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CS 621 Artificial Intelligence

Lecture 34 - 08/11/05

Guest Lecture byProf. 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

Cerebellum: Motor Control

Midbrain: Information Routing; involuntary controls

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– Housefly brain: 1011 operations/sec

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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 neuronin the pathway

http://www.educarer.com/images/brain-nerve-axon.jpg

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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

– Vm = Vi - Vo

– ICF and ECF at isopotential separately. – ECF and ICF are different from each other.

+

_

ICF

ECF

-40 to -90 mV

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Resting Membrane Potential -recording

• Electrode wires can not be inserted in the cells without damaging them (cell membrane thickness: 7nm)

– Solution: Glass microelectrodes (Tip diameter: 10 nm)• 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.

ICF

ECF

-40 to -90 mV+

_

KCl

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R.m.p. - towards a theory

• Ionic concentration gradients across biological cell membrane

Mammalian muscle (rmp = -75mV)

ECF ICFCationsNa+ 145 mM 12 mMK+ 4 mM 155 mMAnionsCl- 120 mM 4 mM 1.5 mM77 mMCl-

Anions

124 mM2.2 mMK+

4 mM109 mMNa+

Cations

ICFECF

Frog muscle (rmp = -80 mV)

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R.m.p. - towards a theory

• Ionic concentration gradients: squid axon (rmp = -60 mV)

40 mM550 mMCl-Anions

400 mM10 mMK+

50 mM440 mMNa+

CationsICFECF

3325Clo/Cli

Anions5652Ki/Ko

2812Nao/Nai

CationsFrogMammal

• Ionic concentration ratios

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Ionic concentration ratios across biological cell membranes

1000.021,065Paramecium1.040.90.5Nitella

Plant cells1830Eel electroplaque2532Cat cardiac1252Rat cardiac

332856Frog sartoriusmuscle

4360Frog nerve38Crab axon

1136Cuttlefish axon14940Squid axon

Clo/CliNao/Nai_Ki / KoSpecies,tissue

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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: NernstEqn

Clo

im

Nai

om

Ki

om

EClCl

FRTV

ENaNa

FRTV

EKK

FRTV

=⎭⎬⎫

⎩⎨⎧

=

=⎭⎬⎫

⎩⎨⎧

=

=⎭⎬⎫

⎩⎨⎧

=

−

−

+

+

+

+

][][

][][

][][

EquationsNernst 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

Nai

om

Ki

om

iNaiK

oNaoKm

ENaNa

FRTV

EKK

FRTV

NaPKPNaPKP

FRTV

=⎭⎬⎫

⎩⎨⎧

=

>>

=⎭⎬⎫

⎩⎨⎧

=

>>⎭⎬⎫

⎩⎨⎧

++

=

+

+

+

+

++

++

][][

PP If][][

PP If][][][][

ln

eq.GHK by theedapproximatPotential Membrane Resting

KNa

NaK

K

Na

PP

,mV][][][][

log58 =⎭⎬⎫

⎩⎨⎧

++

= ++

++

ααα

ii

oom NaK

NaKV

Taking values of R,T &F and dividing throughout by PK:

Consider α = V. large, v. small, and intermediate

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Equivalent Circuit Model: Resting Membrane

CmgKgNa

ENa EK

Vm

Out

In

( )( )

KNa

KKNaNa

KNa

KKmK

NaNamNa

gggEgE

IIgEVIgEVI

++

=

=−=−=

mV Therefore,

state,steady At

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Equivalent Circuit Model including Na pump

EKENa IK(p)

gNa gKVm

Out

In

INa(p)

Cm

KNa

pKKNaNam

pKNa

ggIgEgE

V

III

+

++=

=++

Therefore,

0state,steady At

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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

( ) { }( ) { }

4

3

, ( , )

, ( , ) ( , )K m K m

N a m N a m m

g V t g n V t

g V t g m V t h V t

=

=

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Action Potential Propagation

• Non decremental, constant velocityS R R R R R

X = 0 1 2 3 4

VTh

Time

Convex

Concave

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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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Receptors

Neurotransmitter

Chemical Transmission

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Postsynaptic Electrical Effects

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Synaptic Integration: The Canonical Picture

Action potential

Action potential: Output signal

Axon: Output line

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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

wnWn-1

w1

Xn-1

Threshold = θ

x1

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Step function / Threshold functiony = 1 for Σ > θ, y >1

=0 otherwise

Σwixi > θ

θ

1y

Σwixi

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

• 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 …