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Membrane Channels

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Membrane Channels. The Cell Membrane is Selective. Criteria for passage through the phospholipid bilayer : Hydrophobic Net zero charge Nonpolar Size is also a consideration Chemicals that will NOT pass through the phospholipid bilayer : Hydrophillic Charged, ionic Polar - PowerPoint PPT Presentation

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Page 1: Membrane Channels

Membrane Channels

Page 2: Membrane Channels
Page 3: Membrane Channels

The Cell Membrane is Selective• Criteria for passage through the phospholipid bilayer:

1. Hydrophobic

2. Net zero charge

3. Nonpolar

4. Size is also a consideration• Chemicals that will NOT pass through the

phospholipid bilayer:

1. Hydrophillic

2. Charged, ionic

3. Polar

4. Size is also a consideration

Page 4: Membrane Channels

• But, using the preceding criteria, many substances vital to cellular function (e.g., ions) and survival (e.g., glucose) will not gain entry into the cell!

• So, nature has come up with channels, which selectively allow certain substances to gain entry into the cell, even though they do not meet the criteria on the preceding slide.

Page 5: Membrane Channels

Outside

Inside

PlasmaMembrane

Transported Enzyme Activity

Cell SurfaceIdentity Marker

Cell Surface Receptor

Cell Adhesion Attachment to the Cytoskleton

The Many Functions of Membrane Proteins

Page 6: Membrane Channels

Channels are Vital

Without channels it is energetically unfavorable to move ions across a membrane –

1. the phospholipid bilayer is ~6-8 nm thick.

2. the hydrophilic head of the phospholipid molecule projects toward the cytoplasm or the extracellular fluid.

3. the hydrophobic tails of the phospholipid molecules project toward each other.

Page 7: Membrane Channels

Transmembrane Transport

a) communication among neurons• neural systems: * action potential * synaptic signaling b) receptor – brain communication• heart muscle • signaling and regulatory processes

Cystic fibrosisEpilepsyDiabetesMigrainesNeurotoxins

Channel malfunction

Page 8: Membrane Channels

For the Cation to Move Through the Phospholipid Bilayer…,

1) It must lose its waters of hydration so that it is not so huge and charged; requires energy to break attractive forces between the ion and the waters.

2) Energy is also required to move a charged highly hydrophilic particle into the highly hydrophobic area of the lipid bilayer that contains the “tails” of the phospholipid molecules.

3) Based on thermodynamic calculations, so much energy would be required for this process that it would never occur.

Page 9: Membrane Channels

The rate of the reaction is determined by the energy of activation, the energy input required to produce the transition state.

A + B AB C + D

Reactants transition products

(substrates) state

The uncatalyzedreaction requires a higheractivation energy than the catalyzed one does. So, thelatter runs more quickly.

There is no difference in freeenergy (ΔG) betweenuncatalyzed and catalyzedreactions. The ΔG is thethermodynamic driving forcefor the reaction and determinesthe direction of the reaction.

Transition State

Channels are thermodynamically similar to Enzymes in that the former lower the Activation Energy required to move ions across

the Membrane

Page 10: Membrane Channels

Ion Flow Across the Membrane

• A Chemical can move across the membrane through one of two ways:

1. Movement through the phospholipid bilayer.

2. Movement through a H2O-filled protein channel.

Page 11: Membrane Channels

The rate of diffusion is determined by the “energy of activation”, the energy input required to produce the “transition state”. (Remove H2Os of hydration and/or move into hydro-phobic environ-ment.)

A + B AB C + D

Reactants transition products

(substrates) state

Movement through a channel only requires shedding of waters of hydration (energy input would be infinite to move through the bilayer). So. Diffusion occurs more quickly.

Change in free energy is the thermodynamic driving force for diffusion and determines the direction of ion movement

Transition State

Channels are thermodynamically similar to Enzymes in that the former lower the Activation Energy required to move ions across

the Membrane

ΔG determines this!!

Page 12: Membrane Channels

What do we know about the structure of gated ion channels?

