Jan 10: Neurons and the Brain
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1 Geometry of Neuroscience Matilde Marcolli & Doris Tsao Jan 10: Neurons and the Brain Material largely from Principles of Neurobiology by Liqun Luo
2 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
3 Brains of different animals Human Mouse Fruit fly Zebrafish C. Elegans Jellyfish 700 mya
4 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)
5 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
6 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 mm 3
7 Homology between mouse and primate Mouse Monkey
8 Expansion of neocortex Mouse Human Normal mouse (left) vs mouse expressing B-catenin in neuroepithelial progenitors (right) Brain of an early mammal from 85 million years ago (reconstructed based on fossil record) Double cortex
9 Organization of Central Nervous System
10 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
11 The Neuron Dendrites Axons
12 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
13 The Neuron Basket cell Motor neuron Pyramidal cell
14 Circuit motifs
15
16 Signaling between neurons
17 Signaling between neurons
18 Signaling between neurons
19 Synaptic transmission
20 Voltage-gated calcium channels Calcium influx is necessary for neurotransmitter release
21 Synaptotagmin functions as a calcium sensor, promoting vesicle fusion
22
23 Resting potential Each ion has a reversal potential, where diffusion potential exactly counterbalances electrical potential.
24 Resting potential
25 Action potential
26 Signaling between neurons
27 Comparing signaling in computers vs the brain
28 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
29 Organization of Central Nervous System Brain of Mr. Leborgne aka Tan Tan
30 Hierarchical organization of brain
31 If one wants to understand function in biology, one should study structure. Francis Crick
32 The fruitfulness of following the anatomy Hubel and Wiesel: Orientation Selectivity Edvard & May-Britt Moser: Grid Cells Michael Fee: Sparse HVC neurons
33 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
34 Learning and Memory
35 Forming a long-term memory
36 Hippocampus
37 Long-term potentiation
38 Hippocampus provides an indexing system
39 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
40 Understanding the mechanism for flexible behavior Mante and Newsome 2013
41 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)
42 Regression coefficients for individual neurons
43 Step 4: Orthogonalize regression vectors (Gramm Schmidt) b 2 Q 2 b 1 Q 1
44
45 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???
46 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
47 . Search for fixed points (where x = 0)
48 Red crosses: fixed points (same in both contexts)
49
50 Context-depending integration is explained by different neural dynamics in the two situations!
51 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.
52 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
53 Is hippocampus necessary for retrieval?
54 Replay: Linking spatial navigation to episodic memory
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