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Resting Membrane Potential
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Cell Membranes
F5-1
• Cell membrane distinguishes one cell from the next.
• Cell membranes do the following:
•
a) Regulates exchange of salts, nutrients and waste with the environment.
•
b) Mediate communication between the cytosol and environment.
•
c) Maintain cell shape.
Fig. 03.02
Uneven Distribution of Solutes Amongst Body
Compartments
F5-28
•Solutes are molecules which dissolve in liquid. Cell membranes prevent most
solutes from diffusing amongst compartments.
• Active transport of solutes helps create and maintain differences in solute
concentrations.
• The body is kept in a state of chemical disequilibrium.
Uneven Distribution of Major Ions in the
Intracellular and Extracellular Compartments
(mM)
Ion
K+
Na+
ClOrganic
Anions
Intracellular Extracellular Normal
Plasma
Value
150
5
3.5-5.0
12
140
135-145
10
105
100-108
65
0
T5-9
• The body is in a state of electrical disequilibrium because active transport of
ions across the cell membrane creates an electrical gradient.
• Although the body is electrically neutral, cells have excess negative ions on the
inside and their matching positive ions are found on the outside.
Terminology Associated with Changes in
Membrane
Potential
F8-7, F8-8
• Depolarization- a decrease in the potential difference between the inside and
outside of the cell.
•Hyperpolarization- an increase in the potential difference between the inside and
outside of the cell.
• Repolarization- returning to the RMP from either direction.
•Overshoot- when the inside of the cell becomes +ve due to the reversal of the
membrane potential polarity.
Resting Membrane Potential (Difference)
• The resting membrane potential is the electrical gradient across the
cell membrane.
• Resting: the membrane potential has reached a steady state and is not
changing.
• Potential: the electrical gradient created by the active transport of
ions is a source of stored or potential energy, like chemical gradients
are a form of potential energy. When oppositely charged molecules
come back together again, they release energy which can be used to do
work (eg. molecules moving down their concentration gradient).
• Difference: the difference in the electrical charge inside and outside
the cell (this term is usually omitted)
K+ Ions Contribute to the Resting Membrane
Potential
• In electrical equilibrium and chemical disequilibrium.
• Membrane is more permeable to K+ ions.
• K+ leaks out of the cell down its concentration gradient.
• Excess -ve charge buildup inside the cell as Pr- cannot
cross the membrane. An electrical gradient is formed.
• The -ve charges attract K+ ions back into the cell down
the electrical gradient.
• Net movement of K+ stops. The membrane potential at
which the electrical gradient opposes the chemical
gradient is known as the equilibrium potential (E). EK= 90 mV.
F5-33
Nerst Equation
• The equilibrium potential is calculated using the Nerst equation:
RT [I]out
Eion 
ln
Fz [I]in
(mV)
• Derived under resting membrane conditions when the work required to move
an ion across the membrane (up its concentration gradient) equals the electrical
work required to move an ion against a voltage gradient.
R= gas constant (8.314 jules/oK.mol)
T= temperature (oK)
F= Faraday constant (96, 000
coulombs/mol)
z= the electric charge on the ion
[I]out= ion concentration outside the cell
[I] in= ion concentration inside the cell
RMP Dependence on [K+]o
Contribution of Na+ to the Resting Membrane
Potential
• Membrane permeable to Na+ only.
• Same principles hold as in the case of K+ movement across the membrane.
• The equilibrium potential for Na+ is, ENa= +60 mV.
F5-34
Goldman Equation
• It is used to calculate the membrane potential resulting from all the
participating ions when Vm is not changing:



RT PK [K ]out  PNa [Na ]out  PCl[Cl ]in
Vm 
ln
zF PK [K  ]in  PNa [Na  ]in  PCl[Cl  ]out
• PX= the relative permeability of the membrane to ion X (measured
in cm/s). An ion’s contribution to the membrane potential is
proportional to its ability to cross the membrane.
• PK: PNa: PCl= 1.0: 0.04: 0.45 at rest.
Electrodiffusion Model of the Cell Membrane
GHK Current Eqn.:
z 2 F 2Vm Px [X]i [X]o ezFVm / RT  
Ix 


zFVm / RT 
RT  1 e

Current of ion X through the membrane

I-V Relationship Predicted by GHK Current
Equation
Direction of Current Rectification is Dependent On
The Ratio of Ion Concentration On Both Sides Of
The Membrane As Predicted by GHK Current
Equation
RMP Dependence on [K+]o And 
Vrev
[K  ]o  [Na ]
 (61.5mV) * log10  
 
[K ]i  [Na ] 
Resting Membrane Potential in Real Cells
• Most cells are 40x more permeable to K+ than
Na+. As a result, the resting membrane potential is
much closer to EK than ENa.
• In actual cells, the resting membrane potential is
much closer to -70 mV because a small amount of
Na+ leaks into the cell.
• The Na+ is pumped out and the K+ pumped in by
the Na+/K+-ATPase. It pumps 3 Na+ ions out and 2
K+ ions in.
• Na+/K+-ATPase is also known as an electrogenic pump because it helps maintain
an electrical gradient. 7-20% of the RMP is generated by the pump.
• Not all transporters are electrogenic pumps:
•Na+/K+/2Cl- symporter moves one +ve charge for every -ve charge.
• HCO3-/Cl- antiport in red blood cells moves these ions in a one-for-one
fashion.
F5-35
Electrical Model of the Cell Membrane
References
1.
Boron, W.F. & Boulpaep, E.L. (2005). Medical
Physiology: Elsevier. Ch.3 & 6
2.
Tortora, G.J. & Grabowski, S.R (2003). Principles of
Anatomy & Physiology.New Jersey: John Wiley & Sons.
Ch.12, pp.396-398.
3.
Silverthorn, D.U (1998). Human Physiology: An
Integrated Approach. New Jersey: Prentice Hall. Ch.5,
pp.131-133, 136-141.
4.
Johnston, D. & Wu, S. (1999). Foundations of Cellular
Neurophysiology: Cambridge, Mass.:MIT Press. Ch.2