Structural description of the biological membrane. Physical property of biological membrane.
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Transcript of Structural description of the biological membrane. Physical property of biological membrane.
![Page 1: Structural description of the biological membrane. Physical property of biological membrane.](https://reader036.fdocuments.us/reader036/viewer/2022062409/5697bfea1a28abf838cb77c3/html5/thumbnails/1.jpg)
Structural description of the biological membrane. Physical
property of biological membrane
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Transfer of water soluble molecules across cell membranes by transport proteins
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Two classes of membran proteins
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Comparison of passive and active transport
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Examples of sbubstances transported across cellmembranes by carrier proteins
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Bacteriorhodopsin: A carrier protein
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Conformational change in protein to passivelycarry glucose
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Two components of an electrochemical gradient
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Three ways of driving active transport
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Three types of transport by carrier proteins
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Two types of glucose carriers for transfer of glucoseacross the gut lining
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The Na-K pump
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The Na-K pumpcycle
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Osmosis
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Avoiding osmotic swelling
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Carrier mediated solute transport in animal and plant cells
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The structure of an ion channel
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Patch-clamp recording
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Current through a single ion channel
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Gated ion channels
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Stress activated ion channels allow us to hear
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Distribution of ions gives rise to membranepotential
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K+ is responsible for generating a membrane potential
Nernst equation: V = 62log10(Co/Ci)
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Neurons
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Action Potenetial
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Three conformations of the voltage gated Na channel
----------
+++++ +++++
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Ion Flows and the Action Potential
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The propogation of an action potential along an axon
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The Action Potential
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Synapses
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Synapses
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Synapses
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Excitatory vs. Inhibitory Synapse
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Synapses
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Ion Channels
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Lecture 2
• Membrane potentials
• Ion channels
• Hodgkin-Huxley model
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Cell membranes
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Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
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Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
Ion channels conductance
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Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
Ion channels conductance
Typical A = .01 - .1 mm2 C ~ .1 – 1 nF
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Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
Ion channels conductance
Typical A = .01 - .1 mm2 C ~ .1 – 1 nFQ=CV, Q= 109 ions |V| ~ 65 mV
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Membrane potentialFixed potential concentration gradient
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Membrane potentialFixed potential concentration gradient
Concentration difference Potential difference
Concentration difference maintained by ion pumps, which aretransmembrane proteins
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Nernst potential
)](exp[ 212
1 VVqznn
Concentration ratio for a specific ion (inside/outside):
= 1/kBT
(q = proton charge, z = ionic charge in units of q)
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Nernst potential
)](exp[ 212
1 VVqznn
Concentration ratio for a specific ion (inside/outside):
= 1/kBT
2
1lognn
qzTk
V B
(q = proton charge, z = ionic charge in units of q)
No flow at this potential difference
Called Nernst potential or reversal potential for that ion
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Reversal potentialsNote: VT = kBT/q = (for chemists) RT/F ~ 25 mv
Some reversal potentials:
K: -70 - -90 mVNa: +50 mVCl: -60 - -65 mVCa: 150 mV
Rest potential: ~ -65 mV ~2.5 VT
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Effective circuit model for cell membrane
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Effective circuit model for cell membrane
extii i IVVgdtdV
C )(
(C, gi, Iext all per unit area)(“point model”:ignores spatial structure)
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Effective circuit model for cell membrane
extii i IVVgdtdV
