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From Neuron to Brain: From Neuron to Brain: Pedagogic Approach Pedagogic Approach KAMALES BHAUMIK
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Page 1: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

From Neuron to Brain: From Neuron to Brain: Pedagogic ApproachPedagogic Approach

KAMALES BHAUMIK

Page 2: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 3: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 4: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Movement of charged ions across the cell membrane

aq

V∈

=

aVq

CceCapaci =∈=tan

∈==− 1

221 2

2

aq

CVEenergySelf

480 ≈∈=∈ lipidwater

Page 5: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 6: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Intracellular

fluidExtracellular

Fluid

Voltmeter

Inside of the cell is negative with respect to outside.

Most of the cells have a resting membrane potential in the range of -30mV to -80mV

Page 7: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Resting Membrane Potential

Nernst Potential

Page 8: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Nernst Potential

Chemical Potential = Partial Molar Gibbs Free Energy

Chemical Potential CRTcc ln0 += µµ

Electrochemical Potential zFVCRT ++= ln0µµV∆

1V 2V

1C 2C

11ln zFVCRT +

22ln zFVCRT +=

Page 9: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Nernst Potential

2

112 ln

CC

zFRT

VVV =−=∆

mVzFRT

25=

( )2

1log303.225CC

V Na ×=∆

mVCC

2

1log60≈

Page 10: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 11: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 12: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

NernstPlanck

Page 13: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Nernst-Planck Equation

FVzCRT iiii ++= ln0µµ12 −−= TLmolFluxJ i

dxd

CuJ iiii

µ−=

xV

FzCuxC

RTuJ iiii

ii ∂∂−

∂∂−=

lationsEinsteinRTuD ii Re'=

FICK’s Law

OHM’s Law

Page 14: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Integration of Nernst Planck Equation

CONSTANT FIELD MODEL

Goldmann Hodgkin Katz (GHK) Model

122

211

lnClClKKNaNa

ClClKKNaNa

CPCPCPCPCPCP

FRT

V++++=

Page 15: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Excitation of cells at resting membrane potential

Passive Response

Excitable Cells

Action Potential

All or None response

Page 16: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 17: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 18: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 19: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 20: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 21: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 22: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Currents Flowing in and out of the membrane During Action Potential

Capacitative current

dtdV

Cm

Resting membrane potential = K-Nernst potential

Peak of action potential = Na-Nernst Potential

Nonlinearity in the current flow

Necessity of a voltage clamp machine

Page 23: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Separation of ionic currents

TTX (Tetrodotoxin) Na-Channel Blocker

TEA (Tetra-ethyl-ammonium) K-channel blocker

Na and K channel conductance depends on membrane voltage

Chloride and non-specific ions follow Ohm’s law

Page 24: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Equivalent Circuit

Page 25: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 26: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 27: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 28: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 29: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 30: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Propagation of Axon Potential

mIxV

factor=

∂∂

2

21

2

2

22

2 1ty

vxy

∂∂=

∂∂

∑+∂∂==

∂∂

iimm I

tV

CItV

vfactor 2

2

2

11

Page 31: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 32: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 33: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 34: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 35: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 36: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 37: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Rods and cones

Bipolar Cells

Ganglion Cells

Page 38: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Rods and Cones

Bipolar cells

Ganglion Cells

Receptive field of Ganglion cell

Page 39: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 40: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

+ve -ve-ve

Page 41: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 42: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

+ve contribution-ve -ve

Distance

Intensity of

signal

-2 -1 0 1 2

Page 43: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

A Gaussian function, whose mean value is kept at zero, is given by:

)2

exp(2

1),(

2

2

2 σπσσ x

xg −=

where σ is called the standard deviation

Small σ

Large σ

Page 44: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

+ve contribution-ve -ve

Page 45: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

22

2

21

2

2

2

2

121 2

121

),( σσ

σπσπσσ

xx

eeDOG−−

−=

Page 46: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 47: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 48: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 49: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 50: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 51: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 52: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 53: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 54: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 55: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self
Page 56: From Neuron to Brain: Pedagogic Approach Fellows/kamalesh_bhowmik.pdf · Movement of charged ions across the cell membrane a q V ∈ = a V q Capacitance C= =∈ 1 2 2 1 2 2 a q Self

Thank you


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