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Structural description of the biological membrane. Physical
property of biological membrane
Transfer of water soluble molecules across cell membranes by transport proteins
Two classes of membran proteins
Comparison of passive and active transport
Examples of sbubstances transported across cellmembranes by carrier proteins
Bacteriorhodopsin: A carrier protein
Conformational change in protein to passivelycarry glucose
Two components of an electrochemical gradient
Three ways of driving active transport
Three types of transport by carrier proteins
Two types of glucose carriers for transfer of glucoseacross the gut lining
The Na-K pump
The Na-K pumpcycle
Osmosis
Avoiding osmotic swelling
Carrier mediated solute transport in animal and plant cells
The structure of an ion channel
Patch-clamp recording
Current through a single ion channel
Gated ion channels
Stress activated ion channels allow us to hear
Distribution of ions gives rise to membranepotential
K+ is responsible for generating a membrane potential
Nernst equation: V = 62log10(Co/Ci)
Neurons
Action Potenetial
Three conformations of the voltage gated Na channel
----------
+++++ +++++
Ion Flows and the Action Potential
The propogation of an action potential along an axon
The Action Potential
Synapses
Synapses
Synapses
Excitatory vs. Inhibitory Synapse
Synapses
Ion Channels
Lecture 2
• Membrane potentials
• Ion channels
• Hodgkin-Huxley model
Cell membranes
Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
Cell membranes
Lipid bilayer, 3-4 nm thick capacitancec = C/A ~ 10 nF/mm2
Ion channels conductance
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
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
Membrane potentialFixed potential concentration gradient
Membrane potentialFixed potential concentration gradient
Concentration difference Potential difference
Concentration difference maintained by ion pumps, which aretransmembrane proteins
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)
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
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
Effective circuit model for cell membrane
Effective circuit model for cell membrane
extii i IVVgdtdV
C )(
(C, gi, Iext all per unit area)(“point model”:ignores spatial structure)
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, …
Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
membrane time const
Ohmic model
gCg
tIVVV
tIVVgVC
/)(
)()(
0
0
One gi = g = const
or
Start at rest: V= V0 at t=0membrane time const
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
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
channels are stochastic
channels are stochastic
Many channels: effective g = g open * (prob to be open) * N
Voltage-dependent channels
K channel4 knP k
K
Open probability: 4 independent,equivalent, conformational changes
K channel4 knP k
K
nVnVdtdn
nn )()1)((
Open probability: 4 independent,equivalent, conformational changes
Kinetic equation:
K channel4 knP k
K
nVnVdtdn
nn )()1)((
nVndtdn
V
nn
n
nnn
)()(
)(
Open probability: 4 independent,equivalent, conformational changes
Kinetic equation:
Rearrange:
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
Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( u1, u2: barriers
Thermal rates:TVu
nnTVu
nn bVaV /)(/)( 21 e)(e)( 0,)()( 212211 ccVVcuVVcu nn
u1, u2: barriers
Assume linear in V:
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:
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
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,
Hodgkin-Huxley K channel
)]65(0125.0exp[125.0)]55(1.exp[1
)55(01.
VV
Vnn
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)
Transient conductance: HH Na channel
1,3 lkhmP lkNa
4 independent conformational changes,3 alike, 1 different (see picture)
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:
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:
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)
Hodgkin-Huxley model
extNaNaKKLL IVVhmgVVngVVgdtdV
C )()()( 34
hVhdtdh
VmVmdtdm
VnVndtdn
V hmn )()()()()()(
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
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
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
Spike generation (2)
Regular firing, rate vs Iext
Step increase in current
Noisy input current, refractoriness
