THE BRAIN

I INTRODUCTION

A Human Brain

mass  kg in mature adult

a ab out of b o dy weight

i uses of oxygen of glucose of blo o d ow

b mass at birth ab out of nal value

i mass increase due to growth of axons dendrites synapses myelin sheaths

B Cortex

size of cortex separates humans from other sp ecies



a area cm for rat  cm for chimp  cm for human

i extra area in human cortex obtained by folding

ii thickness of cortex cm



b  neurons in human cortex



i mammalian cortex has  neurons p er cm



c synapses in human cortex



i synapses p er neuron

human genome do es not carry detailed wiring diagram for cortex

a its information content is far to o small



i wiring diagram would require bits of information



b genome carries ab out  bits of information

i h uman genome is ab out one meter of DNA

ii typ es of base pairs



iii separation of  cm b etween base pairs

iv much of genome may b e nonsense

cortex develops in resp onse to external stimuli

a molecular markers involved in initial wiring

b renements due to activity

c numb er of synapses pared back during development

C Explosion In Size Of Cortex Due To Limited Genetic Instructions

comparison of evolution of genome and cortex

a genome length cm for fruit y cm for chicken m for mouse m for human



b numb er of neurons for fruit y for mouse for human

rapid evolution during past  yr

I I FUNCTION

A Neuron

comp onents cell b o dy axon dendrites

nominal dimensions for pyramidal cell in cortex

a cell b o dy blob with r m

b axon cylinder with r m and l cm



c total surface area ab out  cm

i dominated byaxon

 

d total volume ab out cm

i comparable contributions from axon and cell b o dy

electrical prop erties

a axons are output devices

i actively propagate signals

ii contain rep eater stations

b dendrites are input devices

i electrically passive

ii some may pro duce spikes

synapses

a connect axons to dendrites

i signals transmitted chemically across synapses

ii synaptic space   cm

iii time delay ms due to diusion

iv to achieve p ost synaptic threshold may takemuch longer

b can b e excitatory or inhibitory

i excitatory glutamate transmitter op ens Na channels MSG

ii inhibitory gaba transmitter op ens Cl or K channels

iii most common neurotransmitters in cortex

iv amino acids

v inhibitory synapses usually more proximal to cell b o dy

B Action Potentials

neuron sums inputs

a strength related to distance of synapse on dendrite from cell b o dy

b sum determines whether ring o ccurs

spikes initiated on axon close to cell b o dy

a can travel in b oth directions along axon

pulses are quantized all the same

a pulse length ms

b pulse strength V mV

c length and strength determined by kinetics of ion channels

signal strength co ded in ring rate

a at rest Hz typically Hz

b excited Hz typically Hz



Hz by refractory p erio d of ion channels i limited to

propagation sp eed

a dep ends on axon diameter and myelination



i v ms typical value for brain



ii up to v ms in spinal cord

C Axon Mo deled As Coaxial Cable

parameters

a radius a membrane thickness t length l



i typical values a m t  cm l cm

b longitudinal resistance R a l

a a

i salt solution  ohm cm

a



i R  ma l cm ohm

a

c membrane capacitance C Kalt

m 

i dielectric constant of lipid membrane K 



ii C   a ml cm F

m

iii C A  Fcm

m

d membrane resistance R tal

m m



i   ohm cm

m



ii t  ohm cm

m

iii R   ma cm l ohm

m

e inductance negligible

D Action Potential Propagation Along Unmyelinated Neuron

longitudinal diusion

a neglect current through membrane

V I l



t C z

m

V R

a

 I

z l

b diusion equation

l V V

t R C z

a m



ii diusion constant D  l R C a m cm s

a m



c D t spreading length for pulse of duration t

 

i  a cm t ms cm

d propagation sp eed along axon





a



v cm s

t m

i evaluated for t  ms

leakage through membrane

a clamp voltage of axoplasm

V V



t R C

m m

b voltage decays exp onentially with time constant R C

m m



i  s

combined equation reads

V V l V

t R C R C z

m m a m

a impulse regeneration not included in equation

E Action Potential Propagation Along Myelinated Neuron

myelin sheath decreases C

m

a  wraps of myelin sheath p er micron diameter of axon

i like pap er towels on cardb oard roller

b C  l cm F

m

i note C indep endentof a

m

cross membrane currents restricted to no des of Ranvier

a separated bya fewmm

a size a few m

myelination increases propagation sp eed at xed size



a  a m cm



b v a m m s

i note v  a

F Power Requirements

P C V



a P  watt for our canonical neuron



b neurons ring at Hz yields a total p ower watt

c based on unmyelinated axons

i myelination decreases p ower usage

ii do small unmyelinated axons use most of electic p ower

iii could dendrites use signicantpower

total p ower used bybrain watt

a howmuc h for ion pumps

b howmuch for axon transp ort

i molecular motors

exp erimental indications

a ion transp ort is ma jor part of metab olism

i barbiturate anesthesia pro ducing iso electric EEG reduces metab olism to of

normal value

ii inhibiting NaK pump using ouabain reduces metab olism to of normal value

I I I INFORMATION INPUT AND STORAGE

A Eye

retina is cm b ehind cornea pupil size p cm



a cones



i maximum density in center of fovea  cm



b ro ds

 

i maximum density from center of fovea  cm

ii can detect single photon

c cone acuity times ro d acuity less convergence



d cone sensitivityatfovea times smaller than ro d sensitivityat



resolution of eyeatfovea  rad arcminutes

a density of cones matches diraction limited resolution of eye



i diraction limit p 



ii cone spacing

input from visual receptors funnels into neurons in optic nerve



a optic nerve can transmit bits p er second



auditory nerve has  neurons



a auditory bandwidth is  Hz

B Television

standard TV channel uses  MHz in range  MHz

a only  MHz for picture

b  picture elements

i horizontal lines

c raster scans at frames p er second

i more than frames p er second needed to avoid ick er



d elements p er second

angular scale of picture element

a cm  cm screen

i element size x  y  cm

b viewed at distance of d  m



c  rad

match of visual input to TV

a  MHz matches capacity of optic nerve

i neurons ring at Hz



b  rad matches angular separation of picture elements

aliens mightwonder which came rst the TV or the eye

C Memory

Hebb prop osed that information is stored in strength of synaptic connections

a supp ose that there are there N discernible levels of synaptic strength



b human brain might b e able to store ln N bits

i every bit in one full year of viewing TV