resting membrane potential
RESTING MEMBRANE POTENTIAL Objectives:
•
Measure resting membrane potential (Vm) in frog muscle using glass microelectrodes.
•
Examine how Vm depends on extracellular [K+]o.
RESTING MEMBRANE POTENTIAL All living cells under resting conditions have an electrical potential difference.
• Inside - Negative • Outside - Zero (by convention)
RESTING MEMBRANE POTENTIAL Charge Separation: How many ions involved in charge separation? •An estimate can be made using Coulomb’s Law and basic trigonometry. • Estimate surface area of the cell • Capacitance per unit area is fairly constant from one cell to another; It is ~ 1micro Farad/cm2 • If one knows both – cell surface area and capacitance per unit area then one can calculate cell capacitance (C ). • Since resting membrane potential can be measured and cell capacitance C is known by using Coulomb’s Law one obtains Q = C*U. • Number of charges on the membrane is Q/e; • e – elementary charge (1.6* 10-19 C). • Finally the total positive and negative charge in the cell can be calculated from cell volume and ionic concentration. •Number of charges in the cell is calculated from total charges divided by the elementary charge. •A very small fraction of ions involved in charge separation.
RESTING MEMBRANE POTENTIAL
Resting Membrane Potential: Ranges from –60 to –90 mV. • It is a function of the ratio of ion concentrations in the cell and in the extracellular space, but also of membrane permeability to these ions . •Relevant ions: Na+, K+, and Cl-.
RESTING MEMBRANE POTENTIAL Ionic Asymmetry:
•
K+ - High concentration intracellularly
•
Na+ - High concentration extracellularly [Na+]out > [Na+]in
[K+]out < [K+]in
[KMaintenance of Ionic Asymmetry: • Ion pumps K+ is pumped into the cell Na+ is pumped outside the cell
IONIC ASYMMETRY AND SELECTIVE MEMBRANE PERMEABILITY LEAD INEVITABLY TO RESTING MEMBRANE POTENTIAL Assume a simple model: 1) 2 compartments 2) Same ionic composition on both sides (K+ and Cl-), but different concentrations. 3) Membrane permeable only to one ion (K+). 4) Initial electrical neutrality on both sides of semi-permeable membrane.
IONIC ASYMMETRY AND SELECTIVE MEMBRANE PERMEABILITY LEAD INEVITABLY TO RESTING MEMBRANE POTENTIAL
Chemical K+Cl(100mM)
K+Cl(10mM)
Electrical Forces acting on movement of ions: Chemical - Due to concentration gradient Electrical - Due to potential difference (electrical gradient)
Equilibrium: Chemical force = Electrical force
NERNST EQUATION EK = (RT / zF) ln ([K+]0 / [K+]i) EK = 58 log10 ([K+]0 / [K+]i) (at room temperature) R - gas constant (8.31 joules / °Kelvin – mole) T - absolute temperature (°Kelvin) F - Faraday constant (9.65 x 104 coulomb/mole) z - valence of ion (in this case: 1) [K+]0 - extracellular K+ concentration (mM) [K+]i - intracellular K+ concentration (mM)
WORKING HYPOTHESIS At rest, muscle membrane is permeable to K+ ONLY. If this is so >> Vm = EK
If [K+]o concentration increases 10x If [K+]o concentration increases 100x Semilog scale
-
EK is depolarized by 58mV EK is depolarized by 116mV
Linear relationship
EK is a function of concentration ratio ONLY
ELECTRICAL CIRCUIT Eb
E Recording Electrode
Reference Electrode
muscle
Extracellular potential
Tip potential = Vt = E - Eb
ELECTRICAL CIRCUIT (–)
Eb Reference Electrode
E Recording Electrode
muscle Vx = E - Eb + membrane potential (Vm)
Vt Vm
Vx
Vm = membrane potential Vx = potential between two electrodes
Measurement: Vm = Vx - Vt Glass electrode: Tip Size How to measure tip size? a) Optical >> possible but too expensive? b) Electrical R ~ 10M for dtip = 1 m Electrode Solution: 3M KCl Can one use other solutions such as NaCl? Yes but they are not as good. Why?
Recording Instrument: Can one directly connect electrodes to the recording instrument? Ve Re (107 ) Em =
100mV
– inside
CELL MEMBRANE
+ outside
Ro (106 )
Vo
Recording Instrument I =
Em
______
R e + Ro
V e = Em
Re _______ x
Vo = E m
Ro _______ x
R e + Ro R e + Ro
Recording Instrument Ve Re (107 )
Em =
100mV
– inside
CELL MEMBRANE
+ outside
Rr (1010 )
Vr
Recording Instrument I =
Em
_______
R e + Rr
Vr = E m
x
R r _______ R e + Rr
Therefore, the recorded potential ~= actual Em
CONCLUSION High input resistance recording instrument is needed: a) to reduce current flow through recording electrode. b) to accurately measure resting membrane potential. c) To make measurements of resting membrane potential insensitive to changes of electrode resistance.
MEMBRANE POTENTIAL IS DETERMINED BY: ELECTROCHEMICAL GRADIENT (i.e. by a concentration gradient AND by an electrical gradient)
MEMBRANE PERMEABILITY
PK = Potassium permeability PNa = Sodium permeability
TETRAETHYLAMMONIUM • Blocker of K+ conductance. • How should a complete block of K+ conductance alter Vm vs. [K+]o relationship? • How should a partial block of K+ conductance alter Vm vs. [K+]o relationship? • Assume that membrane is: a) not permeable to Na+ or b) that its permeability is small. • Does TEA block ALL K+ conductances?
