Resting Membrane Potential

Uneven Distribution of Solutes Amongst Body Compartments

•Cell membranes prevent most solutes from diffusing amongst compartments. Solutes are molecules which dissolve in liquid.

• 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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Water Distribution Throughout the Body Affects Solute Concentration

• Women have less water (esp. in 17-39 yr olds) than men because they have more adipose (fat) tissue; large fat droplets occupy most of the cell, and thereby reduce the water content of the cytosol.

•In clinical practice, the body’s water content needs to be taken into consideration when drugs are prescribed. Eg. since women and older people have less water than young men, the drug concentration in plasma will be higher in them than young males if administered equal drug dose per kg.

Distribution of Water in the Body: Osmosis

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• In osmosis, water moves to dilute the area of more concentrated solute. In other words, water moves down its concentration gradient.

•Osmosis stops when the concentration of solute is equal in each compartment. In other words, water moves freely between compartments until its distribution is equal. The equal distribution of water is known as osmotic equilibrium.

•The compartments of our body are in osmotic equilibrium.

• Osmotic pressure is the pressure applied to stop osmosis.

Membrane permeable to water

Osmotic Pressure

Osmolarity•Determining the concentration of the solutions in different compartments will indicate whether osmosis can takes place. Water moves into the compartment of higher solute concentration.

•Definition: Measure of the number of solute particles in a given volume of solution (osmol/L). This is different to molarity (mol/L) which measures the number of molecules per given volume of solution.

•Concentration in osmosis is concerned with the number of particles, rather than with the number of molecules in a given volume of solution, since water moves osmotically in response to the total concentration of particles in solution. Eg.one molecule of glucose yields one particle when dissolved in water, whereas NaCl yields two particles; namely, Na+ and Cl-

•Conversion of molarity (M) into osmolarity (OsM): Molarity * (# of particles/ molecule in solution)

•Osmolarity of the human body can range from 280-296 mOsM.

Comparison of Osmolarities Between Two Solutions

•Isosmotic = If two solutions have the same number solute particles per unit volume.

•If the osmolarity of solution A is greater than in solution B, we say that A is hyperosmotic to solution B, whereas solution B is hyposmotic to solution A.

• Compartments of the body are in a state of osmotic equilibrium but in a state of chemical and electrical disequilibrium.

• The electrical disequilibrium (resulting from separation of charge across the membrane) is of prime importance to electrical signalling in nerve and muscle.

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.

Electricity Review• A) Law of conservation of charge: the net amount of electric charge produced in a system is zero. ie. for every +ve charge on an ion, there is an electron on another ion. Overall, the body is electrically neutral.

• B) Opposite charges attract and like charges repel.

• C) Energy is needed to separate charge.

• D) If separated charges could move towards one another, the material through which they are moving is called a conductor.

• E) If the material prevents the movement of separate charges, the material is called an insulator. The cell membrane is a good insulator.

• Static electricity arises from the separation of electric charge.

Separation of Electric Charge Across the Cell Membrane

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• The system is in chemical, electrical and

osmotic equilibrium.

• The system is in osmotic equilibrium,

but chemical and electrical

disequilibrium.

•The input of energy to transport ions across a membrane has created an electrical gradient.

•The active transport of positive ions out of the cell has created a chemical gradient. The combination of an electrical and chemical gradient is called an electrochemical gradient.

•However, the cell remains in osmotic equilibrium.

• Physiological measurements are carried out on a relative scale.

• The -ve ion will try and move down the electrical gradient and follow the +ve ion out of the cell, but the membrane inhibits its flow as it’s a good insulator.

Electrochemical Gradient

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)

Measuring the Resting Membrane Potential•It is measured with glass micropipets filled with solutions which conduct charge. The micropipet is inserted through the membrane into the cell.

• The voltmeter measures the difference in electrical charge between two points, in other words, the potential difference; it is measured in millivolts (mV).

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• The resting membrane potential is measured on a relative scale.

• The reference electrode is placed in the extracellular fluid. The extracellular fluid is designated as the ground and assigned a charge of 0 mV. In reality, the extracellular fluid is not neutral and has an excess of +ve charge that balances the excess of -ve charge in the cell.

• The resting membrane potential is between -40 to -90 mV in nerve and muscle.

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.

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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.

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.

• 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.

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.

References

1. Tortora, G.J. & Grabowski, S.R (2003). Principles of Anatomy & Physiology.New Jersey: John Wiley & Sons. Ch.12, pp.396-398.

2. Silverthorn, D.U (1998). Human Physiology: An Integrated Approach. New Jersey: Prentice Hall. Ch.5, pp.131-133, 136-141.

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