Nernst and Goldman equation in resting membrane potential action potential

1. RestingMembrane Potential & Action Potential
Dr. Dina Hamdy Merzeban
Lecturer of physiology Fayoum university
www.facebook.com/merzeban physiology

2. Excitable Tissues
• Excitability is the ability of living cells to respond
to changes in their environment (stimulus)
• ( i.e. generation and transmission of electrochemical
impulses along the membrane)
Nerve

3. Excitable tissues
excitable Non-excitable
Red cell
GIT
•RBC
•Intestinal cells
•Fibroblasts
•Adipocytes
neuron
muscle
•Nerve
•Muscle
•Skeletal
•Cardiac
•Smooth

4. Membrane potential
• A potential difference exists across all cell
membranes
• This is called
– Resting Membrane Potential (RMP)

5. Excitability
Types of stimuli:
1. Electrical
2. Chemical
3. Mechanical
4. Thermal

6. Membrane potential
– Inside is negative with respect to the outside
– This is measured using microelectrodes and
oscilloscope
– This is about -70 to -90 mV

7. Excitable tissues
• Excitable tissues have more
negative RMP
( - 70 mV to - 90 mV)
excitable Non-excitable
neuron
muscle
•
Red cell
GIT
Non-excitable tissues
have less negative RMP
-53 mV epithelial cells
-8.4 mV RBC
-20 to -30 mV fibroblasts
-58 mV adipocytes

8. Factors affecting degree of
response to the stimulus
-Strength.
-Duration.
-Rate of application.

9. 1- Rate of Application
Suddenly applied stimulus of
certain intensity is more effective
than if a weaker stimulus applied
and gradually increased to the
same intensity
Slow changes >>> adaptation ( ↓
response by continuous stimulation)

10. 2- Strength-Duration curve
Utilization Time
Chronaxie
Minimal time

11. Resting Membrane Potential
• This depends on following factors
– Ionic distribution across the membrane
– Membrane permeability
– Other factors
• Na+/K+ pump

12. Ionic distribution
• Major ions
– Extracellular ions
• Sodium, Chloride
– Intracellular ions
• Potassium, Proteinate
K+
Pr-
Na+ Cl-

13. Ionic distribution
Intracellular Extracellular
10 142
140 4
4 103
0 2.4
10 28
Ion
Na+
K+
Cl-
Ca2+
HCO3
-

14. Ionic channels
• Leaky channels (leak channels)
– Allow free flow of ions
– K+ channels (large number)
– Na+ channels (fewer in number)
– Therefore membrane is more permeable to K+

15. Gibbs Donnan Equilibrium
 When two solutions containing
ions are separated by
semipermeable membrane
 Electrical and chemical
energies on either side of the
membrane are equal and
opposite to each other

16. • Potassium concentration intracellular is more
• Membrane is freely permeable to K+
• There is an efflux of K+
K+
K+K+
K+
K+
K+ K+ K+
Flow of Potassium
K+ K+

17. • Entry of positive ions in to the extracellular fluid
creates positivity outside and negativity inside
K+
K+K+
K+
K+
K+ K+ K+
Flow of Potassium
K+ K+

18. • Outside positivity resists efflux of K+
(since K+is a positive ion)
• At a certain voltage an equilibrium is reached
and K+ efflux stops
K+
K+K+
K+
K+
K+ K+ K+
Flow of Potassium
K+ K+

19. • Sodium concentration extracellular is more
• Membrane is freely permeable to Na+
• There is an influx of Na+
• Entry of positive ions into the intracellular fluid creates positivity inside
and negativity outside
• inside positivity resists influx of Na+
• At a certain voltage an equilibrium is reached and Na+ influx stops
Na+
Na+
Na+
Na+
Na+ Na+
Na+
Flow of sodium
Na+ Na+
_
+

20. EMF = ± 61 x log (Cin / Cout)
Where 61 is constant & is = RT / z F
Where R= Universal Gas constant
T = Absolute temperature z = ion Valence
F = Faraday, an electrical Constant.
Nernst potential (Equilibrium potential)
• The potential level across the membrane that
will prevent net diffusion of an ion
• Nernst equation determines this potential
E = ± 61 x log (Cin / Cout)
Where 61 is constant & is = RT / z F
the sign of the potential is positive (+) if the ion diffusing is a negative ion,
and it is negative (-) if the ion is positive.