A. Biochemical Information –1. MWs range from 25-250 kDal.

2. They are integral membrane glycoproteins.

3. They usually consist of 2 or more subunits.

4. The genes that code for the proteins have been isolated, cloned and sequenced. These sequences have been grouped into 6-7 protein families.

5. The primary (amino acid) sequences of these channels is known.

Page 13: Membrane Channels

Use of the Hydrophobicity Plots

1) Propose 3-D structures of the channels

2) Propose functions for specific regions of the channel proteins

Page 14: Membrane Channels

Amino Acid Sequence Enables Ion Channel Structure Determination

Page 15: Membrane Channels

Many Techniques Can be Used to Test the Proposed Functions of Portions of

the Channel Proteins1) Sequence Homologies – used to determine which

portions of primary sequences of ion channels are the same/very similar

a) Same channel from several different species – what is conserved must be critical to channel function

e.g., Ach-gated channel – Ach receptor portion of the channel is highly conserved

Page 16: Membrane Channels

Many Techniques Can be Used to Test the Proposed Functions of Portions of

the Channel Proteins1) Sequence Homologies – used to determine which

portions of primary sequences of ion channels are the same/very similar (continued)

b) Different channels with the same basic function from many tissues in one species – what is conserved must be critical to channel function

e.g., Voltage gated channels (K+, Na+, Ca2+) – all have a presumed membrane-spanning region with charged AAs at each third position (voltage sensor?), while ligand-gated channels lack this structure

Page 17: Membrane Channels

Many Techniques Can be Used to Test the Proposed Functions of Portions of the

Channel Proteins2) Immunocytochemistry – a) raise antibodies to a portion of the molecule thought to be

on the intracellular or extracellular surface of the membraneb) Incubate neurons with the labeled antibodiesc) Do antibodies bind to intact neurons? (Note: antibodies are

too large to fit into a channel)Yes – sequence is on extracellular surfaceNo – sequence may be in pore or on intracellular surfaced) Next step: lyse cells and repeat exp. to see if there is

binding, i.e. is it an intracellular sequence?

Page 18: Membrane Channels

Many Techniques Can be Used to Test the Proposed Functions of Portions of the

Channel Proteins3) Site-directed mutagenesis – use molecular biology

techniques to modify specific regions of a channel with a predicted function – does modification alter channel function in a predicted fashion?

4) Chimaeric Channel Construction – construct a mutant channel from sequences from 2 or more channel genes – which “parent” channel does the mutant resemble?

Page 19: Membrane Channels

•Most channels have this basic structure: multimeric (quarternary structure), membrane-spanning, and, by definition, have a pore running longitudinally through the structure.•Vary in the number of subunits and complexity.

Page 20: Membrane Channels

Remember your amino acids?

• Primary, secondary, and tertiary structures of proteins.

• In addition, recall that multimeric proteins are formed from the attraction of individual subunits, forming the quarternary structure.

• Recall the structure and ionization of the each of the amino acid side-chains (R).

-It wouldn’t hurt if you reviewed what a pI is.

Page 21: Membrane Channels

The amino acid side –chains (R)

Page 22: Membrane Channels

•The primary amino acid sequence and higher –order structures determine the channel topology.

Interior of the channel will be lined with hydrophilic amino acids.

Exterior of the channel will be lined with hydrophobic amino acids.

Page 23: Membrane Channels

Selectivity Filter

• Many channels are selective for only 1 or 2 different chemicals (ions, sugars, etc.).

• The K+ channel has such a filter, which is a narrow region towards the extracellular surface of the membrane.

• Two K+ ions can occupy the selectivity filter simultaneously, with a third in a H2O-filled cavity deeper in the pore.

