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CS 621 Artificial Intelligence
Lecture 34 - 08/11/05
Guest Lecture by
Prof. Rohit Manchanda
Biological Neurons - II
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The human brain
Seat of consciousness and cognition
Perhaps the most complex information processing
machine in nature
Historically, considered as a monolithic information
processing machine
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Beginner’s Brain Map
Forebrain (Cerebral Cortex):
Language, maths, sensation,
movement, cognition, emotion
Midbrain: Information Routing;
involuntary controls
Cerebellum: Motor
Control
Hindbrain: Control of
breathing, heartbeat, blood
circulation
Spinal cord: Reflexes,
information highways between
body & brain
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Brain : a computational machine?
Information processing: brains vs computers
- brains better at perception / cognition
- slower at numerical calculations
• Evolutionarily, brain has developed algorithms
most suitable for survival
• Algorithms unknown: the search is on
• Brain astonishing in the amount of information it
processes
– Typical computers: 109 operations/sec
11 operations/sec
–
Housefly
brain:
10
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Brain facts & figures
• Basic building block of nervous system: nerve
cell (neuron)
• ~ 1012 neurons in brain
• ~ 1015 connections between them
• Connections made at “synapses”
• The speed: events on millisecond scale in
neurons, nanosecond scale in silicon chips
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Neuron - “classical”
• Dendrites
– Receiving stations of neurons
– Don't generate action potentials
• Cell body
– Site at which information received is
integrated
• Axon
– Generate and relay action potential
– Terminal
• Relays information to next neuronhttp://www.educarer.com/images/brain-nerve-axon.jpg
in the pathway
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Membrane Biophysics: Overview
Part 1: Resting membrane potential
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Resting Membrane Potential
• Measurement of potential between ICF
and ECF
ECF
ICF
_
+
-40 to -90 mV
– Vm = Vi - Vo
– ICF and ECF at isopotential separately.
– ECF and ICF are different from each other.
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Resting Membrane Potential recording
• Electrode wires can not be inserted in the cells
without damaging them (cell membrane
thickness: 7nm)
ECF
_
ICF
+
-40 to -90 mV
KCl
– Solution: Glass microelectrodes (Tip diameter: 10 nm)
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• Glass  Non conductor
• Therefore, while pulling a capillary after heating, it is filled
with KCl and tip of electrode is open and KCl is interfaced
with a wire.
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R.m.p. - towards a theory
• Ionic concentration gradients across
biological cell membrane
Mammalian muscle (rmp = -75
mV)
ECF
ICF
Cations
Na+
145 mM
12 mM
K+
4 mM
155 mM
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ECF
ICF
Na+
109 mM
4 mM
K+
2.2 mM
124 mM
77 mM
1.5 mM
Cations
Anions
Anions
Cl-
Frog muscle (rmp = -80 mV)
120 mM
4 mM
Cl-
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R.m.p. - towards a theory
• Ionic concentration
gradients: squid axon
(rmp = -60 mV)
ECF
• Ionic concentration
ratios
ICF
Cations
Mammal
Frog
Cations
Na+
440 mM
50 mM
Nao/Nai
12
28
K+
10 mM
400 mM
Ki/Ko
52
56
25
33
Anions
Cl08.11.05
Anions
550 mM
40 mM
Clo/Cli
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Ionic concentration ratios across biological cell
membranes
Species,
tissue
_Ki /
Ko
Nao/Nai
Clo/Cli
14
Squid axon
40
9
Cuttlefish axon
36
11
Crab axon
38
Frog nerve
60
3
4
Frog sartorius
muscle
56
28
33
Rat cardiac
52
12
Cat cardiac
32
25
Eel electroplaque
30
18
Nitella
0.5
0.9
1.04
Paramecium
1,065
0.02
100
Plant cells
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Trans-membrane Ionic Distributions
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Resting potential as a K+ equilibrium (Nernst)
potential
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Resting Membrane Potential: Nernst
Eqn
Nernst Equations
RT
Vm 
F
Vm 
RT
F
RT
Vm 
F
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[ K  ]o 
    EK
 [ K ]i 
[ Na ]o 

  E Na

 [ Na ]i 

 [Cl  ]i 
    ECl
[Cl ]o 
Consider values for typical
concentration ratios
EK = -90 mV
ENa = +60 mV
r.m.p. = {-60 to –80} mV
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Goldman-Hodgkin-Katz (GHK) eqn
Resting Membrane Potential approximat ed by the GHK eq.
RT  PK [ K  ]o  PNa [ Na  ]o 
Vm 
ln 



F
 PK [ K ]i  PNa [ Na ]i 
If PK  PNa
RT
Vm 
F
[ K  ] o 
    EK
 [ K ]i 
RT
Vm 
F
[ Na  ]o 

  E Na

[
Na
]
i 

If PNa  PK
Taking values of R,T &F and dividing throughout by PK:
[ K  ]o   [ Na  ]o 
PNa
Vm  58 log  
mV
,




PK
 [ K ]i   [ Na ]i 
Consider  = V. large, v. small, and intermediate
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Equivalent Circuit Model: Resting Membrane
Out
gNa
gK
Vm
ENa
Cm
EK
In
I Na  Vm  E Na g Na
I K  Vm  EK g K
At steady state, I Na  I K
Therefore, Vm 
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E Na g Na  EK g K
g Na  g K
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Equivalent Circuit Model including Na pump
Out
INa(p)
gK
Cm
ENa
EK
IK(p)
In
At steady state,
I Na  I K  I p  0
Therefore,
Vm 
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E Na g Na  EK g K  I p
g Na  g K
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Membrane Biophysics: Overview
Part 2: Action potential
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ACTION POTENTIAL
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ACTION POTENTIAL: Ionic mechanisms
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Action Potential: Na+ and K+ Conductance
g K Vm , t   g K n(Vm , t )
4
g Na Vm , t   g Na m(Vm , t ) h(Vm , t )
3
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Action Potential Propagation
• NonS decremental,
constant
velocity
R
R
R
R
R
X=0
1
2
3
4
Convex
VTh
Concave
Time
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Hippocampus: location
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Hippocampal Network &
Connections
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Membrane Biophysics: Overview
Part 3: Synaptic transmission &
potentials
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“Canonical” neurons: Neuroscience
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Synapses : Chemical & Electrical
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Transmission : Chemical & Electrical
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Chemical Transmission
Neurotransmitter
Receptors
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Postsynaptic Electrical Effects
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Synaptic Integration: The Canonical Picture
Action potential: Output signal
Axon: Output line
Action potential
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The Perceptron Model
A perceptron is a computing element with input
lines having associated weights and the cell
having a threshold value. The perceptron model is
motivated by the biological neuron.
Output = y
Threshold = θ
wn
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w1
Wn-1
Xn-1
x1
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y
1
θ
Σwixi
Step function / Threshold
Σwixi > θ
function
y
= 1 for
Σ > θ, y >1
=0 otherwise
Features of Perceptron
• Input output behavior is discontinuous and the derivative
does not exist at Σwixi = θ
• Σwixi - θ is the net input denoted as net
• Referred to as a linear threshold element - linearity because
of x appearing with power 1
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• y=
f(net): Relation between y and net is non-linear
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Perceptron / ANN “neuron”
Neurophysiological basis of:
a) Input Signs
b) Input Weights
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Dendrites & Synapses in Real Life !
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Neuron morphologies
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In the Retina …
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