21. EMF = ± 61 x log (Cin / Cout)
Where 61 is constant & is = RT / z F
Where R= Universal Gas constant
T = Absolute temperature z = ion Valence
F = Faraday, an electrical Constant.
Conc K+ ions inside =140 mEq/l
Conc K+ ions outside = 4 mEq/l
E = ± 61 x log (Cin / Cout)
E (mv)= - 61 log 140
4
= -61 log 35
= - 94mv
So , if potassium ions were the only factor
causing the resting potential, the resting
potential would be equal to -94 mv .
Equilibrium (Nernst) Potential for K+

22. EMF = ± 61 x log (Cin / Cout)
Where 61 is constant & is = RT / z F
Where R= Universal Gas constant
T = Absolute temperature z = ion Valence
F = Faraday, an electrical Constant.
Conc of Na+ ions inside the cell=14 mEq/l
Conc of Na+ ions outside the cell= 142 mEq/l
E = ± 61 x log (Cin / Cout)
E = -61 log 14 = - 61 log 0.1
140
= -61X-1 = +61 mv
Therefore, if Na ions were the only factor causing the
resting potential, the resting potential inside the fiber
would be equal to +61 mv.
Equilibrium (Nernst) Potential for Na+

23. Goldman Equation
• When the membrane is permeable to several ions the
equilibrium potential is calculated using Goldman
Equation (or GHK Equation)
• that develops depends on
–Polarity of each ion
–Membrane permeability
–Ionic conc
• In the resting state
– K+ permeability is 50-100 times more than that ofNa+

24. Goldman Equation
• In the resting state
– K+ permeability is 50-100 times more than that ofNa+
E (mv)= -61 X log CNa+
in PNa+ + CK+
in PK+ + CCl-
out PCl-
CNa+
out PNa+ + CK+
out PK+ + CCl- in PCl-
Where ‘C’=Concentration & P= Permeability
the Goldman equation gives a potential inside the
membrane of -86 mv, which is near the potassium
potential.
Nernst potential for Potassium -94mv.
Nernst potential for Sodium +61mv

25. Resting membrane potential in nerves is -90 mv
so , -86mv is due to the equilibrium potential of
several ions as calculated by goldman equation
which is nearer to K+ diffusing potential
And - 4mv is provided by Na- K pump

26. Ionic channels
• Leaky channels (leak channels)
– Allow free flow of ions
– K+ channels (large number)
– Na+ channels (fewer in number)
– Therefore membrane is more permeable to K+

27. Na/K pump
• Active transport system for Na+-K+
exchange using energy
• It is an electrogenic pump since 3 Na+
efflux coupled with 2 K+ influx
• Net effect of causing negative charge
inside the membrane
3 Na+
2 K+
ATP ADP

28. Factors contributing to RMP
• One of the main factors is K+ efflux (Nernst Potential:
-90mV)
• Contribution of Na+ influx is little (Nernst Potential:
+60mV)
• Na+/K+ pump causes more negativity inside the
membrane
• Negatively charged protein ions remaining inside the
membrane contributes to the negativity
• Net result: -70 to -90 mV inside

29. Action potential

30. Action Potential (A.P.)
• When an impulse is generated
– Inside becomes positive
– Causes depolarisation
– Nerve impulses are transmitted as AP

31. +30
RMP -70
Hyperpolarisation

32. Inside of the membrane is
• Negative
– During RMP
• Positive
– When an AP is generated
-70
+30

33. • Initially membrane is slowly depolarised
• Until the threshold level is reached
– (This may be caused by the stimulus)
+30
Threshold level
-70

34. • Then a sudden
change in polarisation
causes sharp
upstroke
(depolarisation) which
goes beyond the zero
level up to +35 mV
-70
+30