Page 24: Membrane Channels

Proposed Mechanisms for Channel Ion Selectivity

Ach receptor channel - 6.5 A in diameter

Voltage-gated Na+ channel - 4 A in diameter

Voltage-gated K+ channel – 3.3 A in diameter

Non-specific cation channel, i.e. little selectivity other than for cations

10-20 X more Na+ than K+

100 X more K+ than Na+

Page 25: Membrane Channels

Proposed Mechanisms for Channel Ion Selectivity by Channels: Ionic size

Ach receptor channel - 6.5 A in diameter

Voltage-gated Na+ channel - 4 A in diameter

Voltage-gated K+ channel – 3.3 A in diameter

Non-specific cation channel, i.e. little selectivity other than for cations

10-20 X more Na+ than K+

100 X more K+ than Na+

Non-hydrated K+ ion = 2.7 A in diameter

Non-hydrated Na+ ion = 1.9 A in diameter

If ionic size explains channel selectivity, why is the K+ channel so selective for K+ since Na+ is smaller?

Page 26: Membrane Channels

Proposed Mechanisms for Ion Selectivity by Channels: Ionic size

Ach receptor channel - 6.5 A in diameter

Voltage-gated Na+ channel - 4 A in diameter

Voltage-gated K+ channel – 3.3 A in diameter

Non-specific cation channel, i.e. little selectivity other than for cations

10-20 X more Na+ than K+

100 X more K+ than Na+

Hydrated K+ ion = 3.3 A in diameter

Hydrated Na+ ion = 3.3-4 A in diameter

Modified Model = perhaps channels select based on hydrated ionic radius?

(K+ is larger, has a lower charge density and so attracts fewer waters of hydration.)

Page 27: Membrane Channels

Proposed Mechanisms for Ion Selectivity by Channels: Ionic size

The modified model explains K+ channel selectivity, i.e. the hydrated K+ just fits into the channel and the hydrated Na+ is too big to fit. However, how do we explain the +/- sodium channel selectivity?

A selectivity filter exists inside the channel

Page 28: Membrane Channels

Proposed Mechanisms for Ion Selectivity by Channels: Ionic size

Sodium recognition site = selectivity filter

Na+

Na+

How might it work? Similar to enzymes, but much faster?

Page 29: Membrane Channels

Evidence for a Selectivity Filter

If channels are simple resistors, than movement through an open channel should be a function of the concentration gradient for the ion across the membrane

Rate of ion movement = a x [ion]I/[ion]o

(current flow = diffusion)Linear relationship with slope = a

Page 30: Membrane Channels

Evidence for a Selectivity Filter

Unitary current (pa) = recordings from single channels

External [Na+] mM

Observed data for Na+ channel

Expected data

Page 31: Membrane Channels

Evidence for a Selectivity Filter

Data for voltage-gated Na+ channel do not fit the model of a channel as a simple resistor in the membrane. Instead, the current flow through the Na+ channel plateaus or “saturates” at high [Na+]. This relationship looks like what happens to an enzyme at high [substrate]. Perhaps some channels select ions based on the same biochemical mechanisms used by enzymes to select their substrates?

In the end, the final determinations of channel gating mechanisms and ion selectivities will come from X-ray crystallography of the purified channels.

Page 32: Membrane Channels

The K+ channel is structure such that a very narrowtube through the inverted cone shape allows for only50 H2O molecules and only 2 K+ in succession.

Because they strongly repel each other, when one enters,one will be forced out.

Crystal Structure of the K+ Channel from above and from the side

Page 33: Membrane Channels

Methods for Studying Ion Channels - 1

Biochemistry– agonist, antagonist or drug binding– isolation and purification– reconstitution

Molecular biology– sequencing, cloning, mutagenesis

Structural biology– microscopy, crystallography, NMR, ...

Page 34: Membrane Channels

Methods for Studying Ion Channels - 2

Electrophysiology– tissue slice– extracellular recording– intracellular recording– whole-cell recording– single channel recording

Biochemistry– radioactive ion flux

Voltage clamp

Current clamp

Concentration jump

Page 35: Membrane Channels

Electric eel

Na channel proteins

ProteinPurification

Pure Na channelproteins

Microsequence

Amino acid sequence of smallregion of Na channel protein

Designprobe

Oligonucleotide probe withsequence corresponding

to aa sequence

Hybridize to cDNAlibrary containingNa channel cDNA

s s s s s s s s s s s s s s s s

Isolate and sequenceNa channel cDNA

Deduce proteinsequence

AA sequenceof entire Na

channel proteinSynthesize cDNAlibrary containing

Na channel cDNA (s)

sss

sss

sss

Isolate mRNAs includingone encoding Na channel

Cloning via Protein Purification

Page 36: Membrane Channels

• Positional cloning – Shaker flies

• Cloning by sequence homology- Use the same strategy as that used in preceding slide, except that the sequence on which the cloning is based comes not from the purified protein, but rather from the already-isolated cDNA.

