Part 4B: Real Neurons
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IV.B. Biological Neural Networks
1. Overview
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A Very Brief Tour of
Real Neurons
(and Real Brains)
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(fig. from internet)
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Left Hemisphere
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Typical Neuron
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The brain is organized over sizes that span 6 orders of magnitude
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Part 4B: Real Neurons
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Overview of Brain to Neurons
<http://www.youtube.com/watch?v=DF04XPBj5uc>
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(play flash video)
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Animation of Neuron
•
•
•
•
An animated film about nicotine addiction
A good visualization of a single neuron
©2006, Hurd Studios
Winner of NSF/AAAS Visualization
Challenge
View Flash Video
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Grey Matter vs. White Matter
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(fig. from Carter 1998)
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Part 4B: Real Neurons
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Neural Density in Cortex
• 148 000 neurons / sq. mm
• Hence, about 15 million / sq. cm
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Cortical Areas
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Intercortical Connections
• (1) Short arcuate bundles, (2) Superior longitudinal
fasciculus, (3) External capsule, (4) Inferior occipitofrontal
fasciculus, (5) Uncinate fasciculus, (6) Sagittal stratum,
(7) Inferior longitudinal fasciculus
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Part 4B: Real Neurons
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Intercortical Connections
(diffusion spectrum imaging)
G. Miller Science 330, 164 (2010) (2010)
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Publis hed by AAAS
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Brodmann’s Areas
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Somatosensory & Motor Homunculi
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Part 4B: Real Neurons
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Reorganization of Cortex
• Median nerve
sectioned to show
fluidity of cortical
organization
• (C) before
• (D) immediately
after
• (E) several months
later
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(fig. < M cClelland & al, Par . Dis tr . Pr oc. II)
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Macaque Visual System
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(fig. from Clark, Being Ther e, 1997)
Hierarchy
of
Macaque
Visual
Areas
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(fig. from Van Es s en & al. 1992)
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Part 4B: Real Neurons
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2. Neurons
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Typical Neuron
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Dendritic Trees of Some Neurons
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
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inferior olivary nucleus
granule cell of cerebellar cortex
small cell of reticular formation
small gelatinosa cell of spinal
trigeminal nucleus
ovoid cell, nucleus of tractus solitarius
large cell of reticular formation
spindle-shaped cell, substantia
gelatinosa of spinal chord
large cell of spinal trigeminal nucleus
putamen of lenticular nucleus
double pyramidal cell, Ammon’s horn
of hippocampal cortex
thalamic nucleus
globus pallidus of lenticular nucleus
(fig. from Trues & Carpenter, 1964)
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Part 4B: Real Neurons
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Axonal
Terminations
(Tectum of Turtle)
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(fig. from Sereno & Ulins ki 1987)
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Axonal Net
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(fig. from Arbib 1995)
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Neural Connections
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(array tomography by O’Shea at SmithLab, Stanford)
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Part 4B: Real Neurons
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Minicolumn
• Up to ∼100 neurons
– 75–80% pyramidal
– 20–25% interneurons
• 20–50µ diameter
• Length: 0.8 (mouse) to
3mm (human)
• ∼ 6×10 5 synapses
• 75–90% synapses outside
minicolumn
• Interacts with 1.2×10 5
other minicolumns
• Mutually excitable
• Also called microcolumn
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Layers and Minicolumns
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(fig. from Arbib 1995, p. 270)
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Macrocolumns
•
•
•
•
•
∼ 70 inhibitorally-coupled minicolumns in humans
70% of minicol. connections are within macrocol.
Basket neurons provide shunting inhibition between minicolumns
Winner-takes-all networks
Represent microfeatures
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Part 4B: Real Neurons
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(fig. from Arbib 1995, p. 270)
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Intracortical Connections
• Dendrites extend 2–4
minicol. diameters
• Axons extend 5× (or
even 30–40× minicol.
diameter
• Periodic spacing of
axon terminal clusters
causes entrainment
• ∼ 2×10 7 connections
to macrocolumn
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Neural
Networks in
Visual
System of
Frog
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(fig. from Arbib 1995, p. 1039)
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Part 4B: Real Neurons
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Synapses
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video by Hybrid Medical Animation
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Chemical Synapse
1.
2.
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Action potential
arrives at synapse
Ca ions enter cell
3.
Vesicles move to
membrane, release
neurotransmitter
4.
Transmitter
crosses cleft,
causes
postsynaptic
voltage change
(fig. from Anders on, Intr . Neur . Nets )
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Typical Receptor
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(fig. from Anders on, Intr . Neur . Nets )
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Part 4B: Real Neurons
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Fig. 3 Activity-dependent modulation of pre-, post-, and trans-synaptic components.
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Fig. 4 Local regulation of the synaptic proteome.
V M Ho e t a l. Sc ie nc e 2 0 1 1 ;3 3 4 :6 2 3 -6 2 8
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Fig. 3: A 3D model of synaptic
architecture.
(A)A s ec tion through the s ynaptic
bouton, indic ating 60 proteins.
(A)High-z oom v iew of the ac tiv e z one
area.
(B)High-z oom v iew of one v es icle
within the v es ic le c lus ter.
