Introduction to

electrophysiology

Dr. Tóth András

Topics

• Transmembran transport

• Donnan equilibrium

• Resting potential

• Ion channels

• Local and action potentials

• Intra- and extracellular propagation of the stimulus

Level of significance

• “Entry” level (even under 6)

• “Student” level (for most of you)

• “Gourmand” level (only for the pros)

1. Transmembran transport

Major types of transmembran transport

1

dx

dcA

JD

x

cDAJ

dx

dcDAJ

=

∆∆

−=

−=J: net rate (flux) of diffusion

A: area

dc/dx: concentrationgradient

D: diffusion coefficient

(D: cm2/s)

Fick’s first law of diffusion

2

ηπ r

kTD

6=

Diffusion of solutes as a consequence of the random

thermal (Brownian) motion of the particles

Stokes–Einstein

equation

Einstein relation____

(∆x2) = 2 Dt

3

Time required for diffusion as a function of diffusion

distance

4

Fick’s law for membrane

x

DK

x

cDAJ

x

cDAJ

∆=

∆∆

−=

∆∆

−=

β

β

Diffusion across a semipermeable membrane

ββββ: partition coefficient

K: permeability coefficient

5

Osmotic motion across a semipermeable membrane

6

Definition of the osmotic pressure

ΦΦΦΦ: osmotic coefficient

ΦΦΦΦic: osmotically effective concentration - osmolality

van’t Hoff’s Law

π= iRTm

π= iRTc

π = RTΦic

Φic = ∆Tf /1.86

I.e.: 154 mM NaCl solution

ππππ = 6.42 atm

Φ Φ Φ Φic = 0.286 osmol/L

7

Mechanism of facilitated diffusion

8

Principle of transport of ions across ion channels

9

The principle of function of the Na+/K+–ATPase

10

Secondary active transport processes

11

Transport via proteins shows saturation kinetics

Michaelis-Menten

equation

Vmax: maximal rate of

transport

Km: concentration of

the substrate for which the rate of

transport is equal

to Vmax/2

12

2. Ionic equilibrium

[ ][ ] ( )BA

B

A

o

EEzFX

XRT

zFECRT

−+=∆

++=

+

+

ln

ln

µ

µµ

Electrochemical potential (difference)

13

Nernst equation

[ ][ ] ( )

( ) [ ][ ]

[ ][ ]B

ABA

B

ABA

BA

B

A

X

X

zF

RTEE

X

XRTEEzF

EEzFX

XRT

mEquilibriu

+

+

+

+

+

+

−=−

=−−

−+=

ln

ln

ln0

[ ][ ] lg60

B

A

X X

XmVE

+

+

−=+

For monovalent cations

Z = 1

14

A B

0.1 M

K+

0.01 M

K+

EA – EB = -60 mV

Examples of uses of the Nernst equation 1.

0.1 M

HCO3-

EA – EB = +100 mV

A B

1 M

HCO3-

Is there equilibrium in any of the two cases?

15

A B

0.1 M

K+

0.01 M

K+

EA – EB = −−−−60 mV

Examples of uses of the Nernst equation 2.

A B

At –60 mV the K+ is in electrochemical equilibrium

across the membran

No electric force !!!

+++++++

–––––––

16

1 M

HCO3-

0.1 M

HCO3-

A B

0.1 M

K+

0.01 M

K+

EA – EB = −−−−60 mV

Examples of uses of the Nernst equation 3.

EA – EB = +100 mV

A B

At –60 mV the K+ is in electrochemical equilibrium

across the membran

No electric force

At the given membran potential the HCO3

- is not in electrochemical equilibrium

Electric force: +40 mV

+++++++

–––––––

––––––––

++++++++

17

1 M

HCO3-

0.1 M

HCO3-

A B

[K+] = 0.1 M

[P-] = 0.1 M

[K+] = 0.1 M

[Cl-] = 0.1 M

A B

[K+] =

[Cl-] =

[P-] = 0.1 M

[K+] =

[Cl-] =

Initial state

Before Gibbs-Donnan equilibrium is established

1. The principle of electroneutrality should be preserved !!!

2. The electrochemical potential should be zero for each diffusible ion !!! (Not for the undiffusible ion !!!)

Equilibrium?

18

A B

[K+] = 0.1 M

[P-] = 0.1 M

[K+] = 0.1 M

[Cl-] = 0.1 M

A B

[K+] = 0.133 M*

[Cl-] = 0.033 M*

[P-] = 0.1 M

[K+] = 0.066 M*

[Cl-] = 0.066 M*

Initial state Equilibrium state* (!?)

Gibbs-Donnan equilibrium has been attained

1. The principle of elektroneutrality is, indeed, valid !!!

2. The electrochemical potential is zero for K+ and Cl- !!!

3. * So, is there any problem ???