35. • Then a sudden
decrease in
polarisation causes
initial sharp down
stroke (repolarisation)
-70
+30

36. • Spike potential
– Sharp upstroke and
downstroke
• Time duration of AP
– 1 msec
-70
+30
1 msec

37. All or none law
• Until the threshold level the potential is graded
• Once the threshold level is reached
– AP is set off and no one can stop it !
– Like a gun

38. All or none law
• The principle that the strength by which a nerve
or muscle fiber responds to a stimulus is not
dependent on the strength of the stimulus
• If the stimulus strength is above threshold, the
nerve or muscle fiber will give a complete
response or otherwise no response at all

39. • Sub-threshold stimulus No action potential
• Threshold stimulus Action potential is
triggered
• Supra-threshold stimulus Action potential is
triggered
• Strength of the stimulus above the threshold is coded
as the frequency of action potentials

40. Physiological basis of AP
-70
• When the threshold level is reached
– Voltage-gated Na+ channels open up
– Since Na+ conc outside is more than the inside
– Na+ influx will occur
– Positive ion coming inside increases the positivity of the
membrane potential and causes depolarisation
+30
outside
inside
Na+
Voltage-gated Na+ channel

41. Physiological basis of AP
– When membrane potential reaches +30, Na+
channels are inactivated
– Then Voltage-gated K+ channels open up
– K+ efflux occurs
– Positive ion leaving the inside causes more negativity inside
the membrane
– Repolarisation occurs
-70
+30
outside
inside
At +30
K+

42. • Depolarisation
– Change of polarity of the membrane
• from -70 to + 30 mV
• Repolarisation
– Reversal of polarity of the membrane
• from +30 to -70 mV
-70
+30
-70
+30

43. Hyperpolarisation
• When reaching the
Resting level rate
slows down
• Can go beyond the
resting level
– Hyperpolarisation
• (membrane becoming
more negative)
-70
+30

44. Role of Na+/K+ pump
• Since Na+ has come in and K+ has gone out
• Membrane has become negative
• But ionic distribution has become unequal
• Na+/K+ pump restores Na+ and K+ conc slowly
– By pumping 3 Na+ ions outward and 2+ K ions
inward

45. VOLTAGE-GATED ION CHANNELS
Activation gate
outside
inside
Inactivation gate
• Na+ channel
– This has two gates
• Activation and inactivation gates

46. •
•
At rest: the activation gate is closed
At threshold level: activation gate opens
–
–
Na+ influx will occur
Na+ permeability increases to 500 fold
•
•
•
when reaching +30, inactivation gate closes
– Na influx stops
Inactivation gate will not reopen until resting membrane potential is reached
Na+ channel opens fast
outside
inside
-70
Na+
Threshold level
Na+
outside
inside
+30
Na+m gate
outside
inside
h gate

47. Voltage-gated Na+ channel
• There is a voltage
sensor
• Which opens up
activation gate
• Na+ influx occurs
• Membrane becomes
more positive

48. • When Na+ channel opens
• Na+ influx will occur
• Membrane depolarises
• Rising level of voltage causes many channels to open
• This will cause further Na+ influx
• Thus there a positive feedback cycle
• It does not reach Na+ equilibrium potential (+60mV)
• Because Na+ channels inactivates after opening
• Voltage-gated K+ channels open
• This will bring membrane towards K+ equilibrium
potential

49. VOLTAGE-GATED K+ Channel
• K+ channel
– This has only one gate
outside
inside

50. – At rest: K+ channel is closed
– At +30
• K+ channel open up slowly
• This slow activation causes K+ efflux
• This will cause membrane to become more negative
• Repolarisation occurs
outside
inside
-70 At +30
K+ K+
n gate
outside
inside

51. Basis of hyperpolarisation
• After reaching the resting
still slow K+ channels
may remain open:
causing further negativity
of the membrane
• This is known as
hyperpolarisation
-70
+30
outside
inside
K+

52. Summary

53. Animation

54. Refractory Period
• Absolute refractory
period
– During this period nerve
membrane cannot be
excited again
– Because of the closure
of inactivation gate
-70
+30
outside
inside

55. Refractory Period
• Relative refractory
period
– During this period nerve
membrane can be
excited by supra
threshold stimuli
– At the end of
repolarisation phase
inactivation gate opens
and activation gate
closes
– This can be opened by
greater stimuli strength
-70
+30
outside
inside

57. Na+ and K+ concentrations do not change
during an action potential
• Although during an action potential, large changes
take place in the membrane potential as a result of
Na+entry into the cell and K+exit from the cell
• Actual Na+and K+concentrations inside and outside of
the cell generally do not change
• This is because compared to the total number of Na+
and K+ions in the intracellular and extracellular
solutions, only a small number moves across the
membrane during the action potential

58. Propagation of action potential
(Basis of nerve conduction)

59. Propagation of AP
• When one area is depolarised
• A potential difference exists between that site
and the adjacent membrane
• A current flow is initiated
• Current flow through this local circuit is
completed by extra cellular fluid

60. Propagation of AP
• This local current flow will cause opening of
voltage-gated Na+ channel in the adjacent
membrane
• Na+ influx will occur
• Membrane is depolarised

61. Propagation of AP
• Then the previous area become repolarised
• This process continue to work
• Resulting in propagation of AP

62. Propagation of AP

63. Propagation of AP

64. Propagation of AP

65. Propagation of AP

66. Propagation of AP

67. Propagation of AP

68. Propagation of AP

69. Propagation of AP

70. Animation

71. AP propagation along myelinated
nerves
• Na+ channels are conc
around nodes
• Therefore depolarisation
mainly occurs at nodes

72. Distribution of Na+ channels
• Number of Na+ channels per
square micrometer of membrane
in mammalian neurons
50 to 75
350 – 500
< 25
2000 – 12,000
20 – 75
in the cell body
in the initial
segment
on the surface
of myelin
at the nodes of
Ranvier
at the axon
terminal

73. AP propagation along myelinated
nerves
•
•
Local current will flow from one node to another
Thus propagation of action potential and therefore nerve
conduction through myelinated fibres is faster than
unmyelinated fibre
– Conduction velocity of thick myelinated A alpha fibres is
about 70-100 m/s whereas in unmyelinated fibres it is about
1-2 m/s

74. Saltatory conduction
• This fast conduction through myelinated fibres
is called “saltatory conduction”
• Saltatory word means “jumping”
• This serves many purposes
– By causing depolarisation process to jump at long
intervals it increases the conduction velocity
– It conserves energy for the axon because less loss
of ions due to action potential occurring only at the
nodes

77. Animation

78. Na+/K+ pump
3 Na+
• Re-establishment of Na+ & K+ concentration
after action potential
– Na+/K+ Pump is responsible for this
– Energy is consumed
– Turnover rate of Na+/K+ is pump is much slower
than the Na+, K+ diffusion through channels
2 K+
ATP ADP

79. Clinical importance
• Local anaesthetics (eg. procaine) block voltage
gated sodium channels in pain nerve fibres
• Thereby pain signal transmission is blocked

80. Clinical importance
• Demyelinating diseases
– In certain diseases antibodies would form against myelin
and demyelination occurs
– Nerve conduction slows down drastically
• eg. Guillain-Barre Syndrome (a patient suddenly find difficult to walk,
weakness rapidly progress to upper limbs and respiratory difficulty
will also occur)

81. Muscle action potentials
• Skeletal muscle
• Cardiac muscle
• Smooth muscle

82. Skeletal muscle
• Skeletal muscle is supplied by
somatic nerve
• When there is a signal to the
muscle it contracts and relaxes
• Thus there are two events in the
skeletal muscle
– Electrical - action potential
– Mechanical - contraction

83. Muscle contraction
• Excitation - contraction coupling
– Excitation : electrical event
– Contraction : mechanical event
Mechanical event follows electrical event

84. Skeletal muscle
• Electrical event in a skeletal muscle membrane
is exactly similar to nerve action potential
• Same duration = 1 msec
• Same voltage difference = from -70 to +30 mV

85. Cardiac muscle
• Innervated by autonomic nerves (sympathetic
and parasympathetic)
• Similar to skeletal muscle
– Electrical event - action potential
– Mechanical event – muscle contraction
• However cardiac muscle action potential is
completely different to that of skeletal muscle

86. Cardiac muscle action potential
Phases
• 0: depolarisation
• 1: short repolarisation
• 2: plateau phase
• 3: repolarisation
• 4: resting
Duration is about 200 to 300 msec

87. Cardiac muscle action potential
Phases
• 0: depolarisation
(Na+ influx through fast Na+
channels)
• 1: short repolarisation
(K+ efflux through K+
channels, Cl- influx as well)
•
•
2: plateau phase
(Ca2+ influx through slow
Ca2+ channels)
3: repolarisation
(K+ efflux through K+
channels)
• 4: resting

88. Differences
• Prolonged plateau phase
• Due to opening of slow Ca2+ channels
• Which causes Ca2+ influx
• Membrane is not repolarised immediately
• Mechanical event occurs together with the
electrical event
Excitation
Contraction
: electrical event
: mechanical event

89. Refractory period
• Cardiac muscle refractory period is about 200
msec
• Equal to the period of depolarisation, plateau
phase & part of repolarisation phases
• The reason for this is that the fast sodium
channels are not fully reactivated and therefore
cannot reopen to normal depolarizing stimuli

91. Smooth muscle
• eg. gut wall, bronchi, uterus
• Controlled by nerve supply (autonomic nerves)
or hormonal control

92. Smooth muscle
• Resting membrane potential may be about -55mV
• There are different types of action potentials
• Spikes
– Slow waves -
– Plateau waves -
duration 10-50 ms
voltage from -55 to 0 mV
similar to cardiac muscles
• Ca2+ influx is more important that Na+ influx

93. Pacemaker cells
• Cardiac – SA node
• Spontaneous action potentials
• RMP = -40 mV

95. Depolarisation
• Activation of nerve membrane
• Membrane potential becomes positive
• Due to influx of Na+ or Ca++

96. Hyperpolarisation
• Inhibition of nerve membrane
• Membrane potential becomes more negative
• Due to efflux of K+ or influx of Cl-

97. Channel blockers
• Tetrodotoxin (TTX) is a naturally-found poison
that inhibits the voltage-gated Na+channels
• Tetraethyl ammonium (TEA), a quaternary
ammonium cation, is an agent that inhibits the
voltage-gated K+ channels

98. Other substances
• Oubain
– Plant poison which blocks Na+/K+ pump
• Digitalis
– Drug used in cardiac conditions
– blocks Na+/K+ pump

99. Effect of serum hypocalcaemia
• Concentration of calcium in ECF has a
profound effect on voltage level at which Na+
channels activated
• Hypocalcaemia causes hyperexcitability of the
membrane
• When there is a deficit of Ca2+ (50% below
normal) sodium channels open (activated) by a
small increase in the membrane potential from
its normal level
– Ca2+ ions binds to the Na+ channel and alters the
voltage sensor

100. Effect of serum hypocalcaemia
• Therefore membrane becomes hyperexcitable
• Sometimes discharging spontaneously
repetitively
– tetanyoccurs
• This is the reason for hypocalcaemia causing
tetany

101. Carpopedal spasms

102. Membrane stabilisers
• Membrane stabilisers (these decrease
excitability)
• Increased serum Ca++
– Hypocalcaemia causes membrane instability and
spontaneous activation of nerve membrane
– Reduced Ca level facilitates Na entry
– Spontaneous activation
• Decreased serum K+
• Local anaesthetics
• Acidosis
• Hypoxia

103. Membrane stabilisers
• Membrane destabilisers (these increase
excitability)
•Decreased serum Ca++
•Increased serum K+
•Alkalosis