jan 10: neurons and the brain - california institute of ...matilde/lecture2brainsneurons.pdf · •...
TRANSCRIPT
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Geometry of Neuroscience
Matilde Marcolli & Doris Tsao
Jan 10: Neurons and the Brain
Material largely from Principles of Neurobiology by Liqun Luo
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks, specialized cell types
• Learning and memory
• Population dynamics: a case study
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Jellyfish
Fruit fly
Zebrafish
MouseHuman
C. Elegans
Brains of different animals
700 mya
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Brains of different animals
Jellyfish:• Simplest form of brain: “Nerve net”• 5600 neurons• Sensation/feeding/locomotion• Box jellyfish has 24 eyes
Worm (C. Elegans):• 302 neurons
(sensory/motor/interneurons)• 7000 connections completely
mapped• Allows full understanding of simple
circuits (e.g., response to touch)
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Brains of different animals
Insects (Drosophila):• 100,000 neurons• Display sophisticated social and
cognitive behaviors (memory, spatial navigation)
Fish (Zebrafish):• 100,000 neurons• Transparent in larval stage: can
image every single neuron during behavior
• Interesting behaviors: prey capture, sleep
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Brains of different animals
Mouse:• 4 million neurons• Shares many of the same features
as human brain (both anatomically and functionally)
Human:• 100 billion neurons• Each hemisphere is size of extra
large pizza• 4 km of axons per mm3
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Homology between mouse and primate
MonkeyMouse
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Expansion of neocortex
Brain of an early mammal from 85 million years ago(reconstructed based on fossil record)
Mouse
Human
Normal mouse (left) vs mouse expressing B-catenin in neuroepithelialprogenitors (right)
Double cortex
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Organization of Central Nervous System
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks, specialized cell types
• Learning and memory
• Population dynamics: a case study
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The Neuron
Dendrites
Axons
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The Neuron
“Golgi” stain Brainbow stain
“I expressed the surprise which I experienced upon seeing with my own eyes the wonderful revelatory powers of the chrome-silver reaction and the absence of any excitement in the scientific world aroused by its discovery.” -Cajal
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The Neuron
Pyramidal cell
Basket cell
Motor neuron
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Circuit motifs
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Signaling between neurons
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Signaling between neurons
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Signaling between neurons
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Synaptic transmission
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Calcium influx is necessary for neurotransmitter release
Voltage-gated
calcium
channels
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Synaptotagmin functions as a calcium sensor, promoting vesicle fusion
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Resting potential
Each ion has a reversal potential, where
diffusion potential exactly counterbalances
electrical potential.
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Resting potential
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Action potential
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Signaling between neurons
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Comparing signaling in computers vs the brain
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks,
specialized cell types
• Learning and memory
• Population dynamics: a case study
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Organization of Central Nervous System
Brain of Mr. Leborgne aka “Tan Tan”
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Hierarchical organization of brain
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“If one wants to understand function in biology, one should study structure.”
–Francis Crick
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The fruitfulness of “following the anatomy”
Hubel and Wiesel: Orientation Selectivity Edvard & May-Britt Moser: Grid Cells
Michael Fee: Sparse HVC neurons
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks,
specialized cell types
• Learning and memory
• Population dynamics: a case study
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Learning and Memory
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Forming a long-term memory
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Hippocampus
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Long-term potentiation
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Hippocampus provides an indexing system
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks,
specialized cell types
• Learning and memory
• Population dynamics: a case study
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Mante and Newsome 2013
Understanding the mechanism for flexible behavior
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Step 1: Compute top 12 PCs of population data
D = matrix of eigenvectors
Step 2: Demixing (goal: plot neural state in meaningful coordinates)
Step 3: Denoise the regression vectors (project onto 12 PCs)
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Regression coefficients for individual neurons
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Step 4: Orthogonalize regression vectors (Gramm Schmidt)
b1
b2Q2
Q1
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…So far, not THAT surprising (a fancy way of showing that both color and
motion information are represented regardless of context)
How is he able to do the task???
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Recurrent Neural Network
• x represents activation of neuron, r represents firing rate, J represents recurrent connections, u represents input, c represents offsets, rho represents noise
• J, b, c are modified through training
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Search for fixed points (where x = 0).
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Red crosses: fixed points (same in both contexts)
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• Context-depending integration is explained by different neural dynamics in the two situations!
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“We conclude that the observed complexity and functional roles of single neurons are readily understood in the framework of a dynamical process unfolding at the level of a population .”
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Outline
• Brains of different animals
• Neurons: structure & signaling mechanism
• Organization of the brain: lobes, networks, specialized cell types
• Learning and memory
• Population dynamics: a case study
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Is hippocampus necessary for retrieval?
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Replay: Linking spatial navigation to episodic memory