The Nernst Equation

Question 1

What is the Nernst equation and what does it predict?

Answer 1

E = RT/zF ln [ion outside cell]/[ion inside cell]

- predicts when an electrical gradient (E) and a chemical gradient are in balance

Question 2

What is the definition of a volt?

Answer 2

If the potential is 1 volt it takes 1 joule of work to move 1 coulomb of charge

Question 3

How many coulombs of charge in 1 mole of univalent ions?

Answer 3

F coulombs of charge (96500)

Question 4

how much work does it take to move 1 mole of z-valent ion through a membrane of Vm volts?

Answer 4

Work = z.F.Vm (joules)

Question 5

How much work does it take to move 1 mole of a substance from a concentration ci (inside cell) to co (outside cell)?

Answer 5

• Work = R.T.ln (ci/co) (joules)
• R = gas constant
• T = temperature (K)
• Ln = natural logarithm (e – 2.718)

Question 6

What is the equation for total work?

Answer 6

z.F.Vm + R.T.ln(ci/co)

Question 7

What are the three possible cases about how much work is needed to move something across a membrane?

Answer 7

• Work > 0: energy is needed to move ion across membrane (active transport)
• Work <0: energy is released when ion moves across membrane (downhill – occurs spontaneously)
• Work = 0: no energy required or released i.e. at equilibrium

Question 8

What is the equilibrium case to do with work?

Answer 8

• Total work = 0 = z.F.Vm +R.T.ln (ci/co)
• z.F.Vm = -R.T.ln(ci/co)
• Ln(1/a) = -ln(a) therefore:
• Vm = R.T/z.F .ln(co/ci)
• Convert to log10:; Vm = 2.303.R.T/z.F . log10(co/ci)
• Z = +1 for K+ or Na+; -1 for cl-, +2 for Ca2+
• Answers are in V (volts)
• R = 8.314
  T = temperature in kelvin
  F = 96500

Question 9

What Nernst equation is given to us in the textbook?

Answer 9

• Vm = 61.5/z . log10(co/ci)
• This version of equation gives answer in mV
• This version of equation refers to body temperature (37 degrees)

Question 10

What are the different permeabilities of the ions in a typical cell and why?

Answer 10

• PK = 1
• PNa = 0.025
• PCl = 0.45
  • This shows that potassium ions are the most permeable species when the membrane is at rest. This is because there is a type of potassium channel known as the ‘leak channel’ that disobeys the rule of ‘most ion channels are closed, most of the time’. As a consequence of the high permeability to potassium is that the value of the resting membrane potential is largely determined by EK

Question 11

What happens to potassium at different membrane potentials?

Answer 11

• RMP = 0mV
   K+ leaves down concentration gradient (no electrical gradient)
   K+ exit makes inside of cell more -ve
• RMP negative -30mV
   K+ still leaves down concentration gradient but electrical gradient opposes this and slows it
   Further K+ exit which increases the electrical gradient
• RMP – 80mV = Nernst Ek
   So electrical gradient exactly balances concentration gradient
   No net K+ movement
   Equilibrium
• If there are equal concentrations of potassium inside and outside the cell the Ek will be 0mV

Question 12

What does the Nernst equation give us?

Answer 12

The equilibrium potential for a particular ion

Question 13

What is the equilibrium potential?

Answer 13

The voltage at which the membrane potential balances the concentration gradient

Question 14

At the equilibrium potential what is the net movement of the ion?

Answer 14

There is no net movement of the ion

Question 15

What do we need to factor in as well as equilibrium potential when thinking about a cell’s membrane potential?

Answer 15

Permeabilities

Question 16

Why is the resting membrane potential not the same as the potassium equilibrium potential?

Answer 16

• Na+ can also cross the membrane: consequences for RMP
• With a negative RMP Na+ will enter cell down both electrical and concentration gradients
• Na+ would only be at equilibrium at Na equilibrium potential (+61.5mV)
• Permeability to Na+ means that RMP is more positive than Ek
• Pk&raquo_space; PNa (40 fold) so RMP is much closer to Ek than Ena
• If PNa increases, RMP will become more positive

Question 17

What resting membrane potential do we end up with, taking sodium and potassium permeabilities into account?

Answer 17

-65 mV

Question 18

Why does the concentration of K+ remain constant when the membrane potential is changing?

Answer 18

You hardly have to move any ions to get changes in membrane potential

Question 19

What is a capacitator?

Answer 19

• A device for storing energy via separation of electrical charge
• Charge ‘stored’ on two plates separated by an insulator
   E.g. defibrillator

Question 20

How does the cell membrane act as a capacitor?

Answer 20

• In the cell we have two charged plates separated by an insulator (cell membrane).
   On the outside of the membrane we have a line of Na+ ions
   In the inside of the cell membrane we have Anions lining the cell membrane
   So there is a separation of charge across the cell membrane

Question 21

what is the Goldman-Hodgkin-Katz equation?

Answer 21

• A weighted form of the Nernst equation
• It allows us to calculate the resting membrane potential. You need to plug in the numbers for the ion concentrations and permeabilities and you will be able to calculate a value for Vm