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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.
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Fig. 03.02
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Uneven Distribution of Solutes Amongst Body Compartments
•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.
F5-28
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Ion Intracellular Extracellular Normal Plasma Value
K+ 150 5 3.5-5.0 Na+ 12 140 135-145 Cl- 10 105 100-108 Organic Anions
65 0
Uneven Distribution of Major Ions in the Intracellular and Extracellular Compartments
(mM)
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.
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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.
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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)
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K+ Ions Contribute to the Resting Membrane Potential
F5-33
• 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.
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Nerst Equation• The equilibrium potential is calculated using the Nerst equation:
in
oution [I]
[I]ln
FzRT
E = (mV)
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
• 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.
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RMP Dependence on [K+]o
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F5-34
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.
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Goldman Equation
• It is used to calculate the membrane potential resulting from all the participating ions when Vm is not changing:
outClinNainK
inCloutNaoutKm
][ClP][NaP][KP
][ClP][NaP][KPlnV −++
−++
++++=
zFRT
• 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.
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Electrodiffusion Model of the Cell Membrane
€
Ix =z2F 2VmPxRT
[X]i −[X]oe−zFVm /RT( )
1− e −zFVm /RT( )
⎛
⎝ ⎜
⎞
⎠ ⎟
GHK Current Eqn.:
Current of ion X through the membrane
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I-V Relationship Predicted by GHK Current Equation
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Direction of Current Rectification is Dependent On The Ratio of Ion Concentration On Both Sides Of
The Membrane As Predicted by GHK Current Equation
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€
Vrev = (61.5mV ) * log10
[K +]o +α [Na+]
[K +]i +α [Na+]
⎛
⎝ ⎜
⎞
⎠ ⎟
RMP Dependence on [K+]o And
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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.
F5-35
• 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.
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Electrical Model of the Cell Membrane
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References1. 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