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