Normal Shaker

Page 37: Membrane Channels

Positional Cloning Enabled Determination of the Shaker K Channel

Page 38: Membrane Channels

Heterologous Expression Systems

Page 39: Membrane Channels

Typical Ion Channels with Known Structure:

Acetylcholine receptor M2 transmembrane segment

K+ channel (KCSA)

Types of ion channels: Simple pores (GA, GAP junctions) Substrate gated channels (Nicotinic receptor) Voltage-gated channels (K-channels) Pumps (ATP-synthase, K+,Na+-ATPase)

Page 40: Membrane Channels

Ion Channels• ion channels in the PM of neurons and muscles contributes

to their excitability• when open - ions move down their concentration gradients• channels possess gates to open and close them• two types: gated and non-gated

2. Gated channels: open and close in response to a stimulusA. voltage-gated: open in response to change in voltage - participate in the AP

B. ligand-gated: open & close in response to particular chemical stimuli (hormone, neurotransmitter, ion)

C. mechanically-gated: open with mechanical stimulation

1. Leakage (non-gated) or Resting channels: are always open, contribute to the resting potential-nerve cells have more K+ than Na+ leakage channels -as a result, membrane permeability to K+ is higher-K+ leaks out of cell - inside becomes more negative-K+ is then pumped back in

Page 41: Membrane Channels

Types of Biochemical Mechanisms that Open and Close Channels (Cont’d)

• Nt or hormone binding to receptor causes a 2nd messenger to activate a protein kinase that phosphorylates a channel and thus opens it.

• Changes in membrane potential.• Membrane deformation (e.g., mechanical

pressure).• Selectivity by charge (i.e., positively lined pore

allows anions through; negatively lined pore allows cations through).

Page 42: Membrane Channels

Na+ Channels have Gates

At rest, one is closed (the activation gate) and the other is open (the inactivation gate).

Suprathreshold depolarization affects both of them.

Page 43: Membrane Channels
Page 44: Membrane Channels

The resting potential, recall, is generated mainly by open “resting”, non-gated K+ channels

AXON ECF

-the number of K+ channelsdramatically outnumbers thatof Na+-however, there are a few Na leak channels along the axonalmembrane

Page 45: Membrane Channels

Channel Gating Mechanisms AChR: Proposed gating mechanism

(Unwin, 1995)

OpenClosed

Page 46: Membrane Channels

Channel Families

• Voltage-gated• Extracellular ligand-gated• Intracellular ligand-gated• Inward rectifier• Intercellular• Other

Page 47: Membrane Channels

Voltage-gated

• sodium: I, II, III, µ1, H1, PN3• potassium: KA, Kv (1-5), Kv(r), Kv(s),KSR, BKCa, IKCa, SKCa,

KM, KACh

• calcium: L, N, P, Q, T• chloride: ClC-0 - ClC-8

Page 48: Membrane Channels

Extracellular ligand-gated

• nicotinic ACh (muscle): 2 (embryonic), 2 (adult)

• nicotinic ACh (neuronal): (2-10), (2-4)• glutamate: NMDA, kainate, AMPA• P2X (ATP)• 5-HT3