19

A B

[K+] = 0.1 M

[P-] = 0.1 M

[K+] = 0.1 M

[Cl-] = 0.1 M

A B

[K+] = 0.133 M

[Cl-] = 0.033 M

[P-] = 0.1 M

[K+] = 0.066 M

[Cl-] = 0.066 M

Starting state Equilibrium state

In Gibbs-Donnan equilibrium a transmembrane

hydrostatic pressure gradient is present

(There is no equilibrium between pressures !!!)

∆∆∆∆PH = 2.99 atm !!!

20

3. Resting potential

The „concentration battery”

A B

0.1 M

NaCl

0.01 M

NaCl

If the membrane is permeable for cations, but unpermeable for anions, cation current is

needed to reach equilibrium !!!

21

The „concentration battery”

A B

+

+

+

+

+

+

+

–

–

–

–

–

–

–

In case of electrochemical equilibrium

EA – EB = - 60 mV

Na+

22

0.1 M

NaCl

0.01 M

NaCl

“Measured” intra- and extracellular ionconcentrations

23

A simplified model of the resting membrane potential in

the human skeletal muscle

mV

P

mV

mV

mV

Na

90E 4)

0Prot 3)

P )2

- - 150 Prot

90- 115 3,6 Cl

100- 3,5 160 K

65 145 12 Na

E (mM) EC (mM) IC 1)

m

100K

-

-

eq

−=

=

⟩⟩

+

++

+

+

-90 mV

Cl- Na+

cc cc

cc

E E

E

K+

24

+++

+++

−−−

−=

−=

≈−=

=∆

=

KKmK

NaNamNa

ClClmCl

gEEI

gEEI

gEEI

Rg

R

UI

)(

)(

0)(

1

Conditions for the “chord conductance” equation

Theoretical estimation for the resting potential 1.

25

+

++

+

+

++

+

++++

++

++

+=

−−=−

=+

Na

NaK

Na

K

NaK

Km

KKmNaNam

KNa

Egg

gE

gg

gE

gEEgEE

II

)()(

0

++

++

+=

NaKm EEE1100

1

1100

100

+6

0

0

-70

-90

Na+

K+

Em

The “chord conductance” equation

gNa+ = 1 gK+ = 100

26

The “constant field” (Goldman-Hodgkin-Katz) equation

opClipNaipK

ipClopNaopKm

ClkNakKk

ClkNakKk

F

RTE

][][][

][][][ln

−++

−++

++++

=

Theoretical estimation for the resting potential 2.

27

Major factors affecting resting potential

C

28

Also in cardiac cells the resting potential is supposed to

be [K+] dependent

29

In cardiac cells the resting potential is, indeed, primarily

[K+] dependent

30

4. Ion channels

4.1 Experimental techniques

Major configurations of the „patch clamp” technique

31

„Single channel” current

32

Determination of the mean open time

33

Current-voltage relationship of the „inward” and

„outward” rectifying channels

34

4.2 Principles of regulation

State diagram of a simple, “dual-state” ion channel

35

State diagram of a “multiple-state” ion channel

36

Basic regulatory mechanisms of ion channels

37

„Background” channels spontaneously oscillate between

open and closed states

37

a

„Voltage-gated” channels also oscillate between the two

states, but voltage shifts the equilibrium

37

b

The open state of „neurotransmitter-gated” channels is

altered by the binding of a neurotransmitter to the

channel (e.g. nicotinic receptor)

37

c

The open state of “G-protein gated” channels is altered

by binding of activated G-protein subunits to the channel

(following receptor activation – e.g. muscarinic receptor)

37

d

„Modulated” channels may be voltage-gated, but the

ability of voltage to open the channel may be influenced

by covalent modification (e.g. phosphorilation)

37

e

4.3 Structure

Ion channel “superfamilies”

38

2D model of the Na+ channel 1.

39

2D model of the Na+ channel 2.

40

4.4 Structure-function relation

S4 helices are the “voltage-sensors” of voltage-gated

channels –amino acid homology is extensive

41

Model of the function of the S4 helix as „voltage sensor”

A total of 6 charges should relocare in the membrane to open the channel

42

Top view of the Na+ channel showing how the central ion

channel is proposed to be lined by one of the helices

from each domain

43

Functional model of a K+ channel

44

Cardiac ion channels

45

5. Local and action potentials

5.1 Local response

Local (subthreshold) response

46

Temporal summation

47

Spatial summation

48

5.2 Action potential

Responses in the membrane potential to increasing

pulses of depolarizing current

49

Action potentials from three vertebrate cell types

50

5.3 Action potentials in the heart

Ion concentrations in mammalian heart

51

“Fast” and “slow” response in the heart

52

Regional variations in the shape of the action potential of

the heart cells

53

Explanation of the kinetic differences

„Fast”

sodium

„Funny”

„Delayed

rectifier”

Calcium

„Tranzient

outward”

„Background”

Sodium

„Inward

rectifier”

Ion currents

∅∅∅∅!

I

≈≈≈≈0

≈≈≈≈0

∃∃∃∃

„L”

„T+L”

54

The effect of tetrodotoxin on the fast response

55

6. Propagation of the stimulus

6.1 Basic principles of propagation

Potential changes recorded by an extracellular electrode

located at different distances from the current electrode

56

Maximum change in recorded membrane potential plott-

ed versus distance from the point of current passage

57

Potencial changes in a model RC-circuit

58

Electric model of the axon membrane

59

Time constant determined in a membrane

CRR im ⋅

60

Model of decremental propagation (voltage divider -

resistance ratio)

61

Length constant determined in the membrane

i

m

R

R

62

Model of conduction of the local (subthreshold) response

63

Electric model for the propagation of potential changes

64

Model of conduction of the AP in nonmyelinated fibers

65

“Saltatory” conduction of the action potential in

myelinated fibers

66

Conduction velocity of the action potential determined in

unmyelinated and myelinated fibers

67

6.2 AP propagation in heart

Structure of the electric synapse (gap junction)

MW <<<< 1500Ca2+ ↑↑↑↑pH ↓↓↓↓Em ↑↑↑↑

68

Electric model of the cardiac cells

69

Computer simulation of impulse propagation at the

microscopic level

70

The significance of gap junctions in

normal stimulus propagation in the

heart

Subcellular stimulus propagation

71

Differences in delays of intra- and intercellular activation

– single cell wide network

72

Differences in delays of intra- and intercellular activation

– multi-cell wide network

73

Impulse propagation (isochron lines) in case of normal

gap junction coupling (homogenious AP-population)

74

Impulse propagation (isochron lines) in severe gap

junction uncoupling (heterogenous AP-population)

75

In severe gap junction uncoupling propagation velocity

may decrease TWO orders of magnitude (!!!)

(from 36.7 cm/s to only 0.31 cm/s)

76

In case of normal gap junction coupling isochron lines

are relatively regularly placed, AP-population is

homogenous

77

In case of critical gap junction uncoupling action

potentials form ”clusters” with significant delays

78

Distribution of the cells forming the different clusters in

case of critical uncoupling – turn back behaviour of the

stimulus easily leading to „reentry” can be observed

79

Questions

What are the principal differences between the following iontransporters?

Sodium-calcium exchanger

Sodium-hidrogen exchanger

Calcium pump of the sarcolemma

What does equilibrium potential mean for a given ion?

How the Nernst equation can be used to analyze ion movements in case of

diffusible ions?

What will happen, if the membrane is not permeable for at least one ion?

When is Gibbs-Donnan equilibrium present across a living cell membrane?

In Fig. 22 how much Na+ has to pass the membrane to reach equilibrium?

Which are the primary conditions for establishing and maintaining steady

resting potential ?

What is the reason, for in one cell type (rbc) the resting potential equals –30 mV,

while in an other (cardiac) cell type it equals –90 mV?

What are the major factors determining the actual value of the membrane

potential?

Questions

What is the difference between a membrane receptor and an ion channel?

Are there membrane receptors, which are also ion channels?

How is possible, that Na+ ions can pass an ion channel, but K+ ions don’t?

How is possible, that K+ ions can pass an ion channel, but Na+ ions don’t?

Which are the most important properties of the ion channels?

What is the difference between electrochemical potential and membrane potential?

Which are the most important features of the local response?

Special forms of local response?

What are the major differences between local response and action potential?

What is the reason for the very different kinetic properties of the action potentials

recorded in different cell types?

How could you change the shape of the action potential?

What is the effect of tetrodotoxin on fast response?

Why is “good for us” to maintain a resting potential in the cells of our body, if it

costs such a substantial amount of energy (ATP)?

Questions

What is the explanation for the fact, that postsynaptic action potentials are

generated at the axon hillock?

Which factors determine action potential conduction velocity in myelinated fibers?

And in unmyelinated fibers?

Why is conduction velocity significantly higher in myelinated than in unmyelinated

fibers?

How would you explain the expression that cardiac muscle is “functional

syncytium”?

Where are electric synapses (i.e. gap junctions) located in the mammalian body?

Which are the major functional differences between electric and chemical

synapses?

What is the prime factor determining direction of impulse propagation in the three

dimensional cardiac muscle?

Why is the transmission of stimulus through AV node dramatically slower than in

other parts of the heart?

Is there „fast” and „slow” action potential propagation? What may be the reason?

THE END