVC specifies a note to be sung; the temporal sequence of notes (trajectory) defines the song and is read out and sent to the motor execution system by the subsequent stages.

(F) Interneuronal activity is also temporally organized and relates to the syntactic structure of the song.

now: some attention to BRAIN OSCILLATIONS

Simultaneous ECoG–laminar recordings reveal traveling alpha waves which propagate through supragranular cortex (from Halgren et al. 2019).

1. Average circular distance of each ECoG (circles) and layer I laminar (diamond) contact’s alpha phase from the spatial mean phase throughout the ECoG grid.
2. Representative drawing of a traveling alpha wave (as measured with ECoG) propagating through superficial layers (as measured by a laminar probe).
3. Example traces from ECoG contacts posterior (red) and anterior (blue) to the laminar probe (CSD: current source density).

how alpha waves could mediate feedback

(from Halgren et al. 2019)

1. Alpha propagates as a traveling wave from higher-order (middle temporal) toward lower-order visual areas.
2. Alpha is strongest within supragranular cortex and may carry TOP-DOWN information via short-range feedback connections to constrain lower-level processing; for instance, alpha may play a role in RESOLVING AMBIGUOUS VISUAL IMAGERY, such as the picture of a woman and a horse’s snout shown above. Cortical alpha in layer VI might influence alpha activity within the pulvinar.

how alpha frequency affects the attentional blink

(from Samaha & Postle, 2015)

• Individuals with higher alpha frequencies have vision with finer temporal resolution.
• Eyes-closed and prestimulus peak alpha frequency both show this relationship.
• Within an individual, spontaneous fluctuations in alpha frequency predict perception.
• Alpha oscillations may dictate the resolution of conscious visual updating.

lessons?

So, what is it that neurons compute natively?

• Do linear algebra (vector projection / inner product, matrix multiplication).
• Implement dimensionality reduction (from many dimensions to one), including similarity-preserving DR by random projections.
• Perform function approximation (when arranged in multilayer networks).
• Respond selectively (exhibit tuning) [and thus serve as landmarks/prototypes in a similarity-based representation scheme, a.k.a. the Chorus Transform].
• Form spatial maps, presumably to facilitate navigation, episodic memory and prospection, and social cognition.
• Form abstract maps (retinotopic, tonotopic, chronotopic, etc.), presumably to facilitate similarity-based readout.
• Organize themselves in dynamic assemblies (note the importance of time) implemented by readout mechanisms.
• Collectively generate oscillating local electrical fields and interact with these fields to implement attention etc.