C )(
(C, gi, Iext all per unit area)(“point model”:ignores spatial structure)
gi can depend on V, Ca concentration, synaptic transmitter binding, …
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Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
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Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
membrane time const
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Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
Start at rest: V= V0 at t=0membrane time const
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Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
gIVV /0
One gi = g = const
or
Final state:
Start at rest: V= V0 at t=0membrane time const
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Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
gIVV /0
One gi = g = const
)e1)(/(
e)/()(/
0
/
t
t
gIV
gIVtV
or
Final state:
Start at rest: V= V0 at t=0
Solution:
membrane time const
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channels are stochastic
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channels are stochastic
Many channels: effective g = g open * (prob to be open) * N
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Voltage-dependent channels
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K channel4 knP k
K
Open probability: 4 independent,equivalent, conformational changes
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K channel4 knP k
K
nVnVdtdn
nn )()1)((
Open probability: 4 independent,equivalent, conformational changes
Kinetic equation:
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K channel4 knP k
K
nVnVdtdn
nn )()1)((
nVndtdn
V
nn
n
nnn
)()(
)(
Open probability: 4 independent,equivalent, conformational changes
Kinetic equation:
Rearrange:
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K channel4 knP k
K
nVnVdtdn
nn )()1)((
nVndtdn
V
nn
n
nnn
)()(
)(
)()()(
)(
)()(1
)(
VVV
Vn
VVV
nn
n
nnn
Open probability: 4 independent,equivalent, conformational changes
Kinetic equation:
Rearrange:
relaxation time:
asymptotic value
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Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( u1, u2: barriers
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Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( 0,)()( 212211 ccVVcuVVcu nn
u1, u2: barriers
Assume linear in V:
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Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( 0,)()( 212211 ccVVcuVVcu nn
TVVcn
TVVcnn
nn baV /)(/)(1 21 ee))((
u1, u2: barriers
Assume linear in V:
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Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( 0,)()( 212211 ccVVcuVVcu nn
TVVcn
TVVcnn
nn baV /)(/)(1 21 ee))((
TVVcaaV nnTVVcTVVc
nnnn /)(cosh2)ee())(( /)(/)(1
u1, u2: barriers
Assume linear in V:
Simple model: an=bn, c1=c2
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Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( 0,)()( 212211 ccVVcuVVcu nn
TVVcn
TVVcnn
nn baV /)(/)(1 21 ee))((
TVVcaaV nnTVVcTVVc
nnnn /)(cosh2)ee())(( /)(/)(1
]/)(tanh1[ee
e)( 2
1/)(/)(
/)(
TVVcVn nTVVcTVVc
TVVc
nn
n
u1, u2: barriers
Assume linear in V:
Simple model: an=bn, c1=c2
Similarly,
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Hodgkin-Huxley K channel
)]65(0125.0exp[125.0)]55(1.exp[1
)55(01.
VV
Vnn
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Hodgkin-Huxley K channel
)]65(0125.0exp[125.0)]55(1.exp[1
)55(01.
VV
Vnn
(solid: exponential model for both and Dashed: HH fit)
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Transient conductance: HH Na channel
1,3 lkhmP lkNa
4 independent conformational changes,3 alike, 1 different (see picture)
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Transient conductance: HH Na channel
1,3 lkhmP lkNa
)]35(1.exp[11
)]65(05.exp[07.
)]65(556.0exp[4)]40(1.exp[1
)40(1.
VV
VV
V
hh
mm
4 independent conformational changes,3 alike, 1 different (see picture)
HH fits:
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Transient conductance: HH Na channel
1,3 lkhmP lkNa
)]35(1.exp[11
)]65(05.exp[07.
)]65(556.0exp[4)]40(1.exp[1
)40(1.
VV
VV
V
hh
mm
4 independent conformational changes,3 alike, 1 different (see picture)
HH fits:
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Transient conductance: HH Na channel
1,3 lkhmP lkNa
)]35(1.exp[11
)]65(05.exp[07.
)]65(556.0exp[4)]40(1.exp[1
)40(1.
VV
VV
V
hh
mm
4 independent conformational changes,3 alike, 1 different (see picture)
HH fits:
m is fast (~.5 ms)h,n are slow (~5 ms)
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Hodgkin-Huxley model
extNaNaKKLL IVVhmgVVngVVgdtdV
C )()()( 34
hVhdtdh
VmVmdtdm
VnVndtdn
V hmn )()()()()()(
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Hodgkin-Huxley model
extNaNaKKLL IVVhmgVVngVVgdtdV
C )()()( 34
hVhdtdh
VmVmdtdm
VnVndtdn
V hmn )()()()()()(
Parameters: gL = 0.003 mS/mm2 gK = 0.36 mS/mm2 gNa = 1.2 ms/mm2
VL = -54.387 mV VK = -77 VNa = 50 mV
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Spike generationCurrent flows in, raises V m increases (h slower to react) gNa increases more Na current flows in … V rises rapidly toward VNa
Then h starts to decrease gNa shrinks V falls, aided by n opening for K currentOvershoot, recovery
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Spike generationCurrent flows in, raises V m increases (h slower to react) gNa increases more Na current flows in … V rises rapidly toward VNa
Then h starts to decrease gNa shrinks V falls, aided by n opening for K currentOvershoot, recovery
Threshold effect
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Spike generation (2)
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Regular firing, rate vs Iext
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Step increase in current
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Noisy input current, refractoriness