Resting Membrane Potential

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Cell Membranes

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• 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

•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.

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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)

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• 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

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• 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

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• 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.

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.

RMP Dependence on [K+]o

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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.

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.

Electrodiffusion Model of the Cell Membrane

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Ix =z2F 2VmPxRT

[X]i −[X]oe−zFVm /RT( )

1− e −zFVm /RT( )

⎛

⎝ ⎜

⎞

⎠ ⎟

GHK Current Eqn.:

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

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Vrev = (61.5mV ) * log10

[K +]o +α [Na+]

[K +]i +α [Na+]

⎛

⎝ ⎜

⎞

⎠ ⎟

RMP Dependence on [K+]o And

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.

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• 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.

Electrical Model of the Cell Membrane

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