• GABAA: (1-6), (1-4), (1-4), , , (1-3)• Glycine

Page 49: Membrane Channels

Intracellular ligand-gated

• leukotriene C4-gated Ca2+

• ryanodine receptor Ca2+

• IP3-gated Ca2+

• IP4-gated Ca2+

• Ca2+-gated K+

• Ca2+-gated non-selective cation

• Ca2+-gated Cl– • cAMP cation• cGMP cation• cAMP chloride• ATP Cl–

• volume-regulated Cl–

• arachidonic acid-activated K+

• Na+-gated K+

Page 50: Membrane Channels

Inward rectifier

• Kir – 1.1-1.3– 2.1-2.4– 3.1-3.5– 4.1-4.2– 5.1– 6.1-6.2– 7.1

Page 51: Membrane Channels

Intercellular

• Gap junction channels– Cx26– Cx32– Cx37– Cx40– Cx43– Cx45– Cx50– Cx56

Page 52: Membrane Channels

Other

• Mechanosensitive• Mitochondrial• Nuclear• Aquaporins• Vesicular (synaptophysin)

Page 53: Membrane Channels

G-protein linked receptors coupled to ion channels

• Acetylcholine (muscarinic)• Adenosine & adenine nucleotides• Adrenaline & noradrenaline• Angiotensin• Bombesin• Bradykinin• Calcitonin• Cannabinoid• Chemokine• Cholecystokinin & gastrin• Dopamine• Endothelin• Galinin• GABA (GABAB)• Glutamate (quisqualate)

• Histamine• 5-Hydroxytryptamine (1,2)• Leukotriene• Melatonin• Neuropeptide Y• Neurotensin• Odorant peptides• Opioid peptides• Platelet-activating factor• Prostanoid• Protease-activated• Tachykinins• Taste receptors• VIP• Vasopressin and oxytocin

Page 54: Membrane Channels

Structure of the AChR at 4.6Å

Miyazawa et al, (1999) (left figure was modified)

Page 55: Membrane Channels

Inside Cell

Outside Cell

Na+

Ca2+Cl-

K+

Page 56: Membrane Channels

Schematic model of AChR ligand binding site

based on Arias, 1997

.

NH2

T

DE

NH2

Y

C

CY

WY

ACh orantagonist

W

Page 57: Membrane Channels

empty site in ACh binding protein

Brejc, 2001

Page 58: Membrane Channels

filled site in ACh binding protein

Brejc, 2001

Page 59: Membrane Channels

K Channel Structure at 3Å Resolution

Doyle et al, 1998

Page 60: Membrane Channels

Patch Clamp Recording Technique

A B C D E

electrode

cellchannel

cell- attached patch whole- cell outside- out patch

Page 61: Membrane Channels

Sizing Up Ion Channels

.

Open

ClosedCurrent

Amplitudein Picoamps (pA)

OpenDuration

in Milliseconds (ms)

current

# e

ven

ts

log time

ClosedDuration

in Milliseconds (ms)

log time

time time

# e

ven

ts

# e

ven

ts

# e

ven

ts

# e

ven

ts

Gating and Permeation

Page 62: Membrane Channels

What are the Biochemical Changes that Lead to Channel Gating (Opening or Closing)?

Gating involves some type of conformational change in the protein, but other than that there are few definitive answers to the question.

However, there are several general proposed models for gating.

Page 63: Membrane Channels

Types of Biochemical Mechanisms that Open and Close Channels

• Conformational change occurs in a discrete area of the channel, leading to it opening.

• The entire channel changes conformation (e.g., electrical synapses).

• Ball-and-chain – type mechanism.• Nt or hormone binding causes the channel to

open.

Page 64: Membrane Channels

What are the Biochemical Changes that Lead to Channel Gating (Opening or Closing)?

A. A conformation change occurs in a discrete portion of the channel -

closed

opened

Most popular model, but currently no evidence for it!

Page 65: Membrane Channels

What are the Biochemical Changes that Lead to Channel Gating (Opening or Closing)?

B. Global change occurs in the channel -

closed

opened

Evidence that electrical synapses = gap junctions function in this manner

Page 66: Membrane Channels

What are the Biochemical Changes that Lead to Channel Gating (Opening or Closing)?

C. A blocking portion of the channel changes position -

closed

opened

Evidence that voltage-gated channels function in this manner

Page 67: Membrane Channels

What Types of Stimuli Can Lead to Gating?