(C)High-z oom v iew of a s ection of the
plas ma membrane in the v ic inity of
the ac tiv e z one. Clus ters of s yntax in
(y ellow) and SNAP 25 (red) are
v is ible, as well as a rec ently fus ed
s y naptic v es icle (top). The graphical
legend indic ates the different proteins
(right). Dis play ed s ynaptic v esic les
hav e a diameter of 42 nm.
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Part 4B: Real Neurons
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R ES E A RC H | R E PO R TS
R ES E A RC H | R E PO R TS
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RES
ESEEAARC
RCH
H || R
REEPO
POR
RTS
TS
R
Fig. 3. A 3D model of synaptic architecture. (A) A section through the synaptic bouton, indicating 60 proteins. The proteins are shown in the copy numbers
indicated in tables S1 and S2 and in positions determined according to the imaging data (Fig. 2 and fig. S6) and to the literature (see fig. S6 for details). (B) Highzoom view of the active zone area. (C) High-zoom view of one vesicle within the vesicle cluster. (D) High-zoom view of a section of the plasma membrane in the
vicinity of the active zone. Clusters of syntaxin (yellow) and SNAP 25 (red) are visible, as well as a recently fused synaptic vesicle (top). The graphical legend indicates
the different proteins (right). Displayed synaptic vesicles have a diameter of 42 nm.
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Fig. 3. A 3D model of synaptic architecture. (A) A section through the synaptic bouton, indicating 60 proteins. The proteins are shown in the copy numbers
indicated in tables S1 and S2 and in positions determined according to the imaging data (Fig. 2 and fig. S6) and to the literature (see fig. S6 for details). (B) Highzoom view of the active zone area. (C) High-zoom view of one vesicle within the vesicle cluster. (D) High-zoom view of a section of the plasma membrane in the
vicinity of the active zone. Clusters of syntaxin (yellow) and SNAP 25 (red) are visible, as well as a recently fused synaptic vesicle (top). The graphical legend indicates
the different proteins (right). Displayed synaptic vesicles have a diameter of 42 nm.
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Fig.
bouton, indicating
indicating 60
60 proteins.
proteins. The
The proteins
proteins are
are shown
shown inin the
the copy
copynumbers
numbers
Fig. 3.
3. A
A 3D
3D model
model of
of synaptic
synaptic architecture. (A) A section through the synaptic bouton,
indicated
data (Fig.
(Fig. 22 and
and fig.
fig. S6)
S6) and
and to
to the
the literature
literature(see
(seefig.
fig.S6
S6for
fordetails).
details).(B)
(B)HighHighindicated in
in tables
tables S1
S1 and
and S2
S2 and
and in positions determined according to the imaging data
zoom
vesicle cluster.
cluster. (D)
(D) High-zoom
High-zoom view
view of
of aa section
section of
of the
theplasma
plasmamembrane
membraneininthe
the
zoom view
view of
of the
the active
active zone
zone area.
area. (C) High-zoom view of one vesicle within the vesicle
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39 fused
vicinity
active
as well
well as
as aa recently
recently
fused synaptic
synapticvesicle
vesicle(top).
(top).The
Thegraphical
graphicallegend
legendindicates
indicates
vicinity of
of the
the
active zone.
zone. Clusters
Clusters of syntaxin (yellow) and SNAP 25 (red) are visible, as
the
the different
different proteins
proteins (right).
(right). Displayed
Displayed synaptic vesicles have a diameter of 42 nm.
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MAY 2014
2014 •• VOL
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344 ISSUE
ISSUE 6187
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Part 4B: Real Neurons
4/3/16
Video of 3D Model
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Input Signals
• Excitatory
– about 85% of inputs
– AMPA channels, opened by
glutamate
• Inhibitory
– about 15% of inputs
– GABA channels, opened by
GABA
– produced by inhibitory
interneurons
• Leakage
– potassium channels
• Synaptic efficacy: net
effect of:
– presynaptic neuron to
produce neurotransmitter
– postsynaptic channels to
bind it
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Membrane Potential (Variables)
•
•
•
•
•
•
•
•
g e = excitatory conductance
Ee = excitatory potential (~ 0 mV)
g i = inhibitory conductance
Ei = inhibitory potential (–70 mV)
g l = leakage conductance
El = leakage potential
Vm = membrane potential
θ = threshold
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Part 4B: Real Neurons
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Membrane Potential
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Slow Potential Neuron
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(fig. < Anders on, Intr . Neur . Nets )
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Action Potential Generation
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Part 4B: Real Neurons
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Frequency
Coding
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(fig. from Anders on, Intr . Neur . Nets )
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Variations in Spiking Behavior
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Dendritic computation in pyramidal cells.
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Part 4B: Real Neurons
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Rate Code
Approximation
• Rate-coded (simulated)
neurons:
– short-time avg spike frequency
≈
– avg behavior of microcolumn
(~100 neurons) with similar
inputs and output behavior
• Rate not predicted well by Vm
• Predicted better by g e relative
to a threshold value g eθ
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(fig . < O’Reilly , Co mp . Co g . Neu ro sci.)
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Rate Code Approximation
• g e θ is the
conductance when
Vm = θ
• Rate is a nonlinear
function of relative
conductance
• What is f ?
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Activation Function
• Desired properties:
– threshold (~0 below
threshold)
– saturation
– smooth
• Smooth by convolution
with Gaussian to
account for noise
• Activity update:
yt+1 = yt + C(y − yt )
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(fig . < O’Reilly , Co mp . Co g . Neu ro sci.)
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