•
Measure resting membrane potential (Vm) in frog muscle using glass microelectrodes.
•
Examine how Vm depends on extracellular [K+]o.
RESTING MEMBRANE POTENTIAL All living cells under resting conditions have an electrical potential difference.
• Inside - Negative • Outside - Zero (by convention)
RESTING MEMBRANE POTENTIAL Charge Separation: How many ions involved in charge separation? •An estimate can be made using Coulomb’s Law and basic trigonometry. • Estimate surface area of the cell • Capacitance per unit area is fairly constant from one cell to another; It is ~ 1micro Farad/cm2 • If one knows both – cell surface area and capacitance per unit area then one can calculate cell capacitance (C ). • Since resting membrane potential can be measured and cell capacitance C is known by using Coulomb’s Law one obtains Q = C*U. • Number of charges on the membrane is Q/e; • e – elementary charge (1.6* 10-19 C). • Finally the total positive and negative charge in the cell can be calculated from cell volume and ionic concentration. •Number of charges in the cell is calculated from total charges divided by the elementary charge. •A very small fraction of ions involved in charge separation.
RESTING MEMBRANE POTENTIAL
Resting Membrane Potential: Ranges from –60 to –90 mV. • It is a function of the ratio of ion concentrations in the cell and in the extracellular space, but also of membrane permeability to these ions . •Relevant ions: Na+, K+, and Cl-.
RESTING MEMBRANE POTENTIAL Ionic Asymmetry:
•
K+ - High concentration intracellularly
•
Na+ - High concentration extracellularly [Na+]out > [Na+]in
[K+]out < [K+]in
[KMaintenance of Ionic Asymmetry: • Ion pumps K+ is pumped into the cell Na+ is pumped outside the cell
IONIC ASYMMETRY AND SELECTIVE MEMBRANE PERMEABILITY LEAD INEVITABLY TO RESTING MEMBRANE POTENTIAL Assume a simple model: 1) 2 compartments 2) Same ionic composition on both sides (K+ and Cl-), but different concentrations. 3) Membrane permeable only to one ion (K+). 4) Initial electrical neutrality on both sides of semi-permeable membrane.
IONIC ASYMMETRY AND SELECTIVE MEMBRANE PERMEABILITY LEAD INEVITABLY TO RESTING MEMBRANE POTENTIAL
Chemical K+Cl(100mM)
K+Cl(10mM)
Electrical Forces acting on movement of ions: Chemical - Due to concentration gradient Electrical - Due to potential difference (electrical gradient)
Equilibrium: Chemical force = Electrical force
NERNST EQUATION EK = (RT / zF) ln ([K+]0 / [K+]i) EK = 58 log10 ([K+]0 / [K+]i) (at room temperature) R - gas constant (8.31 joules / °Kelvin – mole) T - absolute temperature (°Kelvin) F - Faraday constant (9.65 x 104 coulomb/mole) z - valence of ion (in this case: 1) [K+]0 - extracellular K+ concentration (mM) [K+]i - intracellular K+ concentration (mM)
WORKING HYPOTHESIS At rest, muscle membrane is permeable to K+ ONLY. If this is so >> Vm = EK
If [K+]o concentration increases 10x If [K+]o concentration increases 100x Semilog scale
-
EK is depolarized by 58mV EK is depolarized by 116mV
Linear relationship
EK is a function of concentration ratio ONLY
ELECTRICAL CIRCUIT Eb
E Recording Electrode
Reference Electrode
muscle
Extracellular potential
Tip potential = Vt = E - Eb
ELECTRICAL CIRCUIT (–)
Eb Reference Electrode
E Recording Electrode
muscle Vx = E - Eb + membrane potential (Vm)
Vt Vm
Vx
Vm = membrane potential Vx = potential between two electrodes
Measurement: Vm = Vx - Vt Glass electrode: Tip Size How to measure tip size? a) Optical >> possible but too expensive? b) Electrical R ~ 10M for dtip = 1 m Electrode Solution: 3M KCl Can one use other solutions such as NaCl? Yes but they are not as good. Why?
Recording Instrument: Can one directly connect electrodes to the recording instrument? Ve Re (107 ) Em =
100mV
– inside
CELL MEMBRANE
+ outside
Ro (106 )
Vo
Recording Instrument I =
Em
______
R e + Ro
V e = Em
Re _______ x
Vo = E m
Ro _______ x
R e + Ro R e + Ro
Recording Instrument Ve Re (107 )
Em =
100mV
– inside
CELL MEMBRANE
+ outside
Rr (1010 )
Vr
Recording Instrument I =
Em
_______
R e + Rr
Vr = E m
x
R r _______ R e + Rr
Therefore, the recorded potential ~= actual Em
CONCLUSION High input resistance recording instrument is needed: a) to reduce current flow through recording electrode. b) to accurately measure resting membrane potential. c) To make measurements of resting membrane potential insensitive to changes of electrode resistance.
MEMBRANE POTENTIAL IS DETERMINED BY: ELECTROCHEMICAL GRADIENT (i.e. by a concentration gradient AND by an electrical gradient)
MEMBRANE PERMEABILITY
PK = Potassium permeability PNa = Sodium permeability
TETRAETHYLAMMONIUM • Blocker of K+ conductance. • How should a complete block of K+ conductance alter Vm vs. [K+]o relationship? • How should a partial block of K+ conductance alter Vm vs. [K+]o relationship? • Assume that membrane is: a) not permeable to Na+ or b) that its permeability is small. • Does TEA block ALL K+ conductances?