A. Binding of Chemicals = Ligand-gated or Chemically-gated Channels

1) Extracellular surface – neurotransmitter or hormone binding causes opening of an ion channel

receptor protein

Neurotransmitter or hormoneBinds to

Opened channel

Page 68: Membrane Channels

What Types of Stimuli Can Lead to Gating?

A. Binding of Chemicals = Ligand-gated or Chemically-gated Channels (continued)

2) Intracellular surface – a second messenger is activated by neurotransmitter or hormone binding to a receptor

receptor protein

Neurotransmitter or hormoneBinds to

2nd messenger

1) Binds directly to a channel and opens/closes it

2) Activates a protein kinase that phosphorylates the channel and opens/closes it

Page 69: Membrane Channels

What Types of Stimuli Can Lead to Gating?

B. Change in Membrane Potential = Voltage-gated channels

C. Membrane Deformation = Mechanically-gated channels (ex. Sensory system where membrane stretch or pressure on the membrane is transmitted to the channel via the cytoskeleton?)

Pressure applied

Page 70: Membrane Channels

What are the Proposed Mechanisms for Ion Selectivity by Channels?

A. Channels can select by charge -Cl-

Cl-

+

+

+

+

+

+

K+

K+

-

-

-

-

-

-

Anion selective channel lined with positively charged AAs

Cation selective channel lined with negatively charged AAs

Page 71: Membrane Channels

What are the Proposed Mechanisms for Ion Selectivity by Channels?

B. Channels can select based on ionic size –

Experimental approach =

1) sequence data were used to propose 3-D structures of the channels and to estimate the pore diameters

2) ionic selectivities were determined using electrophysiological techniques

Page 72: Membrane Channels

A Closer Look at Gating: Kinetics of Gating

Page 73: Membrane Channels

Channel Gating: Two State Model

Closed kc

ko Open

d Closed dt

ko Closed kc Open

d Open

dtko Closed kc Open

Closed=1Open=0

i s RandNum<ko* dt?

Yes No

Closed=0Open=1

Yes No

i s RandNum<kc* dt?

RandNumgenerator

Page 74: Membrane Channels

Channel Gating: 2 State Simulations

43210Time (ms)

43210Time (ms)

1.0

0.8

0.6

0.4

0.2

0.0

Op

en P

rob

43210Time (ms)

Slow kinetics: ko=0.5/ms kc=0.5/ms Fast kinetics: ko=5/ms kc=5/ms

Superposition

Page 75: Membrane Channels

Gating Exercise

average closed time 1ko

steady state popen

k

oko kc

average open time 1kc

onset time 1kokc

Predictions

example ko (1/ms) kc (1/ms)

averageclosed time

(ms)

averageopen time

(ms)

steady-statepopen

onsettime (ms)

1 0.5 0.5 2.0 2.0 0.5 1.0

2 5.0 5.0

3 5.0 0.5

4 0.5 5.0

Closed kc

ko Open

Page 76: Membrane Channels

Channel Gating: More 2 State Simulations

43210Time (ms)

1.0

0.8

0.6

0.4

0.2

0.0

Op

en P

rob

43210Time (ms)

High popen: ko=5/ms kc=0.5/ms

43210Time (ms)

Low popen: ko=0.5/ms kc=5/ms

Superposition

Page 77: Membrane Channels

Channel Gating:3 State Model

d Closed

dt ko Closed kc Open

d Open

dtko Closed kc Open k+i Open k-i Inactive

dInactive dt

k+i Open k-i Inactive

Closed kc

ko Open k-i

k+i Inactive

More realistic model V-gated Na channelsopen channel blockers

Page 78: Membrane Channels

Channel Gating: 3 State Simulation

50403020100time (ms)

Open

Closed

"Supervision"Open

Inactive

Closed

141210864time (ms)

Current

Burst

ko = 0.1/ms kc =0.5/ms k+i = 1/ms k-i = 5/ms

Closed kc

ko Open k-i

k+i Inactive

Page 79: Membrane Channels

Channel Gating: 3 State Superposition

ko = 0.5/ms kc =0.005/ms k+i = 0.25/ms k-i = 0.025/ms

1.0

0.8

0.6

0.4

0.2

0.0

Op

en

Pro

b

50403020100

time (ms)

Popen

k+i = 0/ms k-i = 0/ms

Page 80: Membrane Channels

Channel Gating Mechanisms (1)

A Q K K IEE K Q E L Q E Q Q H Q KQ Q Q Q K K R H QR D E G L G V L G A V A A M

The “Ball and Chain” model of channel inactivation gating

At depolarized potentials, the ball is more stable at the blocking conformation.

Page 81: Membrane Channels

Channel Gating Mechanisms (2)AChR: Open (white) & Closed (blue) conformations

(Unwin, 1995)

Page 82: Membrane Channels

Channel Gating Mechanisms (3)AChR: Proposed gating mechanism

(Unwin, 1995)

Page 83: Membrane Channels

Vr is known as the: Nernst potentialreversal potentialzero current potentialequilibrium potential

Channel Permeation - Nernst

K+

Cl-–Cl-

K+ –

––

––

–––

–K+

Cl-Cl-

K+ –

––

–K+

Cl-Cl-

K+

Vr=RTzF

lncoci

58mVz log

coci

Consider a cell containing a high concentration of KClExternal [KCl] is lowConsider the cell membrane to be permeable to K+ only.

initial condition

K+

Cl-–Cl-

K+ –

––

––

–––

–K+

Cl-Cl-

K+ –

––

–K+

Cl-Cl-

K+

after some diffusion

K+

Cl-–Cl-

K+ –

––

––

–––

–K+

Cl-Cl-

K+ –

––

–K+

Cl-Cl-

K+

equilibrium

Page 84: Membrane Channels

Channel Permeation: ExamplesVr = 58 mV

zlog

coci

VK = 58 mV

+1log 5 mM

150 mM

86 mV

Ion z co (mM) ci (mM) Vr (mV)

K +1 5 150 -86

Na 150 15

Cl 120 10

Ca 2 0.0001

[K]o =5 mM, [K]i=150 mM

Page 85: Membrane Channels

Channel Permeation: GHKGoldman-Hodgkin-Katz Voltage Equation

Cell membrane potential depends on ion gradients and ionic permeabilities (Pi)

Vm=58 mV log PKKo PNaNao PClCliPKKi PNaNai PClClo

1. Neuron at rest (ci, co from previous slide)PK=100, PNa=5, PCl=10 Vm= 63 mV

2. Neuron during an action potential PK=100, PNa=500, PCl=10 Vm=___

Page 86: Membrane Channels

Channel Permeation: Ohm's Law

Current (flow) is equal to voltage (driving force) times conductance (1/resistance)

I = (V-Vr) G

Current (I) is measured in amps (pA, nA, µA)Voltage (V) is measured in volts (mV)Conductance (G) is measured in Siemens (pS, nS)

Page 87: Membrane Channels

Channel Permeation: Turnover

How much is a picoamp of current?

1pA1012A 10 12Coul

s 1 ion1.610 19Coul

107ions/s

Ion channels are enzymes that catalyze the flow of ions across cell membranes. The catalytic rate is on the order of 107 per second.

Page 88: Membrane Channels

Channel Permeation: IV Curvesa) V-independent conductance:

I = (V-Vr) G, G = N popen

1.0

0.8

0.6

0.4

0.2

0.0

Op

en

Pro

bab

ilit

y

-100 -50 0 50 100

Voltage (mV)

-1000

-500

0

500

1000

Cu

rren

t (p

A)

-100 -50 0 50 100

Voltage (mV)

N=200, = 50 pS, Vr=0

Page 89: Membrane Channels

Channel Permeation: IV Curvesb) V-dependent conductance

I = (V-Vr) G(V) G = N popen(V)1.0

0.8

0.6

0.4

0.2

0.0

Op

en

Pro

bab

ilit

y

-100 -50 0 50 100

Voltage (mV)

-1000

-500

0

500

1000

Cu

rren

t (p

A)

-100 -50 0 50 100

Voltage (mV)

N=200, = 50 pS, Vr=+50 mV