A brief tour of everything we know about the brain

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

Máté Lengyel: Intro + Biophysics 1 / 1

Why the brain, which brain, and what specifically within the brain? mind body nervous system peripheral (PNS)

central (CNS)

brain neurons 1:10 glial cells

spinal cord

hindbrain midbrain membrane forebrain ion potential concentrations diencephalon telencephalon basal ganglia subthreshold spikes cortex fluctuations paleocortex archicortex rates temporal patterns neocortex Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Your brain

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Your cortex unfolded neocortex 6 layers ~30 cm ~0.5 cm

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Your cortex unfolded

1 cubic millimeter, ~3*10-5 oz (0.85mg)

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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More numbers... 1 mm3 of cortex:

1 mm2 of a CPU:

50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons

1 million transistors 2 connections/transistor (=> 2 million connections) .002 km of wire

whole brain (2 kg):

whole CPU:

1011 neurons 1015 connections 8 million km of axons

109 transistors 2*109 connections 2 km of wire

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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The elementary unit of the nervous system: the neuron fénymikroszkóppal

neuron dendrite soma nucleus axon initial segment terminal synapse glia myelin sheath node of Ranvier

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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A little cell biology

nucleus plasma membrane

lipid bilayer proteins integral peripheral extracellular space (ECS) intracellular space (ICS)

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Around the cell membrane Factors affecting the membrane transport of ions The permeability of the cell membrane is different for different species of molecules or ions

Membrane transport is made possible by transmembrane proteins • • •

pumps (+energy!) channels transporters

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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The electric cell: the resting membrane potential Phenomenon: voltage difference between the two sides of the membrane

Reason: on the two sides of the membrane • different concentrations of ions, • different permeability for different ions Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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The electric neuron: the action potential Action potential: a momentary deflection of the membrane potetntial

propagating action potential Time: 0 ms

Time: 1 ms

Time: 2 ms

threshold potential resting potential

»all or none« Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Between two neurons: the synapse ionotropic (A) és metabotropic (B,C) receptors

structure and operation of a synapse

excitatory and inhibitory postsynaptic potentials

changes with learning Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Basic biophysics

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Origin of the resting membrane potential

Nernst-equation: relation ship between differences in ionconcentrations and the potential in equilibrium for a single ionic species

R T [C ]ext E=V int !V ext= ln z F [C ]int • multiple

independently moving ionic species • constant field within membrane

Goldman-Hodgkin-Katz-equation (GHK): resting membrane potential as a function of individual ionic concentrations and permeabilities

V rest= Nernst-Planck equation: ion flux (current) as a function of the electrochemical potential

RT F

PK[K

]ext $P Na [ Na+ ]ext$ PCl [ Cl -]int ln + + P K [ K ] ext $P Na [ Na ] int $P Cl [ Cl ] ext

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

+

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Conductance-based modeling EC liquid

V IC Rm= 1/gm

Cm

EC

lipid core: capacitance

dV & t ' V &t ' Cm =! =!V & t ' g m dt Rm ion channel: resistance (conductance)

capacitive current

resisitive or conductive current

IC liquid (plasm) t Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Parallel conductances V Cm

gCl ECl

-90mV

gNa ENa

gK EK

+100mV

V

Iext K+

Current-balance equation:

dV C m = I Cl &t '$I Na &t'$I K &t'$ I ext &t ' dt

Na+

Individual ionic currents:

I leak &t'= g leak & E leak!V & t ' '

I Na &t '=g Na &t ' & E Na !V &t ' ' I K &t '=g K &t ' & E K !V & t ' ' Nernstconductance potential

driving force

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

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Hodgkin-Huxley model / 1 V Cm

gleak Eleak

gNa ENa

gK EK

Iext

Current-balance equation:

Cm

dV & t ' = g leak & E leak!V & t ' ' $g Na & t ' & E Na !V &t ' '$g K & t ' & E K !V & t ' '$ I ext & t ' dt leak (mainly Cl-) current

closed

Ion currents:

open

3

g Na &t '= g% Na #m & t '#h& t ' 4

g K & t ' = g% K #n & t '

probability of being open for an individual gate

maximal probability of being open conductance for an individual channel (channel density)

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

gate

gate

channel

Máté Lengyel: Intro + Biophysics 1 / 17

Hodgkin-Huxley model / 2 at the core of the HH, voltage-dependent gating kinetics:

1-m

?m

9

*h

open m

m & V & t ' '!m & t ' dm & t ' =( m & V &t ' '& 1!m & t ' '!)m &V & t ' ' m & t '= " dt *m & V & t ''

( m &V '$)m & V '

*m

)m

1

(m

0 1

h" m"

[1]

( m & V '$)m & V ' 1

[1, msec]

* m & V '=

(m & V '

*n

0

30 [1/msec]

m " &V '=

[msec]

closed

?m

m"

n"

*m

0 -100

0 -100 V [mV]

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

V [mV]

50

50

Máté Lengyel: Intro + Biophysics 1 / 18

Hodgkin-Huxley model / 3 HH model in operation: 40 V [mV] -80

membrane potential

1

m

n

x [1]

gating variables

h 0 40 g [ S/cm2] 0

Na

channel conductances

K

leak K

0

t [msec]

Theoretical Neuroscience I – Gatsby Computational Neuroscience Unit, UCL, 2006 Fall http://www.gatsby.ucl.ac.uk/teaching/courses/tn1-2006.html

50

I [nA/cm2] -800

channel currents

800

Na

Máté Lengyel: Intro + Biophysics 